I am Paul McCartney

I have long had a theory about the Beatles and Bob Dylan. I know their songs intimately, every note, every cough, every crackle. My theory is, I know the recordings better than they do. Paul McCartney has played Yesterday thousands of times, no two of them identical. What chance has he got against me with the thousands of times I’ve heard the 1965 version?

Today I had the chance to be McCartney. I had a fine afternoon working with my new student Abi Gopal, who seems to have read all my works and knows them backwards. Toward the end of the day I proposed that we try a certain trick adapted from my AAA approximation paper of a couple of years ago. He agreed that this was a good idea, and then gently showed me that I hadn’t remembered the algorithm right.

[10 March 2018]

Advertisements

Metro mean and variance

At the metro every few weeks I run into a nice example of the relationship between mean and variance. My card is running out of credit, so I figure I should recharge it. Now, should I do that before the train ride, or after?

If I recharge the card after the ride, it will take one minute, and that’s that. The mean time spent is one minute and the variance is zero.

If I recharge it before, it’s a lottery. Nine times out of ten, I’ll catch the same train, so I’ll lose zero minutes. The tenth time, I’ll miss the train and spend ten minutes waiting for the next one. The mean is exactly the same, one minute! — but the variance is far from zero.

So which is the right choice? Ah, that depends on my day’s schedule and my mood and my personality. There’s nonlinearity for you.

[24 March 2018]

France, USA, China

Here in France for the year, I marvel that a country can be so advanced and rich and organized, such a complete civilization when you’re living inside it, and yet not seem to matter much to the world at large.

The reason is simply scale. France has 67 million inhabitants, so with 320 million, the USA is four or five times bigger. France has no chance against a disparity of that magnitude.

What if there were a rich, organized country four or five times bigger than the USA? Well, the population of China is around 1380 million. Stay tuned.

[30 January 2018]

Truth in four words

In the last couple of days I’ve had two good examples of somebody saying it all in just four words.

An academic couple were reminiscing about how they got through final exams years ago. She described how she prepared an elaborate diagram detailing what topic she would work on, each quarter-hour throughout the exam period. He said,

“I just read stuff.”

And now here I am at the MONA museum in Hobart listening on the audioguide to the German artist Julius Popp describing his work bit.fall, in which words appear as if by magic in falling water droplets. It’s remarkable when you first see it, and for him after a few years, it seems it’s still remarkable:

“I get sometimes chickenskin.”

[4 February 2018]

Women in science

Women have contributed much less to the physical sciences than men. It’s depressing and it’s glaring and it almost poisons any discussion of the history of, say, physics or mathematics.

Suppose you accept, as I do, that to the best of our knowledge the sexes are equal in intrinsic ability to do science. That leaves a hierarchy of possible explanations:

(1) Women contribute as much as men, but their contributions are not acknowledged.

(2) Women would be able to contribute as much as men, but they are squeezed out of the profession.

(3) Women would be able to contribute as much as men, but too few end up with the right education and career goals.

In the heat of discussion you will hear people claim that it’s all about (1) and (2), or even just (1). In fact, (3) is the biggest explanation, and it is here that we must hope for truly large-scale changes in the future.

[30 November 2017]

Polynomials pure and applied

Algebraic geometry is the purest of pure branches of mathematics, concerned with the intrinsic structure of functions. Its central tool is polynomials, which constitute the very special case of functions you can “write down”.

Chebfun is the most practical of practical branches of mathematics, concerned with machine computing with functions. And its central tool is polynomials too! Mine is the kind of mind that needs to know, are algebraic geometers and Chebfunners interested in polynomials ultimately for the same reason, or different?

I think they are different.  The starting point of algebraic geometry is that, given a function f and a point a, there is a polynomial that exactly matches f and its derivatives at a. The starting point of Chebfun is that, given a function f and an interval [a,b], there is a polynomial that approximately matches f on [a,b] to any prescribed accuracy.

[9 October 2014]

Safety tips

Some maxims seem so natural one assumes they must have been expressed many times before. Here are two that I’ve shared with Emma and Jacob at various ages.

For cyclists (or drivers, or skiers):
Never do anything surprising.

In the restaurant (or the bar, or at home):
Never drink when you’re thirsty.

[6 January 2018]