Big Math

[Richard Zander]

The latest Science News (Feb. 22, 2003) has a nice article on attempts to
solve very difficult math using physical models. Apparently, there are
promising approaches to solving NP-hard problems by "taking appropriate
measurements in a more complicated physical system." Example given was
figuring out the number of twists in transformer wire by measuring the
differences in voltage, or "when a ball s hurled into the air, nature
instantly solves the complicated equations that govern its motion." Examples
of NP-hard problems are labyrinths (you have to check every passage, though
there are some rules that help minimize retracing the route), the traveling
salesman problem (what is the shortest path or minimum retracing that allows
one to visit all the cities?), and evolutionary analysis of large data sets.

Consider then my physical solution to solving a labyrinth, which is to build
it out of pipes, fill it with water, insert a ping pong ball at the entrance
and force water through the pipes. Because water is incompressible, the ping
pong ball follows the moving water to the end of the labyrinth. The hard
part now is making a mathematical analogue to the physical solution to the
labyrinth puzzle.

My puzzle to Taxacomers is more simple:  what is a physical solution to,
say, parsimony analysis of a data set?

______________________
Richard H. Zander
Bryology Group
Missouri Botanical Garden
PO Box 299
St. Louis, MO 63166-0299
richard.zander at mobot.org <mailto:richard.zander at mobot.org>
Voice: 314-577-5180
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Note: this is a second sending of this message, which evidently may not have
made it through the gauntlet of email spam stopper programs. I changed the
title from "A puzzle" to "Big Math" which may be less threatening spam-wise.