for Janet Buck
The Pope is visiting Kenya and his words are reported: “Experience shows that violence, conflicts and terrorism … are born of poverty and frustration.” Is this possible? Can this truly be Jorge Bergoglio, the boy who learned grammar, arithmetic, and Argentine patriotic marches at one of the best schools on the map, the little state school on Calle Varela where I happened to study too? No, Your Holiness, experience shows nothing of the kind. It would be hard to argue that the violence of the likes of Nero or Kim Jong-Un is born of early poverty and frustration, and that the recruits of the new Caliph are coming from the poor—they seem to be coming rather from the bored. It seems that the first Christian martyrs were persuaded that as a prize for their sufferings they were to be admitted, that very day, to the presence of the Lord, and it seems that these modern Islamic fanatics hold a similar persuasion, give or take a few houris. Bergoglio must be aware of that. He would never suggest that St. Stephen and the other palm bearers were motivated by poverty or frustration. Then what is he talking about.
I drank too much yesterday and today Isabel gives me a hard time. “Every time you feel tense or bored you get yourself soused,” she says, and that sends my memory tottering toward Baudelaire: « Il faut être toujours ivre. Tout est là : c’est l’unique question. Pour ne pas sentir l’horrible fardeau du Temps qui brise vos épaules et vous penche vers la terre, il faut vous enivrer sans trêve ». In English: You must always be drunk. That’s the gist of the only thing that matters. If you would not feel the dreadful burden of Time crushing your shoulders and bending you to the ground, you must keep getting drunk.
Homer’s nepenthe was a marvelous drug that made one forget all pain and misery, meant mostly for harried sailors and warriors returning from their battles with monsters. Galen, to calm pain, prescribed opiates (his famous theriac) to the Stoic emperor Marcus Aurelius. When, in the span between Homer and Baudelaire, did the purpose of intoxication change sign? When did opium become an anesthetic for boredom? Coleridge? Or De Quincey? At some point, Virginia Woolf would have us believe, around 0 AM on January 1st 1800.
“Our society distinguishes itself by conquering the centrifugal social forces with Technology rather than Terror, on the dual basis of an overwhelming efficiency and an increasing standard of living.” Thus, Herbert Marcuse in One Dimensional Man. Shortly after publishing this book in 1964, he was denied reappointment as professor at Brandeis University; it was said that President Sachar considered Marcuse too subversive for comfort. So I was hired instead. I took up my lectureship in mathematics at Brandeis in September 1966, just out of graduate school, married and with twin boys aged two. I wasn’t a radical; I was safe, nay, insignificant. In fact, I was terrified. The math department of the University of Buenos Aires, where I had planned to return after my Ph.D., had recently been raided by the police; a number of my friends had been wounded; the Argentine military were convinced that vector analysis was subversive. So we stayed in the U.S.: our ships were burnt, but the future lay in front of us, the big, bright American dream. Those two, the future and the American dream, especially terrified me. I had to keep publishing math papers and constantly thinking math thoughts. I had to make myself, fast, into a one-dimensional man.
Heraclitus on the psyche: “Were you to go in search of the limits of the psyche, you would never find them, even if you tried every path: so deep is the psyche’s logos.” Whatever the Ephesian meant by that last word, logos, I tend to agree about the depth. If you do, too, what more could you conceivably ask of life, how on earth could you feel bored? Fathom, fathom: you’ll never scratch the bottom of yourself. And it is not at all like that bad, boring infinity, die schlechte Unendlichkeit of ever repeating “do the same,” “once more”; of counting one, two, three, and so on; no: by going deeper into the psyche we discover new, unsuspected faunae and florae, new monsters, new miracles, brand new angels and beasts. You, whoever you are, are inexhaustibly interesting. Says the Tao: "Empty of intent, one may be filled with awe." —That’s merely contemplating your navel (you object) instead of fighting for peace and justice. —I beg to differ, my friend. Who says your psyche and mine are not the same? That by trying to fathom my own I’m not trying to fathom yours as well? And if that be so, what could be more conducive to justice and peace?
“Mother of heaven, regina of the clouds, … I wish that I might be a thinking stone” (“Le Monocle de mon oncle”). Yes, that would be an excellent thing to be, a thinking stone, with no secretions to speak of, no excrement, and all the pleasures of the mind without the suffering and the putrefaction. Do you think that Wallace Stevens’ mother, or perhaps his nanny, was an obsessive coprophobic too? In any case, if you believe the rumors that the American poet converted to Catholicism on his deathbed, you must agree he must have had to confess, among other sins, having imitated and poked fun at Dante, at St. Bernard, and even at the Mother of God: “Vergine madre, figlia del tuo Figlio…” This reminds me of my mother—oh no, not because I take myself for God, but because she was at once humble and high, “umile e alta più che creatura”: humble enough to busy herself with my gut and my toilet training, and withal high, floating way above me, omnipotent, urging me to push away all dross and become pure, spiritual, angelical: “Come!, come, Ricardito!, raise yourself to the higher spheres!”
Wherefore the German poet concluded that the Eternal Feminine pulls us upwards: “Das Ewig-Weibliche zieht uns hinan.”
There is an old Gnostic story about the Savior looking down a bottomless well and there, on the deep waters, seeing His own reflection, which was Satan. Long before, Heraclitus had taught that the way up and the way down are one and the same. And long after, in the last few lines of Les Fleurs du mal, in impeccably traditional alexandrines, Baudelaire expressed an indifference in regard to plunging into heaven or into hell, so long as—important proviso—he could find something new that would alleviate his boredom. In my early days, Dante’s Paradiso and his ghostly Beatrice didn’t quite fill Baudelaire’s bill; all those logical knots—a virgin daughter of her Son, the three persons in one of the Trinity, concentric and eccentric circles—all those theological tangles, did not engage my emotions; if anything, I looked upon them with the same mistrust and apprehension I looked upon Pope Pacelli. The Inferno, though, was something else. Canto followed by lower canto, the lower the more exciting, till I got to Taidè, the ravishing courtesan. Ravishing she was in the engraving by Gustave Doré, though perhaps not in the words of Dante’s Virgil:
“… di quella sozza e scapigliata fante
che là si graffia con l’unghie merdose,
e or s’accoscia e ora è in piedi stante.”
(… of that disgusting and disheveled whore, /
there, scratching herself with shitty nails, /
who sits obscenely now, and now stands on her feet.)
Thaïs, the ancient model for the Dantean Taidè, one of whose avatars I got to admire in the novel by Anatole France and in Massenet’s opera, Thaïs with her Alexandrian refinements and inebriating unguents, could not compete in my view with this Taidè sitting on an infernal rock, leaning on her left thigh so as to show her bumptious tokhes to Dante and his guide, her feet dipped in the surrounding pool of excrement, lifting with her right hand her long hair, sewer caked.
Recent breakthroughs in the mathematical theory of graphs hold great promise for computer science, for genomics, robotics, and for the complete mapping of the synaptic connections of the brain: the likely technological applications are simply staggering. I read this announcement yesterday, it was sent to me by one of my sons; then, last night, I dreamt that I had to give a talk about graphs to an audience of distinguished mathematicians; one hour before the event I discover, to my horror, that I had prepared only a few notes on some bits of paper, which I find scattered between the pages of a book hidden in my briefcase. The book is comforting, attractive, much leafed, with scuffed, blue soft covers: it reminds me of the book in a Fantin-Latour still life, lying on a brown table next to a gold-trimmed porcelain teacup. But the notes, my friend, those notes make my heart sink. What have I done? Briefly put, I was trying to impart on those terrifically subtle mathematical minds that seven plus five is twelve.
—I’ve felt that anguish too: once I dreamt I was supposed to play with the New York Giants. Me, a nerdy underweight midget with flabby muscles, butter fingers and bad knees; and I don’t even know the rules of football. I was desperately looking for a substitute, yet I could find none.
—The horror! The horror!
Is it horror, then, and not boredom that holds mankind in thrall? Horror is poorly served by the entertainment industry, which, like traditional metaphysics, is always in search for a subject or an object, viz. an evil character at the heart of it; even in Lovecraft the horror must ultimately adhere to a sensible thing, be it only to a color out of space. Spiders and their webs have long been seen as good candidates for the post, at least ever since Aeschylus launched dramatic arachnophobia with his Oresteia (see my 1996 lecture, Greek Tragedy: Aeschilus, Weaving and Birth.) But the greater prophets of what we are pleased to call modernity knew better: the spider is not the problem; the real horror lies in the web itself, or rather in its formal structure, that is, its mathematical graph. Thus Nietzsche, in Genealogy of Morals, III, 9, mocks the need felt by some weak or pious souls for a spider as agent or boss: “God as some alleged spider of purpose and morality behind the great captious web of causality” („einer angeblichen Zweck- und Sittlichkeits-Spinne hinter dem großen Fangnetz-Gewebe der Ursächlichkeit.“) And Diderot, in his Salon de 1767, in a sort of Kantian-Copernican turn, moves the agent spider to our mind, or rather to the interior of our skulls: « Vous concevez maintenant ce que c’est que le fromage mou qui remplit la capacité de votre crâne et du mien. C’est le corps d’une araignée dont tous les filets nerveux sont les pattes ou la toile. » (“You understand now the nature of the soft cheese that fills your skull and mine. It is the body of a spider, and the nervous nets are its legs or its web.”)
We are tiny flies caught in an immense graph, but no spider is likely to devour us, unless it be the one dwelling inside our skull. That, however, gives us no comfort. A universal spider, a Huitzilopochtli, a gigantic monster like one-eyed Polyphemus, or the many righteous gods, may be exceedingly cruel and impervious to mercy—but try praying to a mathematical structure. Besides, arbitrary monsters or gods have been the source of stories, rituals, theologies, and also of heresies, which at least at some level are accessible to all; but a mathematical structure, e.g. a graph, presents to the mind only objects such as loops, isomorphisms, cycles, connectivity, etc., that are of interest only to very few and accessible to even fewer of us flies. A lack of both concern and the capacity to understand the graphs that hold us in their invisible, unbreakable threads must be at the root of the generalized feeling of boredom, and of the urge to escape it by plunging either into heaven (martyrdom), or into hell (our selves). From Rimbaud’s recommendation of a “long, immense and well-reasoned disorder of all the senses” to Tim Leary’s neo-Cartesian motto, “think for yourself and question authority,” and beyond, advice has followed preposterous advice: as if you and your thinking were isolable chemicals, so that you could be and think “by yourself”; as if you could ask a pharmacist or a liquor salesman for some potion to set you free from the entanglement of all these sticky webs, networks, and graphs.
I think you forget beauty. You are being unfair to mathematics. I must confess I don’t understand what you mean when you say that real horror lies in formal structures like graphs, but I do see very clearly what you omit to say: that therein lies real beauty too. And that is not a trivial omission. Platonism begins with the realization that truth and beauty cohere in math and only there; it ends in our spiritual union with the god, the creator of the cosmos, the One who is always geometrizing: Platonism and our civilization are coterminous. All that is ancient history, but if you are interested in the latest results on the esthetics of math, allow me to direct you to David Mumford’s blog, where you will find a recent post, “Math & Beauty & Brain Areas,” telling, in his words, about “an astonishing experimental investigation of these questions entitled ‘The experience of mathematical beauty and its neural correlates’.” The investigation was carried out by Professor Michael Atiyah (an Oxford mathematician of the first rank) and Semir Zeki (Professor of Neuroesthetics at University College London). Fifteen mathematicians were scanned using fMRI while viewing 60 mathematical formulas and rating them as ugly, neutral or beautiful. The areas of the cerebral cortex affected in the fifteen cases appeared to vary a bit too widely from case to case, so Professor Mumford (himself a top mathematician from Harvard and Brown) suggests a way to get better correlations by “dividing mathematicians into several tribes depending on what most strongly drives them into their esoteric world.” Prof. Mumford likes to call these tribes explorers, alchemists, wrestlers and detectives. And he adds, “Of course, many mathematicians move between tribes and some results are not cleanly part the property of one tribe.”
It should be extremely interesting—don’t you think?—to carry out new brain scans taking into account Mumford’s tribes and sub-tribes.
Did I forget about beauty when I spoke of horror? Perhaps I wasn’t fully mindful of the beauty of math, but your mentioning the cerebral cortex brought to mind Rilke’s First Duino Elegy and what he says there about beauty and horror:
„Denn das Schöne ist nichts / als des Schrecklichen Anfang, den wir noch grade ertragen“ (For beauty is nothing / but the beginning of horror, which we bear just barely);
and the next two lines to explain our marvel at beauty: „und wir bewundern es so, weil es gelassen verschmäht / uns zu zerstören. Ein jeder Engel ist schrecklich.“ (and we admire it so much because it calmly spurns / to destroy us. Every angel is terrible.)
Should we try to devise scales so subtle as to let us weigh the horror of the logic that holds us in its rings like Laocoön and his sons, against the manifold harmonies produced by those tense rings?
Perhaps beauty is a word standing for two entirely different referents, like the English word rose—both the flower and what Sleeping Beauty did when she was kissed by the prince— or even a word standing for opposites, like Greek bios, which, as Heraclitus wisely pointed out, means both life and the bow whose arrows deliver death.
Or perhaps there are two kinds of beauty: one celestial—abstract, unfleshed—and another earthly—perishing, pathetic. If such be the case, this coming year may we be able to experience both kinds of beauty, earthly and celestial, as one and the same. And may we keep in mind Wm. Blake’s Proverb of Hell: “Eternity is in love with the productions of time.”