Like phones with their autocorrect, we all make mistakes when typing. Not for the first time, I just typed “as American as applied pie”.

[13 April 2024]

I think it’s not too great an exaggeration to say that for centuries mathematicians and (physical) scientists conceived the world like this,

whereas now many mathematicians have moved to a view more like this,

What an own goal! Some separation is to be expected as disciplines have grown bigger and more specialized. But it has been a vicious circle. As mathematics and science have diverged, mathematicians have come to know less of science, further encouraging them to focus on (1) rigor and (2) generality at the expense of (3) solving problems. Yet solving problems is what inspired Archimedes, Newton, Euler, Laplace, Gauss,….

[2 April 2024]

Everybody in this coffee shop has a computer, but they don’t know what a rarity I am. I’m actually computing!

[17 March 2024]

I have long been exasperated by mathematicians regarding numerical computation as some kind of an engineering add-on to their subject rather than part of mathematics itself. To fully understand and advance mathematics, surely we must apply and explore its ideas, and that means computing. What could be more obvious? Yet many mathematicians seem to believe that, although algorithms grind out numbers usefully for applications, one need hardly pay attention to all that.

Awkwardly, this narrow-minded view about numerical computation and mathematics parallels the view I have held about machine learning and science. All around us, ML is transforming our capabilities. Protein folding, weather prediction, design of materials, discovery of drugs — it’s amazing. I don’t deny the power, but my feeling has been that these new ML tools have little to do with true scientific understanding.

The analogy isn’t perfect, but I think it’s good enough that I should change my opinion. Provisionally, going forward, I shall take the view that machine learning is a true and indispensable part of science.

[29 December 2023]

I saw a rat crawling around a drain as I biked into Harvard this morning. I don’t see many rats, but English has reserved a three-letter word for them. This got me thinking about the set of possible consonant-vowel-consonent triples. How many are words?

Well, somebody could run a program and find out exactly. Meanwhile I enjoy spotting a few cases where all five triples are in play:

bag, beg, big, bog, bug
bat, bet, bit, bot, but
pat, pet, pit, pot, put
pap, pep, pip, pop, pup

Sometimes none of the five are in ordinary use:

fam, fem, fim, fom, fum
lan, len, lin, lon, lun

And there are some nice gaps, ready to be made into words, like internet domain names that nobody has yet picked up:

Rab, rem, rit, rom, rup.
Sab, sep, sig, som, sut.

[24 November 2023]

I just sent Michael Overton a message and noticed that as I soon as I typed the letter “o” it was completed to his name and address. So I got curious. Who are my 26 best friends as seen by Thunderbird?

They are Alex Townsend, Alex Barnett, Yida Chen, Daan Huybrechs, Heather Wilber, Patrick Farrell, Abi Gopal, Daan Huybrechs, Sarah Iams, Jacob Trefethen, Kate McLoughlin, Wanzhou Lei, Kate McLoughlin, Nick Trefethen, Michael Overton, Patrick Farrell, Qiang Du, Rob Corless, Sheng Yang, Nick Trefethen, Catherine Drysdale, Stephanie Vincent, Wanzhou Lei, Yidan Xue, Yuji Nakatsukasa, and Andre Weideman.

So my 26 best friends are 21 in number, and two of them are me.

[21 October 2023]

We often feel out of control, anxious about the innumerable things that need to get done, some real and vivid, others lurking in the shadows and harder to identify.

It seems to me that there are two broad approaches to coping with this anxiety: (1) get more on top of things, or (2) stop worrying so much about them. In my opinion, neither (1) nor (2) is always or entirely the right answer. It depends on the person, their state of mind, their stage of life, whether there are children in the house to be fed and clothed and got to school. For me now, the emphasis is decidedly on the first. My best strategy is (1) to try to stay on top of things, even though there are always a dozen more of them looming; while at the same time I write notes like this one to balance my portfolio with a spoonful of (2).

[21 October 2023]

I’ve arrived in Boston, from whence Route 95 goes all the way south to Miami and Route 90 goes all the way west to Seattle. The opposite corner of the country is Los Angeles, where Route 5 meets Route 10. The USA has this wonderful concept of interstate highways, multiples of 10 east-west and odd multiples of 5 north-south.

So I propose The Interstate Game. I tell you two numbers, and you tell me, what city lies at their intersection? For example: 25+70? 35+80? (Denver, Des Moines.)

Well, reality is a bit of a mess. Some of these highways barely cross a state, let alone a nation, and all told it seems around 47 of the 90 possible intersections actually exist. You also get plenty of oddities where two roads meet that shouldn’t according to Euclid — like San Diego at the intersection of 5 and 15. In fact in Dallas, three roads meet — 20, 30, and 45.

Still, we have plenty of fine cities to play with. And of course, you can run the game equally in reverse. Baltimore? That’s 95+70. Butte, Montana? 15+90. But who ever heard of Sulphurdale? (It’s near Cove Fort.)

[17 September 2023]

There can’t be many people who have traveled around the world without intending to, or indeed without realizing they were doing it until the final hours. But today I have become such a person.

I’m flying back to London from the ICIAM congress in Tokyo. Tokyo is just 1/3 of the way around the world from London, so one would normally fly east to get there and west to return. But Putin’s war has closed Russian airspace, and planes are diverting to new routes. Last Saturday I flew east to Tokyo, a long trip around the southern edge of Russia. And today, on this plane returning to London, I woke up from a nap to discover we were over Alaska, not Kazakhstan! Eastward to Japan, eastward again back to England through 16 time zones.

One of my biographemes has been that I’ve been around the world five times: in 1964-65, 1971-72, 1982, 1990-91, and 2003-04, every one a journey of many months including a drive across the USA with a visit to my Aunt Jane in Tucson. Four times heading west, once east. This week it seems I’ve unwittingly added another eastward circuit to the list.

[26 August 2023]

Today, on the eve of my last regular day in the office, I gave 53 years of index card notes to the Balliol library, about 1200 cards in all. I will keep writing, but I hope this means the collection will be safe no matter what happens up ahead.

My beloved Copernican Principle asserts that if you want to know how long something will last, your best starting estimate is how long it has lasted already. Balliol was founded in 1263. As Copernican precautions go, this looks about as good as it gets.

[10 August 2023]