From: mailbox@dmitry-kazakov.de   
      
   On Fri, 11 Nov 2005 13:55:33 GMT, VirtualThinker wrote:   
      
   > I am extremely interested in using category theory to model   
   > intelligence, and i seek other people with the same interests.   
   >   
   > Just briefly, the reasoning behind this is that category theory was   
   > invented about 50 years ago by pure mathematicians as a tool for   
   > understanding the increasingly complicated ideas they were   
   > constructing, the "canonical" example of which is the functor which   
   > takes a topological space to it's fundamental group. In my opinion,   
   > category theory is essentially a mathematization of the concept of an   
   > "analogy" between two structures or processes. Recently pure   
   > mathematicians have been trying very hard to write down a theory of   
   > "n-categories" which allow analogies _between analogies_ and so on ad   
   > infinitum.  Physicists are timidly starting to try to apply these ideas   
   > to physics.   
      
   I think that category theory might be very useful in programming language   
   design, specifically for type systems, more specifically to formalize the   
   infamous issue of substitutability, aka Liskov Substitutability Principle.   
      
   > Now i personally think that category theory is a very promising place   
   > to start trying to understand intelligence, because intelligence is   
   > about making analogies between known situations and unknown ones, and   
   > ideas themselves seem to me to just be high level analogies between   
   > lots of similar lower level ideas (continue inductively).   
      
   It is an interesting question. Basically categories could be viewed as   
   higher level abstractions. They don't look much like analogies between   
   situations, but rather between the models describing, predicting,   
   perceiving "situations". Imaginary, all observed analogies between various   
   statistical, fuzzy approaches to machine learning, which in the end produce   
   quite similar results, could they be unified into few categories? It might   
   become promising, however, it is not clear which end to start with.   
      
   Good luck!   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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