Dmitry A. Kazakov wrote:   
   > On Sun, 13 Aug 2006 06:48:53 GMT, James A. Bowery wrote:   
   >   
   > [...]   
   > > The proof is based on the Solomonoff distribution of random programs   
   > > (encoded as strings). The only possible probability distribution over   
   > > an infinite set of possible strings is one in which shorter strings   
   > > have higher probabilities than longer ones. Given any string s with   
   > > probability p(s) > 0, there can only be a finite number of strings   
   > > longer than s with probability greater than p(s), but there must be an   
   > > infinite number of strings longer than s with smaller probability.   
   > > Therefore, given any infinite set of programs with nonzero probability,   
   > > with any a-priori distribution, shorter programs must be more probable   
   > > than longer ones.   
   >   
   > It is a logical fallacy. The same way one could prove that any numeric   
   > algorithm should always consider lesser numbers as the most probable   
   > outcome, just because the expectation of any distribution should be finite.   
   >   
   > Also, for any given N (length) one can have an infinite number of   
   > distributions with all programs shorter than N be wrong.   
   >   
   > --   
   > Regards,   
   > Dmitry A. Kazakov   
   > http://www.dmitry-kazakov.de   
      
   I guess I should refer to the original source, which states it more   
   formally.   
   http://www.idsia.ch/~marcus/ai/paixi.htm   
      
   -- Matt Mahoney   
      
   [ comp.ai is moderated ... your article may take a while to appear. ]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)