Ben, et al, *I think I may finally grok the fundamental misdirection that current AGI thinking has taken!
*This is a bit subtle, and hence subject to misunderstanding. Therefore I will first attempt to explain what I see, WITHOUT so much trying to convince you (or anyone) that it is necessarily correct. Once I convey my vision, then let the chips fall where they may. On Sun, Jun 27, 2010 at 6:35 AM, Ben Goertzel <b...@goertzel.org> wrote: > Hutter's AIXI for instance works [very roughly speaking] by choosing the > most compact program that, based on historical data, would have yielded > maximum reward > ... and there it is! What did I see? Example applicable to the lengthy following discussion: 1 - 2 2 - 2 3 - 2 4 - 2 5 - ? What is "?". Now, I'll tell you that the left column represents the distance along a 4.5 unit long table, and the right column represents the distance above the floor that you will be as your walk the length of the table. Knowing this, without ANY supporting physical experience, I would guess "?" to be zero, or maybe a little more if I were to step off of the table and land onto something lower, like the shoes that I left there. In an imaginary world where a GI boots up with a complete understanding of physics, etc., we wouldn't prefer the simplest "program" at all, but rather the simplest representation of the real world that is not physics/math *in*consistent with our observations. All observations would be presumed to be consistent with the response curves of our sensors, showing a world in which Newton's laws prevail, etc. Armed with these presumptions, our physics-complete AGI would look for the simplest set of *UN*observed phenomena that explained the observed phenomena. This theory of a physics-complete AGI seems undeniable, but of course, we are NOT born physics-complete - or are we?! This all comes down to the limits of representational math. At great risk of hand-waving on a keyboard, I'll try to explain by pseudo-translating the concepts into NN/AGI terms. We all know about layering and columns in neural systems, and understand Bayesian math. However, let's dig a little deeper into exactly what is being represented by the "outputs" (or "terms" for died-in-the-wool AGIers). All physical quantities are well known to have value, significance, and dimensionality. Neurons/Terms (N/T) could easily be protein-tagged as to the dimensionality that their functionality is capable of producing, so that only compatible N/Ts could connect to them. However, let's dig a little deeper into "dimensionality" Physicists think we live in an MKS (Meters, Kilograms, Seconds) world, and that all dimensionality can be reduced to MKS. For physics purposes they may be right (see challenge below), but maybe for information processing purposes, they are missing some important things. *Challenge to MKS:* Note that some physicists and most astronomers utilize " *dimensional analysis*" where they experimentally play with the dimensions of observations to inductively find manipulations that would yield the dimensions of unobservable quantities, e.g. the mass of a star, and then run the numbers through the same manipulation to see if the results at least have the right exponent. However, many/most such manipulations produce nonsense, so they simply use this technique to jump from observations to a list of prospective results with wildly different exponents, and discard the results with the ridiculous exponents to find the correct result. The frequent failures of this process indirectly demonstrates that there is more to dimensionality (and hence physics) than just MKS. Let's accept that, and presume that neurons must have already dealt with whatever is missing from current thought. Consider, there is some (hopefully finite) set of reasonable manipulations that could be done to Bayesian measures, with the various competing theories of recognition representing part of that set. The reasonable mathematics to perform on spacial features is probably different than the reasonable mathematics to perform on recognized objects, or the recognition of impossible observations, the manipulation of ideas, etc. Hence, N/Ts could also be tagged for this deeper level of dimensionality, so that ideas don't get mixed up with spacial features, etc. Note that we may not have perfected this process, and further, that this process need not be perfected. Somewhere around the age of 12, many of our neurons DIE. Perhaps these were just the victims of insufficiently precise dimensional tagging? Once things can ONLY connect up in mathematically reasonable ways, what remains between a newborn and a physics-complete AGI? Obviously, the physics, which can be quite different on land than in the water. Hence, the physics must also be learned. My point here is that if we impose a fragile requirement for mathematical correctness against a developing system of physics and REJECT simplistic explanations (not observations) that would violate either the mathematics or the physics, then we don't end up with overly simplistic and useless "programs", but rather we find more complex explanations that are physics and mathematically believable. we should REJECT the concept of "pattern matching" UNLESS the discovered pattern is both physics and mathematically correct. In short, the next number in the "2, 2, 2, 2, ?" example sequence would *obviously* (by this methodology) not be "2". OK, the BIG question here is whether a carefully-designed (or evolved over 100 million years) system of representation can FORCE the construction of systems (like us) that work this way, so that our "programs" aren't "simple" at all, but rather are maximally correct? Anyway, I hope you grok the question above, and agree that the search for the simplest "program" (without every possible reasonable physics and math constraint that can be found) may be a considerable misdirection. Once you impose physics and math constraints, which could potentially be done with simplistic real-world mechanisms like protein tagging in neurons, the problems then shifts to finding ANY solution that fits the complex constraints, rather than finding the SIMPLEST solution without such constraints. Once we can get past the questions, hopefully we can discuss prospective answers. Are we in agreement here? Any thoughts? 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