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]

The bibliographic arrow of time

References in published papers point to previous works. So it has always been possible to follow the graph backward, reference to reference, scooping up more and more of the history of a topic. A consequence is that it has been advantageous to cite later papers for review purposes rather than earlier ones, since they potentially link to more literature.

With Google Scholar and such tools of the internet, this bibliographic arrow of time has lately been eliminated. Now, given a paper X, it is easy to find the subsequent papers that cite X. Links can be followed in both directions. In choosing which paper to cite for review, there is less of a case for preferring the recent one.

All this is in a world where each publication at least has a fixed timestamp. Though it makes me uncomfortable, this too may be changing.

[17 September 2021]

He cllimbed the beach

If you type “He climbed the beech” into Google Translate, the French comes out correctly as “Il a grimpé le hêtre”. But I mistyped it just now as “He cllimbed the beech”. Out came “Il a grimpé sur la plage” — he climbed the beach!

It would take a better computer psychologist than I am to know exactly what happened here with Google’s machine learning algorithm, but the obvious guess is a rather cool one. I’m guessing “cllimbed” established me as a sloppy speller, from whom the most likely interpretation of “beech” was a sandy strip by the sea.

[29 August 2021]

Newton’s precarious PhD descendants

The Mathematics Genealogy Project allows you to track a mathematician’s students, their students, and so on. For example, I am listed with 75 descendants, and Isaac Newton has 21507.

But unlike me, Newton nearly died out! If the Project’s data are correct, he was followed by eight generations consisting each of one man having just one student, for 150 years (from Smith through Sedgwick, to be exact):

Isaac Newton, Cambridge 1668
Roger Cotes, Cambridge 1706
Robert Smith, Cambridge 1715
Walter Taylor, Cambridge 1723
Stephen Whisson, Cambridge 1742
Thomas Postlethwaite, Cambridge 1756
Thomas Jones, Cambridge 1782
Adam Sedgwick, Cambridge 1811
William Hopkins, Cambridge 1830

And then suddenly, we get the Cambrian explosion. As British science flourished in the Victorian era, William Hopkins had students Cayley, Galton, Maxwell, Routh, Stokes, Thomson, and Todhunter, all famous names still and all with hundreds or thousands of descendants of their own. It is to these that Newton owes his 20,000 or so descendants alive today.

If any link in the chain had been missing, Newton would have had no descendants in the present. Of course his actual impact would have been undiminished, so this is a reminder that there are more forms of inheritance than genetic.

[8 August 2021]

Highway traffic and what’s wrong with society

A lot of things feel wrong these days, and it’s tempting to blame this on bad people. The millions of guns in America are pressed upon us by selfish manufacturers with politicians in their pockets. Climate change is brought on by rich oil men who don’t care what destruction they cause, not to mention this week’s billionaires buying their way into space, each boasty launch destroying cubic miles of our atmosphere.

There are indeed bad people out there; there is plenty of corruption and plenty of evil. But I don’t think they provide a very full explanation of our problems. For example, any of us living in a rich country probably contributes more than the average human being to climate change, with our cars and air-conditioned stores offering meat and vegetables flown in from who knows where. Are we to declare that 50 percent of humanity are wicked because they emit more greenhouse gases than the other 50 percent?

My model of this situation is an analogy with driving on the highway (an analogous analogy to “Tall trees as an explanation of capitalism”). Yes, there are awful drivers, aggressive bastards whom I curse and who probably cause a lot of accidents. These people are bad, and the highway would be better without them. And yet most of the time, when traffic is clogged and we’re doing 40 instead of 80, nobody is to blame. It’s me and him and that lady too, all of us driving pretty reasonably, generating these problems in combination. We should find ways to punish and discourage the truly wicked, while also constantly working on engineering solutions to help the rest of us get along.

[20 July 2021]