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delirium happy

Just keep on trying till you run out of cake

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Warning. Contains geeking.
rho meson
(Most of you probably couldn't care less about this, but it's been annoying me and I had to get it out.)

Today's xkcd is bugging the crap out of me. It's bugging the crap out of me because I'm fairly sure that it wouldn't work, but not entirely sure, and I can't quite manage to convince myself that it definitely wouldn't.

See, I think the problem is with randomness and determinism. Quantum physics is an inherently random phenomenon. It's probabilistic; we can say "there is a 72.943% chance that this will happen" but we can't say when it will. Even with complete and absolute knowledge of the current state of the universe, the future is not predictable.

On the other hand, a Turing machine is entirely deterministic. Given its current state, all its future states are implied exactly. A Turing machine is not capable of generating random numbers, and so isn't capable of accurately representing the physics of our universe.

It could manage pseudo-random numbers, for sure, but they wouldn't suffice. With an arbitrarily large Turing machine, you could generate pseudo-random numbers that were arbitrarily close to being truly random numbers, but I don't think that's good enough. Chaos type things would ensure that even the smallest divergence from true randomness could have potentially major implications.

The problem in my reasoning comes with the infinities involved. Yes, I could argue that the Turing machine the character has created isn't infinite, since he mentions a specific, finite length of time, and says the desert is only infinite "as best as [he] can tell", but that sees like a bit of a cop out. What I can't quite manage to get my head around is what the consequences would be if the machine really was infinite. My intuition is that even then it wouldn't be possible to generate the truly random numbers required, but infinities are seriously weird shit, and my instincts aren't terribly reliable with them. Anyone have any insight?

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With an infinitely large turing machine, why not just calculate all the possible outcomes, complete with their respective probabilities? No randomness required.

Not that that's what xkcd say is happening, but they don't say it isn't.

Or, on the basis that Turing-completeness is not the same thing as Turing-equivalence, just hook your universe simulator up to a fresh cup of really hot tea...

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The real numbers are a mathematical construct though, not a physical one. That's the basic underlying tenet of quantum theory. The building blocks of the universe are discrete on a very very tiny scale.

Hmmm. The many worlds approach could work, yes. It does feel like a bit of a cop out, though.

I considered the possibility of hooking up the universe simulator to a true RNG, but I can't think of any way to generate truly random numbers with just sand and rocks.

"Quantum physics is an inherently random phenomenon."
Correction: Quantum physics as we currently understand it appears to be an inherently random phenomenon.

Unfortunately I can't remember the name of the theory off the top of my head, but one alternative approach has been covered in New Scientist quite a few times which does not require a probabilistic system - only that we cannot observe the underlying complexity which results in chaotic effects. Certainly this aspect is of keen interest to many.

The strip itself also offers us an obvious cause of randomness - don't forget, this is not just a turing machine - there is also a person ;) Who, it is acknowledged, may occasionally forget to do things right. There is also no information regarding the regularity of the desert (indeed, it is indicated that rocks had to be placed into rows, hinting at an initial disorder) or of the environment itself, which may also allow a source for random data.

Modified Newtonian dynamics, that's the one!

I confess I'm not familiar with MOND, and a quick flick through Google and Wikipedia wasn't very illuminating. It is possible I'm a little behind the times on this one. Rather, I was thinking of Bell's Theorem, which states that a local hidden variable theory cannot work as an explanation for quantum theory.

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That's definitely just scratching the surface of pi. It has been conclusively and comprehensively proven that the digits of pi carry on indefinitely without ever repeating (trust me, I'm a (pretend) mathematician!)

The problem I have with infinities is trying to figure out which type of infinity we're talking about. Problems like Hilbert's hotel make my brain hurt.

Hilbert's hotel

Augh why did you link to that??! *whimpers and shakes*

*laugh* Yeah, that was my reaction too.

Reminds me of Isaac Asimov's short story "The Last Question" where man, and decendents, create more and more advanced computers throughout time, ending up with a computer which has survived the collapse of the universe, and who's last lines in the story are "Let there be light"

Insufficient data for a meaningful answer.

Anyone have any insight?

Comic made me chuckle.

...wait, was there supposed to be more insight? ~_^

I suppose the character could, in between moving stones around for a very slow simulation, be tossing coins (or some home-made equivalent) to get random numbers.

Oh to have enough time to actually contemplate this.

Ah, but he could be using the Many Worlds interpretation and calculating all possible futures and attendant probabilities.

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