2011 : WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY'S COGNITIVE TOOLKIT?

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Software Pioneer; Philosopher; Author, "The History of the Future", "Frax—the first Realtime Fractals", "Chron—A Timeline of Literature"
Einstein's Blade in Ockham's Razor

In 1971, when I was a teenager, my father died in a big airplane crash. Somehow I began to turn 'serious', trying to understand the world around me and my place in it, looking for meaning and sense, beginning to realize: everything was very different than I had previously assumed in the innocence of childhood.

It was the beginning of my own "building a cognitive toolset" and I remember the pure joy of discovery, reading voraciously and — quite out of sync with friends and school — I devoured encyclopedias, philosophy, biographies and... science fiction.

One such story stayed with me and one paragraph within it especially:
"We need to make use of Thargola's Sword! The principle of Parsimony. 
First put forth by the medieval philosopher Thargola14, who said, 
'We must drive a sword through any hypothesis that is not strictly necessary"

That really made me think — and rethink again...
Finding out who this man might have been took quite a while, but it was also another beginning: a love affair with libraries, large tomes, dusty bindings... surfing knowledge, as it were.

And I did discover: there had been a monk named Guillelmi, from a hamlet surrounded by oaks, apocryphally called 'William of Ockham'. He crossed my path again years later when lecturing in Munich near Occam Street, realizing he had spent the last 20 years of his life there, under King Ludwig IV in the mid 1300s.

Isaac Asimov had pilfered, or let's say homaged, good old Guillelmi for what is now known in many variants as "Ockham's razor", such as 
"Plurality should not be posited without necessity."
"Entities are not to be multiplied beyond necessity"
or more general and colloquial and a bit less transliterated from Latin:
A simpler explanation invoking fewer hypothetical constructs is preferrable.

And there it was, the dancing interplay between Simplex and Complex, which has fascinated me in so many forms ever since. For me, it is very near the center of "understanding the world", as our question posited.

Could it really be true, that the innocent sounding 'keep it simple' is really such an optimal strategy for dealing with questions large and small, scientific as well as personal? Surely, trying to eliminate superflous assumptions can be a useful tenet, and can be found from Sagan to Hawking as part of their approach to thinking in science. But something never quite felt right to me — intuitively it was clear that sometimesthings are just not simple — and that merely "the simplest" of all explanations cannot be taken as truth or proof.

Any detective story would pride itself in not using the most obvious explanation who did it or how it happened. 
Designing a car to 'have the optimal feel going into a curve at high speed' will require hugely complex systems to finally arrive at "simply good". 
Water running downhill will take a meandering path instead of the straight line.

Both are examples for a domain shift: the non-simple solution is still "the easiest" seen from another viewpoint: for the water the least energy used going down the shallowest slope is more important than taking the straightest line from A to B.

And that is one of the issues with Ockham: 
The definition of what "simple" is — can already be anything but simple.
And what "simpler" is — well, it just doesn't get any simpler there.

There is that big difference between simple and simplistic.
And seen more abstractly, the principle of simple things leading to complexity dances in parallel and involved me deeply throughout my life.

In the early seventies I also began tinkering with the first large scale modular synthesizers, finding quickly how hard it is to recreate seemingly 'simple sounds'.
There was unexpected complexity in a single note struck on a piano that eluded even dozens of oscillators and filters, by magnitudes.

Lately one of many projects has been to revisit the aesthetic space of scientific visualizations, and another, which is the epitomy of mathematics made tangible: Fractals — which I had done almost 20 years ago with virtuoso coder Ben Weiss, now enjoying them via realtime flythroughs on a handheld little smartphone. 
Here was the most extreme example: a tiny formula, barely one line on paper, used recursively iterated it yields worlds of complex images of amazing beauty.
(Ben had the distinct pleasure of showing Benoit Mandelbrot an alpha version at the last TED just months before his death)

My hesitation towards overuse of parsimony was expressed perfectly in the quote by Albert Einstein, arguably the counterpart "blade" to Ockham's razor:
"Things should be made as simple as possible — but not simpler"

And there we have the perfect application of its truth, used recursively on itself: Neither Einstein nor Ockham actually used the exact words as quoted!

After I sifted through dozens of books, his collected works and letters in German, the Einstein archives: nowhere there, nor in Britannica, Wikipedia or Wikiquote was anyone able to substantiate exact sources, and the same applies to Ockham. If anything can be found, it is earlier precedences...;)

Surely one can amass retweeted, reblogged and regurgitated instances for both very quickly — they have become memes, of course. One could also take the standpoint that in each case they certainly 'might' have said it 'just like that', since each used several expressions quite similar in form and spirit.
But just to attribute the exact words because they are kind of close would be, well..another case of: it is not that simple!

And there is a huge difference between additional and redundantinformation.
(Or else one could lose the second redundant "ein" in "Einstein" ?)

Linguistic jesting aside: Nonetheless, the Razor and the Blade constitute a very useful combination of approaching analytical thinking. 
Shaving away non-essential conjectures is a good thing, a worthy inclusion in "everybody's toolkit" — and so is the corollary: not to overdo it!

And my own bottom line: There is nothing more complex than simplicity.