In this awful Trump election year, Republicans are announcing that they won’t vote for him; and of course, most of them add, they couldn’t possibly vote for Hillary either. The latest is Miami mayor Tomás Regalado. Today the New York Times reports that Regalado says he’s going to sit this one out.

The idea of sitting out an election gives another illustration of the strange disconnect between the mathematics and the psychology of voting. Mathematically, for a Republican to not vote for anybody has exactly the same effect as voting for Hillary, except with half the magnitude. Who would want their vote to be cut in half? But the human truth of voting has little to do with the mathematics. We all construct personal narratives of how we will or won’t vote, and out of millions of narratives, somehow or other, a president is elected.

[31 May 2016]

Women’s brains are 10% smaller than men’s, yet the sexes are equally intelligent. It might not have turned out like this.  It’s easy to imagine a world in which natural selection had made men brighter than women. The image is an awful one, a dystopia in which the relationship between the sexes would surely have been that of master and slave.  Thank goodness it didn’t turn out like that.

But actually, it did turn out like that: not with brains, but with brawn. We’re so used to men being bigger and stronger that we don’t regard this disparity with horror. Yet most men can dominate most women physically, and I believe this is the main reason why in most societies throughout history, the men have been in control. Why do men dominate women? Because they can.

In recent generations, thanks to the cognitive demands of advancing civilization, we are beginning to rise above the physical differences and approach equality. It might not have turned out like this. If the dimorphism had been in brains rather than brawn, the advance of civilization might have increased the inequality between the sexes rather than diminishing it.

[22 April 2011]

In Madrid this week, I spent a lot of time looking at Las Meninas.  What a friend it became!

A salient feature of art and literature, and a recurring theme in these notes, is the power of ambiguity.  The experience of a great work may be due half to the artist, who brings so much to the canvas, and half to the viewer, in whose eye and mind the image resonates.  Las Meninas has become my archetypical example of this synergy.  Standing in front of it in that great hall of the Prado, I felt that Velazquez and I were working together to create this viewing experience.

It is key that he is looking at us. He’s daring us with the question, what do you think of this?  What do you make of the dog, and the dwarf, and the cavernous dark upper half of my painting?  Can you imagine the secrets I know of this crazy decadent court of Philip IV?

Yet there is so much Velazquez did not know!  He did not know that Britain and its colonies in America would build a new world as Spain declined ever further. He did not know that the infanta Margarita would die at age 21.  It may be just my fancy, but I like to think that Velazquez had a sense of the uncertainty of the future and the genius to craft a work that would take strength from that uncertainty.

[3 April 2016]

What’s the smallest nonprime that is not obviously nonprime? For Ramanujan the answer would have been in the thousands, but for the rest of us, I think it’s 91. The sequence of nonobvious nonprimes runs 91, 119, 133, 143, 161, 187,….

Here’s my reasoning. If a number is divisible by 2, 3, or 5, that’s obvious, and if it is 11 times a single digit, that’s obvious too. Also, perfect squares are pretty familiar. This leaves us with 7•13, 7•17, 7•19, 11•13, 7•23, 11•17,….

[14 May 2016]