Rebooting the cosmos?

[jackfoxy]

http://motls.blogspot.com/2011/06/rebooting-cosmos.html

[jerf]

This debate always reminds me of an older debate, about how the universe must have a maximum speed, and how the universe can not have a maximum speed, as outlined in [1]. The resolution was ultimately that yes, both were actually true, and the failure of understanding was somewhere else entirely: Galilean transforms are the wrong way to add two velocities, you need Lorentz transforms, and both of Zeno's arguments are thus satisfied.

Similarly, while you don't get it from this source as he has made his decision, there are some reasons why everyone has gone to discrete models. But I suspect the ultimate resolution will have both elements, which the essay does mention at the end, and that contra what the author says, there won't be an "ultimate" to either of them; I bet the universe can not be discrete and it can not be continuous, and the truth is some weird combo of the two in which ultimately the question is simply sidestepped, not resolved, much like the resolution to Zeno's paradoxes.

[1]: http://www.mathpages.com/rr/s3-07/3-07.htm

[dto1138]

Hey, I'm not a particle physicist, but I've read a bunch of books by people who think the universe is a computer. (Three Scientists and Their Gods, A New Kind Of Science, and The Recursive Universe (this last is out of print and much better than Wolfram's newer but more turgid ANKOS.)

I don't think the universe is a computer either, but I don't think this guy understands what that would mean anyway.

From the article: "I just find it obvious that pretty much by definition, discrete objects are always less fundamental and less complete than the continuous ones. A discrete description of some object or phenomenon is always an approximation."

Now the whole thrust of the "computer-universe-ism" people's argument, if I read them correctly, is that the universe is really a discrete structure, in which case a discrete model of said structure would not be ANY kind of approximation. I.e. to what are the integers (a discrete structure) a (supposedly poor) approximation? What about the two-element set {0,1} or (say) groups? (The group theory bit is a trick for the author.)

We'd better leave these questions to be answered by empirical data---or if we need philosophers to chime in, better ones than this.

[andrewflnr → dto1138]

I think his point regarding whether discrete or continuous descriptions are more fundamental is that you can (always?) describe a discrete system continuously, but you can't always reduce a continuous system to a discrete description. Continuity is more general, and since we seem to see it a lot, it's probably the way the universe actually works.

At least that's how I feel about it. But hey, I'm not a particle physicist either.

[btilly]

It should be noted the Motl is a prominent physicist who is very smart, very sure of himself, very outspoken, and sometimes very wrong. See http://en.wikipedia.org/wiki/Lubo%C5%A1_Motl for more.

That said he makes good points, and knows physics much, much better than most of the people proposing digital theories.

[russell]

The universe is continuous not discrete and those who believe otherwise are insane. I'll take his word for it. It is certainly outside my comfort zone, but interesting nonetheless.

[shin_lao]

Or you could use Gödel's incompleteness theorems and say the universe cannot be a computer (as we understand it) because computers (as we understand them) are part of the universe and therefore cannot describe the universe.

Then the discussion could go on and you could reach a definition of "computer" vague enough to be able to say "the universe is a computer".

[Sniffnoy → shin_lao]

...that is not what the incompleteness theorem says.

[jackfoxy → Sniffnoy]

Yes. I'm not a mathematician, but I believe Gödel's incompleteness theorems only address arithmetic. I heard of a book that focuses on common misuses of Gödel's theorems, but don't have a reference. Anyone know of such a book?