01 September 2014

Poincaré on time

Digging for authentic quotations is a frustrating business. Most of the time, the alleged source contains nothing comparable to the quote, and you're very lucky to find something that comes close. Even then, the original lacks the wit, conciseness or sharp phrasing of the quote that everyone knows. (Here and here are two examples.) It's not hard to imagine an evolutionary process that explains the phenomenon. A change in the quote would not survive if it did not somehow improve its predecessor, and you end up with a pebble infinitely more polished that the original. One may argue that, in spite of being fake, the counterfeit is somehow "truer" than the original. As Dutch writer Godfried Bomans has put it: "It's not about what someone actually said. It's about what he should have said."

Now for a rare case: for once, we can pinpoint the original and the forgery. French mathematician Henri Poincaré (1854-1912), counting among the very greatest scientists, is often quoted as having stated

Time is defined so that motion looks simple.

Now, that's a profound one and so Poincaré! Time as an artefact invented to make a hard phenomenon like motion (yes, Zeno's paradoxical motion) look simple. In fact, here is what Poincaré actually wrote

Time must be defined in such a way, 
that the equations of mechanics are as simple as possible.

It's on page 6 of a paper called La mesure du temps (Measuring time), in Revue de métaphysique et de morale 6 (1898), 1-13. (Here the French original, and here the English translation.)

"Defining time," not bad, not bad at all, but he only deals with measuring time—a matter of convention—and there is something trivial about the thought that choosing the right framework will  simplify the equations. Now here is what he should have written.

It's on page 23 of Gravitation, by Misner, Thorne and Wheeler, W.H. Freeman and company, San Francisco, 1973. (Here a sneak preview of the book in djvu format.) The name "Poincaré" occurs 12 times throughout the book, but we could not find any link between the great man and the motto of § 1.5. But it's a giant step from one idea to the other, from clepsydra to Zeno's paradoxes!