Many more books

I recognize myself in these notes by Chris Tiee on tensor analysis—the fever of acquisition, the uses of comparison, and the stray insight that makes the whole book worth it (as the one track does for the whole album):

“One way to learn a lot of mathematics is by reading the first chapters of many books.”—Paul R. Halmos

Ah, the dreaded discussion of texts for tensor analysis. I am addicted to collecting math books (I also often have 10 books checked out from the library simultaneously) and reading the first 20 pages of them. Very occasionally I make it through farther than that. Despite the proliferation of bad tensor analysis texts (some would say all of them are bad), I have to admit I have gleaned everything I have learned about Tensor Analysis from reading these books, collecting the knowledge into a gigantic patchwork. The fact is, each text actually has a gem of insight or two that is not presented in any others. There is much overlap in the bad parts, and some in the good parts too, but of course, it’s always hard to consult so many references, since I often forget the transformation laws on those overlaps. . . not to mention also the transformation laws that tell how the notation changes—regarding this, we have the following

A.1. Joke. Differential geometry is the study of those things invariant under change of notation.

Another problem is also that it’s very hard to strike a balance between being intuitive in the explanations of what these things are—and hence being vague—and also developing a precise, formal theory that is the real deal—hence being obfuscatory.

The quote from Halmos isn’t quite right. It’s actually, “I wish I had read the first ten pages of many more books—a splendid mathematical education can be acquired that way.” As for tensors, a newer book rich in intuition is Dwight Neuenschwander’s Tensor Calculus for Physics.

Nothing but a little marrow

From Rabelais’s prologue to the first book of Gargantua and Pantagruel, translated in 1653 by Sir Thomas Urquhart:

Most noble and illustrious drinkers, and you thrice precious pockified blades (for to you, and none else, do I dedicate my writings), Alcibiades, in that dialogue of Plato’s, which is entitled The Banquet, whilst he was setting forth the praises of his schoolmaster Socrates (without all question the prince of philosophers), amongst other discourses to that purpose, said that he resembled the Silenes. Silenes of old were little boxes, like those we now may see in the shops of apothecaries, painted on the outside with wanton toyish figures, as harpies, satyrs, bridled geese, horned hares, saddled ducks, flying goats, thiller harts, and other such-like counterfeited pictures at discretion, to excite people unto laughter, as Silenus himself, who was the foster-father of good Bacchus, was wont to do; but within those capricious caskets were carefully preserved and kept many rich jewels and fine drugs, such as balm, ambergris, amomon, musk, civet, with several kinds of precious stones, and other things of great price. Just such another thing was Socrates. For to have eyed his outside, and esteemed of him by his exterior appearance, you would not have given the peel of an onion for him, so deformed he was in body, and ridiculous in his gesture. He had a sharp pointed nose, with the look of a bull, and countenance of a fool: he was in his carriage simple, boorish in his apparel, in fortune poor, unhappy in his wives, unfit for all offices in the commonwealth, always laughing, tippling, and merrily carousing to everyone, with continual gibes and jeers, the better by those means to conceal his divine knowledge. Now, opening this box you would have found within it a heavenly and inestimable drug, a more than human understanding, an admirable virtue, matchless learning, invincible courage, unimitable sobriety, certain contentment of mind, perfect assurance, and an incredible misregard of all that for which men commonly do so much watch, run, sail, fight, travel, toil and turmoil themselves.

Whereunto (in your opinion) doth this little flourish of a preamble tend? For so much as you, my good disciples, and some other jolly fools of ease and leisure, reading the pleasant titles of some books of our invention, as Gargantua, Pantagruel, Whippot (Fessepinte.), the Dignity of Codpieces, of Pease and Bacon with a Commentary, &c., are too ready to judge that there is nothing in them but jests, mockeries, lascivious discourse, and recreative lies; because the outside (which is the title) is usually, without any farther inquiry, entertained with scoffing and derision. But truly it is very unbeseeming to make so slight account of the works of men, seeing yourselves avouch that it is not the habit makes the monk, many being monasterially accoutred, who inwardly are nothing less than monachal, and that there are of those that wear Spanish capes, who have but little of the valour of Spaniards in them. Therefore is it, that you must open the book, and seriously consider of the matter treated in it. Then shall you find that it containeth things of far higher value than the box did promise; that is to say, that the subject thereof is not so foolish as by the title at the first sight it would appear to be.

And put the case, that in the literal sense you meet with purposes merry and solacious enough, and consequently very correspondent to their inscriptions, yet must not you stop there as at the melody of the charming syrens, but endeavour to interpret that in a sublimer sense which possibly you intended to have spoken in the jollity of your heart. Did you ever pick the lock of a cupboard to steal a bottle of wine out of it? Tell me truly, and, if you did, call to mind the countenance which then you had. Or, did you ever see a dog with a marrowbone in his mouth,—the beast of all other, says Plato, lib. 2, de Republica, the most philosophical? If you have seen him, you might have remarked with what devotion and circumspectness he wards and watcheth it: with what care he keeps it: how fervently he holds it: how prudently he gobbets it: with what affection he breaks it: and with what diligence he sucks it. To what end all this? What moveth him to take all these pains? What are the hopes of his labour? What doth he expect to reap thereby? Nothing but a little marrow. True it is, that this little is more savoury and delicious than the great quantities of other sorts of meat, because the marrow (as Galen testifieth, 5. facult. nat. & 11. de usu partium) is a nourishment most perfectly elaboured by nature.

In imitation of this dog, it becomes you to be wise, to smell, feel and have in estimation these fair goodly books, stuffed with high conceptions, which, though seemingly easy in the pursuit, are in the cope and encounter somewhat difficult. And then, like him, you must, by a sedulous lecture, and frequent meditation, break the bone, and suck out the marrow,—that is, my allegorical sense, or the things I to myself propose to be signified by these Pythagorical symbols, with assured hope, that in so doing you will at last attain to be both well-advised and valiant by the reading of them: for in the perusal of this treatise you shall find another kind of taste, and a doctrine of a more profound and abstruse consideration, which will disclose unto you the most glorious sacraments and dreadful mysteries, as well in what concerneth your religion, as matters of the public state, and life economical.

The varieties of lexicographic experience

Some instances of an understudied genre, predominantly satirical:

Bierce, The Devil’s Dictionary

Flaubert, Dictionary of Received Ideas

Fowler, Dictionary of Modern English Usage [which I include under the banner of satirical for such entries as “genteelism”]

Heifetz, Mrs. Byrne’s Dictionary

Slonimsky, Lexicon of Musical Invective

Voltaire, Philosophical Dictionary

How far can the dictionary form depart from the norm? Can there be a dictionary (or encyclopedia?) of—say, jokes? What else? Another lexicographic genre is that of the collection of keywords (not quite a straightforward glossary or scholarly lexicon)—for a culture, for a theme, for a discipline. Some examples:

Barthes, A Lover’s Discourse

Jay, Cultural Semantics: Keywords of Our Time

Lewis, Studies in Words

Williams, Keywords: A Vocabulary of Culture and Society

Almost unable to despise

The thirty-second of Leopardi’s Pensieri (Thoughts), written in 1837, translated by J.G. Nichols:

As he advances every day in his practical knowledge of life, a man loses some of that severity which makes it difficult for young people, always looking for perfection, and expecting to find it, and judging everything by that idea of it which they have in their minds, to pardon defects and concede that there is some value in virtues that are poor and inadequate, and in good qualities that are unimportant, when they happen to find them in people. Then, seeing how everything is imperfect, and being convinced that there is nothing better in the world than that small good which they despise, and that practically nothing or no one is truly estimable, little by little, altering their standards and comparing what they come across not with perfection any more, but with reality, they grow accustomed to pardoning freely and valuing every mediocre virtue, every shadow of worth, every least ability that they find. So much so that, ultimately, many things and many people seem to them praiseworthy that at first would have seemed to them scarcely endurable. This goes so far that, whereas initially they hardly had the ability to feel esteem, in the course of time they become almost unable to despise. And this to a greater extent the more intelligent they are. Because in fact to be very contemptuous and discontented, once our first youth is past, is not a good sign, and those who are such cannot, either because of the poverty of their intellects or because they have little experience, have been much acquainted with the world. Or else they are among those fools who despise others because of the great esteem in which they hold themselves. In short, it seems hardly probable, but it is true, and it indicates only the extreme baseness of human affairs to say it, that experience of the world teaches us to appreciate rather than to depreciate.

I think of the opening of Marianne Moore’s poem “Poetry”:

I, too, dislike it: there are things that are important
beyond all this fiddle.
Reading it, however, with a perfect contempt for it,
one discovers that there is in
it after all, a place for the genuine.

Perpetual and immense

Some choice passages from Renée Neu Watkins’s translation (Waveland Press, 1999) of Leon Battista Alberti’s magnificently shrewd De commodis litterarum atque incommodis (The advantages and disadvantages of books), written in Latin around 1430:

[…] I have meditated and thought long and hard, searching with all my ingenuity for a subject I could treat adequately and which would prove the quality of my intellect, so as to satisfy them if it lay within me. But nothing came to mind that had not been beautifully dealt with by the divinely inspired classical authors, so that no one of our time, however learned, could deal with it better than they, nor did there seem to be some topic left of the kind they had treated, that I could handle well and with grace. The ancients had encompassed all serious and comic material, leaving to us only the opportunity to read them and the obligation to admire. Older contemporaries of ours have seized on a few subjects that lay hidden, perhaps overlooked by the ancients, and have thus gained honor and fame. If one wants glory, however, one must be willing to write something that is not perfect and ideal rather than allow oneself to grow old in erudite silence.

 

I earnestly beg you, my brother (if I may borrow your own phrasing in Ephebis) to read this little book of ours, correct it according to your own unswerving judgment, and by your emendations kindly make it better and more beautiful.

 

The life men of learning live is necessarily hard and harsh; by this I mean the ones who, as they should, abandon all other things for the sake of intellectual work. No art, however minor, demands less that total dedication if you want to excel in it. What we know to be true of all arts is most especially true of reading and writing; there is no freedom from striving at any age.

 

In my experience, however, you won’t find many rich men who think books, let alone the delights of study, are worth the effort.

 

Who, with a mind occupied by love, will be able to focus whole and steadfast attention on texts? Who can then be fully absorbed in his work, intent on the teachings, ready and able to store up and retain them? Who, when captive to the madness of love, will have the will power and intellectual vigor and enthusiasm to perfect himself in any noble art? Don’t we know how love usually affects people? Sapping energy, corrupting conduct, perverting the intelligence, loading the mind with obsessions, filling the intellect with errors, driving a man to madness: these are its well-known services, the gifts that it bestows.

 

A brief period away from study has the power to disperse more material than many long hours of application can restore; things placed in memory slip away faster than they can be rememorized or recaptured.

[Cf. the pianist’s quip, variously attributed to Liszt, Rubinstein, and Paderewski: “If I miss one day of practice, I notice; two days, and my friends notice; three days, and everybody notices.”]

When you wish to buy clothes, isn’t it true that your library will say to you: “You owe me that money, I forbid…” If you wish to pursue the hunt, or music, or the martial arts or sports, won’t the books says: “You are stealing this energy from us, we will not bring you fame and reputation!” If you inquire into technical knowledge or painting or three dimensional design, the philosophical disciplines will react strongly: “This is the way you defraud us of your energies. From you we will withhold knowledge of the highest things…!”

 

If you want to refresh your spirit by a country excursion […] the vocation you have taken up will pull you back from there to books and writing, and if you do not with much labor and long hours devote yourself totally to these, the books themselves will threaten you with shattering disgrace.

 

But I would not want to obscure the true nature of scholars by concluding that they devote themselves to books with no idea of pleasure. They could not perform such great labors without some notion of pleasure in their minds. There are those who willingly go into mourning, because they take pleasure from being considered very faithful and true to the memory of friendship. Many actions by which we satisfy convention and public opinion seem less painful to us than they really are. The pleasure of study, however, is such that it might better be called pain: sedentary all the time, reading all the time, thinking hard, always alone, renouncing festivities and play. I am not so bitter and hard a man that I would dare call this a pleasant way to live. […] To satisfy the desire to learn is indeed a pleasure, but the very hard work of study and the accompanying anxiety that oppresses the spirit always bring more mental torment than joy. So if we indeed take a certain pleasure in learning, huge cares and labors undermine it. There is a big difference, moreover, between the burden of fighting the intrigues and assault of enemies, which is experienced relatively briefly, and the scholar’s daily anxiety, which is perpetual and immense. For there are innumerable things in books that are supremely worth knowing, nor is it easy to describe how the desire to learn presses upon a scholar. He may participate in difficulty scholarly debates, or explore some elegant, worthy, and learned subject; while he does so, he does not sleep, does not eat, does not rest, and feels almost no satisfaction. The desire to know and to remember it all is constantly gnawing at him. He takes on immense projects, is entangled in an array of possible rhetorical devices, is constantly tense. On top of this, he is always coming across things previously unknown to him: he encounters in his reading adroit, subtle, and clever ideas, finds some unusual illustrative anecdote, or learns new refinements of the power of persuasion; these things provoke in him the desire to learn more, and he is unable to set limits or stop, nor is he granted any peace of mind as long as he has not cleared up every obscurity. Thus, as you see, the scholar is a very complex puzzle himself, and neither physically nor mentally ever, or hardly ever, gets any rest. Bleak solitude, hard labor, endless hours, great anxiety, difficulty questions, total absorption, intense anxiety—as there is no pleasure to be found in this man, so in his whole life there is almost no break in the onslaught of work and worry.

To Alberti’s unremittingly bleak, if otherwise unsurpassed, characterization of the obsessively acquisitive and self-reinforcing anxiety at the heart of bibliophilia (epistemophilia?), one might counterpose a finer appreciation of the compensating blisses and ecstasies: Barthes’s “pleasure of the text,” Feynman’s “pleasure of finding things out,” Morris’s account of “pleasure in the work itself” (which he writes about here and here), something—appropriately, I cannot remember what—in Emerson. See also: Aristotle’s “desire to know,” Wordsworth’s “bliss of solitude,” Joyce’s “luminous silent stasis of aesthetic pleasure.”

διπλοῦν ὁρῶσιν οἱ μαθόντες γράμματα

An inscription at the University of Edinburgh

My title, “Diploun horosin hoi mathontes grammata”—those who learn the letters [or alphabet] see double—appears in the Γνῶμαι Μονόστιχοι, Gnomai Monostichoi, of Menander, a collection of one-line sayings (not necessarily Menander’s own) with a long legacy in literary education. It is line 657, on page 359, in the version collected in Μeineke’s Fragmenta Comicorum Graecorum, Volume IV, Fragmenta Poetarum Comoediae Novae:

The only English translation is by John Maxwell Edmonds, The Fragments of Attic Comedy After Meineke, Bergk, and Kock, volume IIIb, where he renders the line “Who learns to read doubles his power of sight.” (Though it is not at all what Wittgenstein meant, I am reminded of 5.6 in the Tractatus, “Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt”—the limits of my language mean the limits of my world.)

The Gnomai represent the genre of the gnomologium, a sort of textbook anthology or chrestomathy of wisdom for rhetorical or moral instruction, especially popular throughout antiquity and the Middle Ages. Erasmus mentions the genre (and cites Menander) in his Adages:

There were those, especially among the Greeks, who willingly undertook the task of making gnomologies, collections of aphorisms, notably Johannes Stobaeus. I would rather praise their work than imitate it.

Compare the commonplace book.

Double, triple, quadruple hypothesis

from the first chapter, “Parole, Parole, Parole,” of Tobias Jones’s The Dark Heart of Italy (2003):

As I began studying postwar Italian history, it became obvious that surrounding any crime or political event, there are always confusion, suspicion, and “the bacillus of secrecy.” So much so that dietrologia has become a sort of national pastime. It means literally “behindology,” or the attempt to trump even the most fanciful and contorted conspiracy theory. Dietrologia is the “critical analysis of events in an effort to detect, behind the apparent causes, true and hidden designs.” La Stampa has called it “the science of imagination, the culture of suspicion, the philosophy of mistrust, the technique of the double, triple, quadruple hypothesis.” It’s an indispensable sport for a society in which appearance very rarely begets reality. Stendhal wrote about it in The Character-house of Parma: “Italian hearts are much more tormented than ours by the suspicions and the wild ideas which a burning imagination presents to them.”

Consider, as counterpoint, Moravia’s short story “Non approfondire” (Don’t delve too deeply). Compare, of course, the “hermeneutics of suspicion.”

There is an interesting discussion of the word at the Language Log, and it’s the subject of a column in the Economist from 2011.

Stupid for the rest of the day

From the Wikipedia page on Paul Valéry:

Valéry’s most striking achievement is perhaps his monumental intellectual diary, called the Cahiers (Notebooks). Early every morning of his adult life, he contributed something to the Cahiers, prompting him to write: “Having dedicated those hours to the life of the mind, I thereby earn the right to be stupid for the rest of the day.”

The subjects of his Cahiers entries often were, surprisingly, reflections on science and mathematics. In fact, arcane topics in these domains appear to have commanded far more of his considered attention than his celebrated poetry. The Cahiers also contain the first drafts of many aphorisms he later included in his books. To date, the Cahiers have been published in their entirety only as photostatic reproductions, and only since 1980 have they begun to receive scholarly scrutiny. The Cahiers have been translated into English in five volumes published by Peter Lang with the title Cahiers/Notebooks.

The more things have gone wrong

Colonna, in Umberto Eco’s Numero Zero, translated by Richard Dixon:

Losers, like autodidacts, always know much more than winners. If you want to win, you need to know just one thing and not waste your time on anything else: the pleasures of erudition are reserved for losers. The more a person knows, the more things have gone wrong.