My father was one of the first four employees of the National Science Foundation when it was founded in 1950: Personal Assistant to the Director and Executive Secretary of the National Science Board. He remembered those happy days as a bunch of first-rate guys in an office in Washington trying to do the right thing for science and their country. I estimate he took home as his salary about 3% of NSF’s budget of $225,000.

75 years later, having moved to Harvard after decades in England, I have just registered with NSF as a potential investigator so that I can apply for grants. NSF’s budget last year was $9,877,000,000, and my proposal will ask for about 1/20,000 of that. My ID is 0000A0PB5, and Harvard’s is LN53LCFJFL45.

Among the many documents I must upload is my Mentoring Plan. I wish I could show my father NSF’s instructions for this, to be found in Chapter II, section D.2.i(i) of the NSF Proposal & Award Policies & Procedures Guide (PAPPG) (NSF 24-1), which begin as follows: “Pursuant to Section 7008(a) of the America Creating Opportunities to Meaningfully Promote Excellence in Technology, Education, and Science (42 U.S.C. § 1862o(a)) Act,…”.

[14 August 2008]

I love random twists of history like the following. Is there a name for them?

Switzerland leads in luxury watches because in 1541, Calvin banned jewelry. The lawyers managed to argue that watches were about function, not decoration, and that’s how we got Rolex and Patek Philippe.

The British drink sherry and port because during the Napoleonic wars, their access to French claret was cut off. They turned to peripheral countries, whose grapes weren’t as good.

The USA relies on employer-funded health care because in 1942, Roosevelt imposed a wage freeze. Employers had to find a different way to compete for workers, and we’ve been living with the consequences ever since.

Sport utility vehicles dominate the world because in the late 1970s, the USA passed a law mandating miles-per-gallon averages for cars. Automakers figured out that by building bigger vehicles classed as trucks, they could get around the rules.

[28 May 2024]

Most talks I attend have too many slides. Typically the speaker ends up skipping the last ten pages, expressing surprise that their time has run out so quickly. Even senior professors are surprised, though they’ve been giving talks for decades. Today we had 67 pages of mathematics for a 35-minute talk. One wants to laugh, and scream.

What’s going on here? One factor must be that mathematicians, who are geeky people, aren’t good at putting themselves in the heads of the audience. In preparing for the event, they don’t focus much on communication. They focus on their wonderful mathematics, whose details are so captivating!

A more unholy factor is that optimizing communication is never the whole purpose of a presentation. Audiences must be impressed as well as enlightened. If the talk is an incomprehensible torrent, alas, that may impress.

Like talks, papers are also too long. The reasons are the same, minus the comedy. I still want to scream.

[15 May 2024]

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 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-consonant 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]