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A Challenge from Freeman Dyson

45 points by mr_tyzic 12y ago

andrewl 12y ago
The question Dyson was responding to (What do you believe is true even though you cannot prove it?) is similar to this very interesting thread: What's the craziest or weirdest thing in your field that you suspect is true but is not yet supported fully by data? http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_scientists_of_reddit_whats_craziest_or/ http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_sc...
- lukifer 12y ago
  Thanks for sharing. Also worth a read: the other 119 answers to the original EDGE question in 2005. http://edge.org/q2005/q05_print.html http://edge.org/q2005/q05_print.html
  - IvyMike 12y ago
    I remembered Eric Raymond answering this. (Confession: I remember it because his response struck me as very odd.) But I don't see his answer on the site any more. The answer is still on Raymond's site, though. http://esr.ibiblio.org/?p=184 http://esr.ibiblio.org/?p=184
deleted 12y ago
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Someone 12y ago
"But the assumption that digits in a big power of two occur at random" That may not be the best of assumptions, but it doesn't hurt his argument. Benson's law learns us that the initial digits of 2^n tend to be low (empirically, but in this case, also mathematically. See http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-09.html http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-...). Less than 8% of powers of two begins with the digit '5'. Also, fewer powers of five begin with an even digit than with an odd digit. The argument that there is no deep mathematical reason why it has to be true, though, I find more belief than math. We don't know such a reason, but that doesn't mean it doesn't exist.
- tjradcliffe 12y ago
  "Benford" not "Benson". :-) If I were to approach this from the point of view of actual proof, I'd note that the problem is one of representation. In base 2, the result is trivially true since the reverse of all powers of 2 is 1. In base 5, likewise, the reverse of all powers of 5 is 1. Base 10 = 2*5, which may or may not be significant...
  - deleted 12y ago
    [deleted]
    - Chinjut 12y ago
      The (grandparent post's) claim was only for powers of 2; i.e., 1, 10, 100, 1000, etc., in binary.

45 points by mr_tyzic 12y ago

The question Dyson was responding to (What do you believe is true even though you cannot prove it?) is similar to this very interesting thread: What's the craziest or weirdest thing in your field that you suspect is true but is not yet supported fully by data? http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_scientists_of_reddit_whats_craziest_or/ http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_sc...

lukifer 12y ago
Thanks for sharing. Also worth a read: the other 119 answers to the original EDGE question in 2005. http://edge.org/q2005/q05_print.html http://edge.org/q2005/q05_print.html
- IvyMike 12y ago
  I remembered Eric Raymond answering this. (Confession: I remember it because his response struck me as very odd.) But I don't see his answer on the site any more. The answer is still on Raymond's site, though. http://esr.ibiblio.org/?p=184 http://esr.ibiblio.org/?p=184

deleted 12y ago

[deleted]

Someone 12y ago

"But the assumption that digits in a big power of two occur at random" That may not be the best of assumptions, but it doesn't hurt his argument. Benson's law learns us that the initial digits of 2^n tend to be low (empirically, but in this case, also mathematically. See http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-09.html http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-...). Less than 8% of powers of two begins with the digit '5'. Also, fewer powers of five begin with an even digit than with an odd digit. The argument that there is no deep mathematical reason why it has to be true, though, I find more belief than math. We don't know such a reason, but that doesn't mean it doesn't exist.

tjradcliffe 12y ago
"Benford" not "Benson". :-) If I were to approach this from the point of view of actual proof, I'd note that the problem is one of representation. In base 2, the result is trivially true since the reverse of all powers of 2 is 1. In base 5, likewise, the reverse of all powers of 5 is 1. Base 10 = 2*5, which may or may not be significant...
- deleted 12y ago
  [deleted]
  - Chinjut 12y ago
    The (grandparent post's) claim was only for powers of 2; i.e., 1, 10, 100, 1000, etc., in binary.