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Andreas_Giger comments on Simulating Problems - Less Wrong Discussion

1 Post author: Andreas_Giger 30 January 2013 01:14PM

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Tags: newcomb decision theory game

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Comment author: Andreas_Giger 30 January 2013 03:11:02PM *  1 point [-]

I only used Newcomb as an example to show that determining whether a simulation actually simulates a problem isn't trivial. The issue here is not finding particular simulations for Newcomb or other problems, but the general concept of correctly linking problems to simulations. As I said, it's a rather mathematical issue. Your last statement seems the most relevant one to me:

To simulate Newcomb's problem with a real agent, you have the problem of convincing the agent you can predict his decision, even though in fact you can't.

Can we generalize this to mean "if a problem can't exist in reality, an accurate simulation of it can't exist either" or something along those lines? Can we prove this?

Comment author: MrMind 01 February 2013 01:06:38PM 0 points [-]

Can we generalize this to mean "if a problem can't exist in reality, an accurate simulation of it can't exist either" or something along those lines? Can we prove this?

I would cast this sentence in this form, seeing that if a problem contains some infinite it's impossibile for it to exist in reality. Can an infinite transition system be simulated by a finite transition sistem? If there's only one which can be, then this would disprove your conjecture. The converse of course it's not true...

Comment author: Andreas_Giger 01 February 2013 02:27:24PM *  0 points [-]

I'm not sure what you mean by an infinite transition system. Are you referring to circular causality such as in Newcomb, or to an actually infinite number of states such as a variant of Sleeping Beauty in which on each day the coin is tossed anew and the experiment only ends once the coin lands heads?

Regardless, I think I have already disproven the conjecture I made above in another comment:

Omega predicting an otherwise irrelevant random factor such as a fair coin toss can be reduced to the random factor itself, thereby getting rid of Omega. Equivalence can easily be proven because regardless of whether we allow for backwards causality and whatnot, a fair coin is always fair and even if we assume that Omega may be wrong, the probability of error must still be the same for either side of the coin, so in the end Omega is exactly as random as the coin itself no matter Omega's actual accuracy.

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