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At 7:48 PM -0700 8/19/00, John Denker wrote:At 08:54 8/20/00 -0700, Leigh responded:
Science is not serial. It is a very high-dimensional tangled
latticework of facts. There is no natural ordering of the facts.
.... instruct their students according to a
serial schedule which, conventionally, follows an order that is
perceived to be natural in its increasing level of mathematical
sophistication. That is not an intrinsic property of the latticework;
it is largely cultural, arising as it does from the Gibbsian (as
opposed to, for example, the Cliffordian) farmalistic paradigm*.
I guess you can tell that I have to work on a particularly scary apple
tree today (and a couple of rhododendrons). Still, the metaphor is good,
except I really don't like the physicists' locution, "self consistent",
that I have used above. While it is conventional and well understood by
all of us, it is redundant and thus inelegant. Left to my own preference
I would have used the simpler term "consistent".
Leigh
* Don't worry if that makes no sense; it's a whole 'nother discussion.