Regarding the emergent point issue in the induction mapping, does not a simple matrix product operation do something like that? I mean, if the facts lie in a R^M space the induction could lead to R^N, where M>N, is that what you mean? Another related algebraic idea, let us have facts in some space F, and hypothesis in space H, is there a 'suitable' projection from F to M that validates the hypothesis? Whatever suitable means in this case. Perhaps, once we learn the same kind of projector, it can be used/extended to link other spaces. Best Sergio
On Sunday, January 19, 2014, Ben Goertzel <[email protected]> wrote: > > YKY, > > I would now advocate thinking in terms of the nonparametric Fisher > information... see > > *** > > Washington Mio, Dennis Badylans, and Xiuwen Liu. A com- putational > approach to fisher information geometry with appli- cations to image > analysis. EMMCVPR’05 Proceedings of the 5th international conference on > Energy Minimization Methods in Computer Vision and Pattern Recognition, > 2005. > > *** > > for a simple but non-original overview, or the Wikipedia page on Fisher > info... or my discussion in the attached draft (which also covers other > topics)... > > To answer your question, though, in your application theta is a parameter > of a probability distribution over logic-formula space.... > ben > > On Thu, Jan 9, 2014 at 8:04 AM, YKY (Yan King Yin, 甄景贤) < > [email protected] <javascript:_e({}, 'cvml', > '[email protected]');>> wrote: > >> Hi Ben, >> >> In your AGI-11 "geometry of mind" paper, you mentioned a geodesic along a >> path in parameter space M. The path is defined as a function from (I >> assume) a real number t to the space M, and it goes from parameter θ to θ'. >> >> What is unclear to me: >> >> 1. In a logic-based AGI system, what is a typical parameter θ? Is it a >> logical formula with its truth value? >> >> 2. How can the path be continuous? Continuous in the sense that, if the >> parameter space M is discrete, how can you find a function ϒ: t →M such >> that ϒ(t) varies continuously as t moves along [0,1]? >> >> Thanks =) >> >> PS: I find the use of Fisher information to measure the distance between >> 2 probability distributions a very good idea... for formulating the >> geometry of mind... >> >> YKY >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | >> Modify<https://www.listbox.com/member/?&;>Your Subscription >> <http://www.listbox.com> >> > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "In an insane world, the sane man must appear to be insane". -- Capt. > James T. Kirk > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/15717384-a248fe41> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
