Hi Steve, > is the logical extension of this to the *approximate* (by dropping selected terms) *algebraic* (which may include embedded numerical values) solutions to systems of >*simultaneous* *non-linear* and *differential* * equations*. Once this engine is in place, my claim is that much of AGI should easily fall into place, and further, that many of the >present "grand challenges" in AGI are in actuality simply presenting the problems that surface when you try doing AGI-like things without such an engine in place.
OK, I agree - those equations, especially differential, are an expression of the model for prediction/defining the "correlations" between inputs and future inputs/outputs. In terms from my works the differences between samples/patterns are called "correlations", these differences (and delta-encoding) actually are defining differential equations (in a digital way), and that's how to produce/predict following data, given samples and the "correlation" to the future (that's a "pattern"). This can be extended in many levels of abstraction, these are higher order correlations/differential equations. I agree that a general algorithm for finding those general correlations (something AGI is searching for) is like a universal "definer" of differential equations and non-linear equations from data, and it's what an AGI should be capable to do. The wild non-linear equations (especially very complex ones, with raises, falls, spikes) which are hard to represent "simply"/to compress well are just mappings, one vector is mapped to another, because of some kind of coincidence/repetition. >Ben had the right idea in creating an engine like OpenCog rather than trying to do everything with ad hoc programming. I think that Ben's error was working at too >low a level, e.g. of handling probabilities at particular moments in time. I believe it's not him only, after all that's the idea of AGI, to solve everything possible with a smooth integral framework, instead of working ad-hoc. *--- Todor "Tosh" Arnaudov --* *"Twenkid Research*" - http://research.twenkid.com *Self-Improving General Intelligence Conferenc*e Chair : http://artificial-mind.blogspot.com/2012/07/news-sigi-2012-1-first-sigi-agi.html On Fri, Aug 10, 2012 at 1:12 AM, Todor Arnaudov <[email protected]> wrote: > Hi Steve, > > >There have been a number of programs written that were capable of > manipulating algebraic formulas, and some to solve isolated equations. > There have also been programs to solve simultaneous *linear* equations > >via array operations. In the engine I envision, every "formula" would be > presumed to equal zero, and hence would be an equation, despite its missing > = sign, similar to array operator implementations to solving > >simultaneous linear equations. Instead of operators like "addition" or > "subtraction", there would be new operators like "union" that would solve a > system of simultaneous NONlinear equations, etc. > > What are you talking about, solving equations and general algebraic > operations algorithms are mathematically solved (for linear ones - for > sure), we wouldn't be able to solve them by hand if it was not. One of > the *first (some claim it's the first)* electronic computers itself was > designed precisely to solve linear equations with 30 unknowns (the ABC, > Atanassoff-Berry-Computer), because the other methods were too slow for the > needs of John Atanassoff. The computer was conceived in 1937. Vladimir > Turchin has written algebraic programs in the 60-ies with his programming > language REFAL. http://www.encyclopediaofmath.org/index.php/Refal > Functional and Logical Languages in general are > somewhat intrinsically "algebraic", unlike procedural like C, which are > more "computational/arithmetical". > > The "Matrix processors", the first "SIMD-MIMD" etc. and multi-processing > units devices started with multiplication + addition done much quickly than > general purpose computers, because that's a critical operation for > scientific computation, which are largely for computation of "matrices" > including solving linear equations. With the advent of video cards for > PCs, then the GPU, that's now in every PC's GPU with huge parallelism, > sometimes capable of many TFLOPS. > > In computer vision there are such equations for example when triangulating > a stereo image into 3D object, and calibrating a camera parameters from > taken pictures.I've written a simple program to solve such myself as a > student, using the same algorithm as I'd apply manually - Mathematica > solves all kinds of algebraic expressions, AFAIK it's done also in one > extent or another using REFAL: http://integrals.wolfram.com/index.jsp > > > *--- Todor "Tosh" Arnaudov --* > *"Twenkid Research*" - http://research.twenkid.com > *Self-Improving General Intelligence Conferenc*e Chair : > http://artificial-mind.blogspot.com/2012/07/news-sigi-2012-1-first-sigi-agi.html > > > -- *--- Todor "Tosh" Arnaudov ---* * -- Twenkid Research:* http://research.twenkid.com -- *Self-Improving General Intelligence Conference*: http://artificial-mind.blogspot.com/2012/07/news-sigi-2012-1-first-sigi-agi.html *-- Todor Arnaudov's Researches Blog**: *http://artificial-mind.blogspot.com ------------------------------------------- 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
