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Complexity of irrationals

  1. Aug 1, 2013 #1
    How would I figure out the Kolmogorov complexity of an irrational number?
    Could I just look at the shortest formula to compute that number.
    If it is an uncomputable real, does it have infinite complexity?
     
  2. jcsd
  3. Aug 1, 2013 #2
    Yes, and yes.
     
  4. Aug 1, 2013 #3
    I saw an interesting example online the other day. Take a noncomputable number and interperse 0's in every other digit position. Then for each finite-length initial segment, it takes just a little more than half as much information to compute the number with the 0's in every other position as it does to compute the original number. So not all noncomputable numbers are equally random. It's tricker than I'd realized.
     
    Last edited: Aug 1, 2013
  5. Aug 3, 2013 #4
    where did you see this example
     
  6. Aug 5, 2013 #5

    haruspex

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    That sounds suspiciously like infinity/2 = infinity.
     
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