Nosing around, I found other evidence that he was an intellectual Tory. He rejected a lot of modern mathematics, beginning with Cantor's transfinite cardinals, on intuitionist grounds. In one essay, he ridiculed an elementary logic text that gave, as an example, the alternation "x is rich or x is bald". "Rich" & "bald", he maintained, are predicates that have no relation to each other; to couple them in the same alternation is a form of "mania". That made me think of a woman who wanted a rich husband, but also had a thing about baldness (somehow, I even seemed to imagine her as French), saying "The man I marry must be rich or bald" --- inclusive "or", of course. It is, it seems to me, a virtue of logic that it does not constrain what one might imagine.
Poincaré was an expert on nonEuclidean geometry, so you might have expected him to anticipate general as well as special relativity; but quite the contrary, he thought it unlikely that nonEuclidean geometry would have any application in physics. Confronted with an experimental crisis, he said, one would always choose to modify the force laws rather than monkey with the kinematics on which so much else depends. That was a smart remark, but not, it turned out, a wise one.
After all that, a wicked thought occurred to me: "I'll bet that man was an antisemite." So, over the years, I kept an eye open for anything he might have had to say about Jews (most likely, I supposed, some catty remark about Einstein). I was rewarded in 2006 by extracting from the Web the news that during the Dreyfus affair (a notorious frameup, 1894-1906, of a Jewish army officer) he had testified on Dreyfus's behalf. By now, one can find quite a bit about that. The occasion is of interest to legal historians as an early, crude example of the forensic abuse of statistics. It seems that a police chief involved in the accusation, in an attempt to prove that a certain forged document really was written by Dreyfus, had conducted an "analysis" of the frequencies of certain handwritten letter forms. Its absurdity was widely noted, and the policeman did not require the services of a first-rate mathematician to make a fool of him; but Poincaré lent a hand, for what it was worth (nobody paid much attention that that particular "evidence" anyway). So there you have it -- a furious, highly politicized trial, all the antisemites in France on one side, and Poincaré on the other.
A little while after, after lovemaking with a man of blessed memory, we talked about a lot of things as usual, and I mentioned my delight at exonerating Poincaré, and said that if he had actually been an antisemite, he would have been displaying a devotion to scholarly integrity that was rare among antisemites. That whimsical reductio ad absurdum charmed my friend as well as me, and recalling the pillow talk just yesterday was consoling for a while.
But no! I was bluffing, and (as usual) I was lucky. I don't know much about antisemitism. For all I know, there actually have been conscientious scholarly antisemites. Germany might be a good place to look. I am adept at that kind of knowingness without knowledge. I can say everything I know while giving the impression that I know more. In that way, I get a lot more fun out of life than I deserve.