The end of coins

At the Queen’s Lane Coffee House just now I decided to pay for my cappuccino with coins. The server said that was fine, but when I handed them to her, she turned the 20p coin over and around with some curiosity. Evidently she did not recognize it.

[3 October 2022]

Pedantics recapitulates semantics

I enjoy the word prequel, which probably hadn’t even been coined when the first instance I encountered was published: The Magician’s Nephew, in the Narnia series.

Prequel doesn’t come from Latin: it’s a back-formation from sequel, which does. What tickles me is that its derivation aligns thereby with its definition, for a prequel is something constructed backward from something that already exists.

[21 August 2022]

Expansion coefficients of size 10^100,000

Since writing An Applied Mathematician’s Apology I find myself noting more examples of how unquantitative mathematicians may be.

Here’s one. A well-known theorem by Müntz asserts that, for example, the function f(x) = x can be approximated arbitrarily closely for 0< x<1 by linear combinations of the functions 1, x2, x4, x6, … What Müntz’s theorem doesn’t tell you is that to do this, say to 6-digit accuracy, you’ll need 140,000 of those terms with coefficients as large as 10100,000 ! Such approximations would be useless in any conceivable application.

You might think that the discovery that a theorem is useless for any application would be of interest to mathematicians. In fact, most would regard this effect as just a curiosity. It doesn’t touch the essential truth or beauty of the theorem, and indeed, perhaps it enhances it by shining a light on the power of rigorous proof.

(I asked a leading expert in the area whether he knew of this 10100,000 effect. No, he responded, “I am not a numbers man.”)

In other words, a mainstream view among mathematicians is that it is not their business to care whether or not a theorem is capable of being applied. This raises the question, if it is not their business, then whose business is it? Engineers? I imagine most mathematicians would feel that no, one need not go so far as that. It is the business of the numerical analysts, who are, after all, mathematicians of a kind.

[27 July 2022]

Items on our bulletin board

The bulletin board nearest my office has seven color posters on it just now:

(1) Oxford Maths Summer Party
(2) Responsible Bystanders: If you see or hear inappropriate behaviour or language….
(3) The Athena Swan Principles
(4) The University does not tolerate any form of harassment
(5) Her Dark Mathematicals Women’s Coffee (for female and trans students and staff)
(6) Mathematrix (upcoming meetings for minorities/women/LGBTQ+/non-binary)
(7) SECTRA – the LGBTQIA+ Staff Network Pride celebration

Item (1) is an invitation to a party the day after tomorrow. All the others are aimed at special groups of people defined mainly by issues related to gender.

[22 June 2022]

Macron, Scholz, and inequality

During a walk along the Thames by Iffley Lock just now, I listened to the New Year’s speeches of the leaders of France and Germany, Emanuel Macron and Olaf Scholz. I loved both addresses. How reasonable, reassuring, and upbeat! Both Macron and Scholz had the same message: our country will be strong, for we will remain united.

This put me in mind of reflections I’ve had on walks in other, less salubrious neighbourhoods. You find yourself wondering, why does this guy in the scruffy clothes who just parked illegally look a little fishy, and why doesn’t everybody follow the rules? If you’re me, you see the answer to that question pretty fast. The explanation is that those of us who are winners, broadly speaking, have everything to gain from the system, so we generally support it. Those less lucky, gaining less, may not see the point of following the rules so scrupulously. The more extreme the inequality, the more dangerous this gets.

And thus we see why Macron and Scholz had the same common theme. As the elected leaders of their countries, they are the ultimate beneficiaries of the system. Of course they will tell us we should remain united. And I must add: they are right.

[3 January 2022]

Why are aphorisms so annoying?

Some aphorisms are charming,

An apple a day keeps the doctor away,

but too often they are annoying. Here’s a typical example from Taleb’s The Bed of Procrustes:

The three most harmful addictions are heroin, carbohydrates, and a monthly salary.

Here is apparently a one-sentence book review that Rota reprints as the final line of his Indiscrete Thoughts:

When pygmies cast such long shadows, it must be very late in the day.

What it is about such remarks? First of all they seem drenched in ego. On the surface, of course, the aphorism is a timeless truth with no connection to the author; but we know who he is really talking about. The brevity itself begins to feel like part of the egomania. The author affects to be so cool, so busy with more important projects, that he has just a moment to toss a piece of wisdom at us as he flies by.

I try for my own notes to be a little more sincere, and, to put it bluntly, a little longer. But it’s possible that Taleb and Rota think they are being sincere too.

[21 January 2022]

Nevil Shute and Carl Runge

We all have our special loves, as Kate calls them, things we cleave to with a personal feeling that becomes a part of our identity. For me, among authors, it is Nevil Shute, all of whose novels I’d read by age 20. My father was an engineer, and our family spent time in Australia, so Shute was a natural for me even before I became a fellow of his Oxford college, Balliol.

Among mathematicians, my special one is Carl Runge, a German from Bremen who looks just like my German great-grandfather Henry Newman in a formal photograph with his moustache and who understood my kind of mathematics better than anyone else in those pre-computer days. Runge was born 99 years before me on August 30, 1856 and was later appointed at Göttingen as Germany’s first Professor of Applied Mathematics.

[10 January 2022]

January 6 thoughts

It is idiotic to claim that Trump won the last election, or that Covid vaccines are useless. But in the last year we have learned that you can’t force people to give up their idiocies. The harder you try, the more they stick to them, and the angrier they get.

And if this is how it plays out with matters where truth is as clear as sunlight, it’s only worse with more arguable situations like guns or abortions. I believe abortions should be available, at least in the early months, but I don’t believe that finding the right to them in the Constitution and then forcing it upon all 50 states has been good for the USA.

So what do we do? How can we find a positive direction in this dark time? I wish we could stop trying to force other people to share our views. As of today, I am beginning to take seriously a solution where the USA splits into pieces.

This change of my thinking entails a change in my view of the biggest event of US history, the Civil War. Lincoln was an extraordinary man, and yet, maybe we would have been better off without him and his determination to keep the nation together.

[7 January 2022]

No Saturday this week

Harari asks, “In what sense can we say that Peugeot exists?” The idea is that a company, or any institution, has no physical existence, but is just a social construct. The theme builds to his much-quoted summary, “There are no gods, no nations, no money and no human rights, except in our collective imagination”.

Another example crossed my mind as I was writing the heading “Christmas, Saturday, 25 Dec. 2021” on a note card. I had a funny thought that this was unbalanced, for should not “Christmas” be so big as to blow away mere “Saturday”? I got to thinking, what if Parliament passed a law mandating that Christmas this year will not be a Saturday, nor indeed any day of the week at all, just a special space of its own between Friday and Sunday?

No, the collective imagination is too strong. None of us, as you might say King Canute once observed, has the power to stop Saturday being Saturday.

[27 December 2021]


I keep my whiteboard clean. So it was startling coming into the office just now to find it dirtier than I would ever leave it. I think the cleaners must have given it a once-over with a wet, dirty rag.

Instantly I was reminded of how I feel when proofs of a paper come back from the journal with the copy editor’s corrections.

[30 December 2021]