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]

Death before Dishonor

In North Yorkshire last week, it seemed to Kate and me that everybody had tattoos. Tattoos on their arms, legs, backs, faces, necks, chests. A sunny hour at the Saltburn beach was particularly revealing.

Our taxi ride back to the car at the end of the week put me next to a good specimen. The driver’s muscular forearm was filled by a colorful scroll declaring


I wondered, what do these words mean to him? Does he have in mind any particular kind of dishonor to be proudly avoided? Or is it just empty words that mean not much to him at all? For it’s hard not to notice, “dishonor” is the American spelling. Why would a tough guy from Yorkshire get his arm inked for life with a foreign spelling?

My guess is, he doesn’t much care how the words are spelled or exactly what they mean. He got the tattoo because it looks good. And before long I realized, this Death before Dishonor emblem exemplifies a general effect. Most people don’t think through their views very carefully. They put on whatever feels good, if they like the color.

[20 July 2021]

Violations of shoe pairing

There’s a law of physics we all rely on: like quarks, mutatis mutandis, shoes come in pairs. If you find one of your shoes, the other one is nearby.

I hadn’t noticed the shoe-pairing law until recently because only recently has it begun to fail in our house, now that Clancy is on the scene. I believe the physics explanation involves the Casimir force and a puppy-induced increase of entropy.

Even with Clancy, the other shoe can usually be found within 15 feet, so shoe-pairing violations aren’t serious in themselves. Still, they make me wonder what other unnoticed laws hold together our world.

[2 April 2021]

Silver meat skewer

This past year has rooted millions of us in our homes and our routines. I know every square foot of this place so well, it’s like being a child again.

Here’s an illustration of the groove I have worn. Months ago I bought a bright light to keep my study cheery, which sits on the piano three feet to my right. To turn it on, I just need to touch it. But my arm isn’t three feet long. So to turn on the light I get up from my desk, right?

Wrong. Years ago, for a big birthday, my father gave me a foot-long Georgian silver meat skewer to use as a letter opener. Somewhere along the way this pandemic year, I discovered that if you touch the light with the skewer, it switches on as easily as if you’d touched it with your hand. (My father loved silver, and showed me how it conducts heat and electricity even better than copper.) Two feet (arm) plus one foot (skewer) spans the gap. I don’t get out of my chair.

[27 March 2021]

Randomness and applied mathematics

The greatest change in the applied mathematical landscape in my career, apart from the advance of computers, has been the penetration of probabilistic ideas into every corner of our work. Differential equations become stochastic differential equations; deterministic algorithms become randomized; simulation gives way to uncertainty quantification. When I was a graduate student, hardly anyone outside of statistics departments worked on stochastic problems — certainly none of us numerical analysts in Serra House at Stanford. Nowadays if you don’t, you are old-fashioned.

I got a chance to quantify this trend when I gave the keynote lecture yesterday at the annual meeting of the MIT Center for Computational Science and Engineering. At the end of the question period I asked the audience — about 75 graduate students and postdocs, the CSE leaders of the future — how many of you work on problems with a probabilistic component? We did a Zoom poll, and the answer was 63%.

[16 March 2021]

The comfort of words

The other day I finished La Petite Fille de Monsieur Linh by Philippe Claudel. It is a beautiful story of the friendship between two older men, both troubled by loss and loneliness, who sit together on a park bench day after day. They have no language in common, but M. Bark talks endlessly about this and that in his own language, and M. Linh listens. In fact each is the other’s best friend, providing comfort and contact.

A pretty picture, I thought, but could it really be so?

The very same week, Kate and I got our 8-week-old puppy Clancy. A new member of the family! — and the funny thing is, I talk nonstop to him about anything and everything. It feels good, it’s comforting, it somehow deepens our relationship.

[21 February 2021]

An extra billion people

When I was a kid the world’s population was 3 billion, and today’s nearly 8 billion would have seemed the very definition of dystopia. And indeed, high population is to blame for a good fraction of climate change and other problems besides, though it has become unfashionable to speak of population as a problem.

Over these decades, the average weight of a human being has surely increased by 1/8. We’re larger than we were, and we eat more food and need more space and more materials. From the 1960s point of view, from the biomass and bioneeds points of view, it’s as if yet another extra billion had been added.

Looking around on the web, I find a 2012 paper by Sarah Catherine Walpole et al. that gives estimates of around half a billion.

[16 December 2020]