[extropy-chat] three coins in a fountain

Marc Geddes marc.geddes at gmail.com
Fri Oct 21 06:21:06 UTC 2005

Wow, you guys are way too clever in the ways of Bayesian probablity theory
for me! ;)
 I shall none the less post a couple of very simple problems, which, I'm
sure, with your august and vastly superior knowledge of Bayes, you'll all
have no problem in answering.
 Marc's problem set:
 Using the correct Bayesian extension's for mathematical reasoning, please
tell me the likelihood probabilities for each of these pieces of evidence
that the Riemann hypotheses is true:
 (1) Hardy's 1914 result that all infinitely many zeros lie on the critical

(2) The RH implies the PNT, which is known to be true.
 (3) "Denjoy's probabilistic interpretation"—that is, the coin-tossing
 (4) Another 1914 theorem by Landau and Harald Bohr, stating that most
zeros—all but an infinitesimal proportion—are very close to the critical
 (5) The algebraic results of Artin, Weil, and Deligne
 Now, combining the probabilities for 1-5, please tell me the correct
Bayesian probability that the Riemann hypotheses is true.

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THE BRAIN is wider than the sky,
For, put them side by side,
The one the other will include
With ease, and you beside.

-Emily Dickinson

'The brain is wider than the sky'
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