

A Challenge from Freeman Dyson - mr_tyzic
http://rjlipton.wordpress.com/2014/09/09/a-challenge-from-dyson

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andrewl
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_sc...](http://www.reddit.com/r/AskReddit/comments/1kqtgy/serious_scientists_of_reddit_whats_craziest_or/)

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lukifer
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
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)

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Someone
_" 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-...](http://www.johnderbyshire.com/Opinions/Diaries/Puzzles/2004-09.html)).
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.

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tjradcliffe
"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...

