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.