2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

Boscovich's Explanation Of Atomic Forces

A great example how a great deal of amazing insight can be gained from some very simple considerations is the explanation of atomic forces by the 18th century Jesuit polymath Roger Boscovich, who was born in Dubrovnik.

One of the great philosophical arguments at the time took place between the adherents of Descartes who—following Aristotle—thought that forces can only be the result of immediate contact and those who followed Newton and believed in his concept of force acting at a distance. Newton was the revolutionary here, but his opponents argued—with some justification—that "action at a distance" brought back into physics "occult" explanations that do not follow from the "clear and distinct" understanding that Descartes demanded. (In the following I am paraphrasing reference works.) Boscovich, a forceful advocate of the Newtonian point of view, turned the question around: Let's understand exactly what happens during the interaction that we would call immediate contact?

His arguments are very easy to understand and extremely convincing. Let's imagine two bodies, one of which is traveling at a speed of, say, 6 units, the other at a speed of 12 with the faster body catching up with the slower one along the same straight path. We imagine what transpires when the two bodies collide. By conservation of the "quantity of motion," both bodies should continue after collision along the same path, each with a speed of 9 units (in the case of inelastic collision, or in case of elastic collision for a brief period right after the collision)

But how did the velocity of the faster body come to be reduced from 12 to 9, and that of the slower body increased from 6 to 9? Clearly, the time interval for the change in velocities cannot be zero, for then, argued Boscovich, the instantaneous change in speed would violate the law of continuity. Furthermore, we would have to say that at the moment of impact, the speed of one body is simultaneously 12 and 9, which is patently absurd.

It is therefore necessary for the change in speed to take place in a small, yet finite, amount of time. But with this assumption, we arrive at yet another contradiction. Suppose, for example, that after a small interval of time, the speed of the faster body is 11, and that of the slower body is 7. But this would mean that they are not moving at the same velocity, and the front surface of the faster body would advance through the rear surface of the slower body, which is impossible because we have assumed that the bodies are impenetrable. It therefore becomes apparent that the interaction must take place immediately before the impact of the two bodies and that this interaction can only be a repulsive one because it is expressed in the slowing down of one body and the speeding up of the other.

Moreover, this argument is valid for arbitrary speeds, so one can no longer speak of definite dimensions for the particles that were until now thought of as impenetrable, namely, for the atoms. An atom should rather be viewed as a point source of force, with the force emanating from it acting in some complicated fashion that depends on distance.

According to Boscovich, when bodies are far apart, they act on each other through a force corresponding to the gravitational force, which is inversely proportional to the square of the distance. But with decreasing distance, this law must be modified because, in accordance with the above considerations, the force changes sign and must become a repulsive force. Boscovich even plotted fanciful traces of how the force should vary with distance in which the force changed sign several times, hinting to the existence of minima in the potential and the existence of stable bonds between the particles—the atoms.

With this idea Boscovich not only offered a new picture for interactions in place of the Aristotelian-Cartesian theory based on immediate contact, but also presaged our understanding of the structure of matter, especially that of solid bodies.

Why Is Our World Comprehensible?

"The most incomprehensible thing about the world is that it is comprehensible." This is one of the most famous quotes from Albert Einstein. "The fact that it is comprehensible is a miracle." Similarly, Eugene Wigner said that the unreasonable efficiency of mathematics is "a wonderful gift which we neither understand nor deserve." Thus we have a problem that may seem too metaphysical to be addressed in a meaningful way: Why do we live in a comprehensible universe with certain rules, which can be efficiently used for predicting our future?

One could always respond that God created the universe and made it simple enough so that we can comprehend it. This would match the words about a miracle and an undeserved gift. But shall we give up so easily? Let us consider several other questions of a similar type. Why is our universe so large? Why parallel lines do not intersect? Why different parts of the universe look so similar? For a long time such questions looked too metaphysical to be considered seriously. Now we know that inflationary cosmology provides a possible answer to all of these questions. Let us see whether it might help us again.

To understand the issue, consider some examples of an incomprehensible universe where mathematics would be inefficient. Here is the first one: Suppose the universe is in a state with the Planck density r ~ 10⁹⁴ g/cm³. Quantum fluctuations of space-time in this regime are so large that all rulers are rapidly bending and shrinking in an unpredictable way. This happens faster than one could measure distance. All clocks are destroyed faster than one could measure time. All records about the previous events become erased, so one cannot remember anything and predict the future. The universe is incomprehensible for anybody living there, and the laws of mathematics cannot be efficiently used.

If the huge density example looks a bit extreme, rest assured that it is not. There are three basic types of universes: closed, open and flat. A typical closed universe created in the hot Big Bang would collapse in about 10^-43 seconds, in a state with the Planck density. A typical open universe would grow so fast that formation of galaxies would be impossible, and our body would be instantly torn apart. Nobody would be able to live and comprehend the universe in either of these two cases. We can enjoy life in a flat or nearly flat universe, but this requires fine-tuning of initial conditions at the moment of the Big Bang with an incredible accuracy of about 10^-60.

Recent developments in string theory, which is the most popular (though extremely complicated) candidate for the role of the theory of everything, reveal an even broader spectrum of possible but incomprehensible universes. According to the latest developments in string theory, we may have about 10⁵⁰⁰ (or more) choices of the possible state of the world surrounding us. All of these choices follow from the same string theory. However, the universes corresponding to each of these choices would look as if they were governed by different laws of physics; their common roots would be well hidden. Since there are so many different choices, some of them may describe the universe we live in. But most of these choices would lead to a universe where we would be unable to live and efficiently use mathematics and physics to predict the future.

At the time when Einstein and Wigner were trying to understand why our universe is comprehensible, everybody assumed that the universe is uniform and the laws of physics are the same everywhere. In this context, recent developments would only sharpen the formulation of the problem: We must be incredibly lucky to live in the universe where life is possible and the universe is comprehensible. This would indeed look like a miracle, like a "gift that we neither understand nor deserve." Can we do anything better than praying for a miracle?

During the last 30 years the way we think about our world changed profoundly. We found that inflation, the stage of an exponentially rapid expansion of the early universe, makes our part of the universe flat and extremely homogeneous. However, simultaneously with explaining why the observable part of the universe is so uniform, we also found that on a very large scale, well beyond the present visibility horizon of about 10¹⁰ light years, the universe becomes 100% non-uniform due to quantum effects amplified by inflation.

This means that instead of looking like an expanding spherically symmetric ball, our world looks like a multiverse, a collection of an incredibly large number of exponentially large bubbles. For (almost) all practical purposes, each of these bubbles looks like a separate universe. Different laws of the low energy physics operate inside each of these universes.

In some of these universes, quantum fluctuations are so large that any computations are impossible. Mathematics there is inefficient because predictions cannot be memorized and used. Lifetime of some of these universes is too short. Some other universes are long living but laws of physics there do not allow existence of anybody who could live sufficiently long to learn physics and mathematics.

Fortunately, among all possible parts of the multiverse there should be some exponentially large parts where we may live. But our life is possible only if the laws of physics operating in our part of the multiverse allow formation of stable, long-living structures capable of making computations. This implies existence of stable (mathematical) relations that can be used for long-term predictions. Rapid development of the human race was possible only because we live in the part of the multiverse where the long-term predictions are so useful and efficient that they allow us to survive in the hostile environment and win in the competition with other species.

To summarize, the inflationary multiverse consists of myriads of 'universes' with all possible laws of physics and mathematics operating in each of them. We can only live in those universes where the laws of physics allow our existence, which requires making reliable predictions. In other words, mathematicians and physicists can only live in those universes which are comprehensible and where the laws of mathematics are efficient.

One can easily dismiss everything that I just said as a wild speculation. It seems very intriguing, however, that in the context of the new cosmological paradigm, which was developed during the last 30 years, we might be able, for the first time, to approach one of the most complicated and mysterious problems which bothered some of the best scientists of the 20th century.

Fitness Landscapes

The first time I saw a fitness landscape cartoon (in Garrett Hardin's Man And Nature, 1969), I knew it was giving me advice on how not to get stuck over-adapted—hence overspecialized—on some local peak of fitness, when whole mountain ranges of opportunity could be glimpsed in the distance, but getting to them involved venturing "downhill" into regions of lower fitness. I learned to distrust optimality.

Fitness landscapes (sometimes called "adaptive landscapes") keep turning up when people try to figure out how evolution or innovation works in a complex world. An important critique by Marvin Minsky and Seymour Papert of early optimism about artificial intelligence warned that seemingly intelligent agents would dumbly "hill climb" to local peaks of illusory optimality and get stuck there. Complexity theorist Stuart Kauffman used fitness landscapes to visualize his ideas about the "adjacent possible" in 1993 and 2000, and that led in turn to Steven Johnson's celebration of how the "adjacent possible" works for innovation in Where Good Ideas Come From.

The man behind the genius of fitness landscapes was the founding theorist of population genetics, Sewell Wright (1889-1988). In 1932 he came up with the landscape as a way to visualize and explain how biological populations escape the potential trap of a local peak by imagining what might drive their evolutionary "path" downhill from the peak toward other possibilities. Consider these six diagrams of his :

[Image credit: © Sewall Wright, The Role of Mutation, Inbreeding, Crossbreeding, and Selection in Evolution, Sixth International Congress of Genetics, Brooklyn, NY: Brooklyn Botanical Garden, 1932.]

The first two illustrate how low selection pressure or a high rate of mutation (which comes with small populations) can broaden the range of a species whereas intense selection pressure or a low mutation rate can severely limit a species to the very peak of local fitness. The third diagram shows what happens when the landscape itself shifts, and the population has to evolve to shift with it.

The bottom row explores how small populations respond to inbreeding by wandering ineffectively. The best mode of exploration Wright deemed the final diagram, showing how a species can divide into an array of races that interact with one another. That jostling crowd explores well, and it can respond to opportunity.

Fitness landscapes express so much so economically. There's no better way, for example, to show the different modes of evolution of a remote oceanic island and a continental jungle. The jungle is dense and "rugged" with steep peaks and valleys, isolating countless species on their tiny peaks of high specialization. The island, with its few species, is like a rolling landscape of gentle hills with species casually wandering over them, evolving into a whole array of Darwin's finches, say. The island creatures and plants "lazily" become defenseless against invaders from the mainland.

You realize that for each species, its landscape consists almost entirely of other species, all of them busy evolving right back. That's co-evolution. We are all each other's fitness landscapes.

Einstein's Photons

My favorite deep, elegant and beautiful explanation is Albert Einstein's 1905 proposal that light consists of energy quanta, today called photons. Actually, it is little known, even among physicists, but extremely interesting how Einstein came to this position. It is often said that Einstein invented the concept to explain the photoelectric effect. Certainly, that is part of Einstein's 1905 publication, but only towards its end. The idea itself is much deeper, more elegant and, yes, more beautiful.

Imagine a closed container whose walls are at some temperature. The walls are glowing, and as they emit radiation, they also absorb radiation. After some time, there will be some sort of equilibrium distribution of radiation inside the container. This was already well known before Einstein. Max Planck had introduced the idea of quantization that explained the energy distribution of the radiation inside such a volume. Einstein went a step further. He studied how orderly the radiation is distributed inside such a container. For physicists, entropy is a measure of disorder.

To consider a simple example, it is much more probable that books, notes, pencils, photos, pens etc. are cluttered all over my desk than that they are well ordered forming a beautiful stack. Or, if we consider a million atoms inside a container, it is much more probable that they are more or less equally distributed all over the volume of the container than that they are all collected in one corner. In both cases, the first state is less orderly: when the atoms fill a larger volume they have a higher entropy than the second one mentioned. The Austrian physicist Ludwig Boltzmann had shown that the entropy of a system is a measure of how probable its state is.

Einstein then realized in his 1905 paper that the entropy of radiation (including light) changes in the same mathematical way with the volume as for atoms. In both cases, the entropy increases with the logarithm of that volume. For Einstein this could not just be a coincidence. Since we can understand the entropy of the gas because it consists of atoms, the radiation consists also of particles that he calls energy quanta.

Einstein immediately applied his idea for example to his well-known application of the photoelectric effect. But he also realizes very soon a fundamental conflict of the idea of energy quanta with the well-studied and observed phenomenon of interference.

The problem is simply how to understand the two-slit interference pattern. This is the phenomenon that, according to Richard Feynman, contains "the only mystery" of quantum physics. The challenge is very simple. When we have both slits open, we obtain bright and dark stripes on an observation screen, the interference fringes. When we have only one slit open, we get no stripes, no fringes, but a broad distribution of particles. This can easily be understood on the basis of the wave picture. Through each of the two slits, a wave passes, and they extinguish each other at some places of the observation screen and at others, they enforce each other. That way, we obtain dark and bright fringes.

But what to expect if the intensity is so low that only one particle at a time passes through the apparatus? Following Einstein's realist position, it would be natural to assume that the particle has to pass through either slit. We can still do the experiment by putting a photographic plate at the observation screen and sending many photons in, one at a time. After a long enough time, we look at the photographic plate. According to Einstein, if the particle passes through either slit, no fringes should appear, because, simply speaking, how should the individual particle know whether the other slit, the one it does not pass through, is open or not. This was indeed Einstein's opinion, and he suggested that the fringes only appear if many particles go through at the same time, and somehow interact with each other such that they make up the interference pattern.

Today, we know that the pattern even arises if we have such low intensities that only one, say, photon per second passes through the whole apparatus. If we wait long enough and look at the distribution of all of them, we get the interference pattern. The modern explanation is that the interference pattern only arises if there is no information present anywhere in the Universe through which slit the particle passes. But even as Einstein was wrong here, his idea of the energy quanta of light, today called photons pointed far into the future.

In a letter to his friend Habicht in the same year of 1905, the miraculous year where he also wrote his Special Theory of Relativity, he called the paper proposing particles of light "revolutionary". As far as is known, this was the only work of his that he ever called revolutionary. And therefore it is quite fitting that the Nobel Prize was given to him for the discovery of particles of light. This was the Nobel Prize of 1921. That the situation was not as clear a few years before is witnessed by a famous letter signed by Planck, Nernst, Rubens and Warburg, suggesting Einstein for membership in the Prussian Academy of Sciences in 1913. They wrote: "the fact that he (Einstein) occasionally went too far should not be held too strongly against him. Not even in the exact natural sciences can there be progress without occasional speculation." Einstein's deep, elegant and beautiful explanation of the entropy of radiation, proposing particles of light in 1905, is a strong case in point for the usefulness of occasional speculation. 

The Inductive Economy of An Elegant Idea

An elegant and beautiful explanation is, to me, one that corrals a herd of seemingly unrelated facts within a single unifying concept. In our explorations of the worlds, including our own, that orbit the Sun, and in our attempts to find from these efforts what is special and what is commonplace about our own planet, I can think of two examples of this.

The first is an idea that was originally offered in the 1912 but met with such extreme hostility from the scientific establishment—not an unusual response, by the way, to an original idea—that it wasn't generally accepted until 50 years later. By that time, the sheer weight of evidence supporting it became so overwhelming that the notion was rendered irrefutable. And that notion was plate tectonics.

It could be said that the first indications of plate motions, though of course not recognized as such at the time, came from the observations of the early explorers, like Magellan, who noticed the puzzle-like fit of the continents, Africa and South America, for instance, on their maps. Fast forward to the early 20th century…Alfred Wegener, a German geophysicist, proposes movement of the continents (continental drift), to explain this hand-in-glove fit. Having no explanation, however, for how the continents could actually move, he was laughed out of the room.

But the evidence continued to mount: fossils, rock types, ancient climates were shown to be similar within widely separated geographical regions, like the east coast of South America and the west coast of Africa. Studies of magnetized rocks, which if stationary will always indicate a consistent direction to the north magnetic pole regardless where on the globe they form, indicated that either the north pole location varied throughout time or that the rocks themselves were not formed where they are found today. Finally, by the 1960s, it was clear that many of the Earth's presently active geological phenomena, such as the strongest earthquakes and volcanoes, were found within distinct, sinuous belts that wrapped around the planet and carved the Earth's surface into distinct bounded regions. Furthermore, studies of rocks on the floors of the Earth's oceans revealed an alternating north-up/north-down magnetic striping pattern that could only be explained by the upwelling of molten lava from below, creating new oceanic floor, and the consequent spreading of the old floor, pushing the continents farther apart with time. We now know that the tectonic forces driving the motions of the Earth's crustal plates arise from the convective upwelling and downwelling currents of molten rock in the Earth's mantle that drag around the solid plates sitting atop them.

In the end, the notion that bits of the Earth's surface can drift over time is a glorious example of a simple, efficient and even elegant idea that was eventually proven correct yet so radical for its time, it was scorned.

The second is more or less an extraterrestrial version of the same. In an historic mission not unlike Homer's Odyssey, two identical spacecraft—Voyager I and II—spent the 1980s touring the planetary systems of Jupiter, Saturn, Uranus and Neptune. And the images they returned provided humanity its first detailed views of these planets and the moons and rings surrounding them.

Jupiter was the gateway planet, the first of the four encountered, and it was there that we learned just how complex and presently active other planetary bodies could be. Along with the stunningly active moon, Io, which sported at the time about 9 large volcanic eruptions, Voyager imaged the surface of Jupiter's icy moon, Europa. Just a bit smaller than our own Moon, Europa's surface was clearly young, rather free of craters, and scored with a complex pattern of cracks and fractures that were cycloidal in shape and continuous, with many 'loops', like the scales on a fish. From these discoveries and others, it was inferred that Europa might have a thin crust overlying either warm, soft ice or perhaps even liquid water, though how the fracture pattern came to look the way it does was a mystery. The idea of a sub-surface ocean was enticing for the implicit possibility of a habitable zone for extraterrestrial life.

A follow-on spacecraft, Galileo, arrived at Jupiter in 1995 and before too long got an even better look at Europa's cracked ice shell and its cycloidal fractures. It became clear to researchers at the University of Arizona's Lunar and Planetary Lab that the cycloidal fractures, and even their detailed characteristics, like the shapes of the cycloidal segments, and the existence of, the distance between, and orientations of the cusps, could all be explained by the stresses across the moon's thin ice shell created by the tides raised on it by Jupiter. Europa's distance to Jupiter varies over the course of its orbit because of gravitational resonances with the other Jovian moons. And that varying separation causes the magnitude and direction of the tidal stresses on its surface to change. Under these conditions, if a crack in the thin ice shell is initiated at any location by these stresses, then that crack will propagate across the surface over the course of a Europan day and will take the shape of a cycloid. This will continue, day in and day out, scoring the surface of Europa in the manner that we find it today. Furthermore, tidal stresses would be inadequate to affect these kinds of changes to the moon's surface if its ice shell did not overlie a liquid ocean…an exciting possibility by anyone's measure.

And so, a whole array of features on the surface of one of Jupiter's most fascinating moons, the enormous complexity of the patterns they form, and the implication of a subterranean liquid water ocean in which extraterrestrial life might have taken hold, were explained and supported with one very simple, very easily demonstrated, and very elegant idea….an idea which itself, like that of plate tectonics, exemplifies the great beauty and economy derivable from logical induction, one of humankind's most demonstrably powerful intellectual devices.

The Principle of Least Action

Nature is lazy. Scientific paradigms and "ultimate" visions of the universe come and go, but the idea of "least action" has remained remarkably unperturbed. From Newton's classical mechanics to Einstein's general relativity to Schrödinger's quantum field theory, every major theory has been reformulated with this single principle, by Euler, Hilbert, and Feynman, respectively. The reliability of this framework suggests a form for whatever the next major paradigm shift may be.

Action is a strange quantity, in the units of energy multiplied by time. A principle of least action does not explicitly specify what will happen, like an equation of motion does, but simply asserts that the action will be the least of any conceivable actions. In some sense, the universe is maximally efficient. To be precise, the action integrated over any interval of time is always minimal. Euler and Lagrange discovered that not only is this principle true, but one can derive all of Newtonian physics from it. The Newtonian worldview was often characterized as "clockwork," both because clockwork was an apt contemporary technology, and because of the crucially absolute measurement of time.

In Einstein's relativity, absolute time was no longer possible, and totally new equations of motion had to be written. Now we have to deal with four-dimensional spacetime, rather than the familiar three-dimensional space and the special dimension of time. At speeds much less than the speed of light, a first-order approximation can transform Einstein's equations into Newton's, yet the resemblance is hardly obvious. However, the principle of least action remains much the same, but with a difference that intuitively connects to the essence of Einstein's insight: instead of just integrating over time, we must integrate over space too, with the speed of light serving as a constant exchange rate between spatial and temporal units. The essence of relativity is not its well-known consequences—time dilation, length dilation, or even E=mc^2. Rather, it is the more intuitive idea that space and time are simply different ways of looking at the same thing. Much more complicated mathematics is needed to derive Einstein's equations from this principle, but the legendary mathematician David Hilbert was able to do it. Maxwell's theory of electromagnetism, too, can be derived from the least action principle by a generalization of operators. Even more remarkably, combining the least-action tweaks that lead to Einstein's and Maxwell's equations respectively produces modern relativistic electromagnetism.

By this point you may be imagining that practically any physical theory can be formulated using the principle of least action. But in fact, many cannot —for instance, an early attempt at quantum electrodynamics, put forth by Paul Dirac. Such theories tend to have other issues that preclude their practical use; under many conditions, Dirac's theory prescribed infinite energies (clearly a dramatic difference from experiment). Quantum electrodynamics was later "fixed" by Feynman, a feat for which he won the Nobel Prize. In his Nobel lecture, he mentioned that the initial confirmation he was on the right track was that his version, unlike Dirac's, could be formulated as a principle of least action.

I believe it's reasonable to expect it will be possible to explain the next major physical theory using the least action framework, whatever it may be. Perhaps it will benefit us as scientists to explore our theories within this framework, rather than attempting to guess at once the explicit equations, and leaving the inevitable least action derivation as an exercise for some enterprising mathematician to work out.

The essential idea of least action transcends even the deepest of theoretical physics, and enters the domain of metaphysics. Claude Shannon derived a formula to quantify uncertainty, which von Neumann pointed out was identical to the formula used in thermodynamics to compute entropy. Edwin Jaynes put forth an interpretation of thermodynamics, in which entropy simply is uncertainty, nothing more and nothing less. Although the formal mathematical underpinnings remain controversial, I find it very worthwhile, at least as an intuitive explanation. Jaynes' followers propose a profound connection between action and information, such that the principle of least action and the laws of thermodynamics both derive from basic symmetries of logic itself. We need only accept that all conceivable universes are equally likely, a principle of least information. Under this assumption, we can imagine a smooth spectrum from metaphysics to physics, from the omniverse to the multiverse to the universe, where the fundamental axis is information, and the only fundamental law is that you can never assume more than you know.

Starting from nothingness, or the absence of information, there is a flowering of possible refinements toward specifying a universe, one of which leads to our Big Bang, to particles, fields and spacetime, and ultimately to intelligent life. The reason that we had a long period of stellar, planetary and biological evolution is that this is the path to intelligent life, which required the least action. Imagine how much action it would take to create intelligence directly from nothing! Universes without intelligent life might require even less action, but there is nobody in those universes to wonder where they came from.

At least for me, the least action perspective explains all known physics as well as the origin of our universe, and that sure is deep and beautiful.

"We Are Dreaming Machines That Construct Virtual Models Of The Real World"

The most beautiful and elegant explanation should be as strong and overwhelming as a brick smashing your head; it should break your life in two. For instance, as a result of that explanation, you should realize that even if you are dreaming your brain is active doing what he does best: creating models of reality or, in fact, creating the reality where you live in.

Descartes was aware of this fact and that's why he concluded "I think, therefore I am", cogito ergo sum. You can think of yourself as walking on a park, but this could be just a vivid dream. Therefore, it's not possible to conclude anything about your existence based on the apparent fact of walking. However, if you are really walking on a park, or dreaming, you are thinking, therefore existing. Dreaming is so similar to waking, that you can't trust any sensory information as proof of your existence. You can only trust the fact of thinking or, in contemporary words, the fact that your brain is active.

Dreaming and waking are similar cognitive states, as Rodolfo Llinás says in his masterpiece "I of the vortex". The only difference is that while dreaming, your brain is not perceiving or representing the external reality, it is emulating it and providing self-generated inputs.

The explanation is also shocking in its consequence. While waking we are also dreaming, concludes Llinás: "The waking state is a dreamlike state (…) guided and shaped by the senses, whereas regular dreaming does not involve the senses at all".

In both cases our brain generates models of reality.

With this explanation very few entities—the brain and the matter of reality—are enough to remind us how we create what is usually defined as "reality": "The only reality that exists for us is already a virtual one (…). We are basically dreaming machines that construct virtual models of the real world", says Llinás.

This is not only a beautiful explanation because of the poetic fact that reality is self-generated while dreaming, and partially generated while waking. Is there anything more beautiful than understanding how to create reality?

This is not only an elegant explanation because it shows our minuscule and entirely representative place in the ontological and physical reality, in the huge amount of matter defined as universe.

This explanation is overwhelming in practical terms because as a philosopher and social scientist, I cannot explain the physical or the social reality without considering that we live and move in a model of reality. Including the representational, creative and even ontological role of the brain, is a naturalization project usually omitted as a result of hyper-positivism and scientific fragmentation. From Descartes to Llinás, form the understanding of galaxies to the understanding of crime, this explanation should be relevant in most scientific enterprises.

Bounded Rationality As An Explanation For Many of Our Ills

Explanations that are extraordinary, both analytically and aesthetically, share among others, these properties: (a) they are often simpler compared to what was received wisdom, (b) they point to the more true cause as being some place quite removed from the phenomenon, and (c) they make you wish so much that you had come upon the explanation yourself.

Those of us who attempt to understand the mind, have a unique limitation to confront: the object that is the knower is also the known. The mind is the thing doing the explaining; the mind is also the thing to be explained. Distance from one's own mind, distance from attachments to the specialness of one's species or tribe, getting away from introspection and intuition (not as hypothesis generators but as answers and explanations) are all especially hard to achieve when what we seek to do is explain our own minds and those of others of our kind.

For this reason, my candidate for the most deeply satisfying explanation of recent decades is the idea of bounded rationality. The idea that human beings are smart by comparison to other species, but not smart enough by their own standards including behaving in line with basic axioms of rationality is a now a well-honed observation with deep empirical foundation in the form of discoveries in support.

Herbert Simon put one stake in the ground through the study of information processing and AI, showing that both people and organizations follow principles of behavior such as "satisficing" that constrain them to decent but not the best decisions. The second stake was placed by Kahneman and Tversky, who showed the stunning ways in even experts are error-prone—with consequences for not only their own health and happiness but that of their societies broadly.

Together the view of human nature that evolved over the past four decades has systematically changed the explanation for who we are and why we do what we do. We are error-prone in the unique ways in which we are, the explanation goes, not because we have malign intent, but because of the evolutionary basis of our mental architecture, the manner in which we remember and learn information, the way in which we are affected by those around us and so on. The reason we are boundedly rational is because the information space in which we must do our work is large compared to the capacities we have, including severe limits on conscious awareness, the ability to be able to control behavior, and to act in line even with our own intentions.

From these bounds on rationality generally, we can look also at the compromise of ethical standards—again the story is the same; that it is not intention to harm that's the problem. Rather the explanation lies in such sources are the manner in which some information plays a disproportionate role in decision making, the ability to generalize or overgeneralize, and the commonness of wrong doing that typify daily life. These are the more potent causes of the ethical failures of individuals and institutions.

The idea that bad outcomes result from limited minds that cannot store, compute and adapt to the demands of the environment is a radically different explanation of our capacities and thereby our nature. It's elegance and beauty comes from it placing the emphasis on the ordinary and the invisible rather than on specialness and malign motives. This seems not so dissimilar from another shift in explanation from god to natural section and it is likely to be equally resisted. 

What Time Is It? 

A few years ago, I heard said only old-fashioned folk wear watches. But I thought I would always wear a watch. Today I don't wear a watch.

How do I find the time? Either I do without or I keep my eyes fixed on a screen that has the time in the upper-right corner. It's gotten so that I resent that reality doesn't dispay the time in the upper-right corner. 

You Think, Therefore I Am

"I think, therefore I am." Cogito ergo sum. Remember this elegant and deep idea from René Descartes' Principles of Philosophy? The fact that a person is contemplating whether she exists, Descartes argued, is proof that she, indeed, actually does exist. With this single statement, Descartes knit together two central ideas of Western philosophy: 1) thinking is powerful, and 2) individuals play a big role in creating their own I's—that is, their psyches, minds, souls, or selves.

Most of us learn "the cogito" at some point during our formal education. Yet far fewer of us study an equally deep and elegant idea from social psychology: Other people's thinking likewise powerfully shapes the I's that we are. Indeed, in many situations, other people's thinking has a bigger impact on our own thoughts, feelings, and actions than do the thoughts we conjure while philosophizing alone.

In other words, much of the time, "You think, therefore I am." For better and for worse.

An everyday instance of how your thinking affects other people's being is the Pygmalion effect. Psychologists Robert Rosenthal and Lenore Jacobson captured this effect in a classic 1963 study. After giving an IQ test to elementary school students, the researchers told the teachers which students would be "academic spurters" because of their allegedly high IQs. In reality, these students' IQs were no higher than those of the "normal" students. At the end of the school year, the researchers found that the "spurters'" had attained better grades and higher IQs than the "normals." The reason? Teachers had expected more from the spurters, and thus given them more time, attention, and care. And the conclusion? Expect more from students, and get better results.

A less sanguine example of how much our thoughts affect other people's I's is stereotype threat. Stereotypes are clouds of attitudes, beliefs, and expectations that follow around a group of people. A stereotype in the air over African Americans is that they are bad at school. Women labor under the stereotype that they suck at math.

As social psychologist Claude Steele and others have demonstrated in hundreds of studies, when researchers conjure these stereotypes—even subtly, by, say, asking people to write down their race or gender before taking a test—students from the stereotyped groups score lower than the stereotype-free group. But when researchers do not mention other people's negative views, the stereotyped groups meet or even exceed their competition. The researchers show that students under stereotype threat are so anxious about confirming the stereotype that they choke on the test. With repeated failures, they seek their fortunes in other domains. In this tragic way, other people's thoughts deform the I's of promising students.

As the planet gets smaller and hotter, knowing that "You think, therefore I am" could help us more readily understand how we affect our neighbours and how our neighbours affect us. Not acknowledging how much we impact each other, in contrast, could lead us to repeat the same mistakes.

How The Availability Of Some Plants And Animals Can Explain Thousands Of Years Of Human History

One of the most elegant explanations I have encountered in the social sciences comes courtesy of Jared Diamond, and is outlined in his wonderful book "Guns, Germs, and Steel." Diamond attempts to answer an enormously complex and historically controversial question—why certain societies achieved such historical dominance over others—by appealing to a set of very basic differences in the physical environments from which these societies emerged (such as differences in the availability of plants and animals suitable for domestication).

These differences, Diamond argues, gave rise to a number of specific advantages (such as greater immunity to disease) that were directly responsible for the historical success of some societies.

I'm not an expert in this domain, and I accept that Diamond's explanation might be completely misguided. Yet the appeal to such basic mechanisms in order to explain such a wide set of complex observations is so deeply satisfying that I hope he is right.

Subjective Environment

Explanations tend to be at their most elegant, when science distills the meanderings of philosophy into fact. I was looking for explanations for an observation, when I came across the theory of "Umwelt" versus "Umfeld" (vaguely environment versus surroundings) by the Estonian biologist and forefather of biosemiotics Jakob von Uexküll. According to his definition "Umwelt" is the subjective environment as perceived and impacted by an organism, while "Umfeld" is the objective environment which encompasses and impacts all organisms in it's realm.

My observation had been a mere notion of the major difference between my native Europe and America, my adopted continent for a couple of decades. In Europe the present is perceived as the end point of history. In America the present is perceived as the beginning of the future. Philosophy or history, I hoped, would have an explanation for such a fundamental yet simple difference. Both can deliver parts of an explanation of course. The different paths the histories of ideas and the histories of the countries have taken just in the past 200 years are astounding.

Uexküll's definition of the subjective environment as published in his book Umwelt und Innnenwelt der Tiere (Environments and inner worlds of animals, published 1909 in the language of his German exile) puts both philosophy and history into perspective and context though. Distrusting theories he always wanted ideas to persist in nature. Putting his idea of the subjective environment to the test in the Indian Ocean, the Atlantic and the Mediterranean. He observed simple creatures like sea anemones, sea urchins and crustaceans. His most famous example to explain his theory was the tick though. Here he found a creature whose perception and actions could be defined by three parameters each. Ticks perceive their surroundings by the directions of up and down, by warm and cold and the presence or absence of butyric acid. Their actions to survive and procreate are crawling, waiting and gripping.

This model lead him not only to define environment as a subjective notion. He found the perception of time for any organism as subjective as the perception of space, defined by the very perceptions and actions that create the organism's subjective environment. If subjective time is defined by the experiences and actions of an organism, the context of a continent's history with its myriads of parameters turns philosophy and history into mere factors in a complex environment of collective perception. Now there was an elegant explanation for a rather simple observation. Making it even more elegant is the notion that in the context of a continent's evolution geography, climate, food and culture will weigh in as factors of the perception of the subjective environment and time as well, making it impossible to prove or disprove the explanation scientifically. Having rendered philosophy to just one of many parameters it thus reduces its efforts to discredit Jakob von Uexküll's definition of the subjective environment to mere meanderings. 

Sexual Conflict Theory

A fascinating parallel has occurred in the history of the traditionally separate disciplines of evolutionary biology and psychology. Biologists historically viewed reproduction as an inherently cooperative venture. A male and female would couple for the shared goal of reproduction of mutual offspring. In psychology, romantic harmony was presumed to be the normal state. Major conflicts within romantic couples were and still are typically seen as signs of dysfunction. A radical reformulation embodied by sexual conflict theory changes these views.

Sexual conflict occurs whenever the reproductive interests of an individual male and individual female diverge, or more precisely when the "interests" of genes inhabiting individual male and female interactants diverge. Sexual conflict theory defines the many circumstances in which discord is predictable and entirely expected.

Consider deception on the mating market. If a man is pursuing a short-term mating strategy and the woman for whom he has sexual interest is pursuing a long-term mating strategy, conflict between these interactants is virtually inevitable. Men are known to feign long-term commitment, interest, or emotional involvement for the goal of casual sex, interfering with women's long-term mating strategy. Men's have evolved sophisticated strategies of sexual exploitation. Conversely, women sometimes present themselves as costless sexual opportunities, and then intercalate themselves into a man's mating mind to such a profound degree that he wakes up one morning and suddenly realizes that he can't live without her—one version of the ‘bait and switch' tactic in women's evolved arsenal.

Once coupled in a long-term romantic union, a man and a woman often still diverge in their evolutionary interests. A sexual infidelity by the woman might benefit her by securing superior genes for her progeny, an event that comes with catastrophic costs to her hapless partner who unknowingly devotes resources to a rival's child. From a woman's perspective, a man's infidelity risks the diversion of precious resources to rival women and their children. It poses the danger of losing the man's commitment entirely. Sexual infidelity, emotional infidelity, and resource infidelity are such common sources of sexual conflict that theorists have coined distinct phrases for each.

But all is not lost. As evolutionist Helena Cronin has eloquently noted, sexual conflict arises in the context of sexual cooperation. The evolutionary conditions for sexual cooperation are well-specified: When relationships are entirely monogamous; when there is zero probability of infidelity or defection; when the couple produces offspring together, the shared vehicles of their genetic cargo; and when joint resources cannot be differentially channeled, such as to one set of in-laws versus another.

These conditions are sometimes met, leading to great love and harmony between a man and a woman. The prevalence of deception, sexual coercion, stalking, intimate partner violence, murder, and the many forms of infidelity reveal that conflict between the sexes is ubiquitous. Sexual conflict theory, a logical consequence of modern evolutionary genetics, provides the most beautiful theoretical explanation for these darker sides of human sexual interaction.

A Hot Young Earth: Unquestionably Beautiful and Stunningly Wrong

Around 4.567 billion years ago, a giant cloud of dust collapsed in on itself. At the center of the cloud our Sun began to burn, while the outlying dust grains began to stick together as they orbited the new star. Within a million years, those clumps of dust had become protoplanets. Within about 50 million years, our own planet had already reached about half its current size. As more protoplanets crashed into Earth, it continued to grow. All told, it may have taken another fifty million years to reach its full size—a time during which a Mars-sized planet crashed into it, leaving behind a token of its visit: our Moon.

The formation of the Earth commands our greatest powers of imagination. It is primordially magnificent. But elegant is not the word I'd use to describe the explanation I just sketched out. Scientists did not derive it from first principles. There is no equivalent of E=mc² that predicts how the complex violence of the early Solar System produced a watery planet that could support life.

In fact, the only reason that we now know so much about how the Earth formed is because geologists freed themselves from a seductively elegant explanation that was foisted on them 150 years ago. It was unquestionably beautiful, and stunningly wrong.

The explanation was the work of one of the greatest physicists of the nineteenth century, William Thompson (a k a Lord Kelvin). Kelvin's accomplishments ranged from the concrete (figuring out how to lay a telegraph cable from Europe to America) to the abstract (the first and second laws of thermodynamics). Kelvin spent much of his career writing equations that could let him calculate how fast hot things got cold. Kelvin realized that he could use these equations to estimate how old the Earth is. "The mathematical theory on which these estimates are founded is very simple," Kelvin declared when he unveiled it in 1862.

At the time, scientists generally agreed that the Earth had started out as a ball of molten rock and had been cooling ever since. Such a birth would explain why rocks are hot at the bottom of mine shafts: the surface of the Earth was the first part to cool, and ever since, the remaining heat inside the planet has been flowing out into space. Kelvin reasoned that over time, the planet should steadily grow cooler. He used his equations to calculate how long it should take for a molten sphere of rock to cool to Earth's current temperature, with its observed rate of heat flow. His verdict was a brief 98 million years.

Geologists howled in protest. They didn't know how old the Earth was, but they thought in billions of years, not millions. Charles Darwin—who was a geologist first and then a biologist later—estimated that it had taken 300 million years for a valley in England to erode into its current shape. The Earth itself, Darwin argued, was far older. And later, when Darwin published his theory of evolution, he took it for granted that the Earth was inconceivably old. That luxury of time provided room for evolution to work slowly and imperceptibly.

Kelvin didn't care. His explanation was so elegant, so beautiful, so simple that it had to be right. It didn't matter how much trouble it caused for other scientists who would ignore thermodynamics. In fact, Kelvin made even more trouble for geologists when he took another look at his equations. He decided his first estimate had been too generous. The Earth might be only 10 million years old.

It turned out that Kelvin was wrong, but not because his equations were ugly or inelegant. They were flawless. The problem lay in the model of the Earth to which Kelvins applied his equations.

The story of Kelvin's refutation got a bit garbled in later years. Many people (myself included) have mistakenly claimed that his error stemmed from his ignorance of radioactivity. Radioactivity was only discovered in the early 1900s as physicists worked out quantum physics. The physicist Ernst Rutherford declared that the heat released as radioactive atom broke down inside the Earth kept it warmer than it would be otherwise. Thus a hot Earth did not have to be a young Earth.

It's true that radioactivity does give off heat, but there isn't enough inside the planet is to account for the heat flowing out of it. Instead, Kelvin's real mistake was assuming that the Earth was just a solid ball of rock. In reality, the rock flows like syrup, its heat lifting it up towards the crust, where it cools and then sinks back into the depths once more. This stirring of the Earth is what causes earthquakes, drives old crust down into the depths of the planet, and creates fresh crust at ocean ridges. It also drives heat up into the crust at a much greater rate than Kelvin envisioned.

That's not to say that radioactivity didn't have its own part to play in showing that Kelvin was wrong. Physicists realized that the tick-tock of radioactive decay created a clock that they could use to estimate the age of rocks with exquisite precision. Thus we can now say that the Earth is not just billions of years old, but 4.567 billion.

Elegance unquestionably plays a big part in the advancement of science. The mathematical simplicity of quantum physics is lovely to behold. But in the hands of geologists, quantum physics has brought to light the glorious, messy, and very inelegant history of our planet. 

Feynman's Lifeguard

I would like to propose not only a particular explanation, but also a particular exposition and exponent: Richard Feynman's lectures on quantum electrodynamics (QED) delivered at the University of Auckland in 1979. These are surely among the very best ever delivered in the history of science.

For a start, the theory is genuinely profound, having to do with the behaviour and interactions of those (apparently) most fundamental of particles, photons and electrons. And yet it explains a huge range of phenomena, from the reflection, refraction and diffraction of light to the structure and behaviour of electrons in atoms and their resultant chemistry. Feynman may have been exaggerating when he claimed that QED explains all of the phenomena in the world "except for radioactivity and gravity", but only slightly.

Let me give a brief example. Everyone knows that light travels in straight lines—except when it doesn't, such as when it hits glass or water at anything other than a right angle. Why? Feynman explains that light always takes the path of least time from point to point and uses the analogy of a lifeguard racing along a beach to save a drowning swimmer. (This being Feynman, the latter is, of course, a beautiful girl.) The lifeguard could run straight to the water's edge and then swim diagonally along the coast and out to sea, but this would result in a long time spent swimming, which is slower than running on the beach. Alternatively, he could run to the water's edge at the point nearest to the swimmer, and dive in there. But this makes the total distance covered longer than it needs to be. The optimum, if his aim is to reach the girl as quickly as possible, is somewhere in between these two extremes. Light, too, takes such a path of least time from point to point, which is why it bends when passing between different materials.

He goes on to reveal that this is actually an incomplete view. Using the so-called 'path integral formulation' (though he avoids that ugly term), Feynman explains that light actually takes every conceivable path from one point to another, but most of these cancel each other out, and the net result is that it appears to follow only the single path of least time. This also happens to explain why uninterrupted light (along with everything else) travels in straight lines—so fundamental a phenomenon that surely very few people even consider it to be in need of an explanation. While at first sight such a theory may seem preposterously profligate, it achieves the welcome result of minimising that most scientifically unsatisfactory of all attributes: arbitrariness.

My amateurish attempts at compressing and conveying this explanation have perhaps made it sound arcane. But on the contrary, a second reason to marvel is that it is almost unbelievably simple and intuitive. Even I, an innumerate former biologist, came away not merely with a vague appreciation that some experts somewhere had found something novel, but that I was able to share directly in this new conception of reality. Such an experience is all too rare in science generally, but in the abstract, abstruse world of quantum physics is all but unknown. The main reason for this perspicacity was the adoption of a visual grammar (those famous 'Feynman diagrams') and an almost complete eschewal of hardcore mathematics (the fact that the spinning vectors that are central to the theory actually represent complex numbers seems almost incidental). Though the world it introduces is as unfamiliar as can be, it makes complete sense in its own bizarre terms.

How Do You Get From A Lobster To A Cat?

Did you ever notice that the "vein" you are told, for some reason, to remove from shrimp before eating them doesn't seem to ooze anything you'd be inclined to call blood? Doesn't the slime seem more like some sort of alimentary waste? That's because it is. In shrimp, you can get at the digestive system right through its back because that's where it is. The heart's up there too, and this is the way it is in arthropods, the animal phylum that includes crustaceans and insects. Meanwhile, if you were interested in finding the shrimp's main nerve highway, you'd find it running down along its bottom side.

That feels backwards to us, because we're chordates, another big animal phylum. Chordates have the spinal nerve running down the back, with the gut and heart up in front. It's as if our body plans were mirror images of arthropods', and this is a microcosm of a general split between larger classes: arthropods are among the protostomes, with the guts on the back, as opposed to the deuterostomes that we chordates are among, with the guts up front.

Biologists have noticed this since auld lang sine, with naturalist Étienne Geoffroy Saint-Hilaire famously turning a dissected lobster upside down and showing that as such, its innards' arrangement resembled ours. The question was how things got this way, especially as Darwin's natural selection theory became accepted. How could one get step-by-step from guts on the back and the spinal chord up front to the reverse situation? More to the point, why would this be evolutionarily advantageous, which is the only reason we assume it would happen at all?

Short of imagining that the nerve chord glommed upward and took over the gut and a new gut spontaneously developed down below because it was "needed"—this was actually entertained for a while by one venturesome thinker—the best biologists could do for a long time was suppose that the arthropod plan and the chordate plan were alternative pathways of evolution from some primordial creature. It must have just been a matter of the roll of the dice coming out differently one time than the next one, they thought.

Not only was this boring—the problem was that molecular biology started making it ever clearer that arthropods and chordates trace back to the same basic body plan in a good amount of detail. The shrimp's little segments are generated by the same basic genes that create our vertebral column, and so on. Which leads to the old question again—how do you get from a lobster to a cat? Biologists are converging upon an answer that combines elegance with a touch of mystery while occasioning a scintilla of humility in the bargain.

Namely, what is increasingly thought to have happened is that some early worm-like aquatic creature with the arthropod-style body plan started swimming upside-down. Creatures can do that: brine shrimp, today, for example (remember those "sea monkeys"?). Often it's because a creature's coloring is different on the top than the bottom, and having the top color face down makes them harder for predators to see. That is, there would have been evolutionary advantage to such a creature gradually turning upside down forever.

But what this would mean is that in this creature, the spinal chord was up and the guts were down. In itself, that's perhaps cute, maybe a little sad, but little more. But—suppose this little worm then evolved into today's chordates? It's hardly a stretch, given that the most primitive chordates actually are wormish, only vaguely piscine things called lancelets. And of course, if you were moved to rip one open you'd see that nerve chord on the back, not the front.

Molecular biology is quickly showing exactly how developing organisms can be signaled either to develop a shrimp-like or a cat-like body plan along these lines. There even seems to be a "missing link"—there are rather vile, smelly bottom-feeding critters called acorn worms that have nerve chords on the back and on the front, and guts that seem on their way to moving on down.

So—the reason we humans have a backbone is not because it's somehow better to have a spinal column to break a fall backwards or anything of the sort. Roll the dice again and we could be bipedals with spinal columns running down our fronts like zippers and the guts carried in the back (it actually doesn't sound half bad). And beyond this, this explanation of what's called dorsoventral inversion is yet more evidence of how under natural selection, such awesome variety can emerge in unbroken fashion from such humble beginnings. And finally, it's hard not to be heartened by a scientific explanation that early adopters, like Geoffroy-St. Hilaire, were ridiculed for espousing.

Quite often when preparing shrimp, tearing open a lobster, contemplating what it would be like to be forced to dissect an acorn worm, patting my cat on the belly, or giving someone a hug, I think a bit about the fact that all of those bodies are built on the same plan, except that the cats' and the huggees' bodies are the legacy of, of all things, some worm swimming the wrong way up in a Precambrian Ocean over 550 million years ago. It has always struck me as rather gorgeous.

Flocking Behaviour In Birds

My favourite explanation is Craig Reynold's suggestion (first published in 1986, I think) that flocking behaviour in birds can be explained by assuming that each bird follows three simple rules—separation (don't crowd your neighbours), alignment (steer towards the average heading of your neighbours) and cohesion (steer towards the average position of your neighbours). The idea that such complex behaviour can be accounted for in such a breathtakingly simple way is, well, just beautiful.

Life Is a Digital Code

It's hard now to recall just how mysterious life was on the morning of 28 February and just how much that had changed by lunchtime. Look back at all the answers to the question "what is life?" from before that and you get a taste of just how we, as a species, floundered. Life consisted of three-dimensional objects of specificity and complexity (mainly proteins). And it copied itself with accuracy. How? How do you set about making a copy of a three-dimensional object? How to do you grow it and develop it in a predictable way? This is the one scientific question where absolutely nobody came close to guessing the answer. Erwin Schrodinger had a stab, but fell back on quantum mechanics, which was irrelevant. True, he used the phrase "aperiodic crystal" and if you are generous you can see that as a prediction of a linear code, but I think that's stretching generosity.

Indeed, the problem had just got even more baffling thanks to the realization that DNA played a crucial role—and DNA was monotonously simple. All the explanations of life before 28 Feb 1953 are hand-waving waffle and might as well speak of protoplasm and vital sparks for all the insights they gave.

Then came the double helix and the immediate understanding that, as Crick wrote to his son a few weeks later, "some sort of code"—digital, linear two-dimensional, combinatorially infinite and instantly self-replicating—was all the explanation you needed. Here's part of Francis Crick's letter, 17 March 1953:

"My Dear Michael,

Jim Watson and I have probably made a most important discovery...Now we believe that the DNA is a code. That is, the order of the bases (the letters) makes one gene different from another gene (just as one page pf print is different from another). You can see how Nature makes copies of the genes. Because if the two chains unwind into two separate chains, and if each chain makes another chain come together on it, then because A always goes with T, and G with C, we shall get two copies where we had one before. In other words, we think we have found the basic copying mechanismby which life comes from life...You can understand we are excited."

Never has a mystery seemed more baffling in the morning and an explanation more obvious in the afternoon.

One Concidence; Two Deja Vues

I take comfort in the fact that there are two human moments that seem to be doled out equally and democratically within the human condition—and that there is no satisfying ultimate explanation for either. One is coincidence, the other is déja vu. It doesn't matter if you're Queen Elizabeth, one of the thirty-three miners rescued in Chile, a South Korean housewife or a migrant herder in Zimbabwe—in the span of 365 days you will pretty much have two déja vus as well as one coincidence that makes you stop and say, "Wow, that was a coincidence."

The thing about coincidence is that when you imagine the umpteen trillions of coincidences that can happen at any given moment, the fact is, that in practice, coincidences almost never do occur. Coincidences are actually so rare that when they do occur they are, in fact memorable. This suggests to me that the universe is designed to ward of coincidence whenever possible—the universe hates coincidence—I don't know why—it just seems to be true. So when a coincidence happens, that coincidence had to work awfully hard to escape the system. There's a message there. What is it? Look. Look harder. Mathematicians perhaps have a theorem for this, and if they do, it might, by default be a theorem for something larger than what they think it is.

What's both eerie and interesting to me about déja vus is that they occur almost like metronomes throughout our lives, about one every six months, a poetic timekeeping device that, at the very least, reminds us we are alive. I can safely assume that my thirteen year old niece, Stephen Hawking and someone working in a Beijing luggage-making factory each experience two déja vus a year. Not one. Not three. Two.

The underlying biodynamics of déja vus is probably ascribable to some sort of tingling neurons in a certain part of the brain, yet this doesn't tell us why they exist. They seem to me to be a signal from larger point of view that wants to remind us that our lives are distinct, that they have meaning, and that they occur throughout a span of time. We are important, and what makes us valuable to the universe is our sentience and our curse and blessing of perpetual self-awareness.

Structural Realism

Structural realism—in its metaphysical version, championed by the philosopher of science James Ladyman—is the deepest explanation I know, because it serves as a kind of meta-explanation, one that explains the nature of reality and the nature of scientific explanations.

The idea behind structural realism is pretty simple: the world isn't made of things, it's made of mathematical relationships, or structure. A mathematical structure is a set of isomorphic elements, each of which can be perfectly mapped onto the next. To give a trivial example, the numbers 25 and 5² share the same mathematical structure.

When the philosopher John Worrall first introduced structural realism (though he attributes it to physicist Henri Poincaré), he was trying to explain something puzzling: how was it possible that a scientific theory that would later turn out to be wrong could still manage to make accurate predictions? Take Newtonian gravity. Newton said that gravity was a force that masses exert on one another from a distance. That idea was overthrown by Einstein, who showed that gravity was the curvature of spacetime. Given how wrong Newton was about gravity, it seems almost miraculous that he was able to accurately predict the motions of the planets.

Thankfully, we don't have to resort to miracles. Newton may have gotten the physical interpretation of gravity wrong, but he got a piece of the math right. That's why, at weak masses and small velocities, Einstein's equations reduce to Newton's. The problem, Worrall pointed out, was that we mistook an interpretation of the theory for the theory itself. The fact is, in physics, theories are sets of equations, and nothing more. "Quantum field theory" is a group of mathematical structures. "Electrons" are little stories we tell ourselves.

These days, believing in the reality of objects—of physical things like particles, fields, forces, even spacetime geometries—can quickly lead to profound existential crises.

Quantum theory, for instance, strips particles of any sense of "thingness". One electron is not merely similar to another, all electrons are exactly the same. Electrons have no inherent identity—a fact that makes quantum statistics drastically different from the classical kind. Anyone who believes that an electron is a "thing" in its own right is bound to lose big in a quantum casino.

Meanwhile, all of nature's fundamental forces, including electromagnetism and the nuclear forces that operate deep in the cores of atoms, are described by gauge theory, which shows that forces aren't physical things in the world, but discrepancies in different descriptions of the world, in different observers' points of view. Gravity is a gauge force too, which means you can make it blink out of existence just by changing your frame of reference. In fact, that was Einstein's "happiest thought": a person in freefall can't feel their weight. It's often said that you can't disobey the law of gravity, but the truth is you can take it out with a simple coordinate change.

Recent advances in theoretical physics have only made the situation worse. The holographic principle tells us that our four-dimensional spacetime and everything in it is exactly equivalent to physics taking place on the two-dimensional boundary of the universe. Neither description is more "real" than the other—one can be perfectly mapped onto the other with no loss of information. When we try to believe that spacetime is really four-dimensional or really has a particular geometry, the holographic principle pulls the rug out from under us.

The physical nature of reality has been further eroded by M-theory, the theory that many physicists believe can unite general relativity and quantum mechanics. M-theory encompasses five versions of string theory (plus one non-stringy theory known as supergravity) all of which are related by mathematical maps called dualities. What looks like a strong interaction in one theory looks like a weak interaction in another. What look like eleven dimensions in one theory look like ten in another. Big can look like small, strings can look like particles. Virtually any object you can think of will be transformed into something totally different as you move from one theory to the next—and yet, somehow, all of the theories are equally true.

This reality crisis has grown so dire that Stephen Hawking has called for a kind of philosophical surrender, a white flag he terms "model-dependent realism", which basically says that while our theoretical models offer possible descriptions of the world, we'll simply never know the true reality that lies beneath. Perhaps there is no reality at all.

But structural realism offers a way out. An explanation. A reality. The only catch is that it's not made of physical objects. Then again, our theories never said it was. Electrons aren't real, but the mathematical structure of quantum field theory is. Gauge forces aren't real, but the symmetry groups that describe them are. The dimensions, geometries and even strings described by any given string theory aren't real—what's real are the mathematical maps that transform one string theory into another.

Of course, it's only human to want to interpret mathematical structure. There's a reason that "42" is hardly a satisfying answer to life, the universe and everything. We want to know what the world is really like, but we want it in a form that fits our intuitions. A form that means something. And for our narrative-driven brains, meaning comes in the form of stories, stories about things. I doubt we'll ever stop telling stories about how the universe works, and I, for one, am glad. We just have to remember not to mistake the stories for reality.

Structural realism forces us to radically revise the way we think about the universe. But it also provides a powerful explanation for some of the most mystifying aspects of physics. Without it, we'd have to give up on the notion that scientific theories can ever tell us how the world really is. And that, in my humble opinion, makes it a pretty beautiful explanation.

Complexity Out of Simplicity

As a scientist dealing with complex behavioral and cognitive processes, my deep and elegant explanation comes not from psychology (which is rarely elegant) but from the mathematics of physics. For my money, Fourier's theorem has all the simplicity and yet more power than other familiar explanations in science. Stated simply, any complex pattern, whether in time or space, can be described as a series of overlapping sine waves of multiple frequencies and various amplitudes.

I first encountered Fourier's theorem when I was a Ph.D. student in Cambridge working on visual development. There, I met Fergus Campbell who in the 1960's had demonstrated that not only was Fourier theorem an elegant way of analyzing complex visual patterns, but it was also biologically plausible. This insight was later to become a cornerstone of various computational models of vision. But why restrict the analysis to vision?

In effect, any complex physical event can be reduced to the mathematical simplicity of sine waves. It doesn't matter whether it is Van Gogh's Starry Night, Mozart's Requiem, Chanel's No. 5, Rodin's Thinker or a Waldorf salad. Any complex pattern in the environment can be translated into neural patterns that in turn, can be decomposed into the multitude of sine wave activity arising from the output of populations of neurons.

Maybe I have some physics envy, but to quote Lord Kelvin, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." You don't get much higher praise than that.

Birds Are The Direct Descendents Of Dinosaurs

The most graceful example of an elegant scientific idea in one of my fields of expertise is the idea is that dinosaurs were tachyenergetic, that they were endotherms with the high internal energy production and high aerobic exercise capacity typical of birds and mammals that can sustain long periods of intense activity. Although it is not dependent upon it, high powered dinosaurs blends in with the hypothesis that birds are the direct descendents of dinosaurs, that birds literally are flying dinosaurs, much as bats are flying mammals.

 It cannot be overemphasized how much sense the above makes, and how it has revolutionized a big chunk of our understanding of evolution and 230 millions years of earth history relative to what was thought from the mid 1800s to the 1960s. Until then it was generally presumed that dinosaurs were a dead end collection of bradyenergetic reptiles that could achieve high levels of activity for only brief bursts; even walking at 5 mph requires high respiratory capacity beyond that of reptiles who must plod along at a mph or so if they are moving a long distance. Birds were seen as a distinct and feathery group in which energy inefficiency evolved in order to power flight.

Although the latter hypothesis was not inherently illogical, it was divergent from the evolution of bats in which high aerobic capacity was already present in their furry ancestors.

I first learned of "warm-blooded" dinosaurs in my senior year of high school via a blurb in Smithsonian Magazine about Robert Bakker's article in Nature in the summer of 1972. As soon as I read it, it just clicked. I had been illustrating dinosaurs in accord with the reptilian consensus, but it was a bad fit because dinosaurs are so obviously constructed like birds and mammals, not crocs and lizards. About the same time John Ostrom, who also had a hand in discovering dinosaur endothermy, was presenting the evidence that birds are aerial versions of avepod dinosaurs—a concept so obvious that should have become the dominant thesis back in the 1800s.

For a quarter century the hypotheses was highly controversial—the one regarding dinosaur metabolics especially so—and some of the first justifications were flawed. But the evidence has piled up. Growth rings in dinosaur bones show they grew at the fast pace not achievable by reptiles, their trackways show they walked at steady speeds too high for bradyaerobes, many small dinosaurs were feathery, and polar dinosaurs, birds and mammals were living through blizzardy Mesozoic winters that excluded ectotherms.

 Because of the dinorevolution our understanding of the evolution of the animals that dominated the continents is far closer to the truth than it was. Energy efficient amphibians and reptiles dominated the continents for only 70 million years in the later portion of the Paleozoic, the era that had begun with trilobites and nothing on land. For the last 270 million years higher power albeit less energy efficient tachyenergy has reigned supreme on land, starting with protomammalian therapsids near the end of the Paleozoic. When therapsids went belly up early in the Mesozoic (the survivors of the group being the then all small mammals) they were not replaced by lower power dinosaurs for the next 150 million years, but by dinosaurs that quickly took aerobic exercise capacity to even greater levels.

The unusual avian respiratory complex is so effective that some birds fly as high as airliners, but the system did not evolve for flight. That's because the skeletal apparatus for operating air sac ventilated lungs first developed in flightless avepod dinosaurs for terrestrial purposes (some but by no means all offer low global oxygen levels as the selective factor). So the basics of avian energetics appeared in predacious dinosaurs, and only later were used to achieve powered flight. Rather like how internal combustion engines happened to make powered human flight practical, rather than being developed to do so.

The Gravitational Harmony of Quantum Fields

These three terms are all interconnected in my head. While I was about to quit Grad school in theoretical physics, I stumbled across a quantum field theory book on a classmate's desk which, upon reading the introduction, enticed me to finish up. Let me paraphrase the beginning of the book's intro: "The new paradigm of physics describes the totality of nature as an ensemble vibrating fields that interact with each other… in that sense the universe is like an orchestra and we are a result of eons of harmonies, rhythm and improvisation" (I added in the improvisation part). It helped that I was also a student of jazz theory at the time.

As I continued to study quantum field theory over the years (and now teach the subject), I am amazed at the concise parallels between the quantum field paradigm of nature, music and improvisation. Connected to this theme is one of the coolest things I've learned; an idea that was pioneered by a true master in quantum field theory, Leonard Parker. The basic idea is that when we combine Einstein's discovery that the gravitational force arises from the curving of spacetime with the field paradigm of matter we get a very neat physical effect—which underlies Stephen Hawking's information loss paradox and the emergence of matter from the early universe that is devoid of stars and galaxies.

Last month I had the pleasure to finally meet Parker at the University of Wisconsin, Milwaukee. After a seminar on gravitational wave physics, Leonard took me to his office and revealed the pioneering calculations in his PhD dissertation, which established the study of quantum fields in curved spacetime—I'll refer to the effect as the Parker Process.

In quantum field theory, we can think of all matter as a field (similar to the electromagnetic field) that permeates a large region of space. A useful picture is to imagine a smooth blanket of magnetic fields that fills our entire galaxy (which is actually true). Likewise the electron also has a field that can be distributed across regions of space. At this stage, the field is "classical", since it is a smooth, continuous distribution.

To speak of a quantized field means that we can imagine that if the field vibrates, only discrete bundles (quanta) of vibration are allowed, like an individual musical note on a guitar. The quanta of the field are identified with the creation (or annihilation) of a particle. Quantum field theory has new features that classical field theories lack; perhaps the most important one is the notion of the vacuum. The vacuum is a situation where no particles exist, but one can "disturb" the vacuum and create particles by "exciting" the field (usually with an interaction). It is important to know that the vacuum depends on the space-time location of an observer who can measure no particles.

On the other hand we know from General relativity, space-time is curved and observers don't see the same curvature at different places in general. What Parker realized was that in space-times of cosmological interest, such our expanding universe that Hubble discovered, that existed in a state of zero particles would create particles at a later time due to the very expansion of the space. We can think of this effect occurring because of the wave-like nature of particles (a quantum effect).

The quantum matter fields that live in the vacuum also interact with the expanding space-time field (the gravitational field). The expansion acts on the vacuum in a manner that "squeezes" particle quanta out of the vacuum. It is this quantum-field effect, which is used to explain the seeds of stars, and galaxies that now exist in the universe. Similarly, when black holes evaporate, the space-time also becomes time-dependent and particles are created, but this time as a thermal bath of matter/radiation. This physical feature of quantum fields in curved spaces raise the philosophical questions about the observer dependence of particles or the lack of them.

As you read these words, don't try to imagine some strange observer in some far region of the universe that will swear that you don't exist; and don't blame it on Leonard.

The Limits Of Intuition

We sometimes tend to think that ideas and feelings arising from our intuitions are intrinsically superior to those achieved by reason and logic. Intuition—the 'gut'—becomes deified as the Noble Savage of the mind, fearlessly cutting through the pedantry of reason. Artists, working from intuition much of the time, are especially prone to this belief. A couple of experiences have made me more sceptical.

The first is a question that Wittgenstein used to pose to his students. It goes like this: you have a ribbon which you want to tie round the centre of the Earth (let's assume it to be a perfect sphere). Unfortunately you've tied the ribbon a bit too loose: it's a meter too long. The question is this: if you could distribute the resulting slack—the extra meter—evenly round the planet so the ribbon hovered just above the surface, how far above the surface would it be?

Most people's intuitions lead them to an answer in the region of a minute fraction of a millimeter. The actual answer is almost 16 cms. In my experience only two sorts of people intuitively get close to this: mathematicians and dressmakers. I still find it rather astonishing: in fact when I heard it as an art student I spent most of one evening calculating and recalculating it because my intuition was screaming incredulity. 

Not many years later, at the Exploratorium in San Francisco, I had another shock-to-the-intuition. I saw for the first time a computer demonstration of John Conway's Life. For those of you who don't know it, it's a simple grid with dots that are acted on according to an equally simple, and totally deterministic, set of rules. The rules decide which dots will live, die or be born in the next step. There are no tricks, no creative stuff, just the rules. The whole system is so transparent that there should be no surprises at all, but in fact there are plenty: the complexity and 'organic-ness' of the evolution of the dot-patterns completely beggars prediction. You change the position of one dot at the start, and the whole story turns out wildly differently. You tweak one of the rules a tiny bit, and there's an explosion of growth or instant armageddon. You just have no (intuitive) way of guessing which it's going to be.

These two examples elegantly demonstrate the following to me:

a) 'Deterministic' doesn't mean 'predictable', 
b) we aren't good at intuiting the interaction of simple rules with initial conditions (and the bigger point here is that the human brain may be intrinsically limited in its ability to intuit certain things—like quantum physics and probability, for example), and 
c) intuition is not a quasi-mystical voice from outside ourselves speaking through us, but a sort of quick-and-dirty processing of our prior experience (which is why dressmakers get it when the rest of us don't). That processing tool sometimes produces incredibly impressive results at astonishing speed, but it's worth reminding ourselves now and again that it can also be totally wrong.

"Information Is The Resolution Of Uncertainty"

Nearly everything we enjoy in the digital age hinges on this one idea, yet few people know about its originator or the foundations of this simple, elegant theory of information.

Einstein is well rooted in popular culture as the developer of the theory of relativity. Watson and Crick are associated with the visual spectacle of DNA's double helix structure. 

How many know that the information age was not the creation of Gates or Jobs but of Claude Shannon in 1948?

The brilliant mathematician, geneticist and cryptanalyst formulated what would become information theory in the aftermath of World War II, when it was apparent it was not just a war of steel and bullets.

If World War I was the first mechanized war, the second war could be considered the first struggle based around communication technologies. Combat in the Pacific and Atlantic theaters were as much a battle of information as they were about guns, ships and planes. 

Consider the advances of the era that transformed the way wars were fought. 

Unlike previous conflicts, there was heavy utilization of radio communication among military forces. This quick remote coordination quickly pushed the war to all corners of the globe. Because of this, the field of cryptography advanced quickly in order to keep messages secret and hidden from adversaries. Also, for the first time in combat, radar was used to strategically detect and track aircraft, thereby surpassing conventional visual capabilities that ended on the horizon. 

One researcher, Claude Shannon, was working on the problem of anti-aircraft targeting and designing fire-control systems to work directly with radar. How could you determine the current, and future position of enemy aircraft's flight path, so you could properly time artillery fire to shoot it down? The radar information about plane position was a breakthrough, but "noisy" in that it provided an approximation of its location, but not precisely enough to be immediately useful.

After the war, this inspired Shannon and many others to think about the nature of filtering and propagating information, whether it was radar signals, voice for a phone call, or video for television. 

He knew that noise was the enemy of communication, so any way to store and transmit information that rejected noise was of particular interest to his employer, Bell Laboratories, the research arm of the mid-century American telephone monopoly.

Shannon considered communication "the most mathematical of the engineering sciences," and turned his intellectual sights towards this problem. Having worked on the intricacies of Vannevar Bush's differential analyzer analog computer in his early days at MIT, and with a mathematics-heavy Ph.D. thesis on the "Algebra for Theoretical Genetics," Shannon was particularly well-suited to understanding the fundamentals of handling information using knowledge from a variety of disciplines.

By 1948 he had formed his central, simple and powerful thesis:

Information is the resolution of uncertainty. 

As long as something can be relayed that resolves uncertainty, that is the fundamental nature of information. While this sounds surprisingly obvious, it was an important point, given how many different languages people speak and how one utterance could be meaningful to one person, and unintelligible to another. Until Shannon's theory was formulated, it was not known how to compensate for these types of "psychological factors" appropriately. Shannon built on the work of fellow researchers Ralph Hartley and Harry Nyquist to reveal that coding and symbols were the key to resolving whether two sides of a communication had a common understanding of the uncertainty being resolved.

Shannon then considered: what was the simplest resolution of uncertainty? 

To him, it was the flip of the coin—heads or tails, yes or no—as an event with only two outcomes. Shannon concluded that any type of information, then, could be encoded as a series of fundamental yes or no answers. Today, we know these answers as bits of digital information—ones and zeroes—that represent everything from email text, digital photos, compact disc music or high definition video.

That any and all information could be represented and coded in discrete bits not just approximately, but perfectly, without noise or error was a breakthrough which astonished even his brilliant peers at academic institutions and Bell Laboratories who previously thought it was unthinkable to have a simple universal theory of information.

The compact disc, the first ubiquitous digital encoding system for the average consumer, showed the legacy of Shannon's work to the masses in 1982. It provides perfect reproduction of sound by dividing each second of musical audio waves into 44,100 slices (samples), and recording the height of each slice in digital numbers (quantization). Higher sampling rates and finer quantization raise the quality of the sound. Converting this digital stream back to audible analog sound using modern circuitry allowed for consistent high fidelity versus the generation loss people were accustomed to in analog systems, such as compact cassette.

Similar digital approaches have been used for images and video, so that today we enjoy a universe of MP3, DVDs, HDTV, AVCHD multimedia files that can be stored, transmitted and copied without any loss of quality.

Shannon became a professor at MIT, and over the years students of Shannon went on to be the builders of many major breakthroughs of the information age, including digital modems, computer graphics, data compression, artificial intelligence and digital wireless communication. 

But without a sensational origin myth, bombastic personality or iconic tongue-wagging photo, Shannon's contribution is largely unknown to today's digital users.

Shannon was a humble man and intellectual wanderlust who shunned public speaking or granting interviews. He once remarked, "After I had found answers, it was always painful to publish, which is where you get the acclaim. Many things I have done and never written up at all. Too lazy, I guess."

Shannon was perhaps lazy to publish, but he was not a lazy thinker. Later in life, he occupied himself with puzzles he found personally interesting—designing a Rubik's cube solving device and modeling the mathematics of juggling.

The 20th century was a remarkable scientific age, where the fundamental building blocks of matter, life and information were all revealed in interconnected areas of research centered around mathematics. The ability to manipulate atomic and genetic structures found in nature have provided breakthroughs in the fields of energy and medical research. Less expected was discovering the fundamental nature of communication. Information theory as a novel, original and "unthinkable" discovery has completely transformed nearly every aspect of our lives to digital, from how we work, live, love and socialize. 

Beautiful, elegant and deeply powerful.

Falling Into Place: Entropy, Galileo's Frames of Reference, and the Desperate Ingenuity Of Life

The hardest choice I had to make in my early scientific life was whether to give up the beautiful puzzles of quantum mechanics, nonlocality, and cosmology for something equally arresting: To work instead on reverse engineering the code that natural selection had built into the programs that made up our species' circuit architecture. In 1970, the surrounding cultural frenzy and geopolitics made first steps toward a nonideological and computational understanding of our evolved design, "human nature", seem urgent; the recent rise of computer science and cybernetics made it seem possible; the almost complete avoidance of and hostility to evolutionary biology by behavioral and social scientists had nearly neutered those fields, and so made it seem necessary.

What finally pulled me over was that the theory of natural selection was itself such an extraordinarily beautiful and elegant inference engine. Wearing its theoretical lenses was a permanent revelation, populating the mind with chains of deductions that raced like crystal lattices through supersaturated solutions. Even better, it starts from first principles (such as set theory and physics), so much of it is nonoptional.

But still, from the vantage point of physics, beneath natural selection there remained a deep problem in search of an explanation: The world given to us by physics is unrelievedly bleak. It blasts us when it is not burning us or invisibly grinding our cells and macromolecules until we are dead. It wipes out planets, habitats, labors, those we love, ourselves. Gamma ray bursts wipe out entire galactic regions; supernovae, asteroid impacts, supervolcanos, and ice ages devastate ecosystems and end species. Epidemics, strokes, blunt force trauma, oxidative damage, protein cross-linking, thermal noise-scrambled DNA—all are random movements away from the narrowly organized set of states that we value, into increasing disorder or greater entropy. The second law of thermodynamics is the recognition that physical systems tend to move toward more probable states, and in so doing, they tend to move away from less probable states (organization) on their blind toboggan ride toward maximum disorder.

Entropy, then, poses the problem: How are living things at all compatible with a physical world governed by entropy, and, given entropy, how can natural selection lead over the long run to the increasing accumulation of functional organization in living things? Living things stand out as an extraordinary departure from the physically normal (e.g., the earth's metal core, lunar craters, or the solar wind). What sets all organisms—from blackthorn and alder to egrets and otters—apart from everything else in the universe is that woven though their designs are staggeringly unlikely arrays of highly tuned interrelationships—a high order that is highly functional. Yet as highly ordered physical systems, organisms should tend to slide rapidly back toward a state of maximum disorder or maximum probability. As the physicist Erwin Schrödinger put it, "It is by avoiding the rapid decay into the inert state that an organism appears so enigmatic."

The quick answer normally palmed off on creationists is true as far as it goes, but it is far from complete: The earth is not a closed system; organisms are not closed systems, so entropy still increases globally (consistent with the second law of thermodynamics) while (sometimes) decreasing locally in organisms. This permits but does not explain the high levels of organization found in life. Natural selection, however, can (correctly) be invoked to explain order in organisms, including the entropy-delaying adaptations that keep us from oxidizing immediately into a puff of ash.

Natural selection is the only known counterweight to the tendency of physical systems to lose rather than grow functional organization—the only natural physical process that pushes populations of organisms uphill (sometimes) into higher degrees of functional order. But how could this work, exactly?

It is here that, along with entropy and natural selection, the third of our trio of truly elegant scientific ideas can be adapted to the problem: Galileo's brilliant concept of frames of reference, which he used to clarify the physics of motion.

The concept of entropy was originally developed for the study of heat and energy, and if the only kind of real entropy (order/disorder) was the thermodynamic entropy of energy dispersal then we (life) wouldn't be possible. But with Galileo's contribution one can consider multiple kinds of order (improbable physical arrangements), each being defined with respect to a distinct frame of reference.

There can be as many kinds of entropy (order/disorder) as there are meaningful frames of reference. Organisms are defined as self-replicating physical systems. This creates a frame of reference that defines its kind of order in terms of causal interrelationships that promote the replication of the system (replicative rather than thermodynamic order). Indeed, organisms must be physically designed to capture undispersed energy, and like hydroelectric dams using waterfalls to drive turbines, they use this thermodynamic entropic flow to fuel their replication, spreading multiple copies of themselves across the landscape.

Entropy sometimes introduces copying errors into replication, but injected disorder in replicative systems is self-correcting. By definition the less well-organized are worse at replicating themselves, and so are removed from the population. In contrast, copying errors that increase functional order (replicative ability) become more common. This inevitable ratchet effect in replicators is natural selection.

Organisms exploit the trick of deploying different entropic frames of reference in many diverse and subtle ways, but the underlying point is that what is naturally increasing disorder (moving toward maximally probable states) for one frame of reference inside one physical domain can be harnessed to decrease disorder with respect to another frame of reference. Natural selection picks out and links different entropic domains (e.g., cells, organs, membranes) that each impose their own proprietary entropic frames of reference locally.

When the right ones are associated with each other, they do replicative work through harnessing various types of increasing entropy to decrease other kinds of entropy in ways that are useful for the organism. For example: oxygen diffusion from the lungs to the blood stream to the cells is the entropy of chemical mixing—falling toward more probable high entropy states, but increasing order from the perspective of replication-promotion.

Entropy makes things fall, but life ingeniously rigs the game so that when they do they often fall into place. 

Everything Is The Way It Is Because It Got That Way

This aphorism is attributed to the biologist and classicist D'Arcy Thompson, and it's an elegant summary of how Thompson sought to explain the shapes of things, from jellyfish to sand dunes to elephant tusks. I saw this quoted first in an Edge discussion by Daniel Dennett, who made the point that this insight applies to explanation more generally—all sciences are, to at least some extent, historical sciences. 

I think it's a perfect motto for my own field of developmental psychology. Every adult mind has two histories. There is evolution. Few would doubt that some of the most elegant and persuasive explanations in psychology appeal to the constructive process of natural selection. And there is development—how our minds unfold over time, the processes of maturation and learning. 

While evolutionary explanations work best for explaining what humans share, development can sometimes capture how we differ. This can be obvious: Nobody is surprised to hear that adults who are fluent in Korean have usually been exposed to Korean when they were children or that adults who practice Judaism have usually been raised as Jews. But other developmental explanations are rather interesting.

There is evidence that an adult's inability to see in stereo is due to poor vision during a critical period in childhood. Some have argued that the self-confidence of adult males is influenced by how young they were when they reached puberty (because of the boost in status caused by being bigger, even if temporarily, than their peers). It's been claimed that smarter adults are more likely to be firstborns (because later children find themselves in environments that are, on average, less intellectually sophisticated). Creative adults are more likely to be later-borns (because they were forced to find their own distinctive niches.) Romantic attachments in adults are influenced by their relationships as children with their parents. A man's pain-sensitivity later in life is influenced by whether or not he was circumcised as a baby.

With the exception of the stereo-vision example, I don't know if any of these explanations are true. But they are elegant and non-obvious, and some of them verge on beautiful. 

My Favorite Explanation: Why Curry, Wine And Coffee Cure Most Ails

What makes an explanation beautiful? Many elegant explanations in science are those that have been vetted fully but there are just as many beautiful wildly popular explanations where the beauty is just skin deep. I want to give two examples from the field of brain health.

When preliminary mice studies showed that an ingredient in dietary curry spice may have anti-Alzheimer effects, I suspect every vindaloo lover thought that was a beautiful explanation for why India had a low rate of Alzheimer's. But does India really have a low Alzheimer's rate after adjusting for life span and genetic differences? No one really knows.

Likewise when an observational study in the 1990s reported wine drinkers in Bordeaux had lower rates of Alzheimer's, there was a collective "I knew it" from oenophiles.

The latest observational findings now link coffee drinking with lower risk for Alzheimer's, much to the delight of the millions of caffeine addicts.

In reality, neither coffee nor wine nor curry spice have been proven in controlled trials to have any benefits against Alzheimer's. Regardless, the cognitive resonance these "remedies" find with the reader far exceeds the available evidence. One can find similar examples in virtually every field of medicine and science.

I would like to suggest two conditions that might render an explanation unusually beautiful: 1) a ring of truth, 2) confirmation biases. We all favor explanations and test them in a manner that confirms our own beliefs (confirmation bias). A small amount of factual data can be magnified into a beautiful fully proven explanation in one's mind if the right circumstance exist—thus, beauty is in the eye of the beholder. This may occur less often in one's own specialized fields, but we are all vulnerable in fields in which we are less expert in.

Given how often leading scientific explanations are proven wrong in subsequent years, one would do well to bear in mind Santayana's quote that "almost every wise saying has an opposite one, no less wise, to balance it". As for me, I love my curry, coffee and wine but am not yet counting on them to stop Alzheimer's. 

Why Programs Have Bugs

From the earliest days of computer programming up through the present, we are faced with the unfortunate reality that the field does not know how to design error-free programs.

Why can't we tame the writing of computer programs to emulate the successes of other areas of engineering? Perhaps the most lyrical thinker to address this question is Fred Brooks, author most famously of the "The Mythical Man-Month."(If one bears in mind that this unfortunately titled book was first published in 1975, it is a bit easier to ignore the sexist language that litters this otherwise fine work; the points Brooks made more than 35 years ago are almost all accurate today except the assumption that all programmers are "he".)

When espousing the joys of programming, Brooks writes:

"The programmer, like the poet, works only slightly removed from pure thought-stuff. He builds his castles in the air, from air, creating by exertion of the imagination. Few media of creation are so flexible, so easy to polish and rework, so readily capable of realizing grand conceptual structures. ... Yet the program construct, unlike the poet's words, is real in the sense that it moves and works, producing visible outputs separate from the construct itself. It prints results, draws pictures, produces sounds, moves arms. The magic of myth and legend has come true in our time."

But this magic comes with the bite of its flip side:

"In many creative activities the medium of execution is intractable. Lumber splits; paints smear; electrical circuits ring. These physical limitations of the medium constrain the ideas that may be expressed, and they also create unexpected difficulties in the implementation.

... Computer programming, however, creates with an exceedingly tractable medium. The programmer builds from pure thought-stuff: concepts and very flexible representations thereof. Because the medium is tractable, we expect few difficulties in implementation; hence our pervasive optimism. Because our ideas are faulty, we have bugs; henour optimism is unjustified."

Just as there is an arbitrarily large number of ways to arrange the words in an essay, a staggering variety of different programs can be written to perform the same function. The universe of possibility is too wide open, too unconstrained, to permit elimination of errors.

There are additional compelling causes of programming errors, most importantly the complexiting of autonomously interacting independent systems with unpredictable inputs, often driven by even more unpredictable human actions interconnected on a world wide network. But in my view the beautfiul explanation is the one about unfettered thought-stuff.

Beautiful, Unreasonable Mathematics

I find most beautiful not a particular equation or explanation, but the astounding fact that we have beauty and precision in science at all. That exactness comes from using mathematics to measure, check and even predict events. The deepest question is, why does this splendor work?

Beauty is everywhere in science. Physics abounds in symmetries and lovely curves, like the parabola we see in the path of a thrown ball. Equations like e^iΠ+ 1 =0 show that there is exquisite order in mathematics, too.

Why does such beauty exist? That, too, has a beautiful explanation. This may be the most beautiful fact in science.

In 1960, Eugene Wigner published a classic article on the philosophy of physics and mathematics, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner asked, why does mathematics work so well in describing our world? He was unsure.

We use Hilbert spaces in quantum mechanics, differential geometry in general relativity, and in biology difference equations and complex statistics. The role mathematics plays in these theories is also varied. Math both helps with empirical predictions and gives us elegant, economical statements of theories. I can't imagine how we could ever invent quantum mechanics or general relativity without it.

But why is this true? For beautiful reasons? I think so.

Darwin stated his theory of natural selection without mathematics at all, but it can explain why math works for us. It has always seemed to me that evolutionary mechanisms should select for living forms that respond to nature's underlying simplicities. Of course, it is difficult to know in general just what simple patterns the universe has. In a sense they may be like Plato's perfect forms, the geometric constructions such as the circle and polygons. Supposedly we see their abstract perfection with our mind's eye, but the actual world only approximately realizes them. Thinking further in like fashion, we can sense simple, elegant ways to viewing dynamical systems. Here's why that matters.

Imagine a primate ancestor who saw the flight of a stone, thrown after fleeing prey, as a complicated matter, hard to predict. It could try a hunting strategy using stones or even spears, but with limited success, because complicated curves are hard to understand. A cousin who saw in the stone's flight a simple and graceful parabola would have a better chance of predicting where it would fall. The cousin would eat more often and presumably reproduce more as well. Neural wiring could reinforce this behavior by instilling a sense of genuine pleasure at the sight of an artful parabola.

There's a further selection at work, too. To hit running prey, it's no good to ponder the problem for long. Speed drove selection: that primate had to see the beauty fast. This drove cognitive capacities all the harder. Plus, the pleasure of a full belly.

We descend from that appreciative cousin. Baseball outfielders learn to sense a ball's deviations from its parabolic descent, due to air friction and wind, because they are building on mental processing machinery finely tuned to the parabola problem. Other appreciations of natural geometric ordering could emerge from hunting maneuvers on flat plains, from the clever design of simple tools, and the like. We all share an appreciation for the beauty of simplicity, a sense emerging from our origins. Simplicity is evolution's way of saying, this works.

Evolution has primed humans to think mathematicallybecause they struggled to make sense of their world for selective advantage. Those who didn't aren't in our genome.

Many things in nature, inanimate and living, show bilateral, radial, concentric and other mathematically based symmetries. Our rectangular houses, football fields and books spring from engineering constraints, their beauty arising from necessity. We appreciate the curve of a suspension bridge, intuitively sensing the urgencies of gravity and tension.

Our cultures show this. Radial symmetry appears in the mandala patterns of almost every society, from Gothic stoneworks to Chinese rugs. Maybe they echo the sun's glare flattened into two dimensions. In all cultures, small flaws in strict symmetries express artful creativity. So do symmetry breaking particle theories.

Philosophers have three views of the issue: mathematics is objective and real; it arises from our preconceptions; or it is social.   

Physicist Max Tegmark argues the first view, that math so well describes the physical world because reality really is completely mathematical. This radical Platonism says that reality is isomorphic to a mathematical structure. We're just uncovering this bit by bit. I hold the second view: we evolved mathematics because it describes the world and promotes survival. I differ from Tegmark because I don't think mathematics somehow generated reality; as Hawking says, what gives fire to the equations, and makes them construct reality?

Social determinists, the third view, think math emerges by consensus. This is true in that we're social animals, but this view also seems to ignore biology, which brought about humans themselves through evolution. Biology generates society, after all.

But how general were our adaptations to our world?

R. Lemarchand and Jon Lomberg have argued in detail that symmetries and other aesthetic principles should be truly universal, because they arise from fundamental physical properties. Aliens orbiting distant stars will still spring from evolutionary forces that reward a deep, automatic understanding of the laws of mechanics. The universe itself began with a Big Bang that can be envisioned as a four-dimensional symmetric expansion; yet without some flaws, so-called anisotropies, in the symmetry of the Big Bang, galaxies and stars would never happen.

Strategies for the Search for Extra-Terrestrial Intelligence, SETI, have assumed this since their beginnings in the early 1960s. Many supposed that interesting properties such as the prime numbers, which do not appear in nature, would figure in schemes to send messages by radio. Primes come from thinking about our mathematical constructions of the world, not directly from that world. So they're evidence for a high culture based on studying mathematics.       

A case for the universality of mathematics is in turn an argument for the universality of aesthetic principles: evolution should shape all of us to the general contours of physical reality. The specifics will differ enormously, of course, as a glance at the odd creatures in our fossil record shows.

Einstein once remarked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" But it isn't independent—and that's beautiful.

How Apparent Finality Can Emerge

Darwin, no doubt. The beauty and the simplicity of his explanation is astonishing. I am sure that others have pointed out Darwin as their favorite deep, elegant, beautiful explanation, but I still want to emphasize the general reach of Darwin's central intuition, which goes well beyond the already monumental result of having clarified that we share the same ancestors with all living beings on Earth, and is directly relevant to the very core of the entire scientific enterprise.

Shortly after the ancient greek "physicists" started to develop naturalistic explanations of Nature, a general objection came forward. The objection is well articulated in Plato, for instance in the Phaedon, and especially in Aristotle discussion of the theory of the "causes". Naturalistic explanations rely on what Aristotle called the "the efficient cause", namely past phenomena producing effects. But the world appears to be dominated by phenomena that can be understood in terms of "final causes", namely an "aim" or a "purpose". These are evident in the kingdom of life. We have the mouth "so we can" eat. The importance of this objection cannot be underestimated. It is this objection that brought down ancient naturalism and in the minds of many it is still today the principal source of psychological resistance against a naturalistic understanding of the world.

Darwin has discovered the spectacularly simple mechanism where efficient causes can produce phenomena that appear to be governed by final causes: anytime we have phenomena that can reproduce, the actual phenomena that we observe are those that keep reproducing, and therefore are necessarily those better at reproducing, and we can thus read them in terms of final causes. In other words, a final cause can be effective to understanding the world because it is a shortcut for accounting the past history of a continuing phenomenon.

To be sure, the idea has appeared before. Empedocles discusses the idea that the apparent finality in the living kingdom could be the result of selected randomness, and Aristotle himself in his "Physics" mentions a version of this idea for species ("seeds"). But the times where not yet ripe, and the suggestion was lost in the following religious ages. I think that the resistance against Darwin is not just the difficulty of seeing the power of a spectacularly beautiful explanation: it is the fear of realizing the extraordinary power that such an explanation has in shattering rests of old world views.

"So Much From So Little? Now That Explains A Lot!"

There is a deep fascination I have been carrying with me for decades now, ever since earliest childhood: the interplay between simplicity and complexity.

Unable to express it verbally at the time, in hindsight it seems clear: they are all about that penultimate question: what is life and how did this world come into existence?

In many stages and phases I discovered a multitude of ideas that are exactly what is called for here: deep, elegant and beautiful explanations of the principles of nature.

Simplicity is embodied in a reductionist form in the YinYang symbol: being black or white.

In other familiar words: To be or not to be.

Those basic elements combined: that is the process spawning diversity, in myriads of forms.

As a youngster I was totally immersed in 'Lego' blocks. There are a handful of basic shapes (never liked the 'special' ones and clamored instead for a bigger box of basics) and you could put them together in arrangements that become houses, ships, bridges...entire towns I had growing up the sides of my little room to the tops of wardrobes. And I sensed it then: there is something deep about this.

A bit later I got into a mechanical typewriter (what a relief to be able to type clearly, my handwriting had always been horrid—the hand not being able to keep up with the thinking... and relished the ability to put together words, sentences, paragraphs. Freezing a thought in a material fashion, putting it on paper to recall later. What's more—to let someone else follow your thinking! I sensed: this is a thing of beauty.

Then I took up playing the piano. The embryonic roots of the software designer of later decades probably shuddered at the interface: 88 unlabeled keys! Irregular intervals of black ones interspersed... and almost the exact opposite of todays "we need to learn this in one minute and no, we never ever look at manuals" attitude. It took months to make any sense of it, but despite the frustrations, it was deeply fascinating. String together a few notes with mysterious un-definable skill and out comes... deeply moving emotion?

So the plot thickens: a few Lego blocks, a bunch of lettershapes or a dozen musical notes... and you take that simplicity of utterly lame elements, put them together...and out pops complexity, meaning, beauty.

Later in the early 70s I delved into the very first generation of large synthesizers and dealt specifically with complex natural sounds being generated from simple unnatural ingredients and processes. By 1977—now in California—it was computer graphics that became the new frontier—and again: seemingly innocent little pixels combine to make ... any image—as in: anything one can imagine. Deep.

In those days I also began playing chess, and carom billiards—simple rules, a few pieces, 3 balls...but no game is ever the same. Not even close. The most extreme example of this became another real fascination: the game of GO. Just single moves of black and white stones, on a plain grid of lines with barely a handful of rules—but a huge variety of patterns emerges. Elegant.

The earliest computing, in the first computer store in the world, Dick Heyser in Santa Monica, had me try something that I had read in SciAm by Martin Gardner: Conway's 'Game of Life'. The literal incarnation of the initial premise: Simplicity reduced to that YinYang: a cell is On or Off, black or white. But there is one more thing added here now: iteration. With just four rules each cell is said to live or die and in each cycle the pattern changes, iteratively. From dead dots on paper, and static pixels on phospor, it sprang to—life! Not only patterns, but blinkers, gliders, even glider guns, heck glider gun canons! Indeed, it is now seen as a true Turing-complete machine. Artificial Life. Needless to say: very deep.

Another example in that vein are of course fractals. Half an inch of a formula, when iterated, is yielding worlds of unimaginably intricate shapes and patterns. It was a great circle closing after 20 years for me to re-examine this field, now flying through them as "frax" on a little iPhone, in realtime and in real awe.

The entire concept of the computer embodies the principles of simple on/off binary codes, much like YinYang, being put together to form still simplistic gates and then flip-flops, counters, all the way to RAM and complex CPU/GPUs and beyond. And now we have a huge matrix computer with billions of elements networked together (namely 'us', including this charming little side corridor called 'Edge'), just a little over

70 years after Zuse's Z3 we reached untold complexity—with no sign of slowing down.

Surely the ultimate example of 'simplexity' is the genetic code—four core elements being combined by simple rules to extreme complex effect—the DNA to build archaea, felis or homo somewhat sapiens.

Someone once wrote on Edge "A great analogy is like...a diagonal frog" which embodies the un-definable art of what constitutes a deep, beautiful or elegant explanation: Finding the perfect example! The lifelong encounters with "trivial ingredients turning to true beauty" recited here are in themselves neither terse mathematical proofs nor eloquently worded elucidations (such as one could quote easily from almost any Nobel laureate's prize-worthy insights).

Instead of the grandeur of 'the big formulas' I felt that the potpourri of AHA!  moments over six decades may be just as close to that holy grail of scientific thinking: to put all the puzzle pieces together in such away that a logical conclusion converges further on... the truth. And I guess one of the pillars of that truth, in my eyes, is the charmingly disarmingly miniscule insight:

 "So much from so little. Now that explains a lot!"

An Unresolved (And, Therefore, Unbeautiful) Reaction To The Edge Question

This year's Edge question sits uneasily on a deeper question: Where do we get the idea—a fantastic idea if you stop and think about it—that the beauty of an explanation has anything to do with the likelihood of its being true? What do beauty and truth have to do with each other? Is there any good explanation of why the central notion of aesthetics (fluffy) should be inserted into the central notion of science (rigorous)?

You might think that, rather than being a criterion for assessing explanations, the sense of beauty is a phenomenon to be explained away. Take, for example, our impression that symmetrical faces and bodies are beautiful. Symmetry, it turns out, is a good indicator of health and, consequently, of mate-worthiness. It's a significant challenge for an organism to coordinate the production of its billions of cells so that its two sides proceed to develop as perfect matches, warding off disease and escaping injury, mutation and malnutrition. Symmetrical female breasts, for example, are a good predictor of fertility. As our own lustful genes know, the achievement of symmetry is a sign of genetic robustness, and we find lopsidedness a turnoff. So, too, in regard to other components of human beauty—radiant skin, shining eyes, neotony (at least in women). The upshot is that we don't want to mate with people because they're beautiful, but rather they're beautiful because we want to mate with them, and we want to mate with them because our genes are betting on them as replicators.

So, too, you might think that beauty of every sort is to be similarly explained away, an attention-grabbing epiphenomenon with no substance of its own.  Which brings me to the Edge question concerning beautiful explanations. Is there anything to this notion of explanatory beauty, a guide to choosing between explanatory alternatives, or it just that any explanation that's satisfactory will, for that very reason and no other, strike us as beautiful, beautifully explanatory, so that the reference to beauty is once again without any substance? That would be an explanation for the mysterious injection of aesthetics into science. The upshot would be that explanations aren't satisfying because they're beautiful, but rather they're beautiful because they're satisfying: they strip the phenomenon bare of all mystery, and maybe, as a bonus, pull in further phenomena which can be rendered non-mysterious using the same sort of explanation. Can explanatory beauty be explained away, summarily dismissed by way of an eliminative explanation? (Eliminative explanations are beautiful.)

I'd like to stop here, with a beautiful explanation for explaining away explanatory beauty, but somebody is whispering in my ear. It's that damned Plato. Plato is going on about how there is more in the idea of explanatory beauty than is acknowledged in the eliminative explanation. In particular, he's insisting, as he does in his Timaeus, that the beauty of symmetry, especially as it's expressed in the mathematics of physical laws, cannot be explained away with the legerdemain of the preceding paragraph. He's reproaching the eliminative explanation of explanatory beauty with ignoring the many examples in history when the insistence on the beauty of symmetry led to substantive scientific progress. What was it that led James Clerk Maxwell to his four equations of electromagnetism but his trying to impose mathematical symmetry on the domains of electricity and magnetism? What was it that led Einstein to his equations of gravity but an insistence on beautiful mathematics?

Eliminative explanations are beautiful, but only when they truly and thoroughly explain. So instead of offering an answer to this year's Edge question I offer instead an unresolved (and, therefore, unbeautiful) reaction to the deep question on which it rests.   

The Simpleton Ant and the Intelligent Ants

The obvious answer should be the double helix. With the incomparably laconic "It has not escaped our notice….," it explained the very mechanism of inheritance. But the double helix doesn't do it for me. By the time I got around to high school biology, the double helix was ancient history, like pepper moths evolving or mitochondria as the power houses of the cell. Watson and Crick—as comforting but as taken for granted as Baskin and Robbins.

Then there's the work of Hubel and Wiesel, which showed that the cortex processes sensations with a hierarchy of feature extraction. In the visual cortex, for example, neurons in the initial layer each receive inputs from a single photoreceptor in the retina. Thus, when one photoreceptor is stimulated, so is "its" neuron in the primary visual cortex. Stimulate the adjacent photoreceptor, and the adjacent neuron activates. Basically, each of these neurons "knows" one thing, namely how to recognize a particular dot of light. Groups of I-know-a-dot neurons then project onto single neurons in the second cortical layer. Stimulate a particular array of adjacent neurons in that first cortical layer and a single second layer neuron activates. Thus, a second layer neuron knows one thing, which is how to recognize, say, a 45 degree angle line of light oriented. Then groups of I-know-a-line neurons send projections on to the next layer. 

Beautiful, explains everything—just keep going, cortical layer upon layer of feature extraction, dot to line to curve to collection of curves to…….until there'd be the top layer where a neuron would know one complex, specialized thing only, like how to recognize your grandmother.  And it would be the same in the auditory cortex—first layer neurons knowing particular single notes, second layer knowing pairs of notes….some neuron at the top that would recognize the sound of your grandmother singing along with Lawrence Welk.

It turned out, though, that things didn't quite work this way. There are few "Grandmother neurons" in the cortex (although a 2005 Nature paper reported someone with a Jennifer Aniston neuron). The cortex can't rely too much on grandmother neurons, because that requires a gazillion more neurons to accommodate such inefficiency and overspecialization. Moreover, a world of nothing but grandmother neurons on top precludes making multi-modal associations (e.g., where seeing a particular Monet reminds you of croissants and Debussy's music and the disastrous date you had at an Impressionism show at the Met. Instead, we've entered the world of neural networks.

Switching to a more mundane level of beauty, consider the gastrointestinal tract. In addition to teaching neuroscience, I've been asked to be a good departmental citizen and fill in some teaching holes in our core survey course. Choices: photosynthesis, renal filtration or the gastrointestinal tract. I picked the GI tract, despite knowing nothing about it, since the first two subjects terrified me. Gut physiology turns out to be beautiful and elegant amid a huge number of multi-syllabic hormones and enzymes. As the Gentle Reader knows, the GI tract is essentially a tube starting at the mouth and ending at the anus. When a glop of food distends the tube, the distended area secretes some chemical messenger that causes that part of the tube to start doing something (e.g., contracting rhythmically to pulverize food). But the messenger also causes the part of the tract just behind to stop doing its now-completed task and causes area just ahead to prepare for its job. Like shuttling ships through the Panama Canal's locks, all the way to the bathroom.

Beautiful. But even bowelophiles wouldn't argue that this is deep on a fundamental, universe-explaining level. Which brings me to my selection, which is emergence and complexity, as represented by "swarm intelligence."

Observe a single ant, and it doesn't make much sense, walking in one direction, suddenly careening in another for no obvious reason, doubling back on itself. Thoroughly unpredictable.

The same happens with two ants, a handful of ants. But a colony of ants makes fantastic sense. Specialized jobs, efficient means of exploiting new food sources, complex underground nests with temperature regulated within a few degrees. And critically, there's no blueprint or central source of command—each individual ants has algorithms for their behaviors. But this is not wisdom of the crowd, where a bunch of reasonably informed individuals outperform a single expert. The ants aren't reasonably informed about the big picture. Instead, the behavior algorithms of each ant consist of a few simple rules for interacting with the local environment and local ants. And out of this emerges a highly efficient colony.

Ant colonies excel at generating trails that connect locations in the shortest possible way, accomplished with simple rules about when to lay down a pheromone trail and what to do when encountering someone else's trail—approximations of optimal solutions to the Traveling Salesman problem. This has useful applications. In "ant-based routing," simulations using virtual ants with similar rules can generate optimal ways of connecting the nodes in a network, something of great interest to telecommunications companies. It applies to the developing brain, which must wire up vast numbers of neurons with vaster numbers of connections without constructing millions of miles of connecting axons. And migrating fetal neurons generate an efficient solution with a different version of ant-based routine.

A wonderful example is how local rules about attraction and repulsion (i.e., positive and negative charges) allow simple molecules in an organic soup to occasionally form more complex ones. Life may have originated this way without the requirement of bolts of lightening to catalyze the formation of complex molecules.

And why is self-organization so beautiful to my atheistic self? Because if complex, adaptive systems don't require a blue print, they don't require a blue print maker. If they don't require lightening bolts, they don't require Someone hurtling lightening bolts. 

Embodied Metaphors Unify Perception, Cognition and Action

Philosophers and psychologists grappled with a fundamental question for quite some time: How does the brain derive meaning? If thoughts consist of the manipulation of abstract symbols, just like computers are processing 0s and 1s, then how are such abstract symbols translated into meaningful cognitive representations? This so-called "symbol grounding problem" has now been largely overcome because many findings from cognitive science suggest that the brain does not really translate incoming information into abstract symbols in the first place. Instead, sensory and perceptual inputs from every-day experience are taken in their modality-specific form, and they provide the building blocks of thoughts.

British empiricists such as Locke and Berkeley long ago recognized that cognition is inherently perceptual. But following the cognitive revolution in the 1950ies psychology treated the computer as the most appropriate model to study the mind. Now we know that a brain does not work like a computer. Its job is not to store or process information; instead, its job is to drive and control the actions of the brain's large appendage, the body. A new revolution is taking shape, considered by some to bring an end to cognitivism, and giving way to a transformed kind of cognitive science, namely an embodied cognitive science.

The basic claim is thatthe mind thinks in embodied metaphors. Early proponents of this idea were linguists such as George Lakoff, and in recent years social psychologists have been conducting the relevant experiments, providing compelling evidence. But it does not stop here; there is also a reverse pathway: Because thinking is for doing, many bodily processes feed back into the mind to drive action.

Consider the following recent findings that relate to the very basic spatial concept of verticality. Because moving around in space is a common physical experience, concepts such as "up" or "down" are immediately meaningful relative to one's own body. The concrete experience of verticality serves as a perfect scaffold for comprehending abstract concepts, such as morality: Virtue is up, whereas depravity is down: Good people are "high minded" and "upstanding" citizens, whereas bad people are "underhanded" and the "low life" of society. Recent research by Brian Meier, Martin Sellbom and Dustin Wygant illustrated that research participants are faster to categorize moral words when they are presented in an up location, and immoral words when they are presented in a down location. Thus, people intuitively relate the moral domain to verticality; however, Meier and colleagues also found that peoplewho do not recognize moral norms, namely psychopaths, fail to do so, and do not show this effect.

People not only think of all things good and moral as up, but they also think of God as up, and the Devil as down. Further, those in power are conceptualized as being high up relative to those down below over whom they hover and exert control, as shown by Thomas Schubert.All the empirical evidence suggests that there is indeed a conceptual dimension that leads up, both literally and metaphorically. This vertical dimension that pulls the mind up to considering what higher power there might be is deeply rooted in the very basic physical experience of verticality.

However, verticality not only influences people's representation of what is good, moral and divine, but movement through space along the vertical dimension can even change their moral actions. Larry Sanna, Edward Chang, Paul Miceli and Kristjen Lundberg recently demonstrated that manipulating people's location along the vertical dimension can actually turn them into more "high minded" and "upstanding" citizens. They found that people in a shopping mall who had just moved up an escalator were more likely to contribute to a charity donation box than people who had moved down on the escalator. Similarly, research participants who had watched a film depicting a view from high above, namely flying over clouds seen from an airplane window subsequently showed more cooperative behaviour than participants who had watched a more ordinary, and less "elevating" view from a car window. Thus, being physically elevated induced people to act on "higher" moral values.

The growing recognition that embodied metaphors provide one common language of the mind has lead to fundamentally different ways of studying how people think. For example, under the assumption that the mind functions like a computer psychologists hoped to figure out how people think by observing how they play chess, or memorize lists of random words. From an embodied perspective it is evident that such scientific attempts were hopelessly doomed to fail. Instead, it is increasingly clear that cognitive operations of any creature, including humans, have to solve certain adaptive challenges of the physical environment. In the process, embodied metaphors are the building blocks of perception, cognition, and action. It doesn't get much more simple and elegant than that.

The Double Helix

The Double Helix is a strong candidate. 

"It Just Is?"

The concept of an indivisible component of matter, something that cannot be divided further, has been around for at least two and half millennia, first proposed by early Greek and Indian philosophers. Democritus called the smallest indivisible particle of matter "átomos" meaning "uncuttable". Atoms were also simple, eternal, and unalterable. But in Greek thinking (and generally for about 2,000 years after) atoms lost out to the four basic elements of Empedocles—fire, air, water, earth—which were also simple, eternal, and unalterable, but not made up of little particles, Aristotle believing those four elements to be infinitely continuous.

Further progress in our understanding of the world based on the concept of atoms had to wait till the 18^th century. By that time the four elements of Aristotle had been replaced by 33 elements of Lavoisier based on chemical analysis. Dalton then used the concept of atoms to explain why elements always react in ratios of whole numbers, proposing that each element is made up of atoms of a single type, and that these atoms can combine to form chemical compounds. Of course, by the early 20^th century (through the work of Thompson, Rutherford, Bohr and many others) it was realized that atoms were not indivisible and they were thus not the basic units of matter. All atoms were made up of protons, neutrons, and electrons, which took over the title of being the indivisible components (basic building blocks) of matter.

Perhaps because the Rutherford-Bohr model of the atom is now considered transitional to more elaborate models based on quantum mechanics, or perhaps because it evolved over time from the work of many people (and wasn't a single beautiful proposed law), we have forgotten how much about the world can be explained by the concept of protons, neutrons, and electrons—probably more than any other theory ever proposed. With only three basic particles one could explain the properties of 118 atoms/elements and the properties of thousands upon thousands of compounds chemically combined from those elements. A rather amazing feat, and certainly making the Rutherford-Bohr model worthy of being considered a favorite deep, elegant, and beautiful explanation.

Since that great simplification, further developments in our understanding of the physical universe have gotten more complicated, not less. To explain the properties of our three basic particles of matter, we went looking for even-more-basic particles. We ended up needing 12 fermions (6 quarks, 6 leptons) to "explain" the properties of the 3 previously thought-to-be basic particles (as well as the properties of some other particles that were not known to us until we built high energy colliders). And we added 4 other particles, force-carrier particles, to "explain" the 4 basic force fields (electromagnetism, gravitation, strong interaction, and weak interaction) that affect those 3 previously thought-to-be basic particles. Of these 16 now thought-to-be basic particles most are not independently observable (at least at low energies).        

Even if the present Standard Model of particle physics turns out to be true, the question can be asked: "What next?" Every particle (whatever it's level in the hierarchy of particles) will have certain properties or characteristics. When asked "why" quarks have a particular electric charge, color charge, spin, or mass, do we simply say "they just do"? Or do we try to find even-more-basic particles which seem to explain the properties of quarks, and of leptons and bosons? And if so, does this continue on to still-even-more-basic particles? Could that go on forever? Or at some point, when asked the question "why does this particle have these properties", would we simply say "it just does"? At some point would we have to say that there is no "why" to the universe? "It just is."

At what level of our hierarchy of understanding would we resort to saying, "it just is"? The highest (and least understanding) level is religious—the gods of Mount Olympus each responsible for some worldly phenomenon, or the all-knowing monotheistic god creating the world and making everything work by means truly unknowable to humans. In their theories about how the world worked Aristotle and other Greek philosophers incorporated the gods of Mount Olympus (earth, water, fire, and air were all assigned to particular gods), but Democritus and other philosophers were deterministic and materialistic, and they looked for predictable patterns and simple building blocks that might create the complex world they saw around them. Throughout the growth and evolution of scientific thinking there have been various "it just is" moments, where an explanation/theory seems to hit a wall where one might say "it just is", only to have some one else come along and say "maybe not" and goes on to further advance our understanding. But as we get to the most basic questions about our universe (and our existence) the "it just is" answer becomes more likely. One very basic scientific question is whether there will ever be found truly indivisible particles of nature. The accompanying philosophical question is whether there can be truly indivisible particles of nature.

At some level the next group of mathematically derived "particles" may so obviously appear not to be observable/"real", that we will describe them instead as simply entities in a mathematical model that appears to accurately describe the properties of the observable particles in the level above. At which point the answer to the question of why these particles act as described by this mathematical model would be "they just do". How far down we go with such models will probably depend on how much a new level in the model allows us to explain previously unexplainable observed phenomena or to correctly predict new phenomena. (Or perhaps we might be stopped by the model becoming too complex.)

For determinists still unsettled by the probabilities inherent in quantum mechanics or the philosophical question about what would have come before a Big Bang, it is just one more step toward recognizing the true unsolvable mystery of our universe—recognizing it, but maybe still not accepting it; a new much better model could still come along.

The Higgs Mechanism

The beauty of science—in the long run—is its lack of subjectivity. So answering the question "what is your favorite deep, beautiful, or elegant explanation" can be a little disturbing to a scientist, since the only objective words in the question are "what", "is", "or", and (in an ideal scientific world) "explanation." Beauty and elegance do play a part in science but are not the arbiters of truth. But I will admit that simplicity, which is often confused with elegance, can be a useful guide to maximizing explanatory power.

As for the question, I'll stick to an explanation that I think is extremely nice, relatively simple (though subtle), and which might even be verified within the year. That is the Higgs mechanism, named after the physicist Peter Higgs who developed it. The Higgs mechanism is probably responsible for the masses of elementary particles like the electron. If the electron had zero mass (like the photon), it wouldn't be bound into atoms. If that were the case, none of the structure of our Universe (or of life) would be present. That's not the correct description of our world.

 In any case, experiments have measured the masses of elementary particles and they don't vanish. We know they exist. The problem is that these masses violate the underlying symmetry structure we know to be present in the physical description of these particles. More concretely, if elementary particles had mass from the get-go, the theory would make ridiculous predictions about very energetic particles. For example, it would predict interaction probabilities greater than one.

So there is a significant puzzle. How can particles have masses that have physical consequences and can be measured at low energies but act as if they don't have masses at high energies, when predictions would become nonsensical? That is what the Higgs mechanism tells us. We don't yet know for certain that it is indeed responsible for the origin of elementary particle masses but no one has found an alternative satisfactory explanation.

One way to understand the Higgs mechanism is in terms of what is known as "spontaneous symmetry breaking," which I'd say is itself a beautiful idea. A spontaneously broken symmetry is broken by the actual state of nature but not by the physical laws. For example, if you sit at a dinner table and use your glass on the right, so will everyone else. The dinner table is symmetrical—you have a glass on your right and also to your left. Yet everyone chooses the glass on the right and thereby spontaneously breaks the left-right symmetry that would otherwise be present.

Nature does something similar. The physical laws describing an object called a Higgs field respects the symmetry of nature. Yet the actual state of the Higgs field breaks the symmetry. At low energy, it takes a particular value. This nonvanishing Higgs field is somewhat akin to a charge is spread throughout the vacuum (the state of the universe with no actual particles). Particles acquire their masses by interacting with these "charges." Because this value appears only at low energies, particles effectively have masses only at these energies and the apparent bottleneck to elementary particle masses is apparently resolved.

Keep in mind that the Standard Model has worked extremely well, even without yet knowing for sure if the Higgs mechanism is correct. We don't need to know about the Higgs mechanism to know particles have masses and to make many successful predictions with the so-called Standard Model of particle physics. But the Higgs mechanism is essential to explaining how those masses can arise in a sensible theory. So it is rather significant.

The Standard Model's success nonetheless illustrates another beautiful idea essential to all of physics, which is the concept of an "effective theory." The idea is simply that you can focus on measurable quantities when making predictions and leave understanding the source of those quantities to later research when you have better precision.

Fortunately that time has now come for the Higgs mechanism, or at least the simplest implementation which involves a particle called the Higgs boson. The Large Hadron Collider at CERN near Geneva should have a definitive result on whether this particle exists within this coming year. The Higgs boson is one possible (and many think the most likely) consequence of the Higgs mechanism. Evidence last December pointed to a possible discovery, though more data is needed to know for sure. If confirmed, it will demonstrate that the Higgs mechanism is correct and furthermore tell us what is the underlying structure responsible for spontaneous symmetry breaking and spreading "charge" throughout the vacuum. The Higgs boson would furthermore be a new type of particle (a fundamental boson for those versed in physics terminology) and would be in some sense a new type of force. Admittedly, this is all pretty subtle and esoteric. Yet I (and much of the theoretical physics community) find it beautiful, deep, and elegant.

Symmetry is great. But so is symmetry breaking. Over the years many aspects of particle physics were first considered ugly and then considered elegant. Subjectivity in science goes beyond communities to individual scientists. And even those scientists change their minds over time. That's why experiments are critical. As difficult as they are, results are much easier to pin down than the nature of beauty. A discovery of the Higgs boson will tell us how that is done when particles acquire their masses.

Continuity

For me, the answer to this year's Edge question is clear: The Continuity Equations.

These are already familiar to you, at least in anecdotal form. Most everyone has heard of the law of "Conservation of Mass" (sometimes using the word "matter" instead of mass) and probably its partner "Conservation of Energy" too. These laws tell us that for practical, real-world (i.e. non-quantum, non-general relativity) phenomena, matter and energy can never be created or destroyed, only shuffled around. That concept has origins tracing at least as far back as the ancient Greeks, was formally articulated in the 18^th century (a major advance for modern chemistry), and today underpins virtually every aspect of the physical, life, and natural sciences. Conservation of Mass (matter) is what finally quashed the alchemists' quest to transform lead to gold; Conservation of Energy is what consigns the awesome power of a wizard's staff to the imaginations of legions of Lord of the Rings fans.

The Continuity Equations take these laws an important step further, by providing explicit mathematical formulations that track the storage and/or transfers of mass (Mass Continuity) and energy (Energy Continuity) from one compartment or state to another. As such, they are not really a single pair of equations but instead written into a variety of forms, ranging from the very simple to the very complex, in order to best represent the physical/life science/natural world phenomenon they are supposed to describe. The most elegant forms, adored by mathematicians and physicists, have exquisite detail and are therefore the most complex. A classic example is the set of Navier-Stokes equations (sometimes called the Saint-Venant equations) used to understand the movements and accelerations of fluids. The beauty of Navier-Stokes lies in their explicit partitioning and tracking of mass, energy and momentum through space and time. However, in practice such detail also makes them difficult to solve, requiring either hefty computing power or simplifying assumptions to be made to the equations themselves.

But the power of the Continuity Equations is not limited to complex forms comprehensible solely to mathematicians and physicists. A forest manager, for example, might use a simple, so-called "mass balance" form of a mass continuity equation to study her forest, by adding up the number, size, and density of trees, the rate at which seedlings establish, and subtracting the trees' mortality rate and number of truckloads of timber removed to learn if its total wood content (biomass) is increasing, decreasing, or stable. Automotive engineers routinely apply simple "energy balance" equations when, for example, designing a hybrid electric car to recapture kinetic energy from its braking system. None of the energy is truly created or destroyed just recaptured (e.g. from a combustion engine, which got it from breaking apart ancient chemical bonds, which got it from photosynthetic reactions, which got it from the Sun). Any remaining energy not recaptured from the brakes is not really "lost", of course, but instead transferred to the atmosphere as low-grade heat.

The cardinal assumption behind these laws and equations is that mass and energy are conserved (constant) within a closed system. In principle, the hybrid electric car only satisfies energy continuity if its consumption is tracked from start (the Sun) to finish (dissipation of heat into the atmosphere). This a bit cumbersome so it is usually treated as an open system. The metals used in the car's manufacture satisfy mass continuity only if tracked from their source (ores) to landfill. This is more feasible, and such "cradle-to-grave" resource accounting—a high priority for many environmentalists—is thus more compatible with natural laws than our current economic model, which tends to externalize (i.e., assume an open system) such resource flows.

Like the car, our planet, from a practical standpoint, is an open system with respect to energy and a closed system with respect to mass (while it's true that Earth is still being bombarded by meteorites, that input is now small enough to be neglected). The former is what makes life possible: Without the Sun's steady infusion of fresh, external energy, life as we know it would quickly end. An external source is required because although energy cannot be destroyed, it is constantly degraded into weaker, less useful forms in accordance with the 2^nd law of thermodynamics (consider again the hybrid-electric car's brake pads—their dissipated heat is of not much use to anyone). The openness of this system is two-way, because Earth also streams thermal infrared energy back out to space.  Its radiation is invisible to us, but to satellites with "vision" in this range of the electromagnetic spectrum the Earth is a brightly glowing orb, much like the Sun.  

Interestingly, this closed/open dichotomy is yet another reason why the physics of climate change are unassailable. By burning fossil fuels, we shuffle carbon (mass) out of the subsurface—where it has virtually no interaction with the planet's energy balance—to the atmosphere, where it does. It is well understood that carbon in the atmosphere alters the planet's energy balance (the physics of this have been known since 1893) and without carbon-based and other greenhouse gases our planet would be a moribund, ice-covered rock. Greenhouse gases prevent this by selectively altering the Earth's energy balance in the troposphere (the lowest few miles of the atmosphere, where the vast majority of its gases reside), thus raising the amount of thermal infrared radiation that it emits. Because some of this energy streams back down to Earth (as well as out to space) the lower troposphere warms, to achieve energy balance. Continuity of Energy commands this.

Our planet's carbon atoms, however, are stuck here with us forever—Continuity of Mass commands that too. The real question is what choices will make about how much, and how fast, to shuffle them out the ground. The physics of natural resource stocks, climate change and other problems can often be reduced to simple, elegant, equations—if only we had such masterful tools to dictate their solution.

Cosmic Complexity

What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainly did not invent) is that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for the explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemingly improbable events are actually happening all the time?

Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physicists have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features.

Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capacity" in which extracting energy from a gravitating system makes it hotter—clearly the 2^nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the Sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations.

And because of that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called Life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceaseless experimentation would not be able to produce Life elsewhere—but we don't know for sure.

And Life went on to cause new instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles, with predators for every kind of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves.

One of the instabilities is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are in 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verlinde has argued that gravitation, the one force that has so far resisted our efforts at a quantum description, is not even a fundamental force, but is itself a statistical force, like osmosis.

What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

The True Rotational Symmetry of Space

The following deep, elegant, and beautiful explanation of the true rotational symmetry of space comes from the late Sidney Coleman, as presented to his graduate physics class at Harvard. This explanation takes the form of a physical act that you will perform yourself. Although elegant, this explanation is verbally awkward to explain, and physically awkward to perform. It may need to be practised a few times. So limber up and get ready: you are about to experience in a deep and personal way the true rotational symmetry of space!

At bottom, the laws of physics are based on symmetries, and the rotational symmetry of space is one of the most profound of these symmetries. The most rotationally symmetric object is a sphere. So take a sphere such as a soccer—or basket-ball that has a mark, logo, or unique lettering at some spot on the sphere. Rotate the sphere about any axis: the rotational symmetry of space implies that the shape of the sphere is invariant under rotation. In addition, if there is a mark on the sphere, then when you rotate the sphere by three hundred and sixty degrees, the mark returns to its initial position. Go ahead. Try it. Hold the ball in both hands and rotate it by three hundred and sixty degrees until the mark returns.

That's not so awkward, you may say. But that's because you have not yet demonstrated the true rotational symmetry of space. To demonstrate this symmetry requires fancier moves. Now hold the ball cupped in one hand, palm facing up. Your goal is to rotate the sphere while always keeping your palm facing up. This is trickier, but if Michael Jordan can do it, so can you.

The steps are as follows:

Keeping your palm facing up, rotate the ball inward towards your body. At ninety degrees—one quarter of a full rotation—the ball is comfortably tucked under your arm.

Keep on rotating in the same direction, palm facing up. At one hundred and eighty degrees—half a rotation—your arm sticks out in back of your body to keep the ball cupped in your palm.

As you keep rotating to two hundred and seventy degrees—three quarters of a rotation—in order to maintain your palm facing up, your arm sticks awkwardly out to the side, ball precariously perched on top.

At this point, you may feel that it is impossible to rotate the last ninety degrees to complete one full rotation. If you try, however, you will find that you can continue rotating the ball keeping your palm up by raising your upper arm and bending your elbow so that your forearm sticks straight forward. The ball has now rotated by three hundred and sixty degrees—one full rotation. If you've done everything right, however, your arm should be crooked in a maximally painful and awkward position.

To relieve the pain, continue rotating by an additional ninety degrees to one and a quarter turns, palm up all the time. The ball should now be hovering over your head, and the painful tension in your shoulder should be somewhat lessened.

Finally, like a waiter presenting a tray containing the pi'ece de resistance, continue the motion for the final three quarters of a turn, ending with the ball and your arm—what a relief—back in its original position.

If you have managed to perform these steps correctly and without personal damage, you will find that the trajectory of the ball has traced out a kind of twisty figure eight or infinity sign in space, and has rotated around not once but twice. The true symmetry of space is not rotation by three hundred and sixty degrees, but by seven hundred and twenty degrees!

Although this excercise might seem no more than some fancy and painful basketball move, the fact that the true symmetry of space is rotation not once but twice has profound consequences for the nature of the physical world at its most microscopic level. It implies that 'balls' such as electrons, attached to a distant point by a flexible and deformable 'strings,' such as magnetic field lines, must be rotated around twice to return to their original configuration. Digging deeper, the two-fold rotational nature of spherical symmetry implies that two electrons, both spinning in the same direction, cannot be placed in the same place at the same time. This exclusion principle in turn underlies the stability of matter. If the true symmetry of space were rotating around only once, then all the atoms of your body would collapse into nothingness in a tiny fraction of a second. Fortunately, however, the true symmetry of space consists of rotating around twice, and your atoms are stable, a fact that should console you as you ice your shoulder.

Why Things Happen

There is a wonderful simplicity in the view that events occur because things get worse. I have in mind the Second Law of thermodynamics and the fact that all natural change is accompanied by an increase in entropy. Although that is in my mind, I understand those words in terms of the tendency of matter and energy to disperse in disorder. Molecules of a gas undergo ceaseless virtually random motion, and spread into the available volume. The chaotic thermal motion of atoms in a block of hot metal jostle their neighbors into motion, and as the energy spreads into the surroundings so the block cools. All natural change is at root a manifestation of this simple process, that of dispersal in disorder.

The astonishing feature of this perception of natural change is that the dispersal can generate order: through dispersal in disorder structure can emerge. All it needs is a device that can link in to the dispersal, and just as a plunging stream of water can be harnessed and used to drive construction, so the stream of dispersal can be harnessed too. Overall there is an increase in disorder as the world progresses, but locally structures, including cathedrals and brains, dinosaurs and dogs, piety and evil deeds, poetry and diatribes, can be thrown up as local abatements of chaos.

Take, for instance, an internal combustion engine. The spark results in the combustion of the hydrocarbon fuel, with the generation of smaller water and carbon dioxide molecules that tend to disperse and in so doing drive down a piston. At the same time the energy released in the combustion spreads into the surroundings. The mechanical design of the engine harnesses these dispersals and through a string of gears that harnessing can be used to build from bricks a cathedral. Thus, dispersal results in a local structure even though overall the world has sunk a little more into disorder.

The fuel might be our dinner, which as it is metabolised releases molecules and energy that spread. The analog of the gears in a vehicle is the network of biochemical reactions within us, and instead of a pile of bricks molded into a cathedral amino acids are joined together to generate the intricate structure of  a protein. Thus, as we eat, so we grow. We too are local abatements of chaos driven into being by the generation of disorder elsewhere.

Is it then too fanciful to imagine intellectual creativity, or just plain inconsequential reverie, as being driven likewise? At some kind of notional rest, the brain is a hive of electric and synaptic activity. The metabolic processes driven by the digestion of food can result in the ordering, not now of brick into cathedral, not now of amino acid into protein, but now current into concept, work of artistic expression, foolhardy decision, and scientific understanding.

Even that other great principle, natural selection, can be regarded as an extraordinarily complex reticulated unwinding of the world, with the changes that take place in the biosphere and its evolution driven ultimately by descent into disorder. 

Is it then any wonder that I regard the Second Law as a great enlightenment? That from so simple a principle great consequences flow is, in my view, a criterion of the greatness of a scientific principle. No principle, I think, can be simpler than that things get worse, and no consequences greater than the universe of all activity, so surely the Law is the greatest of all?

Furry Rubber Bands

I learned electrodynamics from Mark Heald and his concise text on an even more concise set of equations, Maxwell's. In 4 lines, just 31 characters (or less with some notational tricks), Maxwell's equations unified what had appeared to be unrelated phenomena (the dynamics of electric and magnetic fields), predicted new experimental observations, and contained both theoretical advances to come (including the wave solution for light, and special relativity) and technologies to come (including the fiber optics, coaxial cables, and wireless signals that carry the Internet).

But the explanation that I found to be so memorable was not Maxwell's of electromagnetism, which is well known for its beauty and consequence, it was Mark's that electric field lines behave like furry rubber bands: they want to be as short as possible (the rubber) but don't want to be near each other (the fur). This is an easily-understood qualitative description that has served me in good stead in device design. And it provides a deeper, quantitative insight into the nature of Maxwell's equations: the local solution for the field geometry can be understood as solving a global optimization.

These sorts of scientific similarities that are predictive as well as descriptive help us reason about regimes that our minds didn't evolve to operate in. Unifying forces is not an everyday occurrence, but explaining them can be. Recognizing that something is precisely like something is a kind of object-oriented thinking that helps build bigger thoughts out of smaller ideas.

I understood Berry's phase for spinors by trying to rotate my hand while holding up a glass; I mastered NMR spin echoes by swinging my arms while I revolved; the alignment of semiconductor Fermi levels at a junction made sense when explained as filling buckets with water. Like furry rubber bands and electric fields, these relationships represent analogies between governing equations. Unlike words, they can be exact, providing explanations that connect unfamiliar formalism with familiar experience.

How Psychotherapy Can Be Placed On A Scientific Basis: 5 Easy Lessons

How did psychoanalysis, once a major mode for treating non-psychotic mental disorders fall so badly in the estimation of the medical community in the United States and in the estimation of the public at large. How could it be reversed? Let me try to address this question putting it in a bit of historical perspective.

While an undergraduate at Harvard College I was drawn to Psychiatry—and specifically to Psychoanalysis. During my training from 1960-1965, psychotherapy was the major mode of treating mental illness and this therapy was derived from psychoanalysis and was based on the belief that one needed to understand mental symptoms in terms of their historical roots in childhood. These therapies tended to take years and neither the outcome nor the mechanisms were studied systematically because this was thought to be very difficult. Psychotherapy and in the limit psychoanalysis when successful allowed people to work a bit better and to love a bit and these were dimensions that were thought to be difficult to measure.

In the 1960s Aaron Beck changed all that by introducing five major obvious, but nevertheless elegant and beautiful innovations:

First, he introduced instruments for measuring mental illness. Up until the time of Beck's work, psychiatric research was hampered by a dearth of techniques for operationalizing the various disorders and measuring their severity. Beck developed a number of instruments, beginning with a Depression Inventory, a Hopelessness Scale, and a Suicide Intent Scale. These scales helped to objectify research in psychopathology and facilitated the establishment of better clinical outcome trials.

Second, Beck introduced a new short-term, evidence-based therapy he called Cognitive Behavioral Therapy.

Third, Beck manualized the treatments. He wrote a cookbook so method could be reliably taught to others. You and I could in principle learn to do Cognitive Behavioral Therapy.

Fourth, he carried out with the help of several colleagues, progressively better controlled studies which documented that Cognitive Behavioral Therapy worked more effectively than placebo and as effectively as antidepressants in mild and moderate depression. In severe depression it did not act as effectively as an anti-depressant but acted synergistically with them to enhance recovery.

Fifth and finally, Beck's work was picked up by Helen Mayberg, another one of my heroes in psychiatry. She carried out FMRI studies of depressed patients and discovered that Brodmann area 25 was a focus of abnormal activity in depression. She went on to find that if—and only if—a patient responded to cognitive behavior therapy or to antidepressants SSRI's (selective serotonin reuptake inhibitors) this abnormality reverted to normal.

What I find so interesting in this recital is the Edge question: What elegant, deep explanation did Aaron Beck bring to his work that differentiated him from the rest of my generation of psychotherapists and allowed him to be so original?

Aaron Beck trained as a psychoanalyst in Philadelphia, but soon became impressed with the radical idea that the central issue in many psychiatric disorders is not unconscious conflict but distorted patterns of thinking. Beck conceived of this novel idea from listening with a critical—and open—mind to his patients with depression. In his early work on depression Aaron set out to test a specific psychoanalytic idea: that depression was due to "introjected anger." Patients with depression, it was argued, experienced deep hostility and anger toward someone they loved. They could not deal with having hostile feelings toward someone they valued and so they would repress their anger and direct it inward toward themselves. Beck tested this idea by comparing the dreams—the royal road to the unconscious—of depressed patients with those of non-depressed patients and found that in their dreams depressed patients showed—if anything—less hostility than non-depressed patients. Instead Beck found that in their dreams as in their waking lives depressed patients have a systematic negative bias in their cognitive style, in the way they thought about themselves and their future. They saw themselves as "losers."

Aaron saw these distorted patterns of thinking not simply as a symptom—a reflection of a conflict lying deep within the psyche—but as a key etiological agent in maintaining the disorders.

This led Beck to develop a systematic psychological treatment for depression that focused on distorted thinking. He found that by increasing the patients' objectivity regarding their misinterpretation of situations or their cognitive distortions and their negative expectancies, the patients experienced substantial shifts in their thinking and subsequently improvements in their affect and behavior.

In the course of his work on depression Beck focused on suicide and provided for the first time a rational basis for the classification and assessment of suicidal behaviors that made it possible to identify high-risk individuals. His prospective study of 9,000 patients led to the formulation of an algorithm for predicting future suicide that has proven to have high predictive power. Of particular importance was his identification of clinical and psychological variables such as hopelessness and helplessness to predict future suicides. These proved to be better predictors of suicide than clinical depression per se. Beck's work on suicide, and that of others such as John Mann at Columbia, demonstrated that a short-term cognitive intervention can significantly reduce subsequent suicide attempts when compared to a control group.

In the 1970s, Beck carried out the randomized controlled trials I referred to earlier. Later, the NIMH did similar trials and together these established cognitive therapy as the first ever-psychological treatment that could objectively be shown to be effective in clinical depression.

As soon as cognitive therapy had been found to be effective in the treatment of depression, Beck turned to other disorders. In a number of controlled clinical trials he demonstrated that cognitive therapy is effective in panic disorder, posttraumatic stress disorder, and obsessive-compulsive disorder. In fact even earlier than Helen Mayberg's work on depression—Lewis Baxter at UCLA had imaged patients with obsessive-compulsive disorder and found they had an abnormality in the caudate nucleus that was reversed when patients improved with cognitive behavioral therapy.

Aaron Beck has recently turned his attention to patients with schizophrenia—and has found that cognitive therapy helps improve their cognitive and negative symptoms, particularly their motivational deficits. Another amazing advance.

So—the answer to the decline of psychoanalysis may not simply lie in the limitation of Freud's thought—but perhaps much more so in the lack of a deep, critical scientific attitude of many of the subsequent generation of therapists. I have little doubt that insight therapy is extremely useful as a therapy. And there are studies that support that contention. But an elegant, deep and beautiful proof requires putting a set of highly validated approaches together to make the point in a convincing manner and perhaps even an idea of how the therapeutic result is achieved.

The Wizard of I

Consciousness is the fusion of immediate stimuli with memory that combines the simultaneous feeling of being both the observer and the observed into a smooth, enveloping flow of time that is neither truly the past nor the present but somehow inexplicably each of them. It is the ultimate authority and arbiter of our perceptual reality. That consciousness is still an intractable problem for scientists and philosophers to understand is not surprising. Whatever the final answer turns out to be, I suspect it will be an illusion the mind evolved to hide the messy workings of its parallel modular computing.

Neurophysiologists are finding, as they pull ever so slightly at the veil, which shrouds the "Wizard of I," that this indispensable attentive and observant self monitor called consciousness, is dependent upon a trick in overseeing our perceptions. Our subjective sense of time does not correspond to reality. Cortical evoked potentials, electrical recordings, of the normal brain during routine activity have been shown to precede by almost a third of a second the awareness of an actual willed movement or a response to sensory stimulation. The cortical evoked potentials indicate that the brain is initiating or reacting to what is happening far sooner than the instantaneous perception we experience. On a physiological scale, this represents a huge discrepancy that our mind corrects by falsifying the actual time an action or event occurs, thus enabling our conscious experience to conform to what we perceive.

But even more damaging to our confidence in the reliability of our perceptions comes from studies of rapid eye movements, called saccades that are triggered by novel visual stimuli. During the brief moments of these jerky eye movements, visual input to the brain is actively suppressed such that we are literally blind. Without this involuntary ocular censorship, we would be repeatedly plagued with moments of acute blurred vision that would be unpleasant as well as unsafe. From a survival calculus, this would pose an extremely unfavorable disadvantage since it would invariably occur with novel stimuli, which by its very nature required, not the worst but the best visual acuity.

The Wizard's solution to this intolerable situation was to exclude those intervals from our stream of awareness and to replace it instead with a vision extrapolated from what had just occurred to what was immediately anticipated. But consciousness, like a former president, had to come up with an accounting for the erased period. Evolution provided a much longer epic to work out the bugs in its necessary deception than the limited time frame under the gun of a special prosecutor. Instead of trying to hide the existence of the tape, consciousness came up with a far clever trick of obscuring the deletion. It did this by falsifying the time, backdating those necessary moments so that there is no appearance of any gap.

This illusion of visual continuity from inference and extrapolation poses an innate vulnerability in the brain's software that any good hacker can exploit. Magicians, card sharks, three card monte hustlers have made a nice living working this perceptual flaw. In a comic routine, Richard Pyror expressed this best when caught by his wife with another woman. "Who are you going to believe? Me or your lying eyes?" 

Kepler's Use Of The Platonic Solids To Explain The Relative Distance Of Planets From The Sun

In 1595 Johannes Kepler proposed a deep, elegant and beautiful solution to the problem of determining the distance from the Sun of the six then-known planets. Nesting, as in the case of Russian dolls, each of the five Platonic solids within a sphere, and having those solids arranged in the proper order—octahedron, icosahedron, dodecahedron, tetrahedron, cube- he proposed that the succession of spherical radii would have the same relative ratios as the planetary distances. Of course the deep, elegant and beautiful solution was also wrong but then, as Joe.E.Brown famously said in Some Like it Hot's last line "Nobody's perfect."

Two thousand years earlier, in a notion that would come to be commonly described as Harmony of the Spheres, Pythagoras had already sought a solution by relating those distances to the sites on a string at which it needed to be plucked in order to produce notes pleasing to the ear. And almost two hundred years after Kepler's suggestion, Johann Bode and Johann Titius offered, without an underlying explanation for its existence, a simple numerical formula that supposedly fit the distances in question. So we see that Kepler's explanation was neither the first nor the last attempt to explain the ratios of planetary orbit radii, but in its linking of dynamics to geometry, it remains for me the deepest as well as being the simplest and most elegant.

In a strict sense none of the three proposals is strictly wrong. They are instead solutions to a problem that doesn't exist for we now understand that the location of planets is purely accidental, a byproduct of how the swirling disk of dust that circled our early Sun evolved under the force of gravity into its present configuration. The realization that there was no problem came as our view expanded from one in which our own planetary system was central to a far greater vision in which it was one of an almost limitless number of such systems scattered throughout the vast numbers of galaxies comprising our Universe.

I have been thinking about this because, together with many of my fellow theoretical physicists, I have spent a good part of my career searching for an explanation of the masses of the so-called elementary particles. But perhaps the reason it has eluded us is a proposal that is increasingly gaining credence, namely that our own visible Universe is only a random example of an essentially infinite number of Universes, all of which contain quarks and leptons with masses taking different values. It just happens that in at least one of those Universes, the values allow for there being at least one star and one planet where creatures that worry about such problems have come to life.

In other words a problem that we thought was central may once again have ceased to exist as our conception of the Universe has grown, in this case extended to one of many Universes. If this is indeed true, what grand vistas may lie before us in the future? I only hope that our descendants may have a much deeper understanding of these problems than we do and that they will smile at our attempts at our feeble attempts to provide a deep, elegant and beautiful solution to what they have recognized is a non-existent problem.

Quasi-elegance

My first exposure to true elegance in science was through a short semi-popular book entitled SYMMETRY written by the renowned mathematician Hermann Weyl. I discovered the book in the fourth grade and have returned to reread passages every few years. The book begins with the intuitive aesthetic notion of symmetry for the general reader, drawing interesting examples from art, architecture, biological forms, and ornamental design. By the fourth and final chapter, though, Weyl turns from vagary to precise science as he introduces elements of group theory, the mathematics that transforms symmetry into a powerful tool.

To demonstrate its power, Weyl spends his final chapter outlining how group theory can be used to explain the shapes of crystals. Crystals have fascinated humans throughout history because of the beautiful faceted shapes they form. Most rocks contain an amalgam of different minerals, each of which is crystalline, but which have grown together or crunched together or weathered to the point that facets are unobservable. Occasionally, though, the same minerals form individual large faceted crystals. That is when we find them most aesthetically appealing. "Aluminum oxide" may not sound like something of value, but add a little chromium, give nature sufficient time and you have a ruby worthy of kings.

If you have not done so recently, I urge you to visit the mineral collection in a museum to observe the remarkable variety and beauty of crystal forms. You will discover for yourself a basic mineralogical fact that the crystal facets found in nature meet at only certain angles corresponding to one of a small set of symmetries. But why does matter take some shapes and not others? What scientific information do the shapes convey? Weyl explains how these questions can be answered seemingly unrelated abstract mathematics aimed at answering a different question: namely, what shapes can be used to tessellate a plane or fill space if the shapes are identical, meet edge-to-edge and leave no spaces? Squares, rectangles, triangles, parallelograms and hexagons can do the job. Perhaps you imagine that many other polygons would work as well; however, try and you will discover there are no more possibilities. Pentagons, heptagons, octagons and all other regular polygons cannot fit together without leaving spaces. Weyl's little book describes the mathematics that allows a full classification of possibilities including as distinct patterns with decorated tiles and including reflections, glides and screw axes,. The final tally is only 17 distinct possibilities in two dimensions (the so-called wallpaper patterns) and 230 distinct symmetry possibilities in three dimensions.

The stunning fact about the mathematicians' list was that it precisely matched the list observed for crystals shapes found in nature. The inference is that crystalline matter is like a tessellation made of indivisible, identical building blocks that repeat to make the entire solid. Of course, we know today that these building blocks are clusters of atoms or molecules. However, bear in mind that the connection between the mathematics and real crystals was made in 19^th century when the atomic theory was still in doubt. It is amazing that an abstract study of tiles and building blocks can lead to a keen insight about the fundamental constituents of matter and a classification of all possible arrangements of them. It is a classic example of physicist Eugene Wigner referred to as the "unreasonable effectiveness of mathematics in the natural sciences." The story does not end there. With the development of quantum mechanics, group theory and symmetry principles have been used to predict the electronic, magnetic, elastic and other physical properties of solids. Emulating this triumph, physicists have successfully used symmetry principles to explain the fundamental constituents of nuclei and elementary particles, as well as the forces through which they interact.

As a young student first reading Weyl's book, crystallography seemed like the "ideal" of what one should be aiming for in science: elegant mathematics that provides a complete understanding of all physical possibilities. Ironically, many years later, I played a role in showing that my "ideal" was seriously flawed. In 1984, Dan Shechtman, Ilan Blech, Denis Gratias and John Cahn reported the discovery of a puzzling manmade alloy of aluminumand manganese with icosahedral symmetry. Icosahedral symmetry, with its six five-fold symmetry axes, is the most famous forbidden crystal symmetry. As luck would have it, Dov Levine (Technion) and I had been developing a hypothetical idea of a new form of solid that we dubbed quasicrystals, short for quasiperiodic crystals. (A quasiperiodic atomic arrangement means the atomic positions can be described by a sum of oscillatory functions whose frequencies have an irrational ratio.) We were inspired by a two-dimensional tiling invented by Sir Roger Penrose known as the Penrose tiling, comprised of two tiles arranged in a five-fold symmetric pattern. We showed that quasicrystals could exist in three dimensions and were not subject to the rules of crystallography. In fact, they could have any of the symmetries forbidden to crystals. Furthermore, we showed that the diffraction patterns predicted for icosahedral quasicrystals matched the Shechtman et al. observations. Since 1984, quasicrystals with other forbidden symmetries have been synthesized in the laboratory. The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for his experimental breakthrough that changed our thinking about possible forms of matter. More recently, colleagues and I have found evidence that quasicrystals may have been among the first minerals to have formed in the solar system.

The crystallography I first encountered in Weyl's book, thought to be complete and immutable, turned out to be woefully incomplete, missing literally an uncountable number of possible symmetries for matter. Perhaps there is a lesson to be learned: While elegance and simplicity are often useful criteria for judging theories, they can sometimes mislead us into thinking we are right, when we are actually infinitely wrong. 

Metarepresentations Explain Human Uniqueness

Humans alone fluently understand the mental states of others. Humans alone rely on an open-ended system of communication. Humans alone ponder the reasons for their beliefs. For each of these feats, and for others too, humans rely on their most special gift: the ability to represent representations—the ability to form metarepresentations. Hidden behind such mundane thoughts as "Mary believes that Paul believes that it's going to rain" is the explanation of human uniqueness.

There are two ways to represent representations: one immensely powerful, the other rather clumsy. The clumsy way is to create a new representation for every representation that needs to be represented. Using such a device, Mary would have to form a representation "Paul believes that it's going to rain" completely independent of her representation "it's going to rain." She would then have to learn anew all of the inferences that can be drawn from "Paul believe it's going to rain," such as the negative impact on the willingness to go for a jog or the increased probability to fetch an umbrella. This cumbersome process would have to be repeated for each new representation that Mary wishes to attribute, from "Peter things the weather looks lovely" to "Ruth is afraid that the Dow Jones is going to crash tomorrow." Such a process could not possibly account for humans' amazing abilities to attribute just about any thought to other people. How can we account for these skills then?

The explanation is that we use our own representations to attribute thoughts to others. When Mary wants to attribute to Paul the belief "it's going to rain," she 'simply' uses her representation "it's going to rain" and embeds it in a metarepresentation: "Paul thinks "it's going to rain."" Because the same representation is used, Mary can take advantage of the inferences that she could draw from "it's going to rain" to draw inferences from "Paul believes that "it's going to rain."" This trick opened for humans the doors to an unparalleled understanding of their social environment.

Most of the beliefs we form about others are derived from communication: people keep telling us what they believe, want, desire, fear, love… Here again, metarepresentations play a crucial role, since understanding language requires going from utterances—"It's going to rain"—to metarepresentations—"Paul means that "it will soon rain here.""

Mentalizing (attributing thoughts to others) and communicating are the most well known uses of metarepresentations, but they are not the only ones. Metarepresentations are also essential for people to be able to think about reasons. Specific metarepresentations are relied on when people produce and evaluate arguments, as in: "Mary thinks "it's going to rain" is a good argument for "we should not go out."" Again, Mary uses her representation "it's going to rain" but, instead of attributing it to someone else, she represents its strength as a reason to accept a given conclusion.

Several other properties of representations can be represented, from their esthetic value to their normative status. The representational richness made possible by recycling our own representations to represent other people's representations, or to represent other attributes of representations, is our most distinctive trait, one of these amazingly brilliant solutions that natural selection stumbles upon. However, if it is indeed much simpler to rely on this type of metarepresentations than on the cumbersome solution of creating new representations from scratch every time, we still face a complex computational task.

Using the example of mentalizing, it is apparent that even when we use our own representations to attribute representations to other people, a lot of work remains to be done. It cannot be metarepresentations all the way down: at some point, other inputs—linguistic or behavioral cues—have to be used to attribute representations. Moreover, when a representation is represented not all of the inferences that can be drawn from it are relevant. When Mary believes that John believes it's going to rain, some of the inferences that she would draw from "it's going to rain" may not be attributable to John—maybe he doesn't mind jogging in the rain for instance. Other inferences Mary may not spontaneously draw—maybe John will be worried because he has left his book outside. Still, without a baseline—Mary's own representation—the task would jump from merely difficult to utterly intractable.

Probably more than any other cognitive trait, the ability to use our own representations to represent representations is what explains humans' achievements. Without this skill, the complex forms of social cognition that characterize our species would have been all but impossible. It is also critical for us psychologists to understand these ideas if we want to continue our forays into human cognition.

I leave the last word to Dan Sperber who, more than any other cognitive scientists, has made of metarepresentations the most central explanation of humans' unique cognition: "Humans have the ability to represent representations. I would argue that this meta-representational ability is as distinctive of humans, and as important in understanding their behaviour, as is echolocation for bats."

Larger Groups Produce Fewer Responses

The most elegant explanation in social psychology convinced me to pursue a Ph.D. in the field. Every few years, a prominent tragedy attracts plenty of media attention because no one does anything to help. Just before sunrise on an April morning in 2010, a man lay dying on a sidewalk in Queens. The man, a homeless Guatemalan named Hugo Alfredo Tale-Yax, had intervened to help a woman whose male companion began shouting and shaking her violently. When Tale-Yax intervened, the man stabbed him several times in the torso. For ninety minutes, Tale-Yax lay in a growing pool of his own blood as dozens of passers-by ignored him or stared briefly before continuing on their way. By the time firefighters arrived to help, the sun had risen and Tale-Yax had died.

Almost half a century earlier another New Yorker, Kitty Genovese, was attacked and ultimately killed while dozens of onlookers apparently failed to intervene. A New York Times writer decried the callousness of New Yorkers and experts claimed that life in the city had rendered them soulless. Just as commentators said in response to Tale-Yax's death, experts wondered how dozens of people with functioning moral compasses could possibly fail to help someone on the verge of death.

Social psychologists are taught to overcome the natural tendency to blame people for apparently bad behavior, and to look for explanations in the environment instead. Witnessing the vocal response to Genovese's death, social psychologists John Darley and Bibb Latane were convinced that something else about the situation explained why the bystanders failed to intervene. Their elegant insight was that human responses aren't additive in the same way that objects are additive. Whereas four light bulbs illuminate a room more effectively than three light bulbs, and three loudspeakers fill a room with noise more effectively than two loudspeakers, two people aren't always more effective than a single person. People second-guess situations, they stop to make sense of a chain of events before acting, and sometimes pride and the fear of looking foolish prevent them from acting at all.

In a series of brilliant studies, Darley and Latane videotaped students as they sat in a room that slowly filled with smoke. The experimenters pumped smoke into the room with a smoke machine, hidden behind a door in a room nearby, but the effect suggested that the door may have concealed a fire. When the students sat in the room alone, they usually left the room quickly and told the experimenter that something was amiss; but when the students sat in small groups of two, three or four, they often remained seated even as they lost sight of the other students through the pall of smoke. When interviewed later, the students said they chose not to act because they were embarrassed, because they weren't sure whether the smoke truly signaled an emergency, and because they relied on the other impassive students in the room to help them decide that the smoke was benign.

According to Darley and Latane, the patterns of thinking that distinguish us from objects and lower-order animals ultimately undermine our willingness to help when we try to understand those situations alongside other people who are equally confused.

The Epidemic of Obesity, Diabetes and "Metabolic Syndrome:" Cell Energy Adaptations in a Toxic World?

"Metabolic syndrome" (MetSyn) has been termed the "Epidemic of the 21^st century." MetSyn is an accretion of symptoms, including high body mass index (weight-for-height), high blood sugar, high blood pressure (BP), high blood triglycerides, high waist circumference (central/visceral fat deposition), and/or reduced HDL-cholesterol, the so-called "good" cholesterol. Epidemics of Obesity and diabetes are intertwined with, and accompany, the meteoric rise in MetSyn.

The prevalent view is that MetSyn is due to a glut of food calories ("energy") consumed, and a dearth of exercise energy expended, spurring weight gain—an "energy surfeit"—with the other features arising in consequence. After all, we have more access to calories, and are more often sedentary, than in times gone by. In turn, MetSyn factors are each linked, in otherwise-healthy young populations, to higher mortality.

But this normative view leaves many questions unanswered: Why do elements of MetSyn correlate? Why are overweight people today more likely to have diabetes than hitherto? Why are elements of MetSyn now emerging in infancy? Why is MetSyn materializing in poor and third-world nations?

The customary "explanation" also creates paradoxes. If MetSyn stems from energy surfeit, why do factors that reduce energy supply, or increase demand promote MetSyn—far from protecting against it?

·     Sleep apnea (It’s a stronger MetSyn risk factor than overweight, though oxygen is the primary energy substrate; moreover sleep apnea treatment benefits each MetSyn element)

·     Ultra low-calorie or low-fat diets

·     Fasting, skipped meals

·     Hypoglycemia-promoting diets (high-carbohydrate/low-fat/low-protein diets lead to unopposed insulin surge)

·     Deficient sleep (more energy-expending wake time

·     Illness/injury/surgery (high energy demand)

·     Cold weather (mandating energy expenditure for thermogenesis)

·     Nutrient and antioxidant deficiencies (adequacy required for energy production)

·     Oxidative stressor exposure (impairs function of mitochondria, the energy producing elements of cells)

·     Mitochondrial pathology.

Why do factors that protect from energy-deficit, reduce MetSyn factors—antioxidant cocoa and cinnamon, mitochondria-supportive coenzymeQ10—and exercise, which expends energy during activity, but boosts energy production throughout the day/night, via antioxidant effects, mitochondrial biogenesis, enhanced circulation and cardiopulmonary function—improving oxygen intake, delivery, and conversion to energy.

Why does MetSyn cease to elevate mortality (indeed, sometimes boosts survival) when the group studied has advanced age, heart failure, or severe kidney disease—conditions that all impair cell energy?

Suppose the correct explanation were the complete opposite to the accepted one? Could the features of MetSyn be the adaptive response to inadequate energy? After all, fat depots, glucose, and triglycerides are each accessory energy sources (oxygen is primary), blood pressure is needed to deliver these to tissues, especially when underperfused. Cell energy, central to cell and organism survival, is needed—continuously (we live only minutes without oxygen). The stretch is not so great: populations in which prior generations were energy starved have increased obesity/MetSyn now ("thrifty gene" thesis); and low energy supplyin utero is understood to foster MetSyn in adulthood.

This explains—as the energy surfeit view does not—why MetSyn exists at all: why elevated glucose, triglycerides, blood pressure (carrying oxygen, glucose, nutrients) and abdominal fat deposition cohere statistically. It explains why other energy supportive adaptations accompany them, like free fatty acids—as well as (metabolically active) ectopic fat: fatty-liver, fatty-pancreas, fatty-kidney—even fatty-streaks in the blood vessels; why MetSyn is linked to fatigue, and increased sleep duration (to conserve energy). Indeed, increased calories eaten, and reduced exercise expended—the usual MetSyn explanation—arise, too, as fellow energetic adaptations: Thus, this view is arguably not antithetical to the canonical one, but in one sense subsumes it. It explains, as the energy surfeit view does not, the populations at risk for MetSyn such as elderly (mitochondrial function declines exponentially with age) and those afflicted with sleep apnea—or any cause for recurrent energy production impairment. And it explains why in studies focused on persons with conditions that blight energy, those with MetSyn features "paradoxically" don’t do worse, or even fare better.

Why, then, is MetSyn an epidemic? Numerous energy-adverse secular shifts include nutrient-poor/low-antioxidant/high-prooxidant pseudofoods (nutrients are needed for energy production machinery, antioxidants protect from oxidative stress—for which the chief target is mitochondria, the energy producing bits of cells), decline of regular balanced meals, hypoglycemic-promoting macronutrient composition (simple carbohydrates without fat or protein engender unopposed insulin surges: glucose drops). But a central factor is the explosion of oxidative stressors in our environment which disrupt function of (and DNA in) mitochondria, cells’ energy-producers, E.g.:

·     Metals and heavy metals (mercury in fish, high fructose corn syrup, broken light bulbs; arsenic to promote poultry growth; aluminum vaccine adjuvants—with proliferating childhood vaccinations)

·     Plastics with bisphenol A

·     Personal care products (chemicals in sunscreens, lotions, hairdyes, cosmetics, detergents, fabric softeners/dryer sheets, conditioners)

·     Cleaning products

·     Furnishings/clothes with formaldehyde (pressboard, no-iron cotton)

·     Petrochemicals, combustion products

·     Electromagnetic fields (electronics, cellphones, smart-meters)

·     Fire retardants (pajamas, bedding)

·     Dry-cleaning chemicals

·     Air "fresheners"

·     Pesticides, herbicides (potent oxidative stressors, now routinely applied at homes, recreational-sites, professional buildings)

·     Termite tenting

·     Prescription and OTC drugs including antibiotics—with exposure directly and through our food supply

·     Antimicrobial soaps bearing active ingredients largely unfilterable from the water supply

·     Air and water pollutants/contaminants

·     Artificial ingredients in foods—transfats, artificial-sweeteners, dyes, preservatives.

The energy deficit ("starving cell") hypothesis accounts for scores of facts where the prevailing view provides no insight. Numerous observations deemed "paradoxical" in the standard view emerge seamlessly. It has testable predictions, e.g.: Multiple other oxidative stress- and mitochondrial disruption-inducing exposures that have not yet been assessed will promote one or multiple elements of MetSyn. For factors that relate at both extremes to MetSyn—e.g. short and long sleep duration—the energy disruptive one will prove to cause MetS, and the energy supportive one to serve as a fellow adaptive consequence.

This reframing addresses a pivotally important problem—some think MetSyn is slated to reverse the gains we have made in longevity—with a perhaps surprising conclusion, that should precipitate a revision in our thinking about causes of MetSyn, and importantly, its solutions.

The Oklo Pyramid

New explanations in science are needed when an observation isn't explicable by current theory. The power of the scientific method lies in the extraordinary richness of understanding that can emerge from an attempt to devise a new explanation. It is like an inverted pyramid, with the first observation—often just a slight departure from the norm—as the point and then ever widening layers of inference, each dependent on a lower layer, until the whole pyramid supplies a satisfying and conclusive explanatory whole.

One of my favourite such explanations began with the observation of a small anomaly in a routine sample of uranium ore sent from Oklo, a region near the town of Franceville, in the Haut-Ogooué province of the Central African state of Gabon. Several natural nuclear fission reactorswere discovered in the uranium mines in the region in 1972.Africa and analysed in a French laboratory. Rock samples of naturally occurring uranium usually contain two types of uranium atoms, isotopes U238 and U235. Most of the atoms are U238 but about 0.7% are U235. In fact, to be accurate, the figure is .720%, but the sample that arrived in France had 'only' .717%, meaning that .003% of the expected U235 atoms were missing.

The only place such differences in proportion were known to occur was in the very artificial surroundings of a nuclear reactor, where U235 was bombarded with neutrons in a chain reaction that transformed the atoms and led to the change in the naturally occurring proportions. But the uranium ore had come from mines in the African state of Gabon and at the time there was no nuclear reactor on the whole continent of Africa, so that couldn't be the explanation. Or could it?

Unlike Olber's Paradox, where science had to wait nearly a hundred years for an explanation of an interesting observation, in the case of Oklo the explanation had already been published. Nearly twenty years before, a scientific paper by three scientists had suggested that somewhere on the Earth the conditions might have existed in the past for a uranium deposit to act like a natural nuclear fission reactor. They suggested three necessary conditions: 1. The size of the deposit should be greater than the average length that fission-inducing neutrons travel, which is about 70 centimeters; 2. Uranium235 atoms must be present in a greater abundance than they exist in natural rocks today, as much as 3% instead of .720%; 3. There must be what is called in a nuclear reactor today a moderator, a substance that 'blankets' the emitted neutrons and slows them down so that they are more apt to induce other uranium atoms to break apart.

These three conditions were exactly those that had applied to the Oklo deposits two billion years ago. The Oklo deposits were much larger than the minimum predicted size. Then, uranium235 has a half life of 704 million years and decays about six times faster that the U238 atoms, so several half lives ago, round about 2 billion years, there would have been much more U235 in natural deposits, just the sort of amount that would lead to a sustainable chain reaction. and so, extrapolating backwards, the relative proportions of the two isotopes would have been approximately 97 to 3 rather than 99.3 to .7 as it is today. And finally, the layers of rock had originally been in contact with natural water suggesting that what had happened was the following:

A chain reaction would start in rocks surrounded by water, and the atoms would split and generate heat. The heat would turn the water to steam and destroy its ability to moderate the reactions and the neutrons would escape, stopping the chain reactions. The steam would condense and turn back into water, beginning to blanket the neutrons that were still being emitted by the uranium, more neutrons would be retained, splitting the uranium atoms and restarting the chain reaction.

In explaining a tiny anomaly in the ratio of two types of atom in a piece of rock this size—I—the scientific method has led to a description of a series of events that happened in a specific location on earth billions of years ago. Over a period of 150 million years a natural nuclear reactor would produce heat for about half an hour and then shut down for two and a half hours before starting up again. It had done this over a period of 150 million years at an average power of 100 kilowatts, the kind of power produced in a typical car engine. Not only is this explanation deep, elegant and beautiful. It's also incontrovertible. It doesn't depend on someone's opinion or bias or desires, unlike many other 'explanations' of how the world works, and that's the power of the best science.

The Universal Algorithm For Human Decisions

The ultimate goal of science, as the French physicist Jean Perrin once stated, should be "to substitute visible complexity for an invisible simplicity". Can human psychology achieve this ambitious goal: the discovery of elegant rules behind the apparent variability of human thought? Many scientists still consider psychology as a "soft" science, whose methods and object of study are too fuzzy, too complex, and too suffused with layers of cultural complexity, to ever yield elegant mathematical generalizations.

And yet cognitive scientists know that this prejudice is simply wrong. Human behavior obeys rigorous laws of the utmost mathematical beauty and even necessity. I will nominate just one of them: the mathematical law by which we take our decisions.

All of our mental decisions appear to be captured by a simple rule that weaves together some of the most elegant mathematics of the past centuries: Brownian motion, Bayes' rule, and the Turing machine.

Let us start with the simplest of all decisions: how do we decide that 4 is smaller than 5? Psychological investigation reveals many surprises behind this simple feat. First, our performance is very slow: the decision takes us nearly half a second, from the moment the digit 4 appears on a screen to the point when we respond by clicking a button. Second, our response time is highly variable from trial to trial, anywhere from 300 milliseconds to 800 milliseconds, even though we are responding to the very same digital symbol "4". Third, we make errors—it sounds ridiculous, but even when comparing 4 with 5, we sometimes make the wrong decision. Fourth, our performance varies with the meaning of the objects: we are much faster, and make fewer errors, when the numbers are far from each other (such as 1 and 5) than when they are close (such as 4 and 5).

Well, all of the above facts, and many more, can be explained by a single law: our brain takes decisions by accumulating the available statistical evidence and committing to a decision whenever the total exceeds a threshold.

Let me unpack this statement. The problem that the brain faces when taking a decision is one of sifting the signal from the noise. The input to any of our decision is always noisy: photons hit our retina at random times, neurons transmit the information with partial reliability, and spontaneous neural discharges (spikes) are emitted throughout the brain, adding noise to any decision. Even when the input is a digit, neuronal recordings show that the corresponding quantity is coding by a noisy population of neurons that fires at semi-random times, with some neurons signaling "I think it's 4", others "it's close to 5", or "it's close to 3", etc. Because the brain's decision system only sees unlabelled spikes, not full-fledged symbols, it is a genuine problem for it to separate the wheat from the chaff.

In the presence of noise, how should one take a reliable decision? The mathematical solution to that the problem was first addressed by Alan Turing, when he was cracking the Enigma code at Bletchley Park. Turing found a small glitch in the Enigma machine, which meant that some of the German messages contained small amounts of information—but unfortunately, too little to be certain of the underlying code. Turing realized that Bayes' law could be exploited to combine all of the independent pieces of evidence. Skipping the math, Bayes' law provides a simple way to sum all of the successive hints, plus whatever prior knowledge we have, in order to obtain a combined statistic that tells us what the total evidence is.

With noisy inputs, this sum fluctuates up and down, as some incoming messages support the conclusion while others merely add noise. The outcome is what mathematicians call a "random walk" or "Brownian motion", a fluctuating march of numbers as a function of time. In our case, however, the numbers have a currency: they represent the likelihood that one hypothesis is true (e.g. the probability that the input digit is smaller than 5). Thus, the rational thing to do is to act as a statistician, and wait until the accumulated statistic exceeds a threshold probability value. Setting it to p=0.999 would mean that we have one chance in a thousand to be wrong.

Note that we can set this threshold to any arbitrary value. However, the higher we put it, the longer we have to wait for a decision. There is a speed-accuracy trade-off: we can wait a long time and take a very accurate but conservative decision, or we can hazard a response earlier, but at the cost of making more errors. Whatever our choice, we will always make a few errors.

Suffice it to say that the decision algorithm I sketched, and which simply describes what any rational creature should do in the face of noise, is now considered as a fully general mechanism for human decision making. It explains our response times, their variability, and the entire shape of their distribution. It describes why we make errors, how errors relate to response time, and how we set the speed-accuracy trade-off. It applies to all sorts of the decisions, from sensory choices (did I see movement or not?) to linguistics (did I hear "dog" or "bog"?) and to higher-level conundrums (should I do this task first or second?). And in more complex cases, such as performing a multi-digit calculation or a series of tasks, the model characterizes our behavior as a sequence of accumulate-and-threshold steps, which turns out to be an excellent description of our serial, effortful Turing-like computations.

Furthermore, this behavioral description of decision-making is now leading to major progress in neuroscience. In the monkey brain, neurons can be recorded whose firing rates index an accumulation of relevant sensory signals. The theoretical distinction between evidence, accumulation and threshold helps parse out the brain into specialized subsystems that "make sense" from a decision-theoretic viewpoint.

As with any elegant scientific law, many complexities are waiting to be discovered. There is probably not just one accumulator, but many, as the brain accumulates evidence at each of several successive levels of processing. Indeed, the human brain increasingly fits the bill for a superb Bayesian machine that makes massively parallel inferences and micro-decisions at every stage. Many of us think that our sense of confidence, stability and even conscious awareness may result from such higher-order cerebral "decisions" and will ultimately fall prey to the same mathematical model. Valuation is also a key ingredient that I skipped, although it demonstrably plays a crucial role in weighing our decisions. Finally, the system is ripe with a prioris, biases and time pressures and other top evaluations that draw it away from strict mathematical optimality.

Nevertheless, as a first approximation, this law stands as one of the most elegant and productive discoveries of twentieth-century psychology: humans act as near-optimal statisticians, and any of our decisions corresponds to an accumulation of the available evidence up to some threshold.

Why We Feel Pressed for Time

Recently, I found myself on the side of the road, picking gravel out of my knee and wondering how I’d ended up there. I had been biking from work to meet a friend at the gym, pedalling frantically to make up for being a few minutes behind schedule. I knew I was going too fast, and when I hit a patch of loose gravel while careening through a turn, my bike slid out from under me. How had I gotten myself in this position? Why was I in such a rush? 

I thought I knew the answer. The pace of life is increasing; people are working more and relaxing less than they did 50 years ago. At least that’s the impression I got from the popular media. But as a social psychologist, I wanted to see the data. As it turns out, there is very little evidence that people are now working more and relaxing less than they did in earlier decades. In fact, some of the best studies suggest just the opposite. So, why do people report feeling so pressed for time?

A beautiful explanation for this puzzling phenomenon was recently offered by Sanford DeVoe, at the University of Toronto and Jeffrey Pfeffer, at Stanford. They argue that as time becomes worth more money, time is seen as scarcer. Scarcity and value are perceived as conjoined twins; when a resource—from diamonds to drinking water—is scarce, it is more valuable, and vice versa. So, when our time becomes more valuable, we feel like we have less of it. Indeed, surveys from around the world have shown that people with higher incomes report feeling more pressed for time. But there are lots of plausible reasons for this, including the fact that more affluent people often work longer hours, leaving them with objectively less free time.

DeVoe and Pfeffer proposed, however, that simply perceiving oneself as affluent might be sufficient to generate feelings of time pressure. Going beyond past correlational analyses, they used controlled experiments to put this causal explanation to the test. In one experiment, DeVoe and Pfeffer asked 128 undergraduates to report the total amount of money they had in the bank. All the students answered the question using an 11-point scale, but for half the students, the scale was divided into $50 increments, ranging from $0-$50 (1) to over $500 (11), whereas for the others, the scale was divided into much larger increments, ranging from $0-$500 (1) to over $400,000 (11). When the scale was divided into $50 increments, most undergraduates circled a number near the top of the scale, leaving them with the sense that they were relatively well-off. And this seemingly trivial manipulation led participants to feel that they were rushed, pressed for time, and stressed out. In other words, just feeling affluent led students to experience the same sense of time pressure reported by genuinely affluent individuals. Other studies confirmed that increasing the perceived economic value of time increases its perceived scarcity.

If feelings of time scarcity stem in part from the sense that time is incredibly valuable, then ironically, one of the best things we can do to reduce this sense of pressure may be to give our time away. Indeed, new research suggests that giving time away to help others can actually alleviate feelings of time pressure. Companies like Home Depot provide their employees with opportunities to volunteer their time to help others, potentially reducing feelings of time stress and burnout. And Google encourages employees to use 20% of their time on their own pet project, which may or may not payoff. Although some of these projects have resulted in economically valuable products like Gmail, the greatest value of this program might lie in reducing employees’ sense that their time is scarce.

As well as pointing to innovative solutions to feelings of time pressure, DeVoe and Pfeffer’s work can help to account for important cultural trends. Over the past 50 years, feelings of time pressure have risen dramatically in North America, despite the fact that weekly hours of work have stayed fairly level and weekly hours of leisure have climbed. This apparent paradox may be explained, in no small part, by the fact that incomes have increased substantially during the same period. This causal effect may also help to explain why people walk faster in wealthy cities like Tokyo and Toronto than in cities like Nairobi and Jakarta. And at the level of the individual, this explanation suggests that as incomes grow over the life course, time seems increasingly scarce. Which means that, as my career develops, I might have to force myself to take those turns a little slower.

Darwin's Explanation of the Origin of Coral Reefs

It's Darwin's explanation of the origin of coral reefs (and it was Nick Humphrey who told me this story in the early 1980's—in Tahiti!). What I love is that the question is so easy to grasp but so difficult to answer, and that Darwin's solution is so simple and beautiful—he worked it out by sheer power of imaginative reasoning long before anybody had heard of tectonic plates and more than a hundred years before the theory would be proved (by deep borings on Bikini Atoll).

The mystery, much discussed in the 1830's, was that coral polyps can grow and reproduce only in shallow water, and yet the walls of coral reefs and atolls plunge thousands of feet into the deep ocean. The coral couldn't have grown from the bottom upwards, so how then did the reef and atolls get there? 

By the 1830's, the geologist Charles Lyell had decided that atolls must be coral reefs growing on the crater rims of sunken extinct volcanoes. Darwin didn't agree, and it's wonderful to know that Lyell was thrilled when Darwin came back from the Beagle voyage and told him the real answer: the coral organisms thrive in shallow water but the ocean floor is slowly sinking; the polyps die but new ones are growing on top of them, and over an immense amount of time countless billions of tiny calcareous skeletons accumulate to make up a vast structure reaching from the darkness of the ocean bed to the sunlit surface so far above. 

Deep Time

There is one simple and powerful idea that strikes me as both deep and beautiful in its own right and as the mother of a suite of further elegant theories and explanations. The idea is that of "deep time": that the Earth is extremely old and the life of our species on it has been very short. When that idea first emerged it stood against everything that was then believed and it was to eventually change people's view of themselves as much as the earlier discovery that the Earth revolved around the Sun.

We know when the idea of deep time was borne, or at least first vindicated, for a University of Edinburgh professor named John Playfair recorded his reaction in 1788. "The mind seemed to grow giddy", he wrote, "by looking so far into the abyss of time." He had travelled to the Scottish coast with his geologist friend James Hutton, who later put his ideas together in a book called the Theory of the Earth. Hutton was showing him a set of distinct patterns in the rocks that could be most simply explained by assuming that the present land has been laid down in the sea, then lifted, distorted, eroded and once again covered by new sediments at the bottom of a sea. The Earth was not six thousand years old as then accepted calculations from the Bible decreed; nor had the strata of land precipitated out a vast flood as prevailing scientific views, informed by the best chemistry of the time, said. 

It was an enormous shift to see the world as Hutton did. Appreciating the vastness of space is easy. When we look up at the stars the immensity of the universe is both obvious and awe inspiring. The immensity of time does not lie within human experience. Nature, observed on a human scale, passes only through the repeated cycle of the seasons, interrupted by occasional catastrophic earthquakes, volcanic eruptions and floods. It is for that reason that creationist and catastrophic theories of the Earth's origins appeared more plausible than those that were slow and gradual. But Hutton had faith in what he saw in the rocks, exhorting others to "open the book of Nature and read in her records".

His thinking about time created fertile ground for other grand theories. With huge spans of time available, then imperceptibly slow processes could shape the natural world. After Hutton came modern geology, then the theory of evolution to explain how new species slowly arose, and eventually a theory of the gradual movement of the continents themselves. All are grounded in deep time.

Hutton's views were a huge challenge to religious orthodoxy too, for when he wrote at the close of his book, "we find no vestige of a beginning--no prospect of an end", he challenged both the idea of a creation and of a judgement day.

The beauty of his idea remains. If we look into the abyss of time, we may not grow giddy, but we can simultaneously feel our own insignificance in the Earth's 4.6 billion year history and the significance of the precise moment in this vast span of time in which we live.

The Importance Of Context

In a thriller novel, the explanation comes at the end. In a newspaper article, it usually comes at the beginning. In an executive summary meant to be read by the top management, the explanation, comes at the beginning of the memo. And for a scientific paper, a summary, with findings and hypothesis is presented at the beginning. There is not a single aesthetics of explanations. True: their beauty, deepness, elegance, always rely on the beauty, deepness and elegance of the question to which they answer: but the way the answer is introduced depends on conventional wisdom in different disciplines. 

What changes the structure of the questioning-answering conventions?

The major difference is probably in the importance of context. 

In entertainment, in a novel or in a movie, the context is the world of meanings that is created by storytellers. Questions appear as surprising twists in the context description. And, mastering the whole thing, the storyteller lets the reader enjoy an entertaining experience by explaining everything at the end. In science, in the news, in a company, the context is in a world of meanings that is already present to the mind of the reader, the storyteller doesn't master the whole thing, everybody feels to be part of the story, and the correct approach is to explain everything as soon as possible, and then to share all the specific findings to help everybody evaluate the quality of the explanation.

But what happens when a really great scientific or economic breakthrough needs to be proposed and shared? What happens when an important new notion that will change the paradigm of its discipline is to be explained? And what happens when something even changes the world of meanings in which the discipline is accustomed to develop?

When Nicolaus Copernicus wrote his masterpiece, De revolutionibus orbium coelestium, he had to make a choice. After having dedicated his work to Pope Paul III, he started the first book introducing a vision of the universe, based on his heliocentric idea. He continued writing three books about mathematics, descriptions of stars, movements of the Sun and the Moon. Only at the end did he explained his new system and how to calculate the movements of all astronomical objects in a heliocentric model.

That was a deep, elegant and beautiful explanation of an historic change. It was an explanation that had to create a new vision of everything, of a new paradigm.  

Denumerable Infinities Are The Same Size; No Mind Emerges Through Sorting

My favorites: Cantor's explanation of why all denumerable infinities are the same size—why, eg, the set of all integers is the same size as the set of all positive integers, or all even integers—and why some infinities are bigger than others. (The set of all rational numbers is the same size as the set of all integers, but the set of all real numbers—terminating plus non-terminating decimals—is larger.) The set of all positive integers is the same size as the set of all even, positive integers—to see that, just line them up, one by one. 1 is paired with 2 (the first even positive integer), 2 is paired with 4, 3 with 6, 4 with 8 and so on.

You would think there would be more positive integers than even ones; but this pairing-off shows that no positive integer will ever be left without a partner. (And so they all dance happily off & there are no wallflowers.) The other proofs are similar in their stunning simplicity, but much easier to demo on a blackboard than to describe in words.

Equally favorite: Searle's proof that no digital computer can have mental states (a mental state is, eg, your state of mind when I say "picture a red rose," and you do); that minds can't be built out of software. A digital computer can only do trivial arithmetic and logical instructions. You can do them too; you can execute any instruction that a computer can execute. You can also imagine yourself executing lots & lots of trivial instruction, & then ask yourself: can I picture a new mind emerging on the basis of my doing lots & lots & lots of trivial instructions? (No.) Or: imagine yourself sorting a deck of cards.

Sorting is the sort of thing digital computers do. Now imagine sorting a bigger & bigger & bigger deck; can you see consciousness emerging at some point, when you sort a large enough batch? Nope. (And the inevitable answer to the inevitable first objection: but neurons only do simple signal transmission; can you imagine consciousness emerging out of that? An irrelevant question. The fact that lots of neurons make a mind has no bearing on the question of whether lots of anything else make a mind. I can't imagine being a neuron, but I can imagine executing machine instructions. No mind emerges no matter how many of those instructions I carry out.)

The Principle of Inertia

My favorite explanation in science is the principle of inertia. It explains why the earth moves in spite of the fact that we don't feel any motion, which was perhaps the most counterintuitive revolutionary step taken in all of science. It was first proposed by Galileo and Descartes and has been the core of all the successful explanations in physics in the centuries since.

The principle of inertia is the answer to a very simple question: how would an object that is free, in the sense that no eternal influences or forces affect its motion, move?

This is a seemingly simple question, but notice that to answer it we have to have in mind a definition of motion. What does it mean for something to move?

The modern conception is that motion has to be described relative to an observer.

Consider an object that is sitting at rest relative to you, say a cat sleeping on your lap, and imagine how it appears to move as seen by other observers. Depending on how the observer is moving the cat can appear to have any motion at all. If the observer spins relative to you, the cat will appear to them to spin.

So to make sense of the question of how free objects move we have to refer to a special class of observers. The answer to the question is the following:

There is a special class of observers, relative to whom all free objects appear to either be at rest or to move in straight lines with constant speeds.

I have just stated the principle of inertia.

The power of this principle is that it is completely general. Once a special observer sees one free object move in a straight line with constant speed, she will observe all other free objects to so move.

Furthermore suppose you are a special observer. Any observer who moves in a straight line at a constant speed with respect to you will also see the free objects move at a constant speed in a straight line, with respect to them.

So these special observers form a big class, all of which are moving with respect to each other. These special observers are called inertial observers.

An immediate and momentous consequence is that there is no absolute meaning in not moving. An object may be at rest with respect to one inertial observer, but other inertial observers will see it moving-always in a straight line at constant speed. This can be formulated as a principle:

There is no way, by observing objects in motion, to distinguish observers at rest from other inertial observers.

Thus, any inertial observer has equal rights to say they are at rest and it is the others that are moving.

This is called Galileo's principle of relativity. It explains why the Earth may be moving without us observing gross effects.

To appreciate how revolutionary this was notice that physicists of the 16th Century could disprove Copernicus's claim that the Earth moves by a simple observation. Just drop a ball from the top of a tower. Were the Earth rotating around its axis and revolving around the Sun at the speeds Copernicus required, the ball would land far from the base of the tower. QED. The Earth is at rest.

But this proof assumes that motion is absolute, defined with respect to a special observer at rest, with respect to whom objects with no forces on them come to rest. By altering the definition of motion, Galileo could argue that the very same experiment that previously proved that the Earth is at rest now demonstrates that the Earth could be moving.

The principle of inertia was not just the core of the scientific revolutions of the 17th Century. It contained the seeds of revolutions to come. To see why, notice the qualifier in the statement of the principle of relativity: "by observing objects in motion." For many years it was thought that there would be other kinds of observations that could be used to tell which inertial observers are really moving and which are really at rest. Einstein constructed his theory of special relativity simply by removing this qualifier. Einstein's principle of relativity states:

There is no way to distinguish observers at rest from other inertial observers.

And there was more. A decade after special relativity, the principle of inertia was the seed also for the next revolution—the discovery of general relativity. The principle was generalized by replacing "moving in a straight line with constant speed" to "moving along a geodesic in spacetime." A geodesic is the generalization of a straight line in a curved geometry—it is the shortest distance between two points. So now the principle of inertia reads:

There is a special class of observers, relative to whom all free objects appear to either be at rest or to move along geodesics in spacetime. These are observers who are in free fall in a gravitational field.

And there is consequent generalization of the principle of relativity.

There is no way to distinguish observers in free fall from each other.

This becomes Einstein's equivalence principle that is the core of his general theory of relativity.

But is the principle of inertia really true? So far it has been tested in circumstances where the energy of motion of a particle is as much as eleven orders of magnitude greater than its mass. This is pretty impressive, but there is still a lot of room for the principle of inertia and its twin, the principle of relativity, to fail. Only experiment can tell us if these principles or their failures will be the core of revolutions in science to come.

But whatever happens, no other explanation in science besides the principle of inertia has survived unscathed for so long, nor proved valid over such a range of scales, nor has any other been the seed of several scientific revolutions separated by centuries. 

How To Have a Good Idea

You don't have to be human to have a good idea. You can even be a fish.

There is a large fish in shallow Micronesian waters that feeds on little fish. The little fish dwell in holes in the mud, but swarm out to feed. The big fish starts to gobble up the little fish, one by one, but they immediately retreat back into their holes, when his meal has barely begun. What to do?

I have put this problem to my classes over the years, and I remember only one student who came up with the big fish's Good Idea. Of course he did it after a little thought, not after millions of years of evolution, but who's counting?

Here is the elegant trick. When the school of little fishes appears, instead of gobbling, he swims low so that his belly rubs over the mud and blocks the escape holes. Then he can dine at leisure.

What do we learn? To have a good idea, stop having a bad one. The trick was to inhibit the easy, obvious but ineffective attempts, permitting a better solution to come to mind. That worked for the big fish, by some mechanism of mutation and natural selection in fish antiquity. Instead of tinkering with the obvious, obsessing about eating faster, taking bigger bites, etc. junk plan A, and plan B comes swimming up. For humans, supposing that the second solution still does not work, block that too, and wait. A third floats into awareness, and so on, until the insoluble is solved, even if the most intuitively obvious premises have to be overridden in the process.

To the novice the Good Idea seems magical, a leap of intellectual lightning. More likely, however, it resulted from an iterative process as outlined above, with enough experience in back to help reject seductive but misleading premises. Thus the extraordinary actually arises step by step out of the ordinary.

Having a good idea is far from rare in the evolution of non-human species. Indeed, many if not most species need to have an idea or trick that works well enough for them to continue to exist. Admittedly, they may not be able to extrapolate its principle from the context in which it emerged, and generalize it as (some) people can, courtesy of their prefrontal cortex.

When the finest minds fail to resolve a classical problem, during decades, or centuries of trying, they were probably trapped by a premise that was so culturally "given", that it did not even occur to them to challenge it, or they did not even notice it at all. But cultural context changes and what seemed totally obvious yesterday becomes dubious at best today or tomorrow. Sooner or later someone who may be no more gifted than his/her predecessors, but is unshackled from some very basic and very incorrect assumption, may hit upon the solution with relative ease.

Alternatively, one can be a fish, wait a million years or two, and see what comes up.

Occam's Razor

Ptolemy's Universe

Claudius Ptolemy explained the sky. He was an Egyptian who wrote in Greek in the Roman empire, in the time of emperors like Trajan and Hadrian. His most famous book was called by its Arabic translators the Almagest. He inherited a long ancient tradition of astronomical science going back to Mesopotamia, but he put his name and imprint on the most successful and so far longest-lived mathematical description of the working of the skies.

Ptolemy's geocentric universe is now known mainly as the thing that was rightly abandoned by Copernicus, Kepler, Newton, and Einstein, in progressive waves of the advancement of modern science, but he deserves our deep admiration. Ptolemy's universe actually made sense. He knows the difference between planets and stars and he knows that the planets take some explaining. (The Greek word 'planet' means wanderer, to reflect ancient puzzlement that those bright lights moved according to no pattern that a shepherd or seaman could intuitively predict, unlikely the reassuringly confident annual march of Orion or the rotation of the great bears overhead.) So Ptolemy represents the heavenly machine in a complex mathematical system most notorious for its "epicycles"—the orbits within orbits, so to speak, by which the planets, while orbiting the earth, spun off their orbits in smaller circles that explained their seeming forward and backward motion in the night sky.

We should admire Ptolemy for many reasons, but chief among them is this: he did his job seriously and responsibly with the tools he had. Given what he knew, his system was brilliantly conceived, mathematically sound, and a huge advance over what had gone before. His observations were patient and careful and as complete as could be, his mathematical calculations correct. More, his mathematical system was a complicated as it needed to be and at the same time as simple as it could be, given what he had to work with. He was, in short, a real scientist. He set the standard.

It took a long time and there were some long arguments before astronomy could advance over what he offered—and that's a sign of his achievement. But when advance was possible, Ptolemy had made it impossible for advance to come through wishful thinking, witch doctors, or fantasy. His successors in the great age of modern astronomy had to play by his rules. They needed to observe more carefully, do their math with exacting care, and propose systems at the poise point of complexity and simplicity themselves. Ptolemy challenged the moderns to outdo him—and so they could and did. We owe him a lot.

True or False: Beauty Is Truth

"Beauty is truth, truth beauty," said John Keats. But what did he know? Keats was a poet, not a scientist.

In the world that scientists inhabit, truth is not always beautiful or elegant, though it may be deep. In fact, it's my impression that the deeper an explanation goes, the less likely it is to be beautiful or elegant.

Some years ago, the psychologist B. F. Skinner proposed an elegant explanation of "the behavior of organisms," based on the idea that rewarding a response—he called it reinforcement—increases the probability that the same response will occur again in the future. The theory failed, not because it was false (reinforcement generally does increase the probability of a response) but because it was too simple. It ignored innate components of behavior. It couldn't even handle all learned behavior. Much behavior is acquired or shaped through experience, but not necessarily by means of reinforcement. Organisms learn different things in different ways.

The theory of the modular mind is another way of explaining behavior—in particular, human behavior. The idea is that the human mind is made up of a number of specialized components, often called modules, working more or less independently. These modules collect different kinds of information from the environment and process it in different ways. They issue different commands—occasionally, conflicting commands. It's not an elegant theory; on the contrary, it's the sort of thing that would make Occam whip out his razor. But we shouldn’t judge theories by asking them to compete in a beauty pageant. We should ask whether they can explain more, or explain better, than previous theories were able to do.

The modular theory can explain, for example, the curious effects of brain injuries. Some abilities may be lost while others are spared, with the pattern differing from one patient to another.

More to the point, the modular theory can explain some of the puzzles of everyday life. Consider intergroup conflict. The Montagues and the Capulets hated each other; yet Romeo (a Montague) fell in love with Juliet (a Capulet). How can you love a member of a group, yet go on hating that group? The answer is that two separate mental modules are involved. One deals with groupness (identification with one's group and hostility toward other groups), the other specializes in personal relationships. Both modules collect information about people, but they do different things with the data. The groupness module draws category lines and computes averages within categories; the result is called a stereotype. The relationship module collects and stores detailed information about specific individuals. It takes pleasure in collecting this information, which is why we love to gossip, read novels and biographies, and watch political candidates unravel on our TV screens. No one has to give us food or money to get us to do these things, or even administer a pat on the back, because collecting the data is its own reward.

The theory of the modular mind is not beautiful or elegant. But not being a poet, I prize truth above beauty.

Imposing Randomness

Paul Meier—who passed away in 2011—was primarily known for his introduction of the Kaplan-Meier estimator. But Meier was also a seminal figure in the widespread adoption of an invaluable explanatory tool: the randomized experiment. The decided unsexiness of the term masks a truly elegant form—that in the hands of its best practitioners approaches art. Simply put, experiments offer a unique and powerful means for devising answers to the question that scientists across discipline seek to answer: How do we know if something "works"?

Take a question that appears anew in the media each year: Is red wine good or bad for us? We learn a great deal about how red wine "works" by asking people about their consumption and health and looking for correlations between the two. To estimate the specific impact of red wine on health, though, we need to ask people a lot of questions—about everything they consume (food, prescription medication, more unsavory forms of medication), their habits (exercise, sleep, sexual activity), their past (their health history, their parents' and grandparents' health histories), and on and on – and then try to control for these factors to isolate the impact of wine on health. Think of the length of the survey…

Randomized experiments completely reengineer how we go about understanding how red wine "works." We take it as a given that people vary in the manifold ways described above (and others), but cope with this variance by randomly assigning people to either drink red wine or not; if people who eat donuts and never exercise are equally likely to be in the "wine treatment" or the "control treatment" then we can do a decent job of assessing the average impact of red wine over and above the likely impact of other factors. It sounds simple because, well, it is —but anytime a simple technique yields so much, elegant is a more apt description.

The rise of experiments in the social sciences that began in the 1950s—including Meier's contributions—has exploded in recent years, with the adoption of randomized experiments in fields ranging from medicine (testing interventions like cognitive behavioral therapy) to political science (running voter turnout experiments) to education (assigning kids to be paid for grades) to economics (encouraging savings behavior). The experimental method has also begun to filter into and impact public policy: President Obama appointed behavioral economist Cass Sunstein to head the Office of Information and Regulatory Affairs, and Prime Minister David Cameron instituted a "Behavioural Insights Team."

Experiments are by no means a perfect tool for explanation. Some important questions simply do not lend themselves to experiments, and the experimental method in the wrong hands can cause harm as in the infamous Tuskegee syphilis experiment. But the increasingly widespread application of experiments speaks to their flexibility in informing human understanding of how things "work"—and why they work that way.

Natural Selection Is Simple, But The Systems It Shapes Are Unimaginably Complex

The principle of natural selection is exceedingly simple. If some individuals in a population have a heritable trait associated with having more offspring, that trait will (with a few caveats) become more common in the population over the generations.

The products of natural selection are vastly complex. They are not merely complicated in the way that machines are complicated, they are organically complex in ways that are fundamentally different from any product of design. This makes them difficult for human minds to fully describe or comprehend. So, we use that grand human gambit for understanding, a metaphor, in this case, the body as machine.

This metaphor makes it easy to portray the systems that mediate cell division, immune responses, glucose regulation, and all the rest, using boxes for the parts, and arrows to indicate causes what. Such diagrams summarize important information in ways we can grasp. Teachers teach them. Students dutifully memorize them. But, they fundamentally misrepresent the nature of organic complexity. As Haldane noted in a prescient 1917 book, "a living organism has, in truth, but little resemblance to an ordinary machine." Machines are designed. They have discrete parts with specific functions, and most remain intact when turned off. Individual machines are manufactured following identical copies of a single blueprint. In contrast, organisms are evolved. They have components with indistinct boundaries and multiple functions that interact with myriad other parts and the environment to create self-sustaining reproducing systems that whose survival requires the constant activity and cooperation of thousands of interdependent subsystems. Individual organisms develop from unique combinations of genes interacting with each other and environments to create phenotypes, no two of which are identical.

Thinking about the body as a machine was a grand advance in the 16^th century, when it offered an alternative to vitalism and vague notions of the life force. Now it is outmoded. It distorts our view of biological systems by fostering thinking about them as simpler and more sensibly "designed" than they are. Experts know better. They recognize that the mechanisms that regulate blood clotting are represented only crudely by the neat diagrams medical students memorize; most molecules in the clotting system interact with many others. Experts on the amygdala know that it does not have one or two functions, it has many, and they are mediated by scores of pathways to other brain loci. Serotonin exists not mainly to regulate mood and anxiety, it is essential to vascular tone, intestinal motility, and bone deposition. Leptin is not mainly a fat hormone, it has many functions, serving different ones at different time, even in the same cell. The reality of organic systems is vastly untidy. If only their parts were all distinct, with specific functions for each! Alas, they are not like machines. Our human minds have as little intuitive feeling for organic complexity as they do for quantum physics.

Recent progress in genetics confronts the problem. Naming genes according to postulated functions is as natural as defining chairs and boats by their functions. If each gene were a box on a blueprint labeled with its specific function, biology would be so much more tractable! However, it is increasingly clear that most traits are influenced by many genes, and most genes influence many traits. For instance, about 80% of the variation in human height is accounted for by genetic variation. It would seem straightforward to find the responsible genes. But looking for them has revealed that the 180 loci with the largest effects together account for only about 10% of the phenotypic variation. Recent findings in medical genetics are more discouraging. Just a decade ago, hope was high that we would soon find the variations that account for highly heritable diseases, such as schizophrenia and autism. But scanning the entire genome has revealed that there are no common alleles with large effects on these diseases. Some say we should have known. Natural selection would, after all, tend to eliminate alleles that cause disease. But, thinking about the body as a machine aroused unrealistic hopes.

The grand vision for some neuroscientists is to trace every molecule and pathway to characterize all circuits in order to understand how the brain works. Molecules, loci, and pathways do serve differentiated functions, this is real knowledge with great importance for human health. But, understanding how the brain works by drawing a diagram that describes all the components and their connections and functions is a dream that may be unfulfillable. The problem is not merely fitting a million items on a page, the problem is that no such diagram can adequately describe the structure of organic systems. They are products of miniscule changes, from diverse mutations, migration, drift, and selection, which develop into systems with incompletely differentiated parts and incomprehensible interconnections, that, nonetheless, work very well indeed. Trying to reverse engineer brain systems focuses important attention on functional significance, but it inherently limited, because brain systems were never engineered in the first place.

Natural selection shapes systems whose complexity is indescribable in terms satisfying to human minds.  Some may feel this is nihilistic. It does discourage hopes for finding simple specific descriptions for all biological systems. However, recognizing a quest as hopeless is often the key to progress. As Haldane put it, "We are thus brought face-to-face with the conclusion which to the biologist is just as significant and fundamental, just as true to the facts observed, as the conclusion of mass persists is to the physicists… the structure of a living organism has no real resemblance in its behavior to that of a machine… In the living organisms…the "structure" is only the appearance given by what seems at first to be a constant flow of specific material, beginning and ending in the environment."

If bodies are not like machines, what are they like? They are more like Darwin's "tangled bank" with its "elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner." Lovely. But, can an ecological metaphor replace the metaphor of body as machine? Not likely. Perhaps someday understanding how natural selection shapes organic complexity will be so widely and deeply understood that scientists will be able to say "A body is like…a living body," and everyone will know exactly what that means. 

Cagepatterns

In art, the title of a work can often be its first explanation. And in this context I am thinking especially of the titles of Gerhard Richter. In 2006, when I visited Richter in his studio in Cologne, he had just finished a group of six corresponding abstract paintings which he gave the title "Cage".

There are many relations between Richter's painting and the compositions of John Cage. In a book about the "Cage" series, Robert Storr has traced them from Richter‘s attendance of a Cage performance at the "Festum Fluxorum Fluxus" in Düsseldorf 1963 to analogies in their artistic processes. Cage has often applied chance procedures in his compositions, notably with the use of the "I Ching". Richter in his abstract paintings also intentionally allows effects of chance. In these paintings, he applies the oil paint on the canvas by means of a large squeegee. He selects the colors on the squeegee, but the factual trace that the paint leaves on the canvas is to a large extend the outcome of chance. The result then forms the basis for Richter's decisions how to continue with the next layer. In such an inclusion of ‘controlled chance' an artistic similarity between Cage and Richter can be found. Additionally to the reference to John Cage, Richter's title "Cage" can also be a visual association, as the six paintings have a very hermetic almost impermeable appearance. The title points to different layers of meaning.

Beyond his Richter's abstract paintings, analogies to Cage can be found also in other of his works. His artist book "Patterns" is my favorite book of the year 2011. It shows Richter's experiment of taking an image of his "Abstract Painting [CR: 724-4]" and dividing it vertically into strips: first 2, then 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, up to 4096 strips. This methodology leads to 8190 strips. Throughout the process the strips become thinner and thinner. The experiment then leads to the strips being mirrored and repeated, which leads to a diversity of patterns. The outcomes are 221 patterns that are published on 246 double page images. In "Patterns" Richter set the precise rules, but he didn't manipulate the outcome, so that the pictures are againan interaction of a defined system and chance.

"Patterns" is one of many outstanding artist books Richter has done over the last couple of years, such as "Wald" (2008), or his book "Ice" (1981) which includes a special layout of the artist with his stunning photos of a trip to the Antarctic. The layout of those books is composed of intervals with different arrangements of the photos but also blank spaces–like pauses. Richter told me that his layout has to do with music, Cage and silence.

In 2007 Richter designed a twenty-meter-high arched stained-glass window to fill the south transept of Cologne Cathedral. The "Cologne Cathedral Window" comprises 11,000 hand-blown squares of glass in seventy-two colors derived from the palette of the original Medieval glazing that was destroyed during the Second World War. Half of the squares were allotted by a random generator, the other half then were like a mirror image to them. Control is once more ceded here to some extent, suggesting his interest in Cage's ideas to do with chance and the submission of the individual will to forces beyond one's control. "Coincidences are only useful", Richter has told me, "because they've been worked out—that means either eliminated or allowed or emphasized."

In Halberstadt, Germany, a performance of Cage's piece "ORGAN²/ASLSP" (1987) is taking place at the moment. "ASLSP" stands for "as slow as possible". Cage has not further specified this instruction, so that each performance of the score will be different. The actual performance will take 639 years to be completed. The slowness in Cage's piece is an essential aspect for our time. With globalization and the Internet all processes are accelerated to a speed in which no time for critical reflection remains. The present "Slow movement" thus argues to take time for well-chosen decisions together with a more locally oriented approach. The idea of slowness is one of the many aspects that continue to make Cage mostly relevant for the 21^st Century.

Richter‘s concise title "Cage" can be unfolded into an extensive interpretation of these abstract paintings (and of other works)—but, one can say, the short form already contains everything. The title, like an explanation of a phenomenon, unlocks the works, describing their relation to one of the most important cultural figures of the twentieth century, John Cage, who shares with Richter the great themes of chance and uncertainty.

Sex At Your Fingertips

We all know males and females are different below the neck. There is growing evidence that there are differences above the neck too. Looking into the mind reveals that on average females develop empathy faster and that on average males develop stronger interests in systems, or how things work. These are not necessarily differences in ability, but more differences in cognitive style and patterns of interest. These differences shouldn't stand in the way of achieving equal opportunities in society, or equal representation in all disciplines and fields, but such political aspirations are a separate issue to the scientific observation of cognitive differences.

Looking into the brain also reveals differences: for example, whilst on average males have larger brain volume even correcting for height and weight, on average females reach their peak volume of grey and white matter at least a year earlier than males. There's also a difference in the number of neurons in the neocortex: on average, males have 23 million and females have 19 million, a 16% difference. Looking at regions within the brain also shows sex differences: for example, males on average have a larger amygdala (an emotion area) and females on average have a larger planum temporale (a language area). But all this talk about sex differences. Ultimately what we want to know is what gives rise to these differences, and here is where I at least enjoy some deep, elegant, and beautiful explanations.

My favourite is foetal testosterone, since a few more drops of this special molecule seems to have 'masculinizing' effects on the development of the brain and the mind. The credit for this simple idea must go to Charles Phoenix and colleagues in 1959 (University of Kansas), an idea picked up again by Norman Geschwind in 1985 (Harvard). This is not the only masculinizing mechanism (another is the X chromosome) but it is one that has been elegantly dissected.

How scientists get to see the causal properties of foetal testosterone can however be through unethical animal experiments. Take for example a part of the amygdala called the medial posterodorsal (MePD) nucleus that is larger in male rats than in females. If you castrate the poor male rat (thereby depriving him of the main source of his testosterone) the MePD shrinks to the female volume in just 4 weeks. Or you can do the reverse experiment, giving extra testosterone to a female rat, which makes her MePD grow to the same size as a typical male rat, again in just 4 weeks.

In humans we look for more ethical ways of studying how foetal testosterone does its work! You can measure this special hormone in the amniotic fluid that bathes the foetus in the womb. It gets into the amniotic fluid by being excreted by the foetus, and so is thought to reflect the levels of this hormone in the baby's body and brain. We measured the baby's testosterone in this way and then simply waited for the baby to be born, and then invited them into an MRI brain scanner 10 years later. This allows a test of how individual differences in testosterone levels before birth shape the development of the human brain. In a new paper in the Journal of Neuroscience our group shows for example how the more testosterone there is in the amniotic fluid, the less grey matter in the planum temporale (that language area of the brain).

This fits with a finding we published some 10 years ago: that the more testosterone in the amniotic fluid, the smaller the child's vocabulary size, at the age of 2 years old. This helps make sense of a longstanding puzzle about why girls talk earlier than boys, and why boys are disproportionately represented in clinics for language delays and disorders, since boys in the womb produce at least twice as much testosterone as girls.

It also helps make sense of the puzzle of individual differences in rate of language development in typical children irrespective of their sex: why at 2 years old some children have huge vocabularies (600 words) and other children haven't even started talking. Foetal testosterone is not the only factor involved in language development (so are social influences, since first born children develop language faster than later born children) but it seems to be a key part of the explanation. And foetal testosterone has been shown to be associated with a host of other sex-linked features, from eye contact to empathy, and from detailed attention to autistic traits.

Foetal testosterone is tricky to get your hands on, since the last thing a scientist wants to do is interfere with the delicate homeostasis of the uterine environment. In recent years a proxy for foetal testosterone has been proposed: the ratio between the second and fourth finger digit lengths (or 2D:4D ratio). Males have a lower ratio than females in the population, and this is held to be set during foetal life and remains stable throughout one's life. So scientists no longer have to think of imaginative ways to measure the testosterone levels directly in the womb. They can simply take a xerox of someone's hand, palm down, at any time in their life, to measure a proxy for levels of testosterone in the womb.

[Image credit: Linda Wooldridge and Mathew Clement, in "Resolving the role of prenatal sex steroids in the development of digit ratio", by John T. Manning, PNAS.]

Sleep Is the Interest We Have to Pay on the Capital Which is Called In at Death

Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate
of interest and the more regularly it is paid, the further the date of redemption is postponed.

So wrote Arthur Schopenhauer, comparing life to finance in a universe that must keep its books balanced. At birth you receive a loan, consciousness and light borrowed from the void, leaving a hole in the emptiness. The hole will grow bigger each day. Nightly, by yielding temporarily to the darkness of sleep, you restore some of the emptiness and keep the hole from growing limitlessly. In the end you must pay back the principal, complete the void, and return the life originally lent you.

By focusing on the common periodic nature of sleep and interest payments, Schopenhauer extends the metaphor of borrowing to life itself. Life and consciousness are the principal, death is the final repayment, and sleep is la petite mort, the periodic little death that renews. 

Elegant = Complex

Many would say the opposite, elegance = simplicity. They have (classical) physics envy—for smooth, linear physics, and describably delicious four-letter words, like "F=ma". But modern science has moved on, embracing the complex. Occam now uses a web-enabled, fractal e-razor. Even in mathematics, stripped of awkward realities of non-ideal gases, turbulence, and non-spherical cows, simple statements about integers like Fermat’s aⁿ + bⁿ = cⁿand wrangling maps with four colors take many years and pages (occasionally computers) to prove.

The question is not "What is our favorite elegant explanation?", but "What should it be?" We are capable of changing not only our mind, but changing the whole fabric of human nature. As we engineer, we recurse—successively approximating ourselves as an increasingly survivable force of nature. If so, what will we ultimately admire? Our evolutionary baggage served our ancestors well, but could kill our descendants. Faced with modern foods, our frugal metabolisms feed a diabetes epidemic. Our love of "greedy algorithms" leads to exhausted resources. Our too easy switching from rationality to blind-faith or fear-based decision making can be manipulated politically to drive conspicuous consumption. (Think Easter Island 163 km² of devastation scaled to Earth Island at 510 million km²).  "Humans" someday may be born with bug-fixes for dozens of current cognitive biases as well as intuitive understanding and motivation to manipulate quantum weirdnesses, dimensions beyond three, super rare events, global economics, etc. Agricultural and cultural monocultures are evolutionarily bankrupt. Evolution was only briefly focused on surviving in a sterile world of harsh physics, but ever since has focused on life competing with itself. Elegant explanations are those that predict the future farther and better. Our explanations will help us dodge asteroids, solar red giant flares, and even close-encounters with the Andromeda galaxy. But most of all, we will diversify to deal with our own ever-increasing complexity.  

The Beauty In A Sunrise

This year's Edge Question is about one's personal responses to explanation. When I was first excited by physics, the depths of its explanations were compelling to me in very esoteric contexts. For example, the binding of matter, energy and space-time in General Relativity seemed (and indeed is) an extraordinarily elegant and deep explanation.

Nowadays I am even more compelled by powerful explanations that lie behind the things we see around us that are too easily taken for granted. And in thinking about the Question, I find myself drawn to a context that is experienced every day by just about everybody.

How generous is that himself the sun
—arriving truly, faithfully who goes
(never for a moment ceasing to begin
the mystery of day for someone's eyes)

Thus wrote ee cummings in the opening of his short but lyrical celebration of our star. Those words highlight a daily moment—a sunrise—whose associated human sense of (in)significance and mystery may for some be only deepened by appreciating (at least) three great explanations underlying within the experience. And each of those explanations has at least one of the qualities of depth, elegance and beauty.

If you care about such things, and (like me) live at a northern middle latitude, you will know the range of the horizon visible from your home, between (roughly) south-east and north-east, across which the point of sunrise shifts back and forth over the year, with sunrise getting later as it moves northward and the days shorten, and the motion reversing at the winter solstice. And beyond that quite complex behaviour is the simple truth of the sun's fidelity—we can indeed trust it to come up somewhere in the East every morning.

Like a great work of art, a great scientific explanation loses none of its power to inspire awe afresh whenever one contemplates it. So it is with the explanation that those daily and annual cycles of sunrises are explicable by a tilted rotating Earth orbiting the Sun, whose average axial direction can be considered fixed relative to the stars thanks to a still-mysterious conservation law.

Unlike my two other chosen explanations, this one encountered scepticism from scientists for decades. The heliocentric view of the solar system, articulated by Copernicus in the mid 16^th century, was not widely accepted until well into the 17^th century. For me, that triumph over the combination of scientific scepticism and religious hostility only adds to the explanation's appeal.

Another explanation is certainly elegant and lies behind the changing hues of the sky as the sun rises. Lord Rayleigh succeeded James Clerk Maxwell as Cavendish professor of physics at Cambridge. One of his early achievements was to deduce laws of the scattering of light. His first effort reached the right answer on an invalid foundation – the scattering of light in an elastic aether. Although the existence of such an aether wasn't shown to be a fallacy until some years later, he redid his calculations using Maxwell's deeply unifying theories of electromagnetism. 'Rayleigh scattering' is the expression of those theories in contexts where an electromagnetic wave encounters electrically polarised particles much smaller than its wavelength. The amount of scattering, Rayleigh discovered, is inversely proportional to the fourth power of the wavelength. By 1899, he had shown that air molecules themselves were powerful scatterers.

There, in one bound, is the essential explanation of why the sky is blue and why sunrises are reddened. Blue light is scattered much more by air molecules than light of longer wavelengths. The sun's disk is accordingly reddened and all the more so when seen through the long atmospheric path at sunrise and sunset. (To fully account for the effect, you also need to take into account the sun's spectrum and the visual responses of human eyes.) The pink clouds that can add so much to the beauty of a sunrise consist of comparatively large droplets that scatter the wavelengths of reddened sunlight more equally than air molecules—colourwise, what you see is what they get.

The third explanation behind a sunrise is conceptually and cosmologically the deepest. What is happening in the sun to generate its seemingly eternal light and heat? Understanding the nuclear reactions at the sun's core was just a part of an explanation that (thanks especially to Burbidge, Burbidge, Fowler and Hoyle in 1957) simultaneously allowed us to understand not only the light from many kinds of stars but also how almost all the naturally occurring chemical elements are produced throughout the universe: in chains of reactions occurring within stable and cataclysmically unstable cosmic balls of gas in their various stages of stellar evolution, driven by the shifting influences of all the fundamental forces of nature—gravity, electromagnetism and the strong and weak nuclear forces.

Edge readers know that scientific understanding enhances rather than destroys nature's beauty. All of these explanations for me contribute to the beauty in a sunrise.

Ah, but what is the explanation of beauty? Brain scientists grapple with nuclear-magnetic resonance images—a recent meta-analysis indicated that all of our aesthetic judgements seem to include the use of neural circuits in the right anterior insula, an area of the cerebral cortex typically associated with visceral perception. Perhaps our sense of beauty is a by-product of the evolutionary maintenance of the senses of belonging and of disgust. For what it's worth, as exoplanets pour out of our telescopes, I believe that we will encounter astrochemical evidence for some form of extraterrestrial organism well before we achieve a deep, elegant or beautiful explanation of human aesthetics.

A Beautiful Explanation For Why The Human Mind May Seem To Have An Elegant Explanation Even If It Doesn't

On reading "The Origin of Species" Erasmus Darwin wrote to his brother Charles in 1859: "The a priori reasoning is so entirely satisfactory to me that if the facts won't fit in, why so much the worse for the facts." Some of the facts—such as Kelvin's calculation of the age of the Earth—looked awkard for Darwin's theory at the time. But the theory of natural selection was too beautiful to be wrong. The brother was sure the troublesome facts would have to change. And so they did.

But it doesn't always work that way. Elegance can be misleading. Consider a simple mathematical example. Given the sequence 2, 4, 6, 8, what rule would you guess is operating to generate the series? There are several theoretically possible answers. One would be the simple rule: take the previous number, x, and compute x + 2. But equally valid for these data would be the much more complicated rule, take the previous number, x, and compute

-1/44 xexp3 + 3/11 xexp2 + 34/11

For the sequence as given so far, the first rule is clearly the more elegant. And if someone, let's call her Tracey, were to maintain that, since both rules both work equally well, she was going to make a personal choice of the second, we would surely think she was being deliberately contrarian and anti-elegant. Tracey Emin not Michelangelo.

But suppose now Tracey were to say: "I bet if we look a little further we shall find I was right all along." And suppose, when we do look further, we find to our surprise that the next number in the sequence is not 10, but 8.91 and the next after that not 12 but 8.67, i.e. the sequence we actually discover goes 2, 4, 6, 8, 8.91, 8.67. Then what had previously seemed the better rule would no longer fit the facts at all. Yet—surprise, surprise—the second rule would still fit nicely. In this case we should be forced to concede that Tracey's anti-elegance had won the day.

How often does the real world tease us by seeming to be simpler than it really is? A famous case is Francis Crick's 1959 theory of how DNA passes on instructions for protein synthesis using a "comma free code". As Crick wrote many years later "Naturally [we] were excited by the idea of a comma-free code. It seemed so pretty, almost elegant. You fed in the magic numbers 4 (the 4 bases) and 3 (the triplet) and out come the magic number 20, the number of amino acids." But alas this lovely theory could not be squared with experimental facts. The truth was altogether less elegant.

A tease? I'm not of course suggesting that Nature was deliberately stringing Crick along. As Einstein said, God is subtle but he is not malicious. In this case the failure of the most elegant explanation to be the true one is presumably just a matter of bad luck. And, assuming this doesn't happen often, perhaps in general we can still expect truth and beauty to go together (as no doubt many of the other answers to this Edge Question will prove).

However I believe there is one class of cases where the elegance of an untrue theory may not be luck at all; where indeed complex phenomena have actually been designed to masquerade as simple ones—or at any rate to masquerade as such to human beings. And such cases will arise just when, in the course of evolution, it has been to the the biological advantage of humans to see certain things in a particularly simple way. The designer of the pseudo-elegant explananda has not been God, but natural selection.

Here is my favorite example. Individual humans appear to other humans to be controlled by the remarkable structures we call "Minds". But the surprising and wonderful thing is that human "minds" are quite easy for others to read. We've all been doing it since we were babies, using the "folk theory" known to psychologists as "Theory of Mind" (or sometimes as "belief desire psychology"). Theory of Mind is simple and elegant, and can be understood by a two-year old. There's no question it provides a highly effective way of explaining the way people behave. And this skill at mind-reading has been essential to human survival in social groups. Yet the fact is Theory of Mind could never have worked so well unless natural selection had shaped human brains to be able to read—and to be readable by—one another in this way. Which is where the explanatory sleight of hand comes in. For, as an explanation of how the brain works, Theory of Mind just doesn't add up. It's a purpose-built over-simplified deep, elegant myth. (A myth whose inadequacy may not become apparent perhaps until those "extra numbers" are added by madness or by brain damage—contingencies which selection has not allowed for).

I find this explanation of the elegance of Theory of Mind beautiful. 

We Are Stardust

Where did we come from? I find the explanation that we were made in stars to be deep, elegant, and beautiful. This explanation says that every atom in each of our bodies was built up out of smaller particles produced in the furnaces of long-gone stars. We are the byproducts of nuclear fusion. The intense pressures and temperatures of these giant stoves thickened collapsing clouds of tiny elemental bits into heavier bits, which once fused, were blown out into space as the furnace died. The heaviest atoms in our bones may have required more than one cycle in the star furnaces to fatten up. Uncountable numbers of built-up atoms congealed into a planet, and a strange disequilibrium called life swept up a subset of those atoms into our mortal shells. We are all collected stardust. And by a most elegant and remarkable transformation, our starstuff is capable of looking into the night sky to perceive other stars shining. They seem remote and distant, but we are really very close to them no matter how many lightyears away. All that we see of each other was born in a star. How beautiful is that?

Explaining How Two Systems Of The World Can Both Be True

The situation that I am trying to explain is the existence side by side of two apparently incompatible pictures of the universe. One is the classical picture of our world as a collection of things and facts that we can see and feel, dominated by universal gravitation. The other is the quantum picture of atoms and radiation that behave in an unpredictable fashion, dominated by probabilities and uncertainties. Both pictures appear to be true, but the relationship between them is a mystery.

The orthodox view among physicists is that we must find a unified theory that includes both pictures as special cases. The unified theory must include a quantum theory of gravitation, so that particles called gravitons must exist, combining the properties of gravitation with quantum uncertainties.

I am looking for a different explanation of the mystery. I ask the question, whether a graviton, if it exists, could conceivably be observed. I do not know the answer to this question, but I have one piece of evidence that the answer may be no. The evidence is the behavior of one piece of apparatus, the gravitational wave detector called LIGO that is now operating in Louisiana and in Washington State. The way LIGO works is to measure very accurately the distance between two mirrors by bouncing light from one to the other. When a gravitational wave comes by, the distance between the two mirrors will change very slightly. Because of ambient and instrumental noise, the actual LIGO detectors can only detect waves far stronger than a single graviton. But even in a totally quiet universe, I can answer the question, whether an ideal LIGO detector could detect a single graviton. The answer is no. In a quiet universe, the limit to the accuracy of measurement of distance is set by the quantum uncertainties in the positions of the mirrors. To make the quantum uncertainties small, the mirrors must be heavy. A simple calculation, based on the known laws of gravitation and quantum mechanics, leads to a striking result. To detect a single graviton with a LIGO apparatus, the mirrors must be exactly so heavy that they will attract each other with irresistable force and collapse into a black hole. In other words, nature herself forbids us to observe a single graviton with this kind of apparatus.

I propose as a hypothesis, based on this single thought-experiment, that single gravitons may be unobservable by any conceivable apparatus.

If this hypothesis were true, it would imply that theories of quantum gravity are untestable and scientifically meaningless. The classical universe and the quantum universe could then live together in peaceful coexistence. No incompatibility between the two pictures could ever be demonstrated. Both pictures of the universe could be true, and the search for a unified theory could turn out to be an illusion.

The Origin of Money

Carl Menger's account of the origin of money is my favourite scientific explanation. It is deeply satisfying because it shows how money can develop from barter without anyone consciously inventing it. As such, it is a great example of Adam Smith's invisible hand, or what scientists now call "emergence."

Menger (1840-1921) founded the Austrian school of economics, a heterodox school of thought which is derided by many mainstream economists. Yet their accounts of the origin of money beg the very question which Menger answered. The typical mainstream economics textbook lists the problems of barter exchange, and then explains how money overcomes these problems. However, that does not really explain how money actually got started, any more than listing the advantages of air travel explains how aeroplanes were invented. As Lawrence White puts it in his book on The Theory of Monetary Institutions (1999), "one is left with the impression that barterers, one morning, suddenly became alert to the benefits of monetary exchange, and, by that afternoon, were busy using some good as money."

That, of course, is ridiculous. In Menger's account, money emerges through a series of small steps, each of which is based on self-interested choices by individual traders with limited knowledge. First, individual barterers realize that, when direct exchange is difficult, they can get what they want by indirect exchange. Rather than finding someone who both has what I want and wants what I have, I need only find someone who wants what I have. I can then trade what I have for his good, even though I don't want to consume it myself, and then trade that for something I do want to consume. In that case, I will have used the intermediate good as a medium of exchange.

Menger notes that not all goods are equally marketable. In other words, some goods are easier to trade than others. It therefore pays a trader to accumulate an inventory of highly marketable items for use as media of exchange. Other alert traders in the market catch on, and eventually the market converges on a single common medium of exchange. This is money.

Menger's theory does not merely show how money can evolve without any conscious plan; it also shows that money does not depend on legal decrees or central banks. Yet this too is often overlooked by mainstream economists. Take Michael Woodford for example. Woodford is one of the most influential academic monetary economists alive today, yet in his 2003 book Interest and Prices: Foundations of a Theory of Monetary Policy, a central bank somehow becomes part of the economy within less than a page after the initial assumptions are introduced. In other words, Woodford does not even pause for a page to consider what a banking system would look like without a central bank. Yet free banking has a long history; the first such system began in China in about 995 AD, more than 600 years before the first central bank.

Can we account for the emergence of central banking by the same invisible-hand type of explanation that Menger proposed for money? The answer depends, according to Lawrence White, on just what we mean by the term "central banking." If government sponsorship is among the defining features of a central bank, then the answer is no. In other words, the emergence of central banks cannot be accounted for entirely by market forces. At some point, deliberate state action must enter the story. The government's motives for getting involved are not hard to imagine. For one thing, exclusive supply of banknotes gives the government a source of monopoly profits in the form of a zero-interest loan from the public's holding of these non-interest bearing notes.

In these troubled times, when central banks are expanding the stock of high-powered money through massive quantitative easing, Menger's theory is more relevant than ever. It alerts us to the possibility that the response to the current crisis in the eurozone need not be ever more centralization, but could instead consist of a move in the opposite direction, towards a regime in which any bank is free to issue its own banknotes, and market forces—not central banks—control the money supply.

Implications of Ivan Pavlov's Great Discovery

It's easy to imagine a politician's objecting to federal funds going to study how dogs drool. But failing to support such research would have been very short sighted indeed during the days of the great Russian physiologist Ivan Pavlov (1849—1936). As part of his Nobel Prize-winning research on digestion, he measured the amount of saliva produced when dogs were given food. In the course of this work, he and his colleagues noticed something unexpected: The dogs started to salivate well before they were fed. In fact, they salivated when they first heard the approaching footsteps of the person coming to feed them. That core observation led to the discovery of classical conditioning.

The key idea behind classical conditioning is that a neutral stimulus (such as the sound of approaching footsteps) comes to be associated with a stimulus (such as food) that reflexively produces a response (such as salivation)—and, after awhile, the neutral stimulus comes to elicit the response produced reflexively by the paired stimulus. To be clear about the phenomenon, we'll need to take a few words to explain the jargon. The neutral stimulus becomes "conditioned," and hence is known as the "conditioned stimulus" (CS), whereas the stimulus that reflexively produces the response is known as the unconditioned stimulus (UCS). And the response that is produced by the UCS is called the unconditioned response (UR). Classical conditioning occurs when the CS is presented right before a UCS, so that after a while the CS by itself produces the response. When this occurs, the response is called a conditioned response (CR). In short, at the outset a UCS (such as food) produces a UCR (such as salivation); when a CS (the sound of the feeder's footsteps) is presented before the UCS, it soon comes to produce the response, a CR (salivation), by itself.

This simple process gives rise to a host of elegant and non-intuitive explanations.

For example, consider accidental deaths from drug overdoses. In general, a narcotics user tends to take the drug in a specific setting, such as in his or her bathroom. The setting initially is a neutral stimulus, but after a person takes narcotics in it a few times, the bathroom comes to function as a CS: As soon as the user enters his or her bathroom with narcotics, the user's body responds to the setting by preparing for the ingestion of the drug. Specific physiological reactions allow the body to cope with the drug, and those reactions become conditioned to the bathroom (in other words, the reactions become a CR). To get a sufficient "high," the user must now take enough of the narcotic to overcome the body's preparation. But if the user takes the drug in a different setting, perhaps in a friend's bedroom during a party (and hence the new setting is not a CS), the CR does not occur—the usual physiological preparation for the narcotic does not take place. Thus, the usual amount of the drug functions as if it were a larger dose, and may be more than the user can tolerate without the body's preemptive readiness. Hence, although the process of classical conditioning was formulated to explain very different phenomena, it can be extended directly to explain why drug overdoses sometimes accidentally occur when usual doses are taken in new settings.

By the same token, classical conditioning plays a role in the placebo effect: For those of us who have regularly used analgesics such as ibuprofen or aspirin, such medicines begin to have their effects well before their active ingredients actually have time to take effect. How? From previous experience, the mere act of taking that particular pill has become a CS, which triggers the pain-relieving processes invoked by the medicine itself (and those processes have become a CR).

Classical conditioning also can result from an implanted defibrillator, or "pacemaker." When the heart beats too quickly, this device shocks it and thereby causes it to revert to beating at a normal rate. Until the shock level is properly calibrated, the shock can be very uncomfortable and can function as a UCS that produces fear as a UCR. Because the shock does not occur in a consistent environment, the person associates random aspects of the environment with it—which then function as CSs. And when any of those aspects of the environment are subsequently present, the person can experience severe anxiety, awaiting the possible shock and resulting reaction.

This same process explains why you would find a particular food unappealing if you happen to have eaten it and gotten food poisoning (and thus had significant gastrointestinal problems—the UCR to the UCS of tainted food). That type of food can thus come to function as a CS, and if you eat it—or even think about eating it—you may feel queasy, a CR. You may find yourself avoiding that food, and thus a food aversion is born. In fact, simply pairing pictures of particular types of food (such as French fries) with aversive photographs (such as of a horribly burned body) can change how appealing you find that food.

These examples should be sufficient to give you a sense of how the explanation for anticipatory salivation can be easily and simply extended to a wide range of phenomena. But, that said, we need to point out that Pavlov's original conception of classical conditioning was not quite right; he thought that sensory input was directly connected to specific responses, which led the stimuli to produce the response automatically. We now know that the connection is not so direct; classical conditioning involves many cognitive processes, such as attention and those that underlie the ability to interpret and understand. In fact, classical conditioning is a form of "implicit learning." As such, it allows us to navigate through life with less cognitive effort (and stress) than would otherwise be required. Nevertheless, this sort of conditioning has byproducts that can be powerful, surprising, and even sometimes dangerous.

"Power Tends To Corrupt, And Absolute Power Corrupts Absolutely."

I hope I will not be drummed out of the corps of Social Science if I confess to the fact that I can't think of an explanation in our field that is both elegant and beautiful. Perhaps deep . . . I guess we are still too young to have explanations of that sort . . . But there is one elegant and deep statement (which, alas, is not quite an "explanation") that comes close to fulfilling the criteria, and that I find very useful as well as beautifully simple.

I refer to the well-known lines Lord Acton wrote in a letter from Naples in 1887 to the effect that: "Power tends to corrupt, and absolute power corrupts absolutely." At least one philosopher of science has written that on this sentence an entire science of human beings could be built.

I find that the sentence offers the basis for explaining how a failed painter like Adolph Hitler and a failed seminarian like Joseph Stalin could end up with the blood of millions on their hands; or how the Chinese emperors, the Roman popes, or the French aristocracy failed to resist the allure of power. When a religion or ideology becomes dominant, the lack of controls will result in widening spirals of license leading to degradation and corruption.

It would be nice if Acton's insight could be developed into a full-fledged explanation before the hegemonies of our time, based on blind faith in science and the worship of the Invisible Hand, follow former forms of power in the dustbins of history.

Keys to Behavior: Tinbergen's Four Questions

Why do we—and all other creatures—behave as we do? No answers really exist. I chose the ethologist and ornithologist NikolaasTinbergen's questions for exactly that reason, because sometimes there is no one deep, elegant, and beautiful explanation. Much like a teacher of fishing rather than a giver of fish, Tinbergen did not try to provide any one global explanation, but instead gave us a scaffolding upon which to build our own answers to each individual behavioral pattern we observe, a scaffolding that can be used not only for the ethological paradigms for which he was famous, but all forms of behavior in any domain. Succinctly, Tinbergen asked:

• What is the mechanism?  How does it seem to work?
• What is the ontogeny? How do we observe it develop over time?
• What is its function? What are all the possible reasons it is done?
• What is its origin? What are the many ways in which it could it have arisen?

In attempting to answer each of these questions, one is forced to think at the very least about the interplay of genes and environment, of underlying processes (neuroanatomy, neurophysiology, hormones, etc.), of triggers and timing, what advantages and disadvantages are balanced and how these may have changed over time.

Furthermore, unlike most 'favorite' explanations, Tinbergen's questions are enduring. Answers to his questions often reflect a current zeitgeist in the scientific community, but those answers mutate as additional knowledge becomes available. His questions challenge us to rethink our basic presumptions each and every time another chunk of data lands in our laps, whatever our field of study. Our fascination with simple elegant answers strikes me as a Doug Adams (Hitchhiker's Guide to the Galaxy) pursuit: We may find "42", but unless we know how to formulate the appropriate questions, the answer isn't always very meaningful.

The 19th Century Explanation of the Remarkable Connection Between Electricity And Magnetism

No explanation I know of in all of recent scientific history is as beautiful or deep, or ultimately as elegant, as the 19th century explanation of the remarkable connection between two familiar, but seemingly distinct forces in nature, electricity and magnetism. It represents to me all that is the best about science: surprising empirical discoveries combined with a convoluted path to a remarkably simple and elegant mathematical framework, which then explained far more than was ever bargained for, and in the process produced the very technology that now powers modern civilization.

It all began with strange experiments with jumping frogs and electric circuits, capped by the serendipitous discovery by the self-schooled, yet greatest experimentalist of his time, Michael Faraday of a very strange connection between magnets and electric currents. It was by then well known that a moving electric charge, i.e. a current, created a magnetic field around the current that could repel or attract other magnets located nearby.

What remained an open question was whether magnets could produce any electric force on charged objects. Faraday discovered, by accident, that when he turned on or off a switch to start or stop a current, creating a magnetic field that grew or decreased with time, during the periods when the magnetic field was changing, a force would suddenly arise in a nearby wire, moving the electric charges within it to create a current.

Faraday's law of induction, as it became known, not only is responsible for the basic principle governing all electric generators, from Niagara falls to nuclear power plants, it produced a theoretical conundrum that required the mind of the greatest theoretical physicist of his time, James Clerk Maxwell to set things straight. Maxwell realized that Faraday's result implied that it was the changing magnetic field (a pictorial concept introduced by Faraday himself because he felt more comfortable with pictures than algebra) that produced an electric field that would push the charges around the wire creating a current.

But in order for mathematical symmetry in the equations governing electric and magnetic fields, this then required that a changing electric field, and not merely moving charges, would produce a magnetic field. This not only produced a set of mathematically consistent equations every physics student knows, and some love, called Maxwell's equations, which can fit on a T-Shirt, but it established the physical reality of what was otherwise a mere figment of Faraday's imagination, a field—some quantity associated with every point in space and time.

But even more than this, Maxwell realized that if a changing electric field produced a magnetic field, then a constantly changing electric field, such as that which occurs when I continue to jiggle a charge up and down, would produce a continuously changing magnetic field. But that in turn would create a continuously changing electric field, which in turn would create a continuously changing magnetic field, and so on. This field 'disturbance' would move out from the original source, the jiggling charge, at a rate that Maxwell could calculate on the basis of his equations. The parameters in these equations came from experiment—measuring the strength of the electric force between two known charges, and the strength of the magnetic force between two known currents.

From these two fundamental properties of nature, Maxwell calculated the speed of the disturbance and found out ... you guessed it, that the speed was precisely the speed that light was measured to have! Maxwell thus discovered that light is indeed a wave ... but a wave of electric and magnetic fields that moved through space at a precise speed determined by two fundamental constants in nature thus laying the basis for Einstein to come along a generation or so later and demonstrate that the constant speed of light required a revision in our notions of space and time.

So, from jumping frogs and differential equations we came up for one of the most beautiful unifications in all of physics, the unification of electricity and magnetism in a single theory of electromagnetism, and that theory explained the existence of that which allows us to observe the universe around us, namely light, and the practical implications of the theory produced the mechanisms that power all of modern civilization and the principles that govern essentially all modern electronic devices, and the nature of the theory itself produced a series of further puzzles that allowed Einstein to yield new insights into space and time!

Not bad for a set of experiments whose worth was questioned by Gladstone (or Queen Victoria—depending upon which apocryphal story one buys)—who came into Faraday's laboratory and wondered what all the fuss was about, and what use all of this experimentation was for. He (or she) was told, either: "Of what use is a newborn baby?"—or in my favorite version of the story—"Use? Why one day this will be so useful you will tax us for it!" Beauty, elegance, depth, utility, adventure, and excitement! Science at its best!

Physical Reality Could Be Hugely More Extensive Than the Patch of Space and Time Traditionally Called 'The Universe'

An astonishing concept has entered the mainstream of cosmological thought: physical reality could be hugely more extensive than the patch of space and time traditionally called 'the universe'. A further Copernican demotion may loom ahead. We've learnt that we live in just one planetary system among billions, in one galaxy among billions. But now that's not all. The entire panorama that astronomers can observe could be a tiny part of the aftermath of 'our' big bang, which is itself just one bang among a perhaps-infinite ensemble.

Our cosmic environment could be richly textured, but on scales so vast that our purview is restricted to a tiny fragment; we're not aware of the 'big picture', any more than a plankton whose 'universe' was a liter of water would be aware of the world's topography and biosphere. It is obviously sensible for cosmologists to start off by exploring the simplest models. But there is no more reason to expect simplicity on the grandest scale than in the terrestrial environment—where intricate complexity prevails.

Moreover, string theorists suspect—for reasons quite independent of cosmology—that there may be an immense variety of 'vacuum states'. Were this correct, different 'universes' could be governed by different physics. Some of what we call 'laws of nature' may in this grander perspective be local bylaws, consistent with some overarching theory governing the ensemble, but not uniquely fixed by that theory. More specifically, some aspects may be arbitrary and others not. As an analogy (which I owe to Paul Davies) consider the form of snowflakes. Their ubiquitous six-fold symmetry is a direct consequence of the properties and shape of water molecules. But snowflakes display an immense variety of patterns because each is molded by its distinctive history and micro-environment: how each flake grows is sensitive to the fortuitous temperature and humidity changes during its growth.

If physicists achieved a fundamental theory, it would tell us which aspects of nature were direct consequences of the bedrock theory (just as the symmetrical template of snowflakes is due to the basic structure of a water molecule) and which cosmic numbers are (like the distinctive pattern of a particular snowflake) the outcome of environmental contingencies. .

Our domain wouldn't then be just a random one. It would belong to the unusual subset where there was a 'lucky draw' of cosmic numbers conducive to the emergence of complexity and consciousness. Its seemingly designed or fine -tuned features wouldn't be surprising. We may, by the end of this century, be able to say, with confidence, whether we live in a multiverse, and how much variety its constituent 'universes' display. The answer to this question will, I think, determine crucially how we should interpret the 'biofriendly' universe in which we live (and which we share with any aliens who we might one day make contact with).

It may disappoint some physicists if some of the key numbers they are trying to explain turn out to be mere environmental contingencies—no more 'fundamental' than the parameters of the Earth's orbit round the Sun. But that disappointment would surely be outweighed by the revelation that physical reality was grander and richer than hitherto envisioned.

The Production of Antibodies

An evening in early August 1954 Niels Kaj Jerne had an idea while walking home from work and crossing Copenhagen's beautiful Knippelsbro—a bridge connecting the island of Amager where his laboratory was located at the vaccine-producing national serum institute SSI, and central Copenhagen. The flash of insight was completed even before he had crossed the bridge and so was the idea that would for ever change our understanding of the immune system—and perhaps one day also perception and cognition.

Niels Kaj Jerne had for a long time been worried about a single piece of evidence in the study of antibodies. Our immune system somehow produces these elegant structures that can bind to and escort out invading foreign substances like viruses or bacteria. The shape of the antibody fits the three-dimensional structure of the invader like a hand in a glove or a key in a lock.

But how was that possible: There is not nearly enough information in the genetic system to specify an antibody for each of the many million foreign entities that could enter the body. A favorite explanation at the time was that the antibody was informed by the alien substance: It took its shape from what was entering the body, so that it could bind to it and usher it out.    However, there was a problem that had been known since the 1930'ies: Small amounts of an antibody is present in the blood stream of animals—even though they have never been exposed to the foreign substance, the antigen, that the antibody is perfectly shaped to bind to. So the antibody could not have learned from the antigen.

The summer evening walk home from work gave Jerne an idea that he immediately saw as "fabulous": The body holds a collection of building blocks for antibodies. Whenever something new enters the body, the building blocks are shuffled into a vast array of antibodies. Each will be produced in one copy. One of them will bind particularly well to the shape of the invader. When the "re-cognition" has taken place, that particular antibody will be mass-produced by the immune system.

This immediately explains why it takes time to fight an infection and why vaccination helps (the shuffling and selection has already been done before the invaders arrive in large numbers).

Niels Kaj Jerne told biochemist Günther Stent about the idea. It took Stent "fifteen, maybe twenty minutes" to become convinced that the idea was right. It took thirty years before Jerne was awarded the Nobel Prize.

In a sense it is Darwinism applied to the immune system. A random production of possible shapes is subject to a selection pressure from an outside universe of shapes. When they fit, the shape from inside is multiplied in large numbers. In Darwinism we are talking organisms and the environment, in Jerne's model we are talking antibodies and the environment.

The elegance of the idea is that there is no transfer of information from the environment into the "design" of the antibody/organism. The environment is only selecting between options produced at random.

Is this not like perception: We actually do not see the world around us, but only our own "simulated visual scenery". When our fantasies are "relevant" to our behavior they are selected for and reproduced.

Is this not like cognition and thinking: We make up lots of "lego-brick" models of the empirical data, reject most of them, but eventually when something fits, we keep thinking that way?

Is Niels Kaj Jerne's idea not a prime example of itself: After playing around with numerous small toy models in his mind, discarding all of them as hopeless, suddenly the right one popped up in his mind that August evening crossing Knippelsbro?

He then kept thinking that way. Reproducing the idea again and again.

As we do, right now.

Duchamp's "Fountain"

Marcel Duchamp's 20^th century Readymades upended art history with the same mental earthquake with which Charles Darwin illuminated biological history. Duchamp's objects moved slowly into the mainstream as they appeared to be some sort of institutional blunder, why was a urinal slotted into the history of art instead of the history of plumbing? Why was the snow shovel inside the museum instead of outside tidying the driveway? Therein lies the essence of his Readymade: an object in the wrong place that questions the aura of objects in the right place. Had the urinal been hung fifty feet away in the restroom we would never have heard of it, but misplaced it was juried, crated, photographed, cataloged, critiqued, insured, donated, dissertated, collected, positioned, lighted, cleaned, and paid for. Had his bottle rack, chocolate grinder, pharmacy bottles or other common objects been stashed away in their proper space they would have passed no mention. But by "creating" an artwork from something made for another purpose he exposed the valuation system that produced an appearance of transcendentalism. In one end went butcher scraps and out came fine sausage. 

Duchamp was from a family of artists and mastered painterly cubism prior to breaking with art tradition by designating common objects as art objects. In doing so he exchanged visual space for mental space, a swap of form and color for context and stratified meaning, making him the father of both Pop Art and Conceptual Art, the dominant forms of art today. His Readymades are technically a nominalism, a stock prop of skepticism imported or deported from letters back and forth since the 11^th century. Nominalists believe in no eternal verities or universals, just names that imagine there are and no special objects, just ones gathered by words and privileged according to the metaphysics of the time. Hence the demystifying brilliance of the Readymades.

Duchamp pushed the envelope as far as possible with the urinal prank, also known as "Fountain"—what possibly would be less likely to be regarded as art than a piss receptacle? He signed the urinal "R. Mutt," a pun on "I'm a dog," and submitted it anonymously to the 1917 Society of Independent Artists, a New York show that employed Duchamp as a juror. The bylaws required inclusion of anyone who could pony up the six buck admission, however the jury pronounced "R. Mutt's" urinal not-art, declined to include it in the catalog and hid it behind a partition. Over the next nine decades this piss-pot was the most debated event in art theory: an artist-juror rejects the fake art of his nom de plume. In a 2004 survey art professionals voted the urinal-Fountain the world's most influential piece of modern art, ahead of works by Picasso or Matisse. Copies of the urinal-Fountain are now in eleven major collections including the Centre Pompidou and the Tate Modern. 

Duchamp did not leave behind many writings instead communicating his thought through visual mischief. When he did write it was usually another spoof such as his essay "Texticles" or his bulletin "Rongwrong" that predicted the high-minded goofiness known as deconstruction decades later. His thought became popularized as "everything is art," somewhat of a misnomer as he never spoke those exact words, documents indicate it would be more accurately "everything can be regarded as art." Duchamp fell in and out of favor over his eighty-one years, but he continued the ruse ever announcing more and more preposterous things as art: "Every breath is an artwork" he explained to an interviewer a year before he passed, "I am a breather, I enjoy it tremendously." 

Beauty and Tragedy In the Mathematics of Music

Some things are too good to be true. Others are too good not to be true. The elegant correspondence between musical consonance and simple mathematical ratios is too good not to be true. The infinitely creative system of musical harmony—based on a small set of canonical intervals and chordsarises out of this correspondence.

And yet the system has a flaw—a rip or tear in the musico-mathematical universe.

The most consonant musical interval is the octave, so much so that two tones an octave apart bear the same letter name, for example, A. The next most consonant interval is the fifth (for example, A to E). If you pluck the A string on a guitar and then pluck it again while placing your finger halfway up the fingerboard (allowing only half the string to vibrate and doubling the frequency), the pitch goes up by an octave to A. If instead you place your finger one-third the way up the fingerboard (allowing only the remaining two-thirds of the string to vibrate and increasing the frequency by a factor of 3/2) the pitch goes up by a fifth to E.

On a full size piano keyboard, if you play the lowest note, A, and then go up by twelve successive fifths, you reach A again—which happens to be seven octaves higher than the lowest A. Calculating by fifths, the highest A is (3/2)¹²times the frequency of the lowest A. Calculating by octaves, the highest A is 2⁷ times the frequency of the lowest A.

It should therefore be the case that:

(3/2)¹² = 2⁷

Tragically, this is not the case: (3/2)¹²is 129.7463, while 2⁷ is 128. Close but unequal. If you tune by octaves, the fifths are out-of-tune, and vice versa.

This discrepancy—a variant of the Pythagorian comma—shatters an edifice that rests on the beautiful principle that ratio simplicity underpins musical consonance. While each interval is most purely tuned using these simple ratios (the just tuning system: 2/1 = octave, 3/2 = perfect fifth, 4/3 = perfect fourth, 5/4 = major third and 6/5 = minor third), the mathematics falls apart when these intervals interact in music.

The Pythagorian comma has haunted string players for centuries, requiring annoying adjustments. On the violin, some notes must be played slightly sharper and others flatter to dodge dissonance. The comma held back the development of keyboard instruments, in which notes cannot be adjusted while playing, thus limiting a composition to the musical key for which the instrument was tuned.

The solution to this problem is to forego mathematical purity by fudging tuning. This discovery—which emerged in various forms over a period of centuries—unleashed new creative possibilities and inspired J.S. Bach to write The Well Tempered Clavier, which traverses all major and minor keys without discriminating on the basis of dissonance.

Today, several tuning systems achieve this end. In equal tempered tuning (used in some electronic synthesizers), the octave is divided into twelve equal semitones on a logarithmic scale. In this system, each successive semitone is 2^1/12 times the frequency of the previous one. Thus a fifth is 2^7/12 or 1.498 instead of 3/2 or 1.5; the perfect fourth is 2^5/12 or 1.3348 instead of 4/3 or 1.3333; the major third is 2^4/12 or 1.2599 instead of 5/4 or 1.25; and the minor third is 2^3/12 or 1.1892 instead of 6/5 or 1.2.

By anchoring the octaves and sprinkling the error elsewhere, consonance is compromised slightly but never disturbingly. The edifice of musical harmony is preserved by systematically fudging the very mathematical system upon which it is built. An elegant way to fix inelegance in an elegant musico-mathematical system.

Inverse Power Laws

I'm intrigued by the empirical fact that most aspects of our world and our society are distributed according to so-called inverse power laws. That is, many distribution curves take on the form of a curve that swoops down from a central peak to have a long tail that asymptotically hugs the horizontal axis.

Inverse power laws are elegantly simple, deeply mysterious, but more galling than beautiful. Inverse power laws are self-organizing and self-maintaining. For reasons that aren't entirely understood they emerge spontaneously in a wide range of parallel computations, both social and natural.

One of the first social scientists to notice an inverse power law was George Kingsley Zipf, who formulated an observation now known as Zipf's Law. This is the statistical fact that, in most documents, the frequency with which a given word is used is roughly proportional to the reciprocal of the word's popularity rank. Thus the second most popular word is used half as much as the most popular word, the tenth most popular word is used a tenth as much as the most popular word, and so on.

In society, similar kinds of inverse power laws govern society's rewards. Speaking as an author, I've noticed, for instance, that the hundredth most popular author sells a hundred-fold fewer books than the author at the top. If the top writer sells a million copies, somone like me might sell ten thousand.

Disgruntled scribes sometimes fantasize about a utopian marketplace in which the naturally arising inverse power law distribution would be forcibly replaced by a linear distribution, that is, a sales schedule that lies along a smoothly sloping line instead of taking the form of the present bent curve that starts at an impudently high peak and then swoops down to dawdle along the horizontal axis.

But there's no obvious way that the authors' sales curve could be changed. Certainly there's no hope of having some governing group try and force a different distribution. After all, people make their own choices as to what books to read. Society is a parallel computation, and some aspects of it are beyond control.

 The inverse-power-law aspects of income distribution are particularly disturbing. Thus the second-wealthiest person in a society might own half as much as the richest, with the tenth richest person possessing only a tenth as much, and—out on in the burbs—the thousandth richest person is making only one thousandth as much as the person on the top.

Putting the same phenomenon a little more starkly, while a company's chief executive officer might earn a hundred million dollars a year, a software engineer at the same company might earn only a hundred thousand dollars a year, that is, a thousandth as much. And a worker in one of the company's overseas assembly plants might earn only ten thousand dollars a year—a ten-thousandth as much as the top exec.

Power law distributions can also be found in the opening weekend grosses of movies, in the number of hits that web pages get, and in the audience shares for TV shows. Is there some reason why the top ranks do so overly well, and the bottom ranks seem so unfairly penalized?

The short answer is no—there's no real reason. There need be no conspiracy to skew the rewards. Galling as it seems, inverse power law distributions are a fundamental natural law about the behavior of systems. They're ubiquitous.

Inverse power laws aren't limited to societies—they also dominate the statistics of the natural world. The tenth smallest lake is likely to be a tenth as large as the biggest one, the hundredth largest tree in a forest may be a hundredth as big as the largest tree, the thousandth largest stone on a beach is a thousandth the size of the largest one.

Whether or not we like them, inverse power laws are as inevitable as turbulence, entropy, or the law of gravity. This said, we can somewhat moderate them them in our social context, and it would be too despairing to say we have no control whatsoever over the disparities between our rich and our poor.

But the basic structures of inverse power law curves will never go away. We can rail at an inverse power law if we like—or we can accept it, perhaps hoping to bend the harsh law towards not so steep a swoop.

Why the Greeks Painted Red People On Black Pots

An explanation of something that seems not to need explaining is good. If it leads to further explanations of things that didn't seem to need explaining, that is better. If it makes a massive stink, as academic vested interests attempt to preserve the status quo in the face of far reaching implications, it is one of the best. I have chosen Michael Vickers' simple and immensely influential explanation of why the ancient Greeks painted little red figures on their pots.

The 'red figure vase' is an icon of antiquity. The phrase is frequently seen on museum labels, and the question of why the figures were not white, yellow, purple or black—other colours the Greeks could and did produce in pottery slips and glazes—does not seem important. Practically speaking, Greek pottery buyers could mix and match without fear of clashing styles, and the basic scheme allowed the potters to focus on their real passion: narrative story telling. The black background and red silhouettes make complex scenes—mythological, martial, industrial, domestic, sporting and ambitiously sexual—graphically crisp. Anyone can understand what is going on (for which reason museums often keep their straight, gay, lesbian, group, bestial, and olisbos [dildo-themed] stuff out of public view, in study collections). So clearly there is enough about Greek vases to catch the eye without thinking about the colour scheme.

Michael's brilliance was to take an idea well known to the scholar Vitruvius in the first century BC and apply it in a fresh context. Vitruvius noted that many features of Greek temples that seemed merely decorative were a hangover from earlier practical considerations: little rows of carefully masoned cubes and gaps just under the roof line were in fact a skeuomorph or formal echo of the beam ends and rafters that had projected at that point when the structures were made of wood. Michael argued that Greek pottery was skeuomorphic too, being the cheap substitute for aristocratic precious metal. He argued that the red figures on black imitated gilded figures on silver, while the shapes of the pots, with their sharp carinations and thin, strap-like handles, so easily broken in clay, were direct translations of the silversmith’s craft.

This still seems implausible to many. But to those of us, like myself, working in the wilds of Eastern European Iron Age archaeology, with its ostentatious barbarian grave mounds packed with precious metal luxuries, it made perfect sense. Ancient silver appears black on discovery, and the golden figuration is a strongly contrasting reddish gold. Museums typically used to 'conserve' such vessels, not realising that (as we now know) the sulfidized burnish to the gold was deliberate, and that no Greek would have been seen dead with shiny silver (a style choice of the hated Persians, who flaunted their access to the exotic lemons with which they cleaned it).

For me, an enthusiast from the start, the killer moment was when Michael photographed a set of lekythoi, elegant little cylindrical oil or perfume jars, laid down end to end in decreasing order in an elegant curve. He demonstrated thereby that no lekythos (the only type of major pottery with a white background, and black only for base and lid) had a diameter larger than the largest lamellar cylinder that could be obtained from an elephant tusk. These vessels, he explained, were skeuomorphs of silver-mounted ivory originals.

The implications are not yet settled, but the reputation of ancient Greece as a philosophically-oriented,  art-for-art's sake culture can now be contrasted with an image of a world where everyone wanted desperately to emulate the wealthy owners of slave-powered silver mines with their fleets of trade galleys (in my view, the scale of the ancient economy in every dimension—slavery, trade, population levels, social stratification—has been systematically underestimated, and with it the impact of colonialism and emergent social complexity in prehistoric Eurasia).

The irony for the modern art world is that the red figure vases that change hands for vast sums today are not what the Greeks themselves actually valued. Indeed, it is now clear that the illusion that these intrinsically cheap antiquities were the real McCoy was deliberately fostered, through highly selective use of Greek texts by nineteenth century auction houses intent on creating a market.

Tit For Tat

Selfishness can sometimes seem like the best strategy. It is the rational response to the prisoner's dilemma, for instance, where each individual in a pair can either cooperate or defect, leading to four potential outcomes. No matter what the other person does, selfish behavior always yields greater return. But if both players defect, both do worse than if they had cooperated. Yet when political scientist Robert Axelrod and his colleagues ran hundreds of rounds of the prisoner's dilemma on a computer, the repetition of the game led to a different result.

Experts from a wide range of disciplines submitted 76 different game strategies for Axelrod to try—some of them very elaborate. At the end of 200 rounds, one strategy was far more successful than the others. It was also the simplest. Tit For Tat, a scheme where the player cooperates on the first move and thereafter does what was done on the previous move, was the winner. The importance of cooperation to evolution was detected by humans, but simulated and verified with machines.

This elegant explanation was then documented in living egoists with an elegant experiment. Evolutionary biologist Manfred Milinski noticed Tit For Tat behavior in his subjects, three-spined sticklebacks (Gasterosteus aculeatus). When he watched a pair of these fish approach a predator, he observed four options: they could swim side by side, one could take the lead while the other followed closely behind (or vice versa), or they could both retreat. These four scenarios satisfied the four inequalities that define the prisoner's dilemma. 

For the experiment, Milinski wanted to use pairs of sticklebacks, but they are impossible to train. So he placed in the tank a single stickleback and a set of mirrors that would act like two different types of companions. In the first treatment, a parallel mirror was used to simulate a cooperative companion that swam alongside the subject stickleback. In the second treatment, an oblique mirror system set at a 32-degree angle simulated a defecting partner—that is, as the stickleback approached the cichlid, the companion appeared to fall increasingly and uncooperatively behind. Depending on the mirror, the stickleback felt he was sharing the risk equally or increasingly going it alone.

When the sticklebacks were partnered with a defector, they preferred the safer half of the tank furthest away from the predator. But in the trials with the cooperating mirror, the sticklebacks were two times more likely to venture into the half of the tank closest to the cichlid. The sticklebacks were more adventurous if they had a sidekick. In nature, cooperative behavior would translate to more food, more space, and therefore greater individual reproductive success. Contrary to predictions that selfish behavior or retreat was optimal, Milinski's observation that sticklebacks most often approached the predator together was in line with Axelrod's conclusion that Tit For Tat was the optimal evolutionary strategy.

Milinski's evidence, published in 1987 in the journal Nature, was the first to demonstrate that cooperation based on reciprocity definitely evolved among egoists, albeit small ones. A large body of research now shows that many biological systems, especially human societies, are organized around various cooperative strategies; the scientific methods continue to become more and more sophisticated, but the original experiments and Tit For Tat strategy are beautifully simple.

Boltzmann's Explanation Of The Second Law Of Thermodynamics

"What is your favorite, deep, elegant, or beautiful explanation?" That's a tough question for a theoretical physicist; theoretical physics is all about deep, elegant, beautiful explanations; and there are just so many to choose from.

Personally my favorites are explanations that that get a lot for a little. In physics that means a simple equation or a very general principle. I have to admit though, that no equation or principle appeals to me more than Darwinian evolution, with the selfish gene mechanism thrown in. To me it has what the best physics explanations have: a kind of mathematical inevitability. But there are many people who can explain evolution much better than I, so I will stick to what I know best.

The guiding star for me, as a physicist, has always been Boltzmann's explanation of second law of thermodynamics: the law that says that entropy never decreases. To the physicists of the late 19^th century this was a very serious paradox. Nature is full of irreversible phenomena: things that easily happen but could not possibly happen in reverse order. However, the fundamental laws of physics are completely reversible: any solution of Newton's equations can be run backward and it is still a solution. So if entropy can increase, the laws of physics say it must be able to decrease. But experience says otherwise. For example, if you watch a movie of a nuclear explosion in reverse, you know very well that it's fake. As a rule, things go one way and not the other. Entropy increases.

What Boltzmann realized is that the second law—entropy never decreases—is not a law in the same sense as Newton's law of gravity, or Faraday's law of induction. It's a probabilistic law that has the same status as the following obvious claim; if you flip a coin a million times you will not get a million heads. It simply won't happen. But is it possible? Yes, it is; it violates no law of physics. Is it likely? Not at all. Boltzmann's formulation of the second law was very similar. Instead of saying entropy does not decrease, he said entropy probably doesn't decrease. But if you wait around long enough in a closed environment, you will eventually see entropy decrease: by accident, particles and dust will come together and form a perfectly assembled bomb. How long? According to Boltzmann's principles the answer is the exponential of the entropy created when the bomb explodes. That is a very long time, a lot longer than the time to flip a million heads in a row.

I'll give you a simple example to see how it is possible for things to be more probable one way than the other, despite both being possible. Imagine a high hill that comes to a narrow point—a needle point—at the top. Now imagine a bowling ball balanced at the top of the hill. A tiny breeze comes along. The ball rolls off the hill and you catch it at the bottom. Next, run it in reverse: the ball leaves your hand, rolls up the hill, and with infinite finesse, comes to the top—and stops! Is it possible? It is. Is it likely? It is not. You would have to have almost perfect precision to get the ball to the top, let alone to have it stop dead-balanced. The same is true with the bomb. If you could reverse every atom and particle with sufficient accuracy, you could make the explosion products reassemble themselves. But a tiny inaccuracy in the motion of just one single particle, and all you would get is more junk.

Here's another example: drop a bit of black ink into a tub of water. The ink spreads out and eventually makes the water grey. Will a tub of grey water ever clear up and produce a small drop of ink? Not impossible, but very unlikely.

Boltzmann was the first to understand the statistical foundation for the second law, but he was also the first to understand the inadequacy of his own formulation. Suppose that you came upon a tub that had been filled a zillion years ago, and had not been disturbed since. You notice the odd fact that it contains a somewhat localized cloud of ink. The first thing you might ask is what will happen next. The answer is that the ink will almost certainly spread out more. But by the same token, if you ask what most likely took place a moment before, the answer would be the same: it was probably more spread out a moment ago than it is now. The most likely explanations would be that the ink-blob is just a momentary fluctuation.

Actually I don't think you would come to that conclusion at all. A much more reasonable explanation is that for reasons unknown, the tub started not-so-long-ago with a concentrated drop of ink, which then spread. Understanding why ink and water go one way becomes a problem of "initial conditions". What set up the concentration of ink in the first place?

The water and ink is an analogy for the question of why entropy increases. It increases because it is most likely that it will increase. But the equations say that it is also most likely that it increases toward the past. To understand why we have this sense of direction, one must ask the same question that Boltzmann did: Why was the entropy very small at the beginning? What created the universe in such a special low-entropy way? That's a cosmological question that we are still very uncertain about.

I began telling you what my favorite explanation is, and I ended up telling you what my favorite unsolved problem is. I apologize for not following the instructions. But that's the way of all good explanations. The better they are, the more questions they raise.

The Gaia Hypothesis

For my money, the deepest, most beautiful scientific explanation is the Gaia hypothesis, the idea that Earth's physical and biological processes are inextricably interwoven to form a self-regulating system. This notion—the 1965 brainchild of chemist James Lovelock, further co-developed with microbiologist Lynn Margulis—proposes that air (atmosphere), water (hydrosphere), earth (geosphere or pedosphere) and life (biosphere) interact to form a single evolving system capable of maintaining environmental conditions consistent with life. Lovelock initially put forth the Gaia hypothesis to explain how life on Earth has persisted for 4 billion years despite a 30% increase in the Sun's intensity over that same interval.

But how does Gaia work? Lacking a conscious command-and-control system, Lovelock and Margulis demonstrated that Gaia uses feedback loops to track and adjust key environmental parameters. Take oxygen, a highly reactive by-product of life, generated and continually replenished by photosynthetic algae and plants. The present day atmospheric concentration of oxygen is about 21%. A few percentage points lower and air-breathing life forms could not survive. A few percentage points higher and terrestrial ecosystems would become overly combustible, prone to conflagration. According to the Gaia hypothesis, oxygen-producing organisms have used feedback loops to maintain atmospheric oxygen between these narrow limits for hundreds of millions of years.

Similar arguments, backed by an ever-growing body of research, can be made for other atmospheric constituents, as well as for global surface temperature, oceanic salinity, and other key environmental metrics. Although the Gaia hypothesis highlights cooperation at the scale of the biosphere, researchers have documented multiple examples showing how cooperation at one level could evolve through competition and natural selection at lower levels. Initially criticized by serious scientists as new-age mumbo-jumbo, Lovelock's radical notion has increasingly been incorporated into scientific orthodoxy, and key elements are now often taught as "Earth Systems Science." One timely lesson resulting at least in part from Gaian research is that food web complexity, including higher species diversity, tends to enhance ecological and climate stability.

So, while Earth may inhabit a "Goldilocks zone," neither too close nor too far from the sun, life's rampant success on this "pale blue dot" cannot be ascribed to luck alone. Life has had a direct hand in ensuring its own persistence.

Science has not yet fully embraced the Gaia hypothesis. And it must be admitted that, as an explanation, this idea remains incomplete. The insights cascading from Gaia are unquestionably deep and beautiful, uniting the whole of the biosphere and Earth's surface processes into a single, emergent, self-regulating system

Yet this explanation has yet to achieve the third milestone defined in this year's Edge Annual Question—elegance. The Gaia hypothesis currently lacks the mathematical precision of Einstein's E=Mc². No unified theory of Earth and Life has been presented to explain why life stabilizes more than it destabilizes.

Evolutionary biologist W. D. Hamilton once compared Lovelock's insights to those of Copernicus, adding that we still await the Newton who will define the laws of this grand, seemingly improbable relationship. Hamilton himself became deeply engrossed in seeking an answer to this question, developing a computer model that seemed to show how stability and productivity could increase in tandem. Were it not for his untimely death, Hamilton might have emerged as that modern-day Newton, becoming, in the words of author Tim Flannery, "the most revered biologist of all time."

The cultural implications of Gaia also continue to be debated. Arguably the most profound implication of Lovelock's idea is that Earth, considered as a whole, possesses many qualities of an organism. But is Gaia actually alive, akin to a single life form, or is it more accurate to think of her as a planet-sized ecosystem? Lynn Margulis argued strongly (and convincingly, to my mind) for the latter view. Margulis, whose work revolutionized evolutionary biology at the smallest and grandest of scales, died recently. Always the hard-nosed scientist, she once said,

"Gaia is a tough bitch—a system that has worked for over three billion years without people. This planet's surface and its atmosphere and environment will continue to evolve long after people and prejudice are gone."

While not disagreeing with this blunt assessment, I find considerably greater inspiration in Gaian thinking. Indeed I would go so far as to suggest that this idea can help shift the human perception of nature. In the modernist perspective, the natural world is little more than a collection of virtually infinite resources available for human exploitation. The Gaian lens encourages us to re-envision Earth-bound nature as an intertwined, finite whole from which we evolved, and in which we remain fully embedded. Here, then, is a deep and beautiful perspective in desperate need of broad dissemination.

The Mechanism of Mediocrity

In 1969, a Canadian-born educator named Laurence J. Peter pricked the maidenhead of American capitalism. "In a hierarchy," he stated, "every employee tends to rise to his level of incompetence." He called it the Peter Principle, and it appeared in a book of the same name. The little volume, not even 180 pages long, went on to become the year's top seller, with some 200,000 copies going out bookstore doors. It's not hard to see why. Not only did the Peter Principle confirm what everyone suspected—bosses are dolts—but it explained why this had to be so. When a person excels at a job, he gets promoted. And he keeps getting promoted until he attains a job that he's not very good at. Then the promotions stop. He has found his level of incompetence. And there he stays, interminably.

The Peter Principle was a hook with many barbs. It didn't just expose the dunderhead in the corner office. It took the centerpiece of the American dream—the desire to climb the ladder of success—and revealed it to be a recipe for mass mediocrity. Enterprise was an elaborate ruse, a vector through which the incompetent made their affliction universal. But there was more. The principle had, as a New York Times reviewer put it, "cosmic implications." It wasn't long before scientists developed the "Generalized Peter Principle," which went thus: "In evolution, systems tend to develop up to the limit of their adaptive competence." Everything progresses to the point at which it founders. The shape of existence is the shape of failure.

The most memorable explanations strike us as alarmingly obvious. They take commonplace observations—things we've all experienced—and tease the hidden truth out of them. Most of us go through life bumping into trees. It takes a great explainer, like Laurence J. Peter, to tell us we're in a forest.

The Seen and the Unseen

The simple yet profound explanation of why people get themselves into serious epistemological trouble and propose idiotic policies and harebrained ideas is that they ignore the Law of Unintended Consequences. Often enough, when considering a given idea, proposal, option, or policy, people will focus only its beneficial consequences and ignore the negative or damaging ones, which may be further off in time and harder to foresee. But practically every human action entails a substantial network of consequences, and so a rational assessment of any proposal ought to take into account all of its effects, the obvious and the non-obvious, the intended and the unintended, not just those that immediately leap to the eye.

The core notion was captured most clearly by the French economist Frédéric Bastiat, who in 1850 wrote an essay called "That Which is Seen and That Which is Unseen." In it he describes a little boy's accidentally throwing a ball through a shopkeeper's window. Bystanders console the shopkeeper by telling him that, despite his loss, the accident will be a boon to the glazier, who will replace the window for six francs.  (Today this is known as "job creation.") 

True enough, the glazier benefits. "But," says Bastiat, "that is only what is seen. It is not seen that as our shopkeeper has spent six francs on one thing, he cannot spend them on another. It is not seen that if he had not had a window to replace, he would, perhaps, have replaced his old shoes, or added another book to his library. In short, he would have employed his six francs in some way, which this accident has prevented."

This so-called "parable of the broken window" has been exploited by free-market economists to oppose many ostensibly "humanitarian" government interventions that, they argue, have negative unintended consequences further down the line. Rent control, for example, while keeping some housing affordable is said to reduce the livability and availability of apartments that landlords can no longer afford to maintain. 

But the lesson of the seen and the unseen is far more encompassing in scope than its applications within the dismal science. For example, species are sometimes introduced to ecological systems with a specific, narrow purpose in mind, whereas their actual introduction is accompanied by ripple effects that go well beyond the original purpose it was intended to serve. A well-known example is the importation and breeding of cane toads in Australia in order to control the cane beetle, a pest that ravaged sugar cane crops. But not only didn't they control the cane beetle, the toads themselves soon proliferated so wildly that they became major pests in their own right, and had the further effect of converting kindly, animal-loving citizens into raging maniacs on public roads and highways on which drivers, day and night, would swerve right and left in order to run over and flatten (with a loud "pop") as many of the monsters as came into view. (In addition, a group of otherwise sane golfers placed powerful lights on golf courses to attract the toads so that they could hit them with golf clubs and propel these amphibian golf balls across the fairways to their deaths, a scheme that in any case didn’t work: "Nine times out of ten the cane toad will get up and hop away," said one unamused critic of the practice.) 

More recently, ethanol has been added to gasoline with the intention of reducing our dependence of foreign petroleum. That is what is seen. As for what is unseen, consider the set of ripple effects described by a team of energy specialists (in a 2007 piece actually entitled "The Ripple Effect: Biofuels, Food Security, and the Environment"). Since ethanol was made from corn, the increased demand for corn caused prices to rise (to wit, from $2.60 per bushel in July 2006 to $4.25 per bushel in March 2007). Higher corn prices in turn meant higher prices for corn-fed beef. It also meant that a basic food crop was made more expensive for food-insecure people who could least afford a price rise. Further ripple effects were massive increases in farmland values (making new acreage more dear to farmers), and greater use of artificial fertilizers, with increased runoffs and negative implications for nitrogen and phosphorous losses to groundwater, surface water, and the atmosphere. And so on.

Moral of the story: When entertaining the merits of some grand new miracle idea, look beyond the obvious.

Beautiful, Elegant, And … Absolutely Wrong

On April 25, 1953, in a short note to Nature entitled "Molecular structure of nucleic acids", James Watson and Francis Crick announced their deduction of the double-helix structure of DNA. Their remarkable article famously ends with one of the most laconic understatements in all of science: "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material." Indeed, the double-strands of DNA, each a mirror image of the other, explains how cells can replicate—the "secret of life" as Watson and Crick modestly announced to the startled clientele of The Eagle pub in Cambridge during a break in their labors. But the most remarkable thing about this beautiful and elegant discovery is that it is not remarkable enough to be the topic of this essay.

In fact, their structure held the key to something far more subtle and arguably of even greater fundamental importance than the mechanism for genetic replication. What Watson and Crick had uncovered was a window on the world's oldest fossil, one which sheds light not only on the static structure of modern molecular biology, but also on the dynamical processes leading to the emergence of life on Earth! The unraveling of this story is a fascinating episode in the history of science, because it involves not one, but two beautiful and elegant ideas, each of which is absolutely and unequivocally wrong! And tellingly, each beautiful but flawed idea was conceived by a physicist trying to understand biology as a jigsaw puzzle at the molecular scale. As we proceed into the second decade of this "century of biology", flooded by data but starved of fundamental insight, we will do well to resist the temptation to build biology on naïve, static principles of beauty and elegance that seemingly serve so well in the physical sciences.

Watson and Crick had shown how to pack together the four molecules ("nucleotides"—known concisely by the symbols A,C,G,T) making up DNA into a structure that fitted X-ray measurements of the atomic positions. The precise sequence of the symbols A,C,G,T somehow encoded the composition of proteins, known to be built up from a palette of twenty small molecules known as amino acids. It was the physicist George Gamow who a year later pointed out that the "key-and-lock" relation between the nucleotides of the DNA structure exhibited diamond-shaped holes, and that for geometrical reasons, these diamonds were specified by the three surrounding nucleotides. Gamow enumerated all such holes, and discovered that there were twenty different types of hole—one for each amino acid! Thus was born the idea of a "genetic code": the stupendously complicated biochemical processes going on inside every cell to make proteins could be reduced down to a simple code table, easily able to fit on a tee-shirt, that told you how to read DNA and translate its message into the proteins of living cells.

Gamow's ingenious idea for a genetic code was absolutely wrong, but serendipitously he did get right that triplets of nucleotides ("codons") code for the twenty amino acids of life. But how do they? If you write down all possible triplets of ACGT, you'll find that there are 64 (4x4x4) possible sets of three letters or codons. Evidently some of these possible codons must code for the same amino acid, or else the cell would use 64 amino acids. If the codons were doublets, then there would only be 16 (4x4) possible sets of such letters, and that would not be enough to specify each of the 20 amino acids used by life. So we are stuck with triplets, and evidently some of these triplets code for the same amino acid.

And now there are two mysteries: not only what is the code, but also, why are only 20 amino acids used by life?

These questions were answered in a brilliant article published by Crick, Griffith and Orgel in 1957. Let's follow Crick and friends, as they try to hack the genome, reverse engineering the genetic code by appealing to a logic that one might mischievously call "intelligent design". Let's suppose that we have a section of the message six characters long, some small part of the three billion characters of the human genome:

… ACGGAC …

Knowing about triplet codons, you would parse this as

ACG, GAC,

But, you say, how do we know that the first letter, the A, is actually where the message starts? Maybe the A is the last symbol in the previous codon (the … above), and the message should be parsed as

…A, CGG, AC …

with the last AC the start of the following codon. In other words, if you set out to transmit a code in this way, what would be the smart way to remove this sort of ambiguity? Crick et al. proposed that you construct the code such that it only makes sense when read with the correct starting point. In other words, you make a code in which ACG and GAC stand for meaningful symbols (in this case the amino acids Threonine and Aspartic acid), but CGG would be meaningless. Such a code can be read in only one way, so it requires no punctuation: it is what they called a "comma-less code". The beautiful discovery of Crick et al. is that the maximum number of symbols (ie. amino acids) that can be encoded in this way with triplets is twenty. And so, they concluded, Nature had been forced to work only with twenty amino acids, and not a much larger set, in order to build proteins, because it was a mathematical impossibility to construct a comma-less genetic code with more amino acids.

From their reasoning, it is not difficult to enumerate the possible comma-less genetic codes. There are 288 of them. But the actual genetic code, conclusively determined during the 1960's, is not one of them!

Beautiful, elegant, and absolutely wrong: key-and-lock mechanisms have been important in understanding snapshots of biological structure, but they are misleading clues in the search to understand the dynamical processes of evolution that have led to the phenomenon of life. Far richer than Gamow and Crick conceived, the genetic code is now thought to have been shaped rapidly over evolutionary time through the cooperative dynamics of early organisms, thus ensuring a code that is remarkably robust to errors in translation and mutations of the genome sequence. Only with such a code could such complex organisms as you and me evolve. And that is the real secret of life. 

Fact, Fiction, and Our Probabilistic World

How do we separate fact from fiction? We are frequently struck by seemingly unusual coincidences. Imagine seeing an inscription describing a fish in your morning reading, then at lunch you are served fish and the conversation turns to "April fish" (or April fools). That afternoon a work associate shows you several pictures of fish and in the evening you are presented with an embroidery of fish-like sea monsters. The next morning a colleague tells you she dreamed of fish. This might be starting to seem spooky. It actually turns out that we shouldn't find this surprising. The reason why has a long history resulting in the unintuitive insight of building randomness directly into our understanding of nature, through the probability distribution.

Chance as Ignorance

Tolstoy was skeptical of our understanding of chance. He gave an example of a flock of sheep where one had been chosen for slaughter. This one sheep was given extra food separately from the others and Tolstoy imagined that the flock, with no knowledge of what was coming, must find the continually fattening sheep extraordinary—something he thought the sheep would assign to "chance" due to their limited viewpoint. Tolstoy's solution was for the sheep to stop thinking that things happen only for "the attainment of their sheep aims" and realize that there are hidden aims that explain everything perfectly well, and so there is no need to resort to the concept of chance.

Chance as an Unseen Force

Eighty-three years later Carl Jung published a similar idea in his well-known essay "Synchronicity, An Acausal Connecting Principle." He postulated the existence of a hidden force that is responsible for the occurrence of seemingly related events that otherwise appear to have no causal connection. The initial story of the six fish encounters is Jung's, taken from his book. He finds this string of events unusual, too unusual to be ascribable to chance. He thinks something else must be going on—and labels it the acausal connecting principle.

Persi Diaconis, Stanford Professor and former professor of mine, thinks critically about Jung's example: suppose we encounter the concept of fish once a day on average according to what statisticians call a "Poisson process" (another fish reference!). The Poisson process is a standard mathematical model for counts, for example radioactive decay seems to follow a Poisson process. The model presumes a certain fixed rate at which observations appear on average and otherwise they are random. So we can consider a Poisson process for Jung's example with a long run average rate of one observation per 24 hours and calculate the probability of seeing six or more observations of fish in a 24 hour window. Diaconis finds the chance to be about 22%. Seen from this perspective, Jung shouldn't have been surprised.

The Statistical Revolution: Chance in Models of Data Generation

Only about two decades after Tolstoy penned his lines about sheep, Karl Pearson brought about a statistical revolution in scientific thinking with a new idea of how observations arose, the same idea used by Diaconis in his probability calculation above. Pearson suggested that nature presents data from an unknown distribution but with some random scatter. His insight was that this is a different concept from measurement error, which adds additional error when the observations are actually recorded.

Before Pearson, science dealt with things that were "real," such as laws describing the movement of the planets or blood flow in horses, to use examples from David Salsburg's book, The Lady Tasting Tea. What Pearson made possible was a probabilistic conception of the world. Planets didn't follow laws with exact precision, even after accounting for measurement error. The exact course of blood flow differed in different horses, but the horse circulatory system wasn't purely random. In estimating distributions rather than the phenomena themselves, we are able to abstract a more accurate picture of the world.

Chance Described by Probability Distributions

That measurements themselves have a probability distribution was a marked shift from confining randomness to the errors in the measurement. Pearson's conceptualization is useful because it permits us to estimate whether what we see is likely or not, under the assumptions of the distribution. This reasoning is now our principal tool for judging whether or not we think an explanation is likely to be true.

We can, for example, quantify the likelihood of drug effectiveness or carry out particle detection in high energy physics. Is the distribution of the mean response difference between drug treatment and control groups centered at zero? If that seems likely, we can be skeptical of the drug's effectiveness. Are candidate signals so far from the distribution for known particles that they must be from a different distribution, suggesting a new particle? Detecting the Higgs boson requires such a probabilistic understanding of the data to differentiate Higgs signals from other events. In all these cases the key is that we want to know the characteristics of the underlying distribution that generated the phenomena of interest.

Pearson's incorporation of randomness directly into the probability distribution enables us to think critically about likelihoods and quantify our confidence in particular explanations. We can better evaluate when what we see has special meaning and when it does not, permitting us to better reach our "human aims." 

Evolution By Natural Selection

My Edge answer this year has to be evolution by natural selection. Not only does it explain how we all got here and how we are and behave as we do, it can even explain (at least to my fairly critical satisfaction) why many people refuse to accept it and why even more people believe in an all-powerful Deity. But since other Edge respondents are likely to have natural selection as their favorite deep, elegant, and beautiful explanation (it has all three attributes, in addition to wide ranging explanatory power), I'll have to hone in on one particular instance: the explanation of how humans acquired language—by which I mean grammatical structure.

There is evidence to suggest that our ancestors developed effective means to communicate using verbal utterances starting at least 3 million years ago. But grammar is much more recent, perhaps as recent as 75,000 years ago. How did grammar arise?

Anyone who has traveled abroad knows that to communicate basic needs, desires, and intentions to people in your vicinity, concerning objects within sight, a few referring words, together with gestures, suffice. The only grammar required is to occasionally juxtapose two words—"Me Tarzan, you Jane" being the information- (and innuendo-) rich, classic example from Hollywood. Anthropologists refer to such a simple, word-pairing, communicative system as protolanguage.

But to communicate about things not in the immediate here-and-now, you need more. Significantly, effectively planning future joint activities needs pretty well all of grammatical structure, particularly if the planning involves more than two people, with even more demands put upon the grammar if the planned action requires coordination between different groups not all present at the same place or time.

Given the degree to which human survival depends on our ability to plan and coordinate our actions—and to collectively debrief after things go wrong so we avoid repeating our mistakes (though at a national level we seem really bad at doing that)—it is clear that grammatical structure is hugely important to Homo sapiens. Indeed, many argue that is our defining characteristic. But communication, while arguably the killer app for grammar, clearly cannot be what put it into the gene pool in the first place, and for a very simple reason. Since grammar is required in order for verbal utterances to convey more complex ideas than is possible with protolanguage, it only comes into play when the brain can form such complex ideas. These considerations lead to what I think is accepted (though not without opposition) as the "Standard Explanation" of language acquisition.

In highly simplified terms, the Standard Explanation runs like this.

1. Brains (or the organs that became brains) first evolved to associate motor responses to sensory input stimuli.

2. In some creatures, brains became more complex, performing a mediating role between input stimuli and motor responses.

3. In some of those creatures, the brain became able to over-ride what was previously an automatic stimulus-response sequence.

4. In Homo sapiens, and to a lesser extent in other species, the brain acquired the ability to function "off-line", effectively running simulations of actions without the need for sensory input stimuli and without generating output responses.

Stage 4 is when the brain acquires grammar. What we call grammatical structure is in fact a descriptive/communicative manifestation of a mental structure for modeling the world.

As a mathematician, what I like about this explanation is that it also tells us where the brain got its capacity for mathematical thinking. Namely, mathematical thinking is essentially another manifestation of the brain's simulation capacity, but in quantitative/relational/logical terms rather than descriptive/communicative.

As is usually the case with natural selection arguments, it takes considerable work to flesh out the details of these simplistic explanations, and some days I am less convinced than others about some aspects, but overall they strike me as about right. In particular, the mathematical story explains why doing mathematics carries with it an overpowering Platonistic sense of reasoning not about abstractions but real objects—at least "real" in a Platonic realm. At which point, the lifelong mathematics educator in me says I should leave the proof of that corollary as an exercise for the reader—so I shall.

The Power of Absurdity

The notion of a transcendent force that moves the universe or history or determines what is right and good—and whose existence is fundamentally beyond reason and immune to logical or empirical disproof—is the simplest, most elegant, and most scientifically baffling phenomenon I know of. Its power and absurdity perturbs mightily, and merits careful scientific scrutiny. In an age where many of the most volatile and seemingly intractable conflicts stem from sacred causes, scientific understanding of how to best deal with the subject has also never been more critical.

Call it love of Group or God, or devotion to an Idea or Cause, it matters little in the end. This is the "the privilege of absurdity; to which no living creature is subject, but man only" of which Hobbes wrote in Leviathan. In The Descent of Man, Darwin cast it as the virtue of "morality," with which winning tribes are better endowed in history's spiraling competition for survival and dominance. Unlike other creatures, humans define the groups to which they belong in abstract terms. Often they strive to achieve a lasting intellectual and emotional bonding with anonymous others, and seek to heroically kill and die, not in order to preserve their own lives or those of people they know, but for the sake of an idea—the conception they have formed of themselves, of "who we are."

Sacred and religious ideas are culturally universal, yet content varies markedly across cultures. [Religious conceptions and sacred, or transcendental, values often go together but aren't quite the same: sacred values—like dignity or honor, love of country or racial purity, devotion to jihad or humanity, or even sometimes to science—share with core religious values immunity to cost-benefit considerations and appear to drive actions independently, or all out of proportion, to likely prospects of success]. Sacred values mark the moral boundaries of societies and determine which material transactions are permissible. Material transgressions of the sacred are taboo: we consider people who sell their children or sell out our country to be sociopaths; other societies consider adultery or disregard of the poor equally immoral, but not necessarily selling children or women or denying freedom of expression.

Sacred values usually become terribly relevant only when challenged, much as food takes on overwhelming value in people's lives only when denied. People in one cultural milieu are often unaware of what's sacred for another; or, in becoming aware through conflict, find immoral and absurd the other side's values (pro-life vs pro-choice).Such conflicts cannot be wholly reduced to secular calculations of interest but must be dealt with on their own terms, a logic different from the marketplace or realpolitik. For example, cross-cultural evidence indicates that prospects of crippling economic burdens and huge numbers of deaths don't necessarily sway people from choosing whether or not to go to war, or to opt for revolution or resistance. As Darwin noted, the virtuous and brave do what is right, regardless of consequences, as a moral imperative. Indeed, we have suggestive neuroimaging evidence that people process sacred values in parts of the brain that are devoted to rule-bound behavior rather than utilitarian calculations (think: "Ten Commandments" or "Bill of Rights").

There is an apparent paradox that underlies the formation of large-scale human societies. The religious and ideological rise of civilizations—of larger and larger agglomerations of genetic strangers, including today's nations, transnational movements, and other "imagined communities" of fictive kin — seem to depend upon what Kierkegaard deemed this "power of the preposterous" (as in Abraham's willingness to slit the throat of his most beloved son to show commitment to an invisible, no-name deity, thus making him the world's greatest culture hero, rather than a child abuser, would-be murderer or psychotic). Humankind's strongest social bonds and actions, including the capacity for cooperation and forgiveness, and for killing and allowing oneself to be killed, are born of commitment to causes and courses of action that are "ineffable," that is, fundamentally immune to logical assessment for consistency and to empirical evaluation for costs and consequences. The more materially inexplicable one's devotion and commitment to a sacred cause — that is, the more absurd—the greater the trust others place in it and the more that trust generates commitment on their part.

To be sure, thinkers of all persuasions have tried to give explanations of the paradox, most being ideologically motivated and simple-minded: often to show that religion is good or, more usual, that religion is unreasonably bad. If anything, evolution teaches that humans are creatures of passion, and that reason itself is primarily aimed at social victory and political persuasion rather than philosophical or scientific truth. To insist that persistent rationality is the best means and hope for victory over enduring irrationality—that logical harnessing of facts could someday to do away with the sacred and so end conflict—defies all that science teaches about our passion-driven nature. Throughout the history of our species, as for the most intractable conflicts and greatest collective expressions of joy today, utilitarian logic is a pale prospect to replace the sacred.

For Alfred Russel Wallace, moral behavior (along with mathematics, music and art) was evidence that humans had not evolved through natural selection alone:

"The special faculties we have been discussing clearly point to the existence in man of something which has not derived from his animal progenitors — something which we may best refer to as being of a spiritual essence… beyond all explanation by matter, its laws and forces."

Of course, this didn't sit well with Darwin: "I hope you have not murdered too completely your own and my child," he lamented in a letter to Wallace. But Darwin himself produced no causal account of how humans became moral animals, other than to say that because our ancestors were so physically weak, only group strength could get them through. Religion and the sacred, banned so long from reasoned inquiry by ideological bias of all persuasions—perhaps because the subject is so close to who we want or don't want to be—is still a vast, tangled and largely unexplored domain for science, however simple and elegant for most people everywhere in everyday life.

Observers Observing

Hormesis Is Redundancy

Nature is the master statistician and probabilist. It follows a certain logic based on layers of redundancies, as a central risk-management approach. Nature builds with extra spare parts (two kidneys), and extra capacity in many, many things (say lungs, neural system, arterial apparatus, etc.), while design by humans tend to be spare, overoptimized, and have the opposite attribute of redundancy, that is, leverage—we have a historical track record of engaging in debt, which is the reverse of redundancy (fifty thousand in extra cash in the bank or, better, under the mattress, is redundancy; owing the bank an equivalent amount is debt).

Now, remarkably, the mechanism called hormesis is a form of redundancy and statistically sophisticated in ways human science (so far) has failed us.

Hormesis is when a bit of a harmful substance, or stressor, in the right dose or with the right intensity, stimulates the organism and makes it better, stronger, healthier, and prepared for a stronger dose the next exposure. That's the reason we go to the gym, engage in intermittent fasting, or caloric deprivation, or overcompensate for challenges by getting tougher. Hormesis lost some scientific respect, interest and practice after the 1930s partly because some people mistakenly associated it with the practice of homeopathy. The association was unfairly done as the mechanisms are extremely different. Homeopathy relies on other principles, such as the one that minute, highly diluted parts of the agents of a disease (so small they can hardly be perceptible, hence cannot cause hormesis) could help medicate against the disease itself. It has shown little empirical backing and belongs today to alternative medicine, while hormesis, as an effect, has shown ample scientific evidence.

Now it turns out that the logics of redundancy and overcompensation are the same—as if nature had a simple elegant and uniform style in doing things. If I ingest, say, fifteen milligrams of a poisonous substance, my body will get stronger, preparing for twenty, or more. Stressing my bones (karate practice or carrying water on my head) will cause them to prepare for greater stress, by getting denser and tougher. A system that overcompensates is necessarily in overshooting mode, building extra capacity and strength, in anticipation for the possibility of a worse outcome, in response to information about the possibility of a hazard. This is a very sophisticated form of discovering probabilities via stressors. And of course such extra capacity or strength becomes useful—in itself—as opportunistic as it can be used to some benefit even in the absence of the hazard. Redundancy is an aggressive, not a defensive approach to life.

Alas, our institutional risk management methods are vastly different. Current practice is to look in the past for worst-case scenario, called "stress test" and adjust accordingly, never imagining that, just as the past experienced a large deviation that did not have a predecessor, that such deviation might be insufficient. For instance, current systems take the worst historical recession, the worst war, the worst historical move in interest rates, the worst point in unemployment, etc., as an anchor for the worst future outcome. Many of us have been frustrated—very frustrated—by the method of stress testing in which people never go beyond what has happened before and even had to face the usual expression of naive empiricism, "do you have evidence?" when suggesting that we need to consider worse.

And, of course, these systems don't do the recursive exercise in their mind to see the obvious, that the worst past event itself did not have a predecessor of equal magnitude, and that someone using the past worst case in Europe before the Great War would have been surprised. I've called it the Lucretius underestimation, after the Latin poetic philosopher who wrote that the fool believes that the tallest mountain there is should be equal to tallest one he has observed. Danny Kahneman's wrote, using as backup the works of Howard Kunreuther, that "protective actions, whether by individuals or by governments, are usually designed to be adequate to the worst disaster actually experienced (...) Images of even worse disaster do not come easily to mind." For instance, in Pharaonic Egypt, scribes have tracked the high-water mark of the Nile and used it as worst-case scenario. No economist had tested the obvious: do extreme events fall according to the past? Alas, backtesting says: no, sorry.

The same dangerous recklessness can be seen in the methodology used for the Fukushima nuclear reactor, built to the worst past outcome, and not imagining and extrapolating to much worse. Well, nature, unlike risk engineers, prepares for what has not happened before, assuming worse harm is possible.

So if humans fight the last war, nature fights the next war. Of course, there is a biological limit to our overcompensation.

This form of redundancy remains vastly more extrapolative than our minds that are intrapolative.

The great Benoit Mandelbrot, now gone for a year, saw the same fractal self-similarity in nature and in probabilities of historical and economic events. It is thrilling to see how the two domains unite under the notion of fractal-based redundancy.

p.s. The word "fitness" in the common scientific discourse does not appear to be precise enough. I am unable to figure out if what is called "Darwinian fitness" is merely intrapolative adaptation to current environment, or if it contains an element of statistical extrapolation. In other words, there is a significant difference between robustness (is not harmed by stressor) and what I've called antifragility (i.e., gains from stressors).

A Sphere

Most scientific facts are based on things that we cannot see with the naked eye or hear by our ears or feel by our hands. Many of them are described and guided by mathematical theory. In the end, it becomes difficult to distinguish a mathematical object from objects in nature.

One example is the concept of a sphere. Is the sphere part of nature or it is a mathematical artifact? That is difficult for a mathematician to say. Perhaps the abstract mathematical concept is actually a part of nature. And it is not surprising that this abstract concept actually describes nature quite accurately.