Pascal’s wager and my bowl of ice cream

I have marveled that although my life is far past half-way done, this doesn’t bother me much, which seemed irrational. But I’ve also argued, in connection with Pascal’s wager, that we are decoupled from our past and future selves by decreasing weight functions: that the present value of a pound of pleasure a year from now is only a few ounces.

I still hold to this view, and it explains the ice cream effect. If I assess my stage of life by integrating from birth to death without a weight function, then yes, I am 75% finished. With a weight function in there, however, the early and late years drop away. And that is why, throughout life, until near the end, as long as one is healthy, it can feel like the middle.

Living in the here-and-now is like driving at night with headlights shining on the road. A hazard ahead is nearly invisible until you get quite close.

[14 October 2022]

Bad driving incident

The other day on Holywell Street, I backed up without looking properly and put a couple of pedestrians at risk. This was bad driving. I was at fault.

The man gestured to me to lower my window and yelled at me about my bad driving. He was completely right, and I tried to tell him that I agreed and was deeply sorry. However, he was too mad, and he stalked off without hearing my apology.

And then boy was I mad too.

[4 October 2022]

World’s 5th biggest economy

The New York Times points out on the front page today that “Recently, Britain lost its place as the world’s fifth-largest economy to India.”

What an odd statement — not mentioning that India’s population is 20 times greater.

[5 October 2022]

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]