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Mark Spahn

Joined: 07 Jul 2005
Posts: 62

Posted: Mon Jul 10, 2006 6:12 am    Post subject: horniness and clarity of mind

A chapter in the novel "Cryptonomicon" by Neal Stephenson
discusses a cryptanalyst's thinking about how his
clarity of mind C_m varies with his horniness <sigma>.
The entire chapter, with well-drawn mathematical notation
and graphs, is found here:
http://newark.pardey.org/book/cryptonomicon/slide63.html

The proportionality expression
C_m <is proportional to> lim (as n approaches infinity) 1/(sigma -
sigma_c)^n
makes little sense. The author says that this "amounts to saying that
the moment [sigma] rises above the threshold sigma_c it becomes
totally impossible for Waterhouse [the cryptanalyst] to break
Nipponese cryptographic systems." But the limit expression
to the right of the <is proportional to> symbol
is a simple function of the variable sigma (sigma_c is a constant).
When (sigma - sigma_c) is less than -1, or greater than 1,
the limit is 0; when (sigma - sigma_c) = -1, the limit does not exist,
because (sigma - sigma_c) alternates between -1 and +1
and n alternates between a negative and positive integer;
and when (sigma - sigma_c) = 1, the limit is 1.

Elsewhere in this book, the mathematics is correct, but here it is
incoherent.
It can easily be fixed, however, by eliminating the talk of a limit and
a dummy variable n.

-- Mark Spahn

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