“Yet bridges stand”

A mathematician and poet reflects on the strange powers conferred by a discipline where, as Bertrand Russell once said, you don’t know what you’re talking about or whether what you say is true.

Apropos the science-and-religion question, a reader points me to the work of Clarence Wylie, who wrote his dissertation at Cornell on “Space Curves Belonging to a Linear Line Complex.”

Wylie also wrote:


Not truth, nor certainty. These I forswore

In my novitiate, as young men called

To holy orders must abjure the world.

“If …, then,” this only I assert;

And my successes are but pretty chains

Linking twin doubts, for it is vain to ask

If what I postulate be justified

Or what I prove possess the stamp of fact.

Yet bridges stand, and men no longer crawl

In two dimensions. And such triumphs stem

In no small measure from the power this game,

Played with the thrice attenuated shades

Of things, has over their originals.

How frail the wand, but how profound the spell!

Wylie’s poem assumes the “formalist” view of mathematics, as summed up by Bertrand Russell: “Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” That remains the dominant view among philosphers of mathematics, but the disconnect between the frailty of the wand and its evident power lends some support to the alternative view of Lakoff and Núñez that mathematics starts from basic human experience.

I must confess that my own views remain primitively Platonic; that is, I belive that it was the case that a group consisting of two pairs of trees contained four trees, even before there were humans around to notice that fact.

Author: Mark Kleiman

Professor of Public Policy at the NYU Marron Institute for Urban Management and editor of the Journal of Drug Policy Analysis. Teaches about the methods of policy analysis about drug abuse control and crime control policy, working out the implications of two principles: that swift and certain sanctions don't have to be severe to be effective, and that well-designed threats usually don't have to be carried out. Books: Drugs and Drug Policy: What Everyone Needs to Know (with Jonathan Caulkins and Angela Hawken) When Brute Force Fails: How to Have Less Crime and Less Punishment (Princeton, 2009; named one of the "books of the year" by The Economist Against Excess: Drug Policy for Results (Basic, 1993) Marijuana: Costs of Abuse, Costs of Control (Greenwood, 1989) UCLA Homepage Curriculum Vitae Contact: Markarkleiman-at-gmail.com