If now the element under observation is exactitude itself, if one isolates it and allows it to develop, if one regards it as an intellectual habit and a way of living and lets it exert its exemplary influence on everything that comes into contact with it, the logical conclusion is a human being with the paradoxical combination of precision and indefin-iteness. He possesses an incorruptible, deliberate cold- bloodedness, the temperament that goes with exactitude; but apart from and beyond this quality, all is indefinite.
The point at which Musil comes closest to a possible solution is when he mentions the fact that mathematical problems do not admit of a general solution, but that particular solutions, taken all together, can lead to a general solution (chap. 83). He thinks that this method might be applied to human life. Many years later another writer, Roland Barthes, in whose mind the demon of exactitude lived side by side with the demon of sensitivity, asked himself if it would not be possible to conceive of a science of the unique and unrepeatable: “Pourquoi n'y aurait-il pas, en quelque sorte, une science nouvelle par objet? Une Mathesis sin-gularis (et non plus universalis)TL· chambre claire, 1980, p. 21] (Why couldn't there be, in some way, a new science for every object? A mathesis singularis^ and no longer universalisT).
If Musil's Ulrich soon resigns himself to the defeats that the passion for exactitude is bound to suflFer, Paul Valery's Monsieur Teste, another great intellectual personage of this century, has no doubts about the fact that the human spirit can fulfill itself in the most exact and rigorous way. And if Leopardi, poet of life's sadness, shows the highest degree of exactitude in describing indefinite sensations that give pleasure, Valery, poet of impassive rigor of mind, shows the highest degree of exactitude in putting his Monsieur Teste face to face with pain, and making him combat physical suflfering by an exercise in abstract geometry.
“J'ai,” dit-il … “pas grand'chose. J'ai … un dixieme de seconde qui se montre … Attendez … II y a des instants ou mon corps s'illumine … C'est tres curieux. J'y vois tout a coup en moi… je distingue les profondeurs des couches de ma chair; et je sens des zones de douleur, des anneaux, des poles, des aigrettes de douleur. Voyez-vous ces figures vives? cette geometrie de ma souffrance? II y a de ces eclairs qui ressemblent tout a fait a des idees. Ils font com-prendre—d'ici, jusque-la … Et pourtant ils me laissent incertain. Incertain n'est pas le mot… Quand cela va venir, je trouve en moi quelque chose de confus ou de diffus. II se fait dans mon etre des endroits … brumeux, il y a des etendues qui font leur apparition. Alors, je prends dans ma memoire une question, un probleme quelconque … Je m'y enfonce. Je compte des grains de sable … et, tant que je les vois … — Ma douleur grossissante me force a Pobser-ver. J'y pense!—Je n'attends que mon cri … et des que je Pai entendu—Yobjet, le terrible objet, devenant plus petit, et encore plus petit, se derobe a ma vue interieure.” (Galli-mard edition, 1946, pp. 32-33)
“It is nothing … much,” he said. “Nothing but… a tenth of a second appearing … Wait… At certain moments my body is illuminated … It is very curious. Suddenly I see into myself… I can make out the depths of the layers of my flesh; and I feel zones of pain … rings, poles, plumes of pain. Do you see these living forms, this geometry of my suffering? Some of these flashes are exactly like ideas. They make me understand—from here, to there … And yet they leave me uncertain. Uncertain is not the word … When it is about to appear, I find in myself something confused or diffused. Areas that are … hazy occur inside me, wide spaces come into view. Then I choose a question from my memory, any problem at all … I plunge into it. I count grains of sand … and as long as I can see them … But increasing pain forces me to observe it. I think about it! I only await my cry … and as soon as I have heard it—the object, the terrible object, getting smaller, and still smaller, vanishes from my inner sight.”
In our century Paul Valery is the one who has best defined poetry as a straining toward exactitude. I am speaking chiefly of his work as a critic and essayist, in which the poetics of exactitude may be traced in a straight line through Mallarme to Baudelaire and from Baudelaire to Edgar Allan Poe.
In Poe—the Poe of Baudelaire and Mallarme—Valery sees “le demon de la lucidite, le genie de Panalyse, et Pinventeur des combinaisons les plus neuves et les plus seduisantes de la logique avec Pimagination, de la mysticite avec le calcul, le psychologue de Pexception, Pingenieur litteraire qui approfondit et utilise toutes les ressources de Part” (the demon of lucidity, the genius of analysis, and the inventor of the newest, most seductive combinations of logic and imagination, of mysticism and calculation; the psychologist of the exceptional; the literary engineer who studied and utilized all the resources of art). Valery writes this in his essay “Situation de Baudelaire,” which for me has the value of a poetic manifesto, together with another essay of his on Poe and cosmogony, in which he deals with Eureka.
In the essay on Poe's Eureka, Valery questions himself on cosmogony as a literary genre rather than as scientific speculation and achieves a brilliant refutation of the idea of “universe,” which is also a reaffirmation of the mythic force that every image of “universe” carries with it. Here too, as in Leopardi, we find both attraction and repulsion with regard to the infinite. And here too we find cosmological conjectures as a literary genre, such as Leopardi amused himself with in certain “apocryphal” prose pieces: “Frammento apocrifo di Stratone da Lampsaco” (Apocryphal Fragment of Strato of Lampsacus), on the beginning and particularly the end of the terrestrial globe, which flattens and empties out like the rings of Saturn and is dispersed until it burns up in the sun; or his translation of an apocryphal Talmudic text, “Can-tico del gallo silvestre” (Song of the Great Wild Rooster), where the entire universe is extinguished and disappears: “un silenzio nudo, e una quiete altissima, empieranno lo spazio immenso. Cosi questo arcano mirabile e spaventoso delPesistenza univer-sale, innanzi di essere dichiarato ne inteso, si dileguera e perder-assi” (a naked silence and a most profound quiet will fill the immensity of space. So this marvelous and frightening mystery of universal existence, before being declared or understood, will fade away and be lost). Here we see that what is terrifying and inconceivable is not the infinite void, but existence.
This talk is refusing to be led in the direction I set myself. I began by speaking of exactitude, not of the infinite and the cosmos. I wanted to tell you of my fondness for geometrical forms, for symmetries, for numerical series, for all that is combinatory, for numerical proportions; I wanted to explain the things I had writ ten in terms of my fidelity to the idea of limits, of measure But perhaps it is precisely this idea of forms that evokes the idea of the endless: the sequence of whole numbers, Euclid's straight lines Rather than speak to you of what I have written, perhaps it would be more interesting to tell you about the problems that I have not yet resolved, that I don't know how to resolve, and what these will cause me to write: Sometimes I try to concentrate on the story I would like to write, and I realize that what interests me is something else entirely or, rather, not anything precise but everything that does not fit in with what I ought to write—the relationship between a given argument and all its possible variants and alternatives, everything that can happen in time and space. This is a devouring and destructive obsession, which is enough to render writing impossible. In order to combat it, I try to limit the field of what I have to say, divide it into still more limited fields, then subdivide these again, and so on and on. Then another kind of vertigo seizes me, that of the detail of the detail of the detail, and I am drawn into the infinitesimal, the infinitely small, just as I was previously lost in the infinitely vast.
“Le bon Dieu est dans le detail.” This statement of Flaubert's I would explain in the light of the philosophy of Giordano Bruno, that great visionary cosmologist, who sees the universe as infinite and composed of innumerable worlds but who cannot call it “totally infinite” because each of these worlds is finite. God, on the other hand, is totally infinite: “tutto lui e in tutto il mondo, ed
in ciascuna sua parte infinitamente e totalmente” (the whole of him is in the whole world, and in each of his parts infinitely and totally).
Among the Italian books in the last few years which I have most often read, reread, and thought about is Paolo Zellini's Breve storia dell' infinito (Short History of the Infinite, 1980). It opens with Borges' famous invective against the infinite from “Avatares de la tortuga” (Avatars of the Tortoise)—it is the one concept that corrupts and confuses all others—and then goes on to review all arguments on the subject, with the result that it dissolves and reverses the extension of the infinite into the density of the infinitesimal.
I think that this bond between the formal choices of literary composition and the need for a cosmological model (or else for a general mythological framework) is present even in those authors who do not explicitly declare it. This taste for geometrical composition, of which we could trace a history in world literature starting with Mallarme, is based on the contrast of order and disorder fundamental to contemporary science. The universe disintegrates into a cloud of heat, it falls inevitably into a vortex of entropy, but within this irreversible process there may be areas of order, portions of the existent that tend toward a form, privileged points in which we seem to discern a design or perspective. A work of literature is one of these minimal portions in which the existent crystallizes into a form, acquires a meaning—not fixed, not definitive, not hardened into a mineral immobility, but alive as an organism. Poetry is the great enemy of chance, in spite of also being a daughter of chance and knowing that, in the last resort, chance will win the battle. “Un coup de des n'abolira jamais le hasard” (One throw of the dice will never annul chance).
It is in this context that we should view the reevaluation of logical, geometrical, and metaphysical procedures that prevailed in the figurative arts during the first decades of this century and thereafter in literature. The emblem of the crystal might be used to distinguish a whole constellation of poets and writers, very different from one another, such as Paul Valery in France, Wallace Stevens in the United States, Gottfried Benn in Germany, Fernando Pessoa in Portugal, Ramon Gomez de la Serna in Spain, Massimo Bontempelli in Italy, and Jorge Luis Borges in Argentina.
The crystal, with its precise faceting and its ability to refract light, is the model of perfection that I have always cherished as an emblem, and this predilection has become even more meaningful since we have learned that certain properties of the birth and growth of crystals resemble those of the most rudimentary biological creatures, forming a kind of bridge between the mineral world and living matter.
Among the scientific books into which I poke my nose in search of stimulus for the imagination, I recently happened to read that the models for the process of formation of living beings “are best visualized by the crystal on one side (invariance of specific structures) and thefiame on the other (constancy of external forms in spite of relentless internal agitation).” I am quoting from Massimo Piattelli-Palmarini's introduction to the volume devoted to the debate between Jean Piaget and Noam Chomsky in 1975 at the Centre Royaumont {Language and Uarning, 1980, p. 6). The contrasting images of flame and crystal are used to make visible the alternatives offered to biology, and from this pass on to theories of language and the ability to learn. For the moment I will leave aside the implications for the philosophy of science embodied in the positions stated by Piaget, who is for the principle of “order out of noise”—the flame—and Chomsky, who is for the “self-organizing system,” the crystal.
What interests me here is the juxtaposition of these two symbols, as in one of those sixteenth-century emblems I mentioned in my last lecture. Crystal and flame: two forms of perfect beauty that we cannot tear our eyes away from, two modes of growth in time, of expenditure of the matter surrounding them, two moral symbols, two absolutes, two categories for classifying facts and ideas, styles and feelings. A short while ago I suggested a “Party of the Crystal” in twentieth-century literature, and I think one could draw up a similar list for a “Party of the Flame.” I have always considered myself a partisan of the crystal, but the passage just quoted teaches me not to forget the value of the flame as a way of being, as a mode of existence. In the same way, I would like those who think of themselves as disciples of the flame not to lose sight of the tranquil, arduous lesson of the crystal.
A more complex symbol, which has given me greater possibilities of expressing the tension between geometric rationality and the entanglements of human lives, is that of the city. The book in which I think I managed to say most remains Invisible Cities, because I was able to concentrate all my reflections, experiments, and conjectures on a single symbol; and also because I built up a many-faceted structure in which each brief text is close to the others in a series that does not imply logical sequence or a hierarchy, but a network in which one can follow multiple routes and draw multiple, ramified conclusions.
In my Invisible Cities every concept and value turns out to be double—even exactitude. At a certain point Kublai Khan personifies the intellectual tendency toward rationalization, geometry, and algebra, reducing knowledge of his empire to the combina-toria of pieces on a chessboard. The cities that Marco Polo describes to him with a wealth of detail Kublai represents with various arrangements of castles, bishops, knights, kings, queens, and pawns on black and white squares. The final conclusion to which this operation leads him is that the object of his conquest is nothing other than the block of wood on which each piece rests: an emblem of nothingness. But just at this moment comes a coup de scene, for Marco Polo requests Kublai to look more closely at what he sees as nothingness:
II Gran Kan cercava d'immedesimarsi nel gioco: ma adesso era il perche del gioco a sfuggirgli. II fine d'ogni partita e una vincita o una perdita: ma di cosa? Qual era la vera posta? Allo scacco matto, sotto il piede del re sbalzato via dalla mano del vincitore, resta il nulla: un quadrato nero o bianco. A forza di scorporare le sue conquiste per ridurle alPessenza, Kublai era arrivato alPoperazione estrema: la conquista definitiva, di cui i multiformi tesori delPimpero non erano che involucri illusori, si riduceva a un tassello di legno piallato.
Allora Marco Polo parlo:—La tua scacchiera, sire, e un intarsio di due legni: ebano e acero. Il tassello sul quale si fissa il tuo sguardo illuminato fu tagliato in uno strato del tronco che crebbe in un anno di siccita: vedi come si di-spongono le fibre? Qui si scorge un nodo appena accennato: una gemma tento di spuntare in un giorno di primavera precoce, ma la brina della notte Pobbligo a desistere—. Il Gran Kan non s'era fin'allora reso conto che lo straniero sapesse esprimersi fluentemente nella sua lingua, ma non era questo a stupirlo.—Ecco un poro piu grosso: forse e stato il nido d'una larva; non d'un tarlo, perche appena nato avrebbe continuato a scavare, ma d'un bruco che rosicchio le foglie e fu la causa per cui l'albero fu scelto per essere abbattuto … Questo margine fu inciso dall'ebanista con la sgorbia perche aderisse al quadrato vicino, piu spor-gente…
La quantita di cose che si potevano leggere in un pez-zetto di legno liscio e vuoto sommergeva Kublai; gia Polo era venuto a parlare dei boschi d'ebano, delle zattere di tronchi che discendono i fiumi, degli approdi, delle donne alle finestre …
The Great Khan tried to concentrate on the game: but now it was the game's reason that eluded him. The end of every game is a gain or a loss: but of what? What were the real stakes? At checkmate, beneath the foot of the king, knocked aside by the winner's hand, nothingness remains: a black square, or a white one. By disembodying his conquests to reduce them to the essential, Kublai had arrived at the extreme operation: the definitive conquest, of which the empire's multiform treasures were only illusory envelopes; it was reduced to a square of planed wood.
Then Marco Polo spoke: “Your chessboard, sire, is inlaid with two woods: ebony and maple. The square on which your enlightened gaze is fixed was cut from the ring of a trunk that grew in a year of drought: you see how its fibers are arranged? Here a barely hinted knot can be made out: a bud tried to burgeon on a
premature spring day, but the night's frost forced it to desist.”
Until then the Great Khan had not realized that the foreigner knew how to express himself fluently in his language, but it was not this fluency that amazed him.
“Here is a thicker pore: perhaps it was a larvum's nest; not a woodworm, because, once born, it would have begun to dig, but a caterpillar that gnawed the leaves and was the cause of the tree's being chosen for chopping down… This edge was scored by the wood carver with his gouge so that it would adhere to the next square, more protruding….”
The quantity of things that could be read in a little piece of smooth and empty wood overwhelmed Kublai; Polo was already talking about ebony forests, about rafts laden with logs that come down the rivers, of docks, of women at the windows …*
From the moment I wrote that page it became clear to me that my search for exactitude was branching out in two directions: on the one side, the reduction of secondary events to abstract patterns according to which one can carry out operations and demonstrate theorems; and on the other, the eflFort made by words to present the tangible aspect of things as precisely as possible.
The fact is, my writing has always found itself facing two divergent paths that correspond to two different types of knowledge. One path goes into the mental space of bodiless rationality, where one may trace lines that converge, projections, abstract forms, vectors of force. The other path goes through a space crammed with objects and attempts to create a verbal equivalent of that space by filling the page with words, involving a most careful, painstaking eflFort to adapt what is written to what is not written, to the sum of what is sayable and not sayable. These are two different drives toward exactitude that will never attain com- plete fulfillment, one because “natural” languages always say something more than formalized languages can—natural languages always involve a certain amount of noise that impinges upon the essentiality of the information—and the other because, in representing the density and continuity of the world around us, language is revealed as defective and fragmentary, always saying something less with respect to the sum of what can be experienced.
Six Memos for the Next Millennium Page 7