Todor, There is a disconnect here. You seem to be mixing:
1. The *algebraic* solutions to equations, and 2. The *numerical* solutions to systems of simultaneous linear equations we both agree that these are well known. What isn't so well known (at least to me) 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. 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. Steve =============== On Thu, Aug 9, 2012 at 3:12 PM, 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 > > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/10443978-6f4c28ac> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Full employment can be had with the stoke of a pen. Simply institute a six hour workday. That will easily create enough new jobs to bring back full employment. ------------------------------------------- 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
