Category: Language

I know about Japanese rings (commutative rings A which are integral domains and such that the integral closure of A in any finite extension of the ring of fraction is finite over A), and about Polish spaces (separable complete metric spaces). Are there any other mathematical concepts named after locations on Earth (or elsewhere)?

The only vaguely similar cases I can think of are K3 surfaces, which A. Weil mentions somewhere being named partly as a reference to the K2 mountain; and the recent innovation of esperantist graphs, which are defined in a new preprint of J. Ellenberg, C. Hall and myself (I’ll write about the latter in more detail soonish; the point of the name is that it alliterates with “expanders”, and it is indeed a condition related to, but weaker, than being an expander graph…)

One of the most charming category of words in any language is that of eponyms, nouns taken from the names of actual people (or places), when this origin is completely forgotten (not like euclidean…) Two favorites in French are

Poubelle (garbage container), from the name of the prefect Poubelle, who apparently made the use of such an implement mandatory in 1884;

Silhouette (silhouette), from a French finance minister of the middle 18th Century; here the etymology claims that the French people disliked his economy politics and attributed the name to drawings done equally economically… This word is even more remarkable in that it is now common in at least three languages (in English but also in German according to my dictionary). Are there others?

I’ve just learnt of a new one, a word I’ve used many times without ever wondering where it came from…

Barème: this may roughly be translated as “scale” or ‘table”; it’s commonly used in French for the distribution of points in an exam (e.g., four points for the first exercise, six for the second, and ten for the last problème). The name is from François Barrême (note the change of spelling; I’m using the Grand Robert as dictionary), a now obscure French mathematician from the late 17th century, who was once called ce fameux arithméticien (“this famous arithmetician”) for his works Tarifs et Comptes faits du grand commerce and Livre des comptes faits — see here; these books seem to have been simply conversion tables between units of measurements and money systems of various countries and provinces.

There might be some readers who are currently desperately looking for a suitable epigraph for their mathematical masterwork. The best advice I can give is to spend some time in the company of Thomas Pynchon’s works, which abound in scientific and mathematical wit. Many, though aware that P.G. Wodehouse’s wonderfully more readable oeuvre is unfortunately sadly lacking for this purpose, will still object by pointing out the reputation for incomprehensibility of, say, “Gravity’s Rainbow”, a heavy volume supposedly barely more understandable than “Finnegans wake”. However, it should be kept in mind that this reputation is the work of literary critics, who — and they are more to be pitied than castigated — are unlikely to find that the veil lifts when, around page 670, the dashing Yashmeen Halfcourt of “Against the day” starts conversing cogently in Göttingen with David Hilbert to propose what is commonly referred to as the Polya-Hilbert idea to solve the Riemann Hypothesis. But this, of course, is exactly where a mathematician will think that, after all, it’s not so bad.

Here are some of my favorite quotable excerpts from Pynchon:

• From “Gravity’s Rainbow”, which is also full of Poisson processes, if I remember right:
  

  “The Romans,” Roger and the Reverend Dr. Paul de la Nuit were drunk together one night, or the vicar was, “the ancient Roman priests laid a sieve in the road, and then waited to see which stalks of grass would come up through the holes.”

  (actually, I have to confess, with respect to this citation, to having committed two of the cardinal sins of epigraphists: I’ve used it twice — my excuse being that one time was for my PhD thesis, which was not published as-is –, and I haven’t read the book much further than beyond the place where it appears; and for those who wonder, there is at least one more dreadful faux pas in epigraphing: doctoring a quote to make it just perfect — and I’ve done it at least once).

• In “Mason & Dixon”, we find

  In the partial light, the immense log Structure seems to tower toward the clouds until no more can be seen.

  This novel was published in 1997; one cannot feel anything but impressed to see Pynchon following so closely the latest developments of post-Grothendieck algebraic geometry…

• Still in “Mason & Dixon” (which I am currently re-reading, hoping to vault triumphantly above the 50 percent mark of understanding), we have

  He sets his Lips as for a conventional, or Toroidal, Smoke-Ring, but out instead comes a Ring like a Length of Ribbon clos’d in a Circle, with a single Twist in it, possessing thereby but one Side and one Edge….

  which prompts the obvious question: is it really possible to blow a smoke ring in the shape of a Möbius band? Hopefully some experts will comment on this…

Nature, stretching Horace Davenport out, had forgotten to stretch him sideways, and one could have pictured Euclid, had they met, nudging a friend and saying: “Don’t look now, but this chap coming along illustrates exactly what I was telling you about a straight line having length without breadth.”

(taken from the first pages of Uncle Fred in the Springtime; due to a rather unfortunate fall in the stairs last week, I have to rest and watch my back for a few days, and hence I’ve been in need of light and refreshing literature to pass the time, turning therefore in part to re-reading some novels of P.G. Wodehouse.)

Few words, the OED informs us, have received more etymological examination than average (see the sense “average, n.²“). Ample consideration of this issue, we read, was given by eminent linguists, among whom are listed “Diez, Dozy, Littré, Wedgwood, E. Müller, Skeat, etc”. (The third one, É. Littré, is well-known in France, for his own XIXth Century French dictionary).

It seems that the mathematical sense arose from the following meanings:

2. Any charge or expense over and above the freight incurred in the shipment of goods, and payable by their owner. (In this sense it still occurs in petty average, and the now inoperative phrase, average accustomed in Bills of Lading: see quotations 1540 and 1865.)

3. spec. The expense or loss to owners, arising from damage at sea to the ship or cargo.

4. a. The incidence of any such charge, expense, or loss; esp. the equitable distribution of expense or loss, when of general incidence, among all the parties interested, in proportion to their several interests.

In this sense, it seems that “average” is directly related to the French word avarie (which, roughly, means any damage suffered by a ship or its cargo), both coming ultimately from the old Italian avaria. The OED traces the first use to 1200 (though it’s in an Old French text apparently), with English uses as far back as 1502.

In the mathematical sense, the first recorded uses seem to only come around 1750. One thing which seems to be not quite clear is whether one should say on average, or on an average, or on the average, or at an average, or something else altogether.