[EMAIL PROTECTED] wrote:
 OO  O O        
        O          > > then lim i->inf e(i) = inf.
         O         >
 O                 > This will not give you a uniform
        O          > distribution on infinitely many things.
  O     O       
  O     O       yes. i agree.
    O   O       
   O    O       hm.
 O   O   O      
    O    O      let's try a thought experiment.
 O  O O  O      
    O O         there is a universe which contains a large
 O  O           machine. a factory. which produces self-aware
 O    O O       robots. they are all identical, aside from their
 O  O   O       serial number. it takes a year to make such a
     O OO       robot. this universe exists for 100 years, in
 OOO            which time 100 robots are produced.
     OO  O      
 O   O O O      when the robots come alive - they are able to
 O     OOO      reason about their serial number. a robot may
 OOO   O        
OO O O O        say "there is a 90% chance my serial number is
OO O O O O      greater than ten."
OO O O   O      
O O O O  O      now consider a similar universe - but this one
O O   O  O      exists for 200 years. in it the robots can
OOO O O  O      reason similarly, and can say "there is a 95%
OOO O O  O      chance my serial number is greater than ten."
OO  O O  O      
OO OO O  O      now consider a similar universe - one which
O O O O OO      lasts forever.
O  OO O OO      
O  OO  OOO      by your argument - the robots cannot reason
OO OO  OO       about their serial numbers - because there are
OO OO  OOO      infinitely many robots, and there is no uniform
OO OO  OOO      distribution over them.
OO OOO  OO      
OO OO  OOO      poppycock i say. although YES, I AGREE, THERE IS
OO OO OOO       NO UNIFORM DISTRIBUTION OVER AN INFINITE SET - i
 OOOO OOOO      believe it is still possible for the robots to
O  OOOOOOO      reason about their serial numbers. but they need
OO OOO OOO      to use tricks, like the one i presented earlier.
O   OOOOOO      
OOO  OOOOO      similarly, i think it is possible to reason
OOOOOO OOO      about the complexity of a uniformly chosen
OOO OO OOO      universe - and in doing so, i find that it's
OOOOOO OOO      complexity is extremely high.
OO  OOO OO      
 OOOOOO OO      
OOOOOOO OO      
OO OO OOOO      -k

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