From: Dave Long (email@example.com)
Date: Tue Jan 02 2001 - 10:43:02 PST
> The "Thirty Hypothesis" is the belief that one's useful life ends at
> 30. This rule was first proposed by Rohit as the "Mathematician's rule
> of 25," which states that anything that was ever useful in mathematics
> was discovered and/or proved by a person by the time s/he was 25.
Aristotle (Rhetoric) says young men would rather do noble
deeds than useful ones, but old men would rather do useful
than noble. By his definitions then, this hypothesis
should read "one's noble life ends at 30", for I believe
the reason that the young people make all the discoveries
is the older ones are too busy exploiting what has already
Kaufmann (The Origins of Order) points out that on rugged
fitness landscapes, those which have a large number of
local optima, adaptation shows two phases. In the first
phase, the initial point is poorly adapted and variants
in its vicinity are only slightly fitter, but variants
at a long jump away can be very much fitter. Once a fit
segment of the space has been discovered, however, the
variants at a distance are usually less fit, whereas the
variants found locally may be slightly fitter, and so
adaptation climbs a local hill in the second phase.
Young mathematicians and engineers are in their first
phase, so they make the long jumps, the "discoveries".
Older ones have a sense of gradients in the landscapes
of their fields, as well perhaps as a sense of their
own fortes and foibles, and so limit themselves to the
main chance with the goal of doing useful work.
 "They are too fond of themselves; this is one form
that small mindedness takes. Because of this, they
guide their lives too much by considerations of what
is useful and too little by what is noble -- for the
useful is what is good for oneself, and the noble
what is good absolutely."
 "The race is not always to the swift, nor the battle
to the strong, but that's the way to bet."
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