To clarify what I mean by "observable universe", I am including any part that could be observed in the future, and therefore must be modeled to make accurate predictions. For example, if our universe is computed by one of an enumeration of Turing machines, then the other enumerations are outside our observable universe.
-- Matt Mahoney, [EMAIL PROTECTED] --- On Thu, 9/4/08, Abram Demski <[EMAIL PROTECTED]> wrote: > From: Abram Demski <[EMAIL PROTECTED]> > Subject: Re: Computation as an explanation of the universe (was Re: [agi] > Recursive self-change: some definitions) > To: [email protected] > Date: Thursday, September 4, 2008, 9:43 AM > > OK, then the observable universe has a finite > description length. We don't need to describe anything > else to model it, so by "universe" I mean only the > observable part. > > > > But, what good is it to only have finite description of the > observable > part, since new portions of the universe enter the > observable portion > continually? Physics cannot then be modeled as a computer > program, > because computer programs do not increase in Kolmogorov > complexity as > they run (except by a logarithmic term to count how long it > has been > running). > > > I am saying that the universe *is* deterministic. It > has a definite quantum state, but we would need about 10^122 > bits of memory to describe it. Since we can't do that, > we have to resort to approximate models like quantum > mechanics. > > > > Yes, I understood that you were suggesting a deterministic > universe. > What I'm saying is that it seems plausible for us to be > able to have > an accurate knowledge of that deterministic physics, > lacking only the > exact knowledge of particle locations et cetera. We would > be forced to > use probabilistic methods as you argue, but they would not > necessarily > be built into our physical theories; instead, our physical > theories > act as a deterministic function that is given probabilistic > input and > therefore yields probabilistic output. > > > I believe there is a simpler description. First, the > description length is increasing with the square of the age > of the universe, since it is proportional to area. So it > must have been very small at one time. Second, the most > efficient way to enumerate all possible universes would be > to run each B-bit machine for 2^B steps, starting with B = > 0, 1, 2... until intelligent life is found. For our > universe, B ~ 407. You could reasonably argue that the > algorithmic complexity of the free parameters of string > theory and general relativity is of this magnitude. I > believe that Wolfram also argued that the (observable) > universe is a few lines of code. > > > > I really do not understand your willingness to restrict > "universe" to > "observable universe". The description length of > the observable > universe was very small at one time because at that time > none of the > basic stuffs of the universe had yet interacted, so by > definition the > description length of the observable universe for each > basic entity is > just the description length of that entity. As time moves > forward, the > entities interact and the description lengths of their > observable > universes increase. Similarly, today, one might say that > the > observable universe for each person is slightly different, > and indeed > the universe observable from my right hand would be > slightly different > then the one observable from my left. They could have > differing > description lengths. > > In short, I think you really want to apply your argument to > the > "actual" universe, not merely observable > subsets... or if you don't, > you should, because otherwise it seems like a very strange > argument. > > > But even if we discover this program it does not mean > we could model the universe deterministically. We would need > a computer larger than the universe to do so. > > Agreed... partly thanks to your argument below. > > > There is a simple argument using information theory. > Every system S has a Kolmogorov complexity K(S), which is > the smallest size that you can compress a description of S > to. A model of S must also have complexity K(S). However, > this leaves no space for S to model itself. In particular, > if all of S's memory is used to describe its model, > there is no memory left over to store any results of the > simulation. > > Point conceded. > > > --Abram > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: > https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
