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]

Anonymous referees

The public sphere is in trouble these days, and part of the problem is online anonymity. Disinhibited people say the most brutal things, sometimes intending to hurt, other times just because what should hold them back?

We academics have known an elite version of this effect for years. Perfectly reasonable referees — these are our friends! — lose all sense of politeness when carrying out their anonymous duty. Alex Townsend and I hit an extreme example a few years ago with a manuscript we worked on with great care for many weeks and then submitted to SIAM Review. A referee said the paper was “simplistic,” “unscholarly,” “pointless,” “lacking in insight,” “sloppy,” “misleading,” “outdated,” “unevenly written,” “not up to the standards of SIREV,” and “a severe misrepresentation of the field.” He/she added that rather than consider the theory of matrix factorizations, as was the subject of our manuscript, we should “start with the simulation of a wing attached to an Airbus in turbulence.” If you’ve ever written a paper on theoretical linear algebra, you’ll have an idea of how bewildering such advice can be.

A case so extreme is easily laughed off, and this paper ended up published in the Proceedings of the Royal Society. But less extreme cases can be painful indeed, and in my experience they are the rule, not the exception. Prof. Jekyll becomes another creature entirely when he doesn’t have to sign his name.

[16 December 2020]

Hitler, Trump, and me

There are a hundred notes I’ve wanted to write about this awful Trump era, and mostly I’ve restrained myself. Here though is something that has been with me so persistently, such a permanent puzzle in my thoughts, that I feel I must record it.

The analogy with 1930s Germany is always there. How can the leading people in an educated, sophisticated, world-leading country cave in to the ravings of a madman? And here is what has puzzled me. In 1930s Germany, if you took a stand against the Nazis, you might be killed. But if a leading Republican takes a stand against Trump, yes they might lose their job, but they’ll get another one at a high salary. Almost all the top Republicans must know that Trump is evil. Why do so few take a stand?

This mystery has troubled me for years now. It has always seemed to me that if I were in their shoes, I would behave differently; yet surely that just showed a gap in my understanding. But lately I’ve reached a different conclusion. I think I really would behave differently. If I were a Republican Senator, I think I really would take a stand. I’m not alone in this, but it would seem I’m in a minority. My error was in assuming that ultimately people are all the same.

[16 July 2020]

Impact Factors

I tear my hair out over the widespread habit of listing a journal’s Impact Factor to four digits of precision. Today I attended a journal editorial board meeting in which we were let inside the sausage factory:

Citations in 2 years/no. of papers = \displaystyle{350\over 146} = 2.397.

Abracadabra! Three digits in, four digits out!

But the true problem is larger. With a three-digit sample size, the square-root effect of statistics tells us we should trust the quotient to about 1.5 digits. Not 3. Certainly not 4 — that would require a sample size of 108. This 4-digit Impact Factor is 62.5% garbage.

[4 September 2020]

Breakdown of the traditional teaching model?

Today may mark a turning point for Oxford mathematics. Because of COVID-19, our teaching will be virtual in the coming term. I had been looking forward to live performances, but no, it has been confirmed today that all our lectures must be prerecorded. In fact, we are encouraged to have them in the can before term begins.

This little development stores up a big question for the future. A year from now, will we be allowed to reuse the lectures we have recorded? It’s hard to see how a “yes” would be tolerable to administrators, who would see their faculty as being paid to do nothing at all. But it’s equally hard to see how a “no” would be tolerable to faculty, who would see themselves as chained to a meaningless make-work scheme.

Perhaps an ingenious resolution will emerge. I look forward to seeing it.

[ 31 July 2020]

Memos to papers to books

In recent years I’ve settled into the habit of writing numbered research memos. A typical one might be four pages long and include half a dozen computational experiments and plots along with theorems and references. The time scale of a memo is a matter of days, so they are excellent for day-to-day motivation, unlike papers (months) and books (years). These mathematical memos are the main way I communicate during an ongoing project with my coauthors and my increasingly forgetful self.

The current series, on rational functions, is up to Rat124, and 8 journal articles have come out of these. That’s 15 memos per paper. One level up in this verbal food chain, I note that all together in my career, I have published around 140 papers and 7 books. That’s 20 papers per book.

So my career to date has the heft of around 2100 memos. Actually, I wasn’t always so memo-happy; the true number is more like 400 — plus a few hundred Chebfun Examples, which are psychologically similar.

[27 July 2020]