> In fact Physics are not random. But let's go a little further, > and here's what I want to say. > > Physics are deterministic. "Deterministic" means that given a > system in one state, the following state can be inferred by > applying physics rules. It also works backwards: a given state > has only one previous state - but that is more difficult to see. > This can be seen more clearly by absurd: If Physics were not > deterministic, then things would happen without any cause. > The first author to talk about this was Descartes. > > So, if we had all the information of the universe in a specific > instant, then all the past and future could be calculated. >
What faith...and if I were a TV evangelist this would probably be a good thing, but as a physicist, this turns out to be a bad thing. Nothing in physics should be taken on faith, except of course your initial assumptions ;-) Faith aside, the idea that "Physics are deterministic"...is both a statement of faith and a falsifiable conjecture beyond Newtonian Physics. Let me explain. The story of the evolution of determinism in physics is a story that begins with Newton who, perhaps working off the philosophical legacy of Descartes and the mathematical influence of von Liebnitz, was able to formulate his "Universal Law of Gravitation" and in the process single-handedly solve the so-called "two-body" problem, e.g. the orbital motion of the Earth around the Sun. Unfortunately, he was unable to do the same for the so-called "three-body" problem, e.g. the orbital motion of the Earth and Mars around the Sun. The key in the strictly deterministic Newtonian framework is to find a sufficient number of conserved quantities. Energy, momentum, angular momentum, pointing vectors and the like. These conserved quantities are used to specify and solve integral equations that characterize the "two-body" problem. Even though some of the best minds of Newton's era, Newton included, and subsequent eras worked on the problem, it remained unsolved...and remains so today. The reason for this is that there are not enough conserved quantities in the "three-body" problem to make it ``integrable''. If there are enough conserved quantities, and thereby enough integrals, the motion problem is completely specified and solved. The motion is then described as quasi-periodic motion, or interdependent periodic motions, specified by a motion in phase space that lies on a multi-dimensional torus. Applying your definition of "Deterministic", meaning given a system in one state, the following state can be inferred by applying physics rules, to such a problem, forces us to "dilute" or "water down" the problem by respecifying those states considered or including constraints. Solutions to the constrained "three-body" problem, e.g. specifying that the orbital motion of the Earth and Mars around the Sun lies in a plane, are in fact ``integrable'' and often used in guidance systems for interplanetary spacecraft trajectories (along with empirical models to help specify the "nine-body" problem ;-). Furthermore, it has been shown that the deterministic framework of Newton's "Universal Law of Gravitation" is an approximation for a more complete theory of gravitation via the tensor-deterministic framework of Einstein's "General Relativity". However, I don't recommend that you try to solve Einstein's "General Relativity" just to get your spacecraft to go where you want it to go. Even with advanced software tools like Maple, MatLab, Mathematica, etc. it might take hours to crank out solutions for simple problems and sometimes problems that were thought straight forward turn out to yield solutions only after you pay the ultimate price in patience...depending on the speed of your computer, this could mean receiving your answer as an epitaph on your gravestone. R.I.P. No, it seems to me that Newton's brilliant world model with strict deterministic physics has little import beyond the "two-body" problem, after all who wants to play 2-ball billiards? But deterministic physics aside, more than anything else, Newton's legacy is one characterized as a 1. Mathematical...co-founder of calculus, 2. Experimental...remember the apple ;-), and 3. Universal...father of modern physics...approach. This still remains the cornerstone of modern physics today, although ALOT about the actual physical models have changed since. And whatever shortcomings Newton had in his deterministic physics "Weltansicht", he was more than compensated by his logical, methodical, and scientific approach...things I'm sure that would have made Aristotle or René proud of. What was left in Newton's wake, quite literally, was a mathematical approach to a quasi-deterministic world that the engineers, experimentalists, and empiricists of 18 century England couldn't quite figure out. Here, I'm referring to the early Englishmen trying to design more efficient steam engines (so they could deliver more power to the factories of England and steam the so-called industrial revolution thing along). After plenty of trail and error, a more "intuitive" approach to physical models based on "gross" state specifications using borrowed mathematical approaches from statistics and probabilities lead to...more interesting and predictable results. This "train of thought" that started with Boyles Law, made regular stops along the way at Statistical Physics and Thermodynamics, and eventually steamed its way to the Modern Dynamical Systems and Chaos Theory station. Lost in the approach are strict notions in definition: system components become "black boxes" or require "diluted" definitions to fit a schema. Found in the approach are concepts like "state", "determinism", and "causality" that lead to more interesting and predictable results than ever before. But somewhere in this grab bag of Lost & Found items is a whole new "intuitive" approach to physical models...a new approach to a new paradigm. For example, in the case of ideal gases, it was known that the individual gas molecules that make up the morass of a gaseous system were the little vermin behind any statement about "state", "determinism", and "causality", however since not much could be said about these little vermin, e.g. no clue what was the interaction history of any or all the gas molecule, they were forced to make statements about the "gross" system. It's an approach that has almost nothing to do with the strict determinism of Newton and everything to do with statistics and probabilities of Boltzmann, et al. In fact, had Newton not submitted his "Universal Law of Gravitation" to the scholarly world of his day, the early Englishmen trying to design more efficient steam engines would still have gone on to develop the same "intuitive" approach to physical models leading to the same interesting and predictable results. It was a new approach for a new paradigm that operated at a higher level of abstraction from the old paradigm, specifically local v. global, micro v. macro, individual v. state, etc. And it's an extremely important consideration that comes up in almost everything humans attempt to model...hence its relevance to AGI. It's a consideration that often makes the difference between model applicability and non-applicability, use and disuse, etc. and ultimately success and failure. And although now might be a good time to interject something about the "EPR Paradox" or the "Hidden Variable" dilemma, I'll refrain and stick to the main point. What's the main point? The modern approach to physical modeling is not a strictly "deterministic" approach, but rather an almost exclusively "statistical" approach. It's an approach that permeates almost all our understanding of modern physical world, from Boyles Law to SUSY (SUper SYmmetry models). It's an approach of, for, and by statistics and probabilities. And in as much, what do we really know anymore about the physical world? What can we really know about the physical world? Apparently only what we already know ;-) ...after all the statistics and probabilities relate to something already known. In a real sense, it's an admission that our 1. Tools and 2. Capacity for Understanding the physical world are intimately constrained by our design and relationship to the thing being modeled (I'm not certain, but did I hear someone in the crowd say Heisenberg, Godel, von Neumann?). >From my adventures in physics, I came to the conclusion that my understanding of the physical world had more to do with 1. My ability to create and use tools for modeling, i.e. from the physical tools of an advanced computer system to my internal abstraction tools like a new theorem of group algebra that helps me organize the particle world, 2. My internal mechanism for modeling, i.e. my internal neural structure, than it had to do with any 'physical reality'. But to be constructive here, as well as hopefully instructive, the moral of my story: In today's labor market of approaches to physical modeling, "statistical" determinism works, but "strict" determinism is still out to lunch ;-) BTB: I think there is a strong correlation between considerations of approaches to physical modeling and considerations of approaches to AGI modeling ;-) > Moreover: firstly we were talking about losing patterns as we > considered larger spaces. But if patterns do remain between > sets of information, then as we unite different spaces, we can > recognize more general patterns. Then as we consider larger > sets of information, the universe would become not less > compressible, but more compressible (because the more > general patterns take less bits). > > For imagination only: think of the Big Bang. Possibly the > amount of existing information was much reduced. Consider > that if the complexity of a system is n - the amount of > information when compressed - then that quantity can only > grow if the system receives information from outside itself. > Then, since there should be no system outside the universe > itself, all the information we have is the same we had at the > big bang, that "reduced" amount. Then all the information we > see everyday is the fractal consequence of a reduced set of > information. > > > Cheers > Pablo > > > > Shane Legg wrote: > > > > > > Hi Cliff, > > >> And if the "compressibility of the Universe" is an > assumption, is > > >> there a way we might want to clarify such an > assumption, i.e., aren't > > >> there numerical values that attach to the *likelihood* > of gravity > > >> suddenly reversing direction; numerical values attaching > to the > > >> likelihood of physical phenomena which spontaneously > negate like the > > >> chess-reward pattern; etc.? > > > > > > This depends on your view of statistics and probability. > I'm a > > > Bayesian and so I'd say that these things depend on > your prior > > > and how much evidence you have. Clearly the evidence > that gravity > > > stays the same is rather large and so the probability that > it's > > > going to flip is extremely super hyper low and the prior > doesn't > > > matter to much... > > > > To be specific: The Kolmogorov complexity of a constant > universe is less, > > so the prior probabilities of universes that are consistent > with ours up > > until now, but then suddenly flip tomorrow, are lower under > Solomonoff's > > universal prior. I think Jurgen has also pointed this out. > > (http://www.idsia.ch/~juergen/) > > > > -- > > Eliezer S. Yudkowsky http://singinst.org/ > > Research Fellow, Singularity Institute for Artificial > Intelligence > > > > ------- > > To unsubscribe, change your address, or temporarily > deactivate your subscription, > > please go to http://v2.listbox.com/member/? > [EMAIL PROTECTED] > > > > > ----------------------------------------------------------------------- > Registre su dominio. El primer paso de un proyecto exitoso en Internet. > http://www.montevideo.net.uy/hnnoticiaj1.exe?9,0 > > ------- > 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]
