XPost: comp.theory   
      
   In article <46fb7ff3$1@news.unimelb.edu.au>,   
   David Kinny   wrote:   
   >Equally, no person can reliably determine this, since   
   >some cases would be more complex than they could possibly understand.   
      
   For a simple, explicit example, write a program to search for a   
   counterexample to the Riemann hypothesis or the Goldbach conjecture   
   or some similar unsolved mathematical problem, halting as soon as it   
   finds such a counterexample.  Being able to determine whether the   
   machine halts is equivalent to solving the unsolved math problem.   
   --   
   Tim Chow       tchow-at-alum-dot-mit-dot-edu   
   The range of our projectiles---even ... the artillery---however great, will   
   never exceed four of those miles of which as many thousand separate us from   
   the center of the earth.  ---Galileo, Dialogues Concerning Two New Sciences   
      
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