We spend our lives comparing things with each other, along dimensions of age, beauty, size, color, weight, value, etc. Numbers are the simplest of things, and two numbers, one would think, could always be tested against each other: one is larger and the other smaller, unless they're both equal. Not necessarily! Mathematicians have put a powerful spin on the issue of comparison. They've invented new numbers --- not ordinary "numbers", admittedly, but special ones --- that have strange and useful properties.

Some of these special numbers are positive but closer to zero than any regular numbers, tinier than anything one could name. Some are fuzzy, in that they lie near each other but their order is indeterminate; they quasi-overlap, like wavefunctions of quantum-mechanical particles. When such numbers are added to each other, still more bizarre relationships arise among the results.

Infinitesimal and fuzzy numbers are valuable in understanding difficult-to-compare or conflicting options in real life. Sometimes we have to deal with goals that don't lie along a single axis --- they exist in higher-dimensional spaces, with critical aspects that are independent of each other. Some other goals are of infinite concern --- so important that all others pale to insignificance. The mathematics of incomparables give us a vocabulary and a toolkit to analyze such situations.

So Edgar Rice Burroughs's "incomparable Dejah Thoris", beautiful Martian maiden, perhaps was more than a cliché!

Sunday, October 03, 1999 at 20:28:59 (EDT) = 1999-10-03

*(correlates: DejahThoris, InBalance, GoWords, ...)*