> 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/?member_id=8660244&id_secret=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
