Whether or not the universe is computable, the future will be unpredictable. There are 3 possibilities.
1. The universe cannot be simulated by a Turing machine. 2. The universe can be simulated by a Turing machine but not a finite state machine (unbounded time and memory). 3. The universe can be simulated by a finite state machine (bounded time and memory). -- Matt Mahoney, [EMAIL PROTECTED] In case 1, the universe has infinite Kolmogorov complexity. If we model a rational agent as a Turing machine, then accurate predictions are impossible. Examples of such universes could be where a rational agent is rewarded for guessing true random bits (with a possibly known distribution), or the bits of Omega (the probability that a random Turing machine will halt). In case 2, AIXI proves that optimal behavior is to guess the shortest consistent Turing machine. This problem is known to be undecidable. Furthermore, choosing the shortest machine leaves some uncertainty remaining: there will always be an infinite set of less likely machines with the same past but different futures. In case 3, AIXI^tl provides a computable solution for the case where the agent and environment have their own memory. However a physical realization of the universe is such that the agent is part of it. The agent therefore cannot have as many states (memory) as the universe containing it, so it cannot fully simulate the universe. Note that either time and memory are both bounded or both unbounded. If time is bounded, then only a finite amount of tape can be written. If memory is bounded to n bits, then a machine must either halt or cycle endlessly within 2^n steps. Our current cosmological model of the universe is finite in distance, time, mass, and number of possible quantum states, and therefore in entropy. However, this model is based on observation, not proof. ----- Original Message ---- From: Pei Wang <[EMAIL PROTECTED]> To: agi@v2.listbox.com Sent: Sunday, August 13, 2006 8:08:23 PM Subject: Re: [agi] Marcus Hutter's lossless compression of human knowledge prize On 8/13/06, Shane Legg <[EMAIL PROTECTED]> wrote: > > > On 8/13/06, Pei Wang <[EMAIL PROTECTED]> wrote: > > Shane, > > > > I don't think the statement "the universe is computable" can either be > > proved or disproved, because it is not a mathematical statement. > > However, there can be evidence for or against it. > > > Agreed. To date there is no evidence against it, and the entire field > of standard physics for it. That's a lot of evidence on one side, and > no evidence at all on the other. Thus it is pretty reasonable to make > the assumption that the environment is computable when doing this > kind of work. I'd say that the whole field of Philosophy of Science is against it, and I disagree with your statement about Physics. > Secondly, while one cannot prove that the whole universe is computable, > the observed universe to date has proven to be computable to a very high > degree. Thus, even if this assumption was violated, it would still hold for > much of the universe and to a very high degree of accuracy. Clearly then > any AI based on the computable universe assumption would still continue > to work perfectly well on most of the universe. I don't think so. Let's agree to be disagree, and see which approach will be more fruitful. Pei > > My objection is not any one you anticipated, > > > I didn't expect you to use one of the ones I listed, that's why I > said "before others jump in"... ;-) > > Shane > > > ________________________________ > To unsubscribe, change your address, or temporarily deactivate your > subscription, please go to > http://v2.listbox.com/member/[EMAIL PROTECTED] ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED] ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
