From: mailbox@dmitry-kazakov.de   
      
   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   
      
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