Thomas Pynchon, mathematical epigraphist

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…

P.G. Wodehouse on Euclid

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.)

All along the average

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.

“Würfeln” is German for playing dice

Since finishing Max Jammer’s book on the history of Quantum Mechanics, I’ve read a few more (and more popular) books, articles or reviews about the same general subject. One very striking thing — very obvious because of the outstanding level of the earlier book — was that none of the other texts gave any kind of feeling for the fact that the foundational work (until the middle 30’s at least) was very much a German-speaking affair. A few other languages are represented (de Broglie and the Curies in French, Dirac in English, Bohr at least partly in Danish), but their numbers are dwarfed by those of the German-speaking masters (Planck, Sommerfeld, Born, Einstein, Pauli, Schrödinger, Jordan, Heisenberg, etc). One anecdote emphasizes this clearly: the Indian physicist S. N. Bose sent a crucial paper in the form of a letter to Einstein (presumably in English), asking him if he could arrange for a German translation to be made and for its publication (Einstein did the translation himself).

Jammer gives most of the important quotations (and the crucial words in others) in the original language, with a translation. The other texts I’ve read, even if they briefly mention the original language, give only English translations of older quotes, with rarely a word of German appearing. (Of course, there is a lot of later literature which was first written in English). For most of the quotations, it seems there is no “official” translation, so it’s hard to judge their correctness.

For instance, it seems every source gives a slightly different version of the so-called “God doesn’t play dice” citation. The German original (in a letter from Einstein to Max Born in 1926; Born had been the first to give the standard interpretation of the modulus square of the “wave function” as giving the probability density of finding a quantum particle at a given point) is the following:

Die Quantenmechanik ist sehr Achtung gebietend. Aber eine innere Stimme sagt mir, dass das noch nicht der wahre Jakob ist. Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, dass der Alte nicht würfelt.

which translates fairly literally (the best I can do…) as

Quantum mechanics is very imposing. But an inner voice tells me, that this is not yet the real McCoy. The theory provides a lot, but it brings us little closer to the secrets of the Old Man. At least I am certain, that the Old Man doesn’t play dice.

What is mostly missing from most of the translations I’ve seen is the informality and playfulness of the language. There’s wahre Jakob, which seems really equivalent to the real McCoy. And of course there is der Alte — I have no idea what would be a colloquially equivalent word in English; I can’t say at all whether it really refers to a deity or not (and if yes, at what level of formality). And I also wonder if there isn’t some slight difference of emphasis or subtlety of meaning in the verb würfeln, which contains in a single word the meaning to to play dice (jouer au dé). [Interestingly, it seems that würfeln also means to dice in the cooking-sense of cutting in dices.]

Felicities of the German language

In supermarkets in Zürich (and in other German-speaking parts of the world), aluminium foil is called “Aluminiumfolie” — fairly straightforward, certainly, but since the word “folie” means “madness” in French, every time I see this word, I can’t help thinking of a some kind of craze for aluminium that would justify a name like “aluminium madness”.

Similarly, the word “Art” in German does not mean what the spelling suggests (which is “die Kunst”); much more mundanely, it means “kind” as in “integral of the third kind” or “Stirling-Zahlen zweiter Art”. But, even more than for aluminium, whenever I read a title like

Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen

I can not help translating it as

A new art of non-holomorphic automorphic functions and the determination of Dirichlet series by functional equations

(this is the paper where Hans Maass first introduced what are now called Maass forms, and showed how these non-holomorphic modular forms could lead to Dirichlet series with functional equation related to real quadratic fields, in analogy with the case of imaginary quadratic fields where holomorphic forms occured — both are now understood as cases of “Langlands functoriality”).

Equally romantic is Emil Artin’s title

Über eine neue Art von L-Reihen

for the paper where he introduces what are now called Artin L-functions; translating it as “On a new art of L-functions” seems so much better than just “On a new kind of L-functions”…