Why (some) progressives hurt the cause:

In the New York Times, there is an essay about Ethnomathematics. We'll cut to the chase, and quote from one of the books that takes a multi-cultural outlook:

From 'Ethnomathematics: A Multicultural View of Mathematical Ideas,' by Marcia Ascher

A critical issue is that, as it stands, much of mathematics education depends upon assumptions of Western culture and carries with it Western values.

That is complete nonsense, as anybody familiar with the history of the calculus would know. Carries Western values? Like the use of negative numbers, which were grudgingly accepted by the West long after the Hindus were using them? The Western values as expressed by Bishop Berkeley, who challenged Newton's use of infinitesimals in the book "THE ANALYST; OR, A DISCOURSE Addressed to an Infidel MATHEMATICIAN WHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith" (they had long titles in the 1700's):

And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the Ghosts of departed Quantities?

When the Ethnomathematicians spout nonsense, it gives people like Lynne Cheney ammunition to do real damage in academia (and not just in the mathematics department).

UPDATE: We could go on and on about this issue. "The West" was hostile to non-Euclidian geometry at first. There were heated arguments over the reality (and utility) of infinite numbers. The West inherited the Greeks' notion that there could never be a "completed infinity" but instead, only a "potential infinity". That contributed to the opposition to Cantor's work. Then there was the wrestling match that took place around 1900 between the Formalists (probably the most "Western" of the trio), the Intuitionists, and the Logical School, concerning the foundation of mathematics.

The point is that mathematics proceeds along its own path, and in doing so, has faced opposition at times from philosophers of many schools - including those of the Establishment West. And of course, at other times mathematics was congruent with Western Philosophy. But the notion that mathematics carries "Western values" is absurd. The values of mathematics are consistency, test by proof, and an axiomatic structure. At times, even though the mathematics was legitimate, it was deemed beyone the pale (most notably with non-Euclidian geometry, for Euclidian geometry was thought of as the way the universe was set up, perhaps by God).

'nuff said.

posted by Quiddity at 2/23/2003 10:49:00 AM