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roystgnr comments on Rationality Quotes February 2014 - Less Wrong
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N.B. This assertion seems pretty falsifiable. If the laws of physics turn out to be particularly simple then we'll be forced to conclude that the universe is special.
And, wait for it...
(no, seriously, wait 5 seconds for it)
the laws of physics did turn out to be particularly simple. In the 5 seconds you were waiting, did the air wafting around the room obey Navier-Stokes, or Navier-Stokes+a-dragon-randomly-appears? Both of those are fine, formalizable mathematical rules; one just happens to be much much simpler than the other.
And because the observed laws of physics are so particularly simple, they are dwarfed in number by mathematically possible more complex laws that we never observe. Choose between "Navier-Stokes" and "Navier-Stokes+dragon-after-half-a-second" and "Navier-Stokes+dragon-after-a-quarter-second" and so on; why do you expect to see the former rule rather than any of the infinite collection of latter rules? Without some kind of special privileged probability measure, we have no reason to expect to be in such a special universe, but here we are.
Laws of physics are not some deep mysterious algorithms built into the universe when it was created, they are human approximations of the infinite complexity we observe. As long as the universe is at least somewhat predictable and not completely random, it is possible to construct a series of increasingly accurate ways to predict its behavior. If the universe included predictable dragons after half a second, these approximations would, too. In fact, the Navier Stokes equations happen to describe so many dragons, there is still an open Millennium problem related to them. If the dragons appear unpredictably... well, then, it's just like the universe we already live in, where the unpredictability is everywhere (if you doubt that, please tell me the results of tomorrow's lottery).
So no, our universe is not particularly simple. It's mostly, to quote a historian, "one damned thing after another".
Perhaps "Navier-Stokes" and "complexity" and such are (ironically) overcomplicating things. Let's try to simplify:
I just walked out of a room with blue walls.
Is there a mathematically consistent universe in which, when I walk back in, the walls will have spontaneously turned red? Yellow? Plaid? (hint: for a universe with a set of physical rules S, is there anything mathematically inconsistent about the set "S union that-room-spontaneously-turns-red-in-2-minutes"?)
If all mathematically consistent universes exist and there is no special probability distribution preferring some over others, what subjective probability should I assign to the expectation that I will see the same shade of blue walls?
In the real world, what subjective probability should I assign?
If the previous two answers are different (for example, if the first probability is epsilon and the second is one minus epsilon...), why is that so?
What would you say the complexity of our laws of physics is? Feel free to choose your own definition of complexity and give no better than a back-of-napkin estimate.
I suppose you can estimate the complexity of a particular approximate equation as the number of bit required to simulate it in a particular setup. I did something like that for the Schrodinger equation here a couple of years ago, frustrated by Eliezer's empty theorizing, but I cannot find my comment anymore. Anyway, it was basically the length of the computer code which simulates the equation, so not that large, maybe tens or hundreds of kilobytes. You have to keep adding other codes to describe the necessary math and physics, and pretty soon you have to count a large chunk of the scientific and engineering software required to simulate the physical phenomena and engineering machinery, with a multitude of special cases for special dragons. And we still cannot simulate everything we see.
If the universe is somwhat predictable and not completely random, it is not nfinitely complex.
I don't see what you base this assertion on. Also, consider paying attention to your spellchecker.
The information-theoretic definition of entropy, Chaitin, etc.