EXPONENTIAL ISN'T OWNED BY MATH

Alas, Stolen Meanings are Inevitable Even in “Pure” Mathematics

                                         By

                            Howard Richler

In his New York Times article Stop Saying “Exponential” Sincerely, a Math Nerd of March 4^th,  math professor Manil Suri railed against the increasing use of “exponential” to mean  “a whole lot” and declares this is erroneous because the word should only be applied towards  a trend not a single comparison.  Hence, he believes a Washington Post report on “exponentially richer private-sector jobs” represents a misuse of the term.

Dr  Suri recognizes that “English has  a long history of borrowing specialized words for other purposes – for example, ‘catalyst’ from chemistry being applied to people. But an essential characteristic of mathematics, one it arguably lives and dies by, is precision.”

Oh really?

Let’s look at some “precise”  mathematic terms.  “Corollary” is defined in the Oxford English Dictionary (OED) as “In Geometry, etc. A proposition appended to another which has been demonstrated, and following immediately from it without new proof; hence gen.an immediate inference, deduction, consequence.”  Its first use in this sense is found in Chaucer’s translation of Boethius’s  The  Consolation of Philosophy.   But by 1674, we see this generalized OED definition: “Something that follows in natural course; a practical consequence, result.”

Another mathematical term that has seen added meanings is “tangent.”  The OED shows this 1594 definition “Geometry. Of a line or surface in relation to another (curved) line or surface: Touching, i.e. meeting at a point and (ordinarily) not intersecting” But by 1823 the burgeoning field of crystallography used it to mean “Applied to a plane replacing an edge or solid angle of a crystal (which is more properly a secant plane.”   Alas, even non-scientific senses developed such a “flying off at a tangent” to mean “erratic” and a general sense of something “touching” or “contiguous.”

Similarly, “parameter” originally only had a mathematical sense in the 17^th century but in the interim years is has been adopted by the fields of electricity,  statistics and music and in the 20^th century it has acquired a generalized sense  to refer to any distinguishing or defining characteristic. “Perimiter” has roots in geometry but has been adopted by ophthalmology, the military, and (horrors!) even basketball.

Dr Suri ends his piece by saying “math is one of the few institutions we have left free of doublespeak or embellishment or biased opinion. Its words are supposed to mean exactly what they say.”

As I’ve demonstrated, it ain’t so.   Q.E.D.