Often physicists do something new, and mathematicians later make it rigorous. Generally the physicists couldn’t care less, and as for the mathematicians, they quickly forget the physicists’ part in the story.
Here’s an example in the beloved book by Körner on Fourier series. In 1909 the physicist Jean Perrin, building on Einstein’s paper of 1905, realized that Brownian motion trajectories are continuous but nowhere differentiable. This was made mathematically rigorous in the 1920s by Norbert Wiener and Paul Levy. Körner summarizes Wiener’s construction with the words, “In accordance with Perrin’s prophetic remarks [the Brownian paths] turned out to be continuous and nowhere differentiable”.
Prophetic remarks! Once again, it would seem, a physicist had struck it lucky.
[8 March 2020]
The outstanding mathematician Louis Nirenberg died January 26. I knew him from my own times at NYU, and I liked him very much. Nirenberg was a mensch.
But how exasperating to read the obituary in Nature describing him as “skating above emerging distinctions between pure and applied mathematics”. What nonsense! Nirenberg was the quintessential pure mathematician. He was no more an applied mathematician than Einstein was an electrical engineer.
This imperialist point of view is all too familiar, and it drives me crazy. Pure mathematicians like to think mathematics is one, and as some kind of a corollary, it follows that the great pure mathematicians encompass the applied side too. For a few, like von Neumann, this may be true. For most, it’s preposterous.
[5 March 2020]
Books and movies nowadays have settled on a comfortable position regarding bad people. A bad adult was very likely abused as a child, and this has something to do with why they ended up bad, without, of course, excusing it.
Regarding the influence of countries on their citizens as opposed to families on their children, we take a curiously different position. Some governments are bad, we agree. The people of these countries, however, are good. We may criticize the wicked practices of the regime that has driven country X into the ground in the past 50 years, but we have nothing against the ordinary citizens of X, who are fine, decent people.
I wish it were so, but I think our model of families may be more accurate than our model of nations. My suspicion is that if a society is prosperous and fair, its citizens tend to be trustworthy and open, and if a society is venal and corrupt, they tend to be grasping. Of course, these are statistical statements, with a thousand exceptions. But I suspect it’s true on average.
Americans used to be famous for their corn-fed openness. Here in the age of Trump, they may be changing.
[22 February 2020]
Fifty years ago today, as a young teenager in Lexington, Massachusetts, I typed my first index card note. Naturally I have an interest in others who have followed a similar habit. Lichtenberg, Leopardi, Maugham, Manguso. Emily Dickinson, Michael Frayn, Samuel Butler. B. F. Skinner, N. N. Taleb. I happily regard these as kindred spirits through the ages, and I keep their books on a special shelf.
Lichtenberg wrote notes for more than 30 years, and Butler more than 40. Tomorrow I’ll be past 50!
[14 February 2020]
Edward VII was 59 when he ascended the throne, and Prince Charles is already 71. As Wikipedia puts it, he is “the oldest and longest-serving heir apparent in British history”.
I’ve realized that three different effects conspire to make it particularly unfortunate to succeed a Queen — a perfect storm of actuarial bad luck. First, of course, women live longer than men (Victoria to 81, Elizabeth to 93 so far). Second, women marry younger than men (Victoria was 20, Elizabeth 21).
Now these two effects apply to all of us, making our mothers last a decade longer than our fathers. But there’s a third factor that hits royals especially. If you are the Queen, or destined to be crowned as such, don’t imagine you can spend a few years after the wedding working on the relationship! No, the babies must come immediately. Edward arrived 12 months into the marriage, and Charles 21. Their mothers were practically teenagers.
[8 February 2020]
As I walked in I noticed the LGBT rainbow flag flying over the humanities building. My immediate happy reaction was: good!
Instantly this was followed by a second, unhappy thought as I reflected that these days, flying the rainbow flag is about more than just LGBT rights. Equally, it’s a statement of which side you are on, which public figures you approve of and which you disapprove of. How depressing.
And then my thoughts took a third, bitter turn. Who’s to blame for polarising us? It’s Trump and the Republicans.
All this in five seconds upon seeing that rainbow flying in the breeze.
[28 January 2020]
I don’t exactly often write notes of the kind you might find in the family section of a newspaper. But Kate and I have stumbled upon a delightful game and we’re thrilled to have found it. Try it next time you and a friend are on a drive for a few hours.
Simply pick a word or a theme and take turns choosing songs that mention the word or touch the theme. The magic is, nowadays it’s easy to call up any song on your smartphone and play it over the car speakers. To play the game, the driver drives and the passenger manages the electronics, but you take equal turns picking songs.
We’ve had half a dozen drives like this so far. The theme of “cities” led to Molly Malone, Brownsville Girl, and Jamaica Farewell (along with twenty others of course). “Work” led to the Lumberjack Song, Easy Wind, and 9 to 5. “Sky” led to Penny Lane, Over the Rainbow, and Clouds. “Railroads” gave us King of the Road, This Train, and Casey Jones. We’ve done flowers, girls’ names, animals, American states,….
[22 January 2020]
حصلت على هذا البرنامج النصي من جوجل ترجمة
Arabic script is beautiful, isn’t it?
I find it fascinating that readers of Arabic are incapable of seeing the script as I do. Of course they too can see beauty, but it will be beauty of a different kind, for they can’t turn off the message.
For me there’s a similar effect in the gulf between musical pieces I know and those I do not. I can get pleasure and even emotion from listening to a piece I don’t know, but it’s a formless experience, without any of the meaning that takes over when I’ve heard the piece ten times. Listening to a piece I know is much more satisfying. But once I know it, I’ve lost the ability to hear those sounds as sounds and nothing more.
[3 January 2020]
In the spirit of Occam’s Razor, I’d like to propose a simplification of the current system of rewarding the good with heaven and punishing the bad with hell.
The good spend their days on earth in sober industry, avoiding all excesses of food, drink, sex, and high spirits. Then they go to heaven for an eternity of the same.
The bad break these rules. It seems to me that as punishment, it suffices to send them to heaven too.
[31 December 2019]
I’ve long had the view that there are three main functions of a committee:
(1) Generate good decisions;
(2) Spread responsibility for decisions;
(3) Groom participants for future leadership roles.
[16 September 2019]