Ben, Your posting appears to deal with two distinct issues that have been stirred together. I will discuss them separately:
1. Continuous representation and methods: Sure, some things are binary, but the vast majority of things are at least Bayesian. Regardless of whether you are representing probabilities and doing logic, or representing quantities and doing diffy-Q, you seem to be pretty much pushed into SOME sort of continuous representation. Of course, you could handle logical quantities as binary and carry the uncertainty separately, but that seems (at least to me) to be kludgy at all levels and an unnecessary complication. 2. Diffy-Q vs. logic of some sort. Here, I think our brains are in agreement, but we have had some problems expressing our respective views. When computing physical phenomena, and any phenomena with complex "pushback" that has bidirectional effects, diffy-Q is the clear winner. In "forward logic" situations (that seems to be what AGI has been concentrating on), where correct functionality is expressible as probability functions, put diffy-Qs away, because Bayesian methods are probably about as good as you can do. I think our point of disagreement is in how much of the world works according to "forward logic". Further, diffy-Qs and Bayesian methods are NOT mutually exclusive. You can rewrite ANY unstable simultaneous Bayesian equation (I suspect that substantially ALL complex real-world AGI Bayesian equation are both unstable and simultaneous) as a diffy-Q and directly SOLVE it, rather than letting them rattle around inside some sort of Bayesian engine like OpenCog. Continuing with details... On Tue, Jul 10, 2012 at 12:27 AM, Ben Goertzel <[email protected]> wrote: > > Arguing for use of differential equations to model intelligence, is sorta > like arguing for use of Lie groups and Feynman diagrams to model > biochemistry... > If you look at the zillions of simultaneous Bayesian equations that would be operating an AGI, many of them have "rate effects", e.g. where the world must integrate to see what the AGI is doing, or the AGI must integrate to see what the world is doing, or the AGI must integrate to see the effects of its own actions. If you take these integral calculus equations, differentiate them, and solve the system of simultaneous differential equations, you can then look into the many prospective futures. Here, the equations are fundamentally Bayesian, but with diffy-Q "twists" to be solved. > > After all, the level underlying biochemistry -- which consist of > elementary particles -- is well modeled by Lie groups, Feynman diagrams and > associated math... > > But actually, the math of elementary particle physics is not the simplest > tool for modeling biochemistry, even though it's in principle applicable > I see the diffy-Qs as being at the same high-level as you see that is needed. You seem to believe that diffy-Qs must all be at the subatomic level and not Bayesian. I see no need for this. One of us is failing to express the "obvious" to the other. Let's keep hammering at this until one or the other of us "gets it". > > Similarly, the math of differential equations -- though great for physics > and useful for lower-level neuroscience and many other areas -- is not > necessarily the simplest and most useful tool for modeling cognition... > Unless you have bidirectional effects, which I believe are MUCH more common than you do. However, frequency aside, you MUST be able to handle bidirectional effects to ever be "intelligent". "Honey, when are we going to have dinner?" "When you get hungry?" Even in trivial situations like this you have bidirectional action. > > I studied lots of diff eq in grad school, and I would have a great time > applying them to cognition, if I saw a good way to do so... > I presume that you were modeling physical systems. You can just as easily apply them to Bayesian equations - or not, depending on the problem at hand. I see diffy-Qs as just another computational tool, in addition to the other things that you have been looking at. If there is no feedback of pushback, then there is no need for diffy-Qs. However, I suspect that it would be hard to find hardly any interesting situation that doesn't at least involve pushback. > > I realize it's different from the direction you're pushing in, but here is > a paper of mine that uses continuous math to describe cognitive systems... > > *HTTP://goertzel*.org/papers/*MindGeometry*_agi_11_v2.pdf > > It also explicitly relates continuous math to computational math.... It's > more inspired by general relativity than by classical physics though -- and > more by the geometric aspects than the specific form of equations > involved... > > This is an attempt to use this continuous math to guide the design of an > AI component... > > *HTTP://goertzel*.org/ECAN_v3.pdf > > But while I see the use of continuous math to model and guide aspects of > AGI systems as interesting, I don't see why it's critical... > ... and I don't see why it is NOT critical. Did you see my paper that explained that temporal learning was SO easy that it was almost unavoidable when you represent things as their derivatives rather than as their plain values? Of course, derivatives don't work well with discontinuous quantities, as binary things tend to be. > > I grew up on diff-eq models of complex dynamical systems, it's great stuff. You just haven't (yet) seen our brains as being complex dynamical systems. > However, I don't think one needs to take that approach to build a > mind.... I believe nonlinear dynamics are important for AGI, but I don't > see what you get from continuous-variable diff-eqs that you can't also get > from discrete dynamical systems... > The diffy-Qs are easily solvable, even by wetware, whereas the discrete dynamical systems are more of a challenge and require hyper-complex software to solve. Further, from the quantum theory point of view, we need to consider the full range of prospective solutions, and not just whichever single solution a logic engine might come up with, which is easily possible (I think our neurons are natively doing this) by subtly "guiding" diffy-Q solutions. Hopefully my remarks have refined any differences in our POVs. 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