Category: Language

When the conversation turns to anti-américanisme primaire, as it will every once in a while in France, the first argument I use if I intend to display a contrary argument is the New Yorker. Indeed, this magazine is so much above the level of the available French weeklies that (to use a cliché), it’s not even funny. Not only is the content much better — more art, more poetry, more humor, more fiction, less French politics –, but the difference is even stronger from the purely visual point of view (typography, art, design: no need to be able to read French or English to see which editors/writers/readers have better taste). This is especially shameful, considering that the French penchant for style over substance would seem to guarantee that we would (at least) do much better in this respect. However, it is not for any of the French magazines that J.J. Sempé draws covers, but for The New Yorker. (Sempé is known in France in particular for inventing the second most important fictional Nicolas in history).

I think I first read about The New Yorker in the introduction to a French translation of Woody Allen’s short humor pieces for the magazine (if you’ve never read any of them, I suggest googling for “Gossage Vardebedian”), in which (the introduction) it was identified as “the most snobbish magazine in the world”, which immediately piqued my curiosity. However, I think I read an issue for the first time when I went for a month to the US to work with Henryk Iwaniec in 1992. Then in late 1993, I decided to start subscribing from France. At that time, issues arrived there about one month after publication, so that reading the jazz programme at the Café Carlyle, for instance, was a somewhat quixotic thing to do, but most of the articles were of lasting enough interest that this delay was not much a problem.

My interest for this magazine has been considered somewhat obsessive at times. It is not true that I brought my fledgling (three years old) collection to the US when I went there for Graduate School, but I must admit that I did ship back to France all issues accumulated during that period (and the resulting post-doc), and then had them also sent to Switzerland, together with the issues of the last eight years or so (they are now in storage somewhere in Zürich).

Frankly, my justification for this accumulation was not quite convincing: it is not really useful to have physical issues of The New Yorker somewhere in the basement in a random order, since (until recently) it did not really help to remember vaguely that, say, there was a hilarious story about a mathematics class by some Irish author sometime during the first (or was it second?) Clinton administration — the time to locate it would still be discouraging to consider. Moreover, I couldn’t help feeling terribly jealous of older subscribers who could reach (if they knew where they were located) for issues containing stories by I.B. Singer, for instance, and read them whenever they wanted.

In principle, this two problems were solved a few years ago when The New Yorker published a set of eight DVD’s containing all issues of the magazine (until that date, of course; it has been updated regularly). I bought it immediately, but the fact that the DVD’s were encrypted, and the reader program did not work under Linux was something of a problem. Because we had a Mac in the house, it was still theoretically possible to take advantage of the archive, but in practice it was very inconvenient (except for the fact that the search database was a standard SQLite database, and could thus very well be queried from my Linux computers; so I could say very quickly when the Gossage-Vardebedian papers were published — January 22, 1966 –, but actually reading it involved complicated manipulations and printing to PDF from a very slow Mac whose DVD reader was broken, etc.)

But, at last, this is old history: just recently, The New Yorker started making available both a digital edition (which is convenient, but not so important for me), and the complete archive online, available more or less as in the DVD set, as exact reproductions of the actual magazine (so even the ads, etc, are exactly as in the printed edition, which is quite wonderful actually). Better yet: both services are available free to subscribers.

[Note: I am aware that many older subscribers believe the magazine went downhill starting about 1990; but I can’t really be held responsible for not reading it before, and (1) now I can; (2) it is still much better than the French weeklies…]

As a result of recent moves, the (almost) complete set of Buffon’s monumental Histoire naturelle belonging to my father’s family has recently arrived here in Zürich (it comes from my grand-father, who was director of the Muséum d’histoire naturelle de Nantes). I will keep these in my office for the moment, as it definitely lends it a very scholarly air…

(As far as I can see from the web page above, what is missing from our set is the Histoire naturelle des poissons, which was not written by Buffon anyway, but by the Comte de Lacépède, who also wrote the volumes about snakes, which we do have).

Many probabilists know Buffon for his annoying habit of dropping needles on the parquet, and finding the value of π after doing this sufficiently many times. This game was indeed included in his natural history, more precisely in the Essai d’arithmétique morale (or “Essay of moral arithmetic”) in Volume VII of the Suppléments — at least, it is there in my family’s edition, though it is missing from the web site containing Buffon’s works, where the Essai is in Supplement volume 4.

Here are pictures of the first pages of the description of the problem (click for readable larger picture):

and

Notice the delightful typography and orthography: the “s” that looks like an integral sign (and is barely distinguishable from an “f”), the way the past tense is written demanderoit instead of the current demanderait, etc.

Enlightnement came from a somewhat unexpected source (the manual for my digital camera), and a comment on the earlier post also suggested it: what may be the most natural English rendering of the French encadrement is “bracket”, or “bracketing”.

Indeed, it seems the term “bracket” is used in photography for the operation of taking simultaneously (or as nearly so as possible) three pictures, one with a given selected exposure, and two with higher and lower settings, so that the amateur photographer can then select which is best.

The ever-helpful OED confirms that this is a good choice: we find for Bracket, n., 5(b)

The (specified) distance between a pair of shots fired, one beyond the target and one short of it, in order to find the range for artillery; chiefly in the phrase to establish a bracket.

The quotations that go with this sense are convincing (if somewhat martial); here is the first one:

1899 Daily News 6 Dec. 5/7 At first I fire at 3100 yards, and if I find that my shot is short I fire a second round, say at 3300, in order to go beyond the object. If I see that my shot does go over I am satisfied that I have established what is called ‘a long bracket’, that is to say, I have found two ranges, 200 yards apart, between which the object must lie… I..fire another shot to shorten the distance within which I can then know that the target must be. This we call, on the same principle as the other, ‘a short bracket’.

There is then a further sense 5(c) with similar meaning:

A group bracketed together as of equal standing in some graded system, as income bracket: a class of persons grouped according to income.

And then, finally, bracketing is defined as “The action of furnishing, coupling, uniting, with brackets”. Altogether, it seems one can quite correctly state, in demotic English, something like:

… and so we have the bracket

(although, to my ear, the variant “we have the bracketing” seems better).

Is there a particular word in English for a string of two inequalities which together give both a lower and an upper bound for a certain quantity?  French has encadrement for things like this, as in

Pour tout réel x, on a l’encadrement

This is often quite convenient — of course, one can say “we have the following inequalities…”, but the extra information is useful to have, and it helps avoiding too many repetitions.

Note: The OED only lists encadré as an English word, as a technical term in crystallography:

A crystal is named encadré, when it has facets which form kinds of squares around the planes of a more simple form already existing in the same species, R. Jameson, A treatise on the external characters of minerals, 1805.

Quite by chance, I’ve stumbled in the archive of Nature (alas, not freely available) on a paper by J. Sylvester (dated December 30, 1869) concerning, roughly, the status of mathematics among sciences. He says his text was a reaction to earlier talks and articles by Huxley (the biologist, not the limericks writer…). His esteemed opponent having stated

Mathematics “is that study which knows nothing of observation, nothing of induction, nothing of experiment, nothing of causation”, but knows only deduction,

Sylvester argues strongly in the opposite direction:

I think no statement could have been made more opposite to the fact,

and goes on to give examples from his own work, in particular, where conclusions were reached, and entire theories were constructed, based on simple apparently accidental remarks, by processes of observation, induction and imagination.

Besides this discussion, reading this paper is quite fascinating. Mostly, it must be said, because it is rather incredibly hard to read. Not only physically (the font size is small, and the footnotes even smaller, and printed 2-up, it really exercises your eyesight), but also because of the language, which I believe should cause many a lover of the English language to either faint or burst out laughing; the Gothic Victorian style (cleverly ridiculed by Jane Austen in “Northanger abbey”) is here put into overdrive for the purpose of scientific discussion. There are rather frightening mathematical terms which, presumably, a few living readers can still interpret,

canonisant, octodecadic skew invariant, invariantive criteria, amphigenous surface, a catena of morphological processes

and there are Latin, Greek and French quotations, untranslated, and a German one (which, strangely, Sylvester feels to be in need of translation). The following passage is quite typical:

Now this gigantic outcome of modern analytical thought, itself, only the precursor and progenitor of a future still more heaven-reaching theory, which will comprise a complete study of the interoperation, the actions and reactions, of algebraic forms (Analytical Morphology in its absolute sense), how did this originate? In the accidental observation by Eisenstein, some twenty or more years ago, of a single invariant (the Quadrinvariant of a Binary Quartic) which he met with in the course of certain researches just as accidentally and unexpectedly as M. Du Chaillu might meet a Gorilla in the country of the Fantees, or any one of us in London a White Polar Bear escaped from the Zoological Gardens. Fortunately, he pounced upon his prey and preserved it for the contemplation and study of future mathematicians…

But there are also interesting things, like a discussion of the status of higher-dimensional geometry, and indeed a forecast of Flatland (the book of that title was only published 15 years later):

for as we can conceive beings (like infinitely attenuated book-worms in an infinitely thin sheet of paper) which possess only the notion of space of two dimensions…

The follow-up paper is much in the same style (with beauties such as “the Eikosi-heptagram“, and flights of fancy like “my own latest researches in a field where Geometry, Algebra and the Theory of Numbers melt in a surprising manner into one another, like sunset tints or the colours of the dying dolphin” – this theory is that of “the Reducible Cyclodes”), and also quite insightful sometimes. For instance, there is en passant, the following very convincing footnote:

Is it not the same disregard of principles, the indifference to truth for its own sake, which prompts the question “Where’s the good of it?” in reference to speculative science, and “Where’s the harm of it?” in reference to white lies and pious frauds? In my own experience I have found that the very same people who delight to put the first question are in the habit of acting upon the denial implied in the second. Abit in mores incuria.

(Sylvester writes the “i” in the word “in” in the last quotation as a dotless i; I doubt it’s a typographical error, but I can’t find an indication that this is proper Latin grammar; does any reader here have an insight on this?)