“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]

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]

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 2³⁰ ≈ 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]

So far as I am aware, there is no historical evidence about Jesus Christ’s mother. I believe we just invented her. Thus one of Mary’s most distinctive properties is indeed quite true: she was immaculately conceived.

[21 September 2016]

Here in Oxford’s spectacular mathematics building, we had our weekly meeting of the Chebfun team yesterday. Looking around the table, I realized that the people here working with me were from Italy, France, Germany, the USA, Pakistan, Iran, Japan, and China — and that I was the only one in the room with the right to remain permanently in the UK.

Seven-and-a-half of our nine salaries are paid by sources outside the UK.

More or less accidentally, the British people seem to have voted to bring all this to an end.

[7 July 2016]

The Bible has much to say about sheep, which are cared for by man as man is cared for by God. Walking the South Downs Way past hundreds of them yesterday, I was wondering about what sheep make of this relationship. It’s hard to put myself in the mind of a ewe, but perhaps an approximation goes like this. She probably knows pretty well that people run the show. She probably has a sense that the man who takes care of her and her lambs is on their side. A caregiver.

Being a sheep, she probably doesn’t reflect much on the question of “why?”  Why does that man take care of us? What’s in it for him? Perhaps she dimly supposes that it’s because he likes us.

It doesn’t occur to her that his actual plan is to eat us.

[4 July 2016]

Jeremy Corbyn, leader of the Labour Party, was overwhelmingly defeated this week in a no-confidence vote: 40 votes for him, 172 against. That’s 81.1% against.

The press has been describing this fraction sometimes as “three-quarters”.  I heard that expression on Radio 4 when the vote was first announced, and here it is again in yesterday’s Economist: “Jeremy Corbyn has been rejected by three-quarters of his MPs”. In fact, 81.1% is between four-fifths and five-sixths.

The BBC and the Economist are not sloppy. We can assume their choice of words was intentional. I guess in their editorial judgment, “three-quarters” sounds like English and “four-fifths” sounds like statistics.

[1 July 2016]

Dear NA friends,

I don’t normally sink so low as to send you an image from a movie, but this is irresistible. Kate and I just saw The Martian, in which Matt Damon is stuck on Mars and likely to die. But then the very cool young JPL astrophysicist genius Rich Purnell has the idea of slingshotting a spacecraft around Earth and back to Mars at great speed. Will it work? Cool young Purnell goes to the computer to run the math. He presses Enter, waits a tense moment, and then in one of the film’s big dramatic moments, gets this response on the screen,

==================
| CALCULATIONS CORRECT |
==================

Isn’t this delicious? It’s not every day that Hollywood shows the world the excitement of numerical computation.

[16 May 2016]

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]