On Sat, Jun 13, 2015 at 1:57 PM, Piaget Modeler <[email protected]> wrote:
> What do the linear dependencies mean? > > a3 P3 = a1 P1 + a2 P2 > > > Please give examples. And what do the operators or predicates = and + > mean in the above context? > Well, I mean, P1, P2, P3 are propositions (or any objects to be represented). a1, a2, a3 are scalars. The above expresses linear dependence of the vectors (each vector is a proposition). The superposition principle says that if you want to represent 3 propositions together, you can have P1 + P2 + P3. However, I find that this superposition is problematic when the dimension of the space is lower than the number of things that needs to be represented. Say, if the dimension of the space is 2, then any 3 vectors (propositions) would be linearly dependent. That would mean, for example, "the moon is made of cheese" is somehow related to "yesterday rained" and "Obama is US president". That is undesirable. It seems that a 2D vector space could hold at most 2 propositions without interference, and *n*-dim would hold *n* propositions. This is somewhat contrary to my early (perhaps incorrect) impression that distributive representations can hold many more items than their vector space dimension. ------------------------------------------- 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
