Affirmative fraction

About 19% of SIAM’s non-student members are women, but at the next SIAM Annual Meeting, 9 out of 16 invited speakers will be women. These figures imply that the fraction invited to speak will be around 5.5 times higher for women than for men.

That’s the math, which is easy. The politics? Not so easy.

[6 January 2017]

Pikachu evolves into Raichu

“Did you see the tombs of Mary of Burgundy and Charles of Burgundy in the chancel?”

(Kate asked me this just now in the Church of Our Lady in Bruges.)

I couldn’t help thinking of when Emma and Jacob were little and they knew every detail of Pikachu and Charmander and the other Pokémon characters, each with its particular abilities and weaknesses and path of evolution. Pokémon for the kids, Harry Potter for the teenagers, saints for the Catholics, celebrities for the masses. Our appetite for particulars about people is infinite, and it hardly matters how small the facts are or whether the people are even real.

[31 December 2015]

Why don’t thieves take my bike helmet?

I lock my bike, but often I don’t bother to lock my helmet. Instead I buckle it around the lock so that the casual onlooker would guess that it too is secure.

A thief, however, is no casual onlooker. If thieves were out to steal bike helmets, they’d have stolen mine long ago. This gets me thinking about what makes it rational to be so insouciant about my helmet.

Let’s say the bike costs 300 pounds and the helmet costs 30. Then loss of the helmet means just 1/10th the pain of loss of the bike.

But because it’s worth less, the helmet is also less likely to be stolen! Let’s say, 1/10th as likely. So we have a quadratic effect in play: the expected loss from leaving my helmet unlocked is 1/100th that of leaving my bike unlocked.

[19 December 2016]

Hillary, Donald, and the theory of comparative advantage

“I don’t like either one. Donald’s a racist and Hillary’s a liar”. I heard a voter interviewed along these lines the other day, and it encapsulates the view of millions that has brought us to the edge of a possible Trump victory.

It’s an astonishing view, for by any empirical standard, as many analysts have shown, it’s Donald who’s the liar. In terms of telling the truth, Hillary is a normal politician and Donald is far from normal. Yet by systematically attacking her honesty in every speech and tweet, he has gone a good way to destroying her reputation, just as earlier in the campaign he systematically destroyed Jeb Bush, Ted Cruz, and Marco Rubio.

What Donald is doing is exploiting what economists call the theory of comparative advantage. David Ricardo famously observed that if England is less efficient than Portugal in making cloth but much less efficient in making wine, then it should make cloth anyway and trade it with Portugal. In cloth-making, England has an absolute disadvantage but a comparative advantage.

The same principle determines what insults are traded by Hillary and Donald. On an absolute scale, Trump is the liar, but his dishonesty must be ranged against his other defects of racism, misogyny, ignorance, lack of experience, impetuousness, laziness, narcissism, and contempt for the rule of law. Hillary lacks such defects, so it’s her honesty that gets attacked. Every time Trump speaks of “crooked Hillary”, he is endorsing Ricardo’s analysis of free trade.

[6 November 2016]

Scientists without borders

Yesterday’s numerical analysis seminar here at Oxford was given by an Egyptian who studied in France and the USA before taking his current job in the UK. There were 30 people in the room, and the group seemed even more diverse than usual. We checked and found that we had been born in 21 different countries: Argentina, Australia, Canada, China, Czech Republic, Egypt, Germany, Hungary, India, Iran, Ireland, Italy, Japan, Kazakhstan, Mexico, Romania, Singapore, Slovakia, Switzerland, UK, and USA.

[28 October 2016]


Somewhere along the way, the word “humbled” came in. “I am humbled,” declared the new NYU president at his inauguration last week. It’s a great word, sends all the right signals.

But a little detached, perhaps, from its traditional meaning. As Hillary recalled about one of her achievements in this evening’s Clinton-Trump debate –

“I was very proud and very humbled about that.”

[9 October 2016]

Genghis Khan’s descendants

How differently do mathematicians and historians think? It would seem the factor is about a billion.

I went to a lecture today by a history professor. His abstract had raised the question, “How many people alive today are descendants of Genghis Khan?” The answer he gave in the lecture was, around 16 million.

That was the word he used, simply “descendants”. However, after a question it emerged that he actually meant not just descendants but descendants in a direct male line, male to male to male to male (hence all with the same Y chromosome).

This is a sensational, spectacular, supernova kind of a difference. Suppose Genghis Khan lived 30 generations ago. In principle each of us has up to 2^30 ≈ 1 billion ancestors back then. (The actual number will be less because of overlaps and limited population size.) If one of your ancestors was Genghis Khan or William the Conqueror or Attila the Hun, that’s not very remarkable. But if your father’s father’s father’s … father was Genghis or William or Attila, that’s astonishing.

To this historian, the distinction was evidently a footnote.

[27 September 2016]