> The problem is that there is a large class of physical systems that are > not "computable" by TMs, i.e., they are "intractable". Did you read the > Wolfram quote that I included in one of my posts? Please read the entire > article found here: > Another way of thinking of this is to concider the Laplacean notion > where given the specification of the "initial conditions" and/or "final > conditions" of the universe that all of the kinematics and dynamics of the > universe would be laid out. The modern incarnation of this is the so-called > 4D cube model of the universe. Again, these ideas only work for those who > are willing to completely ignore the facts of computational complexity and > the Heisenberg Uncertainty principle. > Stephen,

Am I correct that you're essentially saying that our universe is algorithmically incompressible? If so I would agree and, interestingly, so does my friend Jim in a parallel thread I sparked from this very thread on the infophysics list a week or so back; thought I'd post it because he represents the "hard" info physical view on this subject much better than I could: From: "Jim Whitescarver" Subject: Re: [InfoPhysics] Fw: Is the universe computable In so far as the universe is logical it can be modeled as a logical information system. The information nature of the quantum makes such a model convenient. It seems surprising how closely nature obeys logic granting validity to science. If we suppose that it is indeed logical and has no other constraints outside that logic, we then find it is an incompressible computation, that cannot be represented with fewer states. The universe is computably as it is a computer, but only a computer larger than the universe itself could model it. In this sense, the universe is not technically computable in practical terms. Intractability, however, is not exclusive of there existing good solutions. Unknowability is inherent in complex systems and we can capitalize on the the uniformity of the unknowable in the world of the known. Consider a pure entropy source, e.g. a stationary uncharged black hole. It effective eats all the information that falls in irretrievably randomizing it into the distant future. It is not that systems falling in stop behaving determistically, it is that we no longer care what their state is effectively randomized and outside our window of observation. Nothing in our world covaries with what happens inside the black hole but we know that there would be correlations due to the determinism that exists independently on the inside and the outside. I am not saying we can compute all of this. What happens at any point is the result of the entire universe acting at that point at this instant. Clearly this is not knowable. Causes are clearly not locally deterministic. But we can represent the black hole as a single integer, its mass in Plank action equivalents. From this all it's relevant properties to our perspective are known in spite of however complex it is internally. All participants, modeled as information systems, are entropy sources like black holes, but we get samplings of their internal state suggesting a finite state nature and deterministic behavior. The distinction is whether we can determine what that deterministic systems is or not. We cannot without communicating with all the participants and that is not always possible. But given a set of perspectives, there is no limit to how closely we can model them. Where no model works randomness may be substituted and often we will get good, if not perfect, results. Even legacy quantum mechanics, misguidedly based on randomness, yields deterministic results for quantum interactions shown accurate to many dozens of decimal places. This suggests that simple deterministic models will most likely be found. Jim CMR <-- insert gratuitous quotation that implies my profundity here -->