Wednesday, January 5, 2011

Our forebears, unWhigged

In writings about the history and philosophy of science, you’ll come across words like Whiggish and Whiggery:  meaning, the post-hoc survey-textbook approach, which sees the past as basically stumbling confusedly towards our contemporary take on things, which, by contrast, is splendid.

It has for some decades now been fashionable to attack that approach -- often for the wrong reasons, nominalism or atavism or just plain political correctness:  the sort of groveling relativism that avers, hand on heart, that the math and the physics of the Patagonians is just as valid as that of Harvard and MIT -- a convenient doctrine which, among other things, excuses the student from the need of ever taking a science class, or understanding anything if she is somehow forced to.     There are valid reconceptions of the history of science, but these are much more difficult to do.

One that struck me like a thunderclap was a lecture, many years ago, by Steven Weinberg, which examined Galileo’s refusal to accept Kepler’s splendid discovery of the elliptical nature of the planetary orbits, continuing to insist on circles.  The ‘Whig’ view:  our forefathers were troglodytes, or Sleepwalkers; next slide please.   The PC view:  Circles are cool;  ovals are cool; wavy scribbles are cool; whatever your tribe subscribes too.   But for Weinberg, fully aware that Galileo was a very intelligent man who had devoted his life to his subject, that won’t wash.   Weinberg’s take, in a nutshell:  Galileo was right to value symmetry highly;  again and again  such considerations have been central to physics.  And a circle is more symmetrical than an ellipse.  Where Galileo went wrong (understandably enough), was in imagining that planets are central to physics or anything else.   In the past, they were given the names of gods;  in a broader view, they are vagrant bits of dirt, very far indeed from the pristine symmetries that lie at the heart of physics, and that are believed to have actually prevailed, for a trice or two, in the early universe.

And now another observation, this time from a mathematician rather than a physicist:

Shlomo Sternberg, Celestial Mechanics (1969), p. 34:

It is the theory of the motion of the planets  that represents the greatest achievement of Ptolemy.  Here, by a clever superposition of many epicycle motions in space, he was able to approximate very closely the motions of the planets.

The attentive lay reader will here be brought up short.  Epicycles -- “clever” -- “greatest achievement”??   One of the very few notions of ancient and medieval science to survive in contemporary vernacular is:  epicycles.  Folks don’t know from deferents, but they do know about epicycles:  useless complications, kludges, crude sticking-plaster on a turkey of a theory that is doomed.

Now, Sternberg does not here develop this observation beyond the passage quoted, since he has other fish to fry than Whigs;  but we know what, as a mathematician, he has in mind -- the moreso as he has already explicitly compared the Babylonians’ use of approximation by spline functions  to that key central topic of mathematics over the past couple of hundred years, Fourier series (quoted in the post “Babylonian mathematics”, below).  Modern mathematics has long prized approximations of problem curves by a series of well-studies ones, such as the trigonometric functions in the Fourier series, or Legendre polynomials, or, more recently, wavelets.

Footnote, and a further refutation of the lazy denigration of Ptolemy:  Copernicus himself, popularly presented as having booted Ptolemy into the trashbin of history, continued to use epicycles. 
The casual reader will be surprised to hear this; thus, Wikipedia, s.v. Copernicus: “Ptolemy's mechanism of eccentrics and epicycles -- the surmounting and discarding of which constituted the first step toward the creation of Copernicus' own doctrine of the structure of the universe.”
A step Copernicus himself did not take.  Thus Arthur Koestler, The Sleepwalkers (1959), p. 195:

Contrary to popular, and even academic belief, Copernicus did not reduce the number of circles [let alone “discard” them altogether] but increased them (from forty for forty-eight).

Incidentally, Sternberg commends Koestler’s Sleepwalkers.

William James, The Will to Believe (1897), p. 106, illustrating the metaphorical, pejorative use:
Epicycle upon epicycle of subsidiary hypothesis will have to be invoked  to give the discrepant terms a temporary appearance of squaring with each other, but at last even this resource will fail.

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