Hi all, I wonder whether most people here grok that the world is fundamentally a gargantuan set of simultaneous nonlinear differential equations for us to solve in order to achieve our goals?
Sure, if we drop something it falls, but how fast, and will it break when it hits? The instantaneous effects of our muscles become forces that produce accelerations, that are integrated to become velocities, that are integrated to become positions, that may be integrated to accumulate food, that may be accumulated to create fat, that will (hopefully) accumulate enough to keep us alive next winter when food is scarce. Of course we can't accurately know these complex systems of equations, so our "solutions" are necessarily approximate. Nonetheless, a coarse solution is still a lot better than no solution. I talked about integrating to get to the end result. Of course, to "go the other way" to see how to get to a desired end result requires differentiation, which is what differential equations are all about. AGI discussions have been about the algebra of Bayesian probabilities, when I think it should be about the differential calculus of computing the muscle activations that are needed now to achieve a desired result in the future, which is fundamentally a problem in differential equations. Sure the "numbers" in these equations are fuzzy, and no one has yet worked out the details of fuzzy differential equations (a good thesis project for someone), so we have some homework to do. I suspect that fuzziness may be represented some way in our own neural signals, e.g. by seemingly "random" separations between spikes. Hence, the systems of simultaneous differential equations may in effect be computing with complex pairs of numbers (or worse, triplets or quadruplets to represent other things we can't now even guess) to represent both a value and its suspected accuracy. Sure, numerical models are complicated, but NOT as complicated as starting with an over-simplified qualitative model (like Bayesian methods), and then trying to patch over the zillions of "cracks" that develop when trying to solve fundamentally numerical problems using qualitative models. Without necessarily agreeing, is everyone on board here with an understanding of what I am saying? Any questions? BTW, I was terrible at differential equations, and nearly flunked the class. I never got much further than understanding what they were all about. Steve ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
