STORIES OF CREATION, by Ricardo Nirenberg
The mathematician Georg Cantor believed that his theory of transfinite numbers had been communicated to him from a "more powerful energy." A divine voice, like the angel who in old paintings whispers the Word to the Evangelist or the Translator, whispered to Cantor the Theorems of Ordered Sets.
Don't smile. To anyone who has puzzled over old questions, Cantor's Set Theory opens vast and surprising views. Take the belief in the soul's survival after the body's death. One of the major objections has been the unmanageable proliferation: where in heaven or hell could there be room enough for the souls of each of us, of every man and woman, perhaps of every animal, of every bacteria, who ever lived or will live? Such multitudes are unimaginable. The philosopher David Hume, shortly before his death, said that he found it impossible to believe that there is an after-life, that "the trash of every age should be preserved, and that new universes must be created to contain such infinite numbers..." Yet consider for a moment Cantor's idea: the material monads in the universe may be infinitely many, but with the mild infinity of the natural numbers, 1, 2, 3, 4, etc., an infinity which Cantor named, in cabalistic style, Aleph Zero. We, whose bodies are made of such monads, are, each of us, finite sets thereof; each living body is a finite set of monads. Now, all such possible finite sets are still only denumerable in number, again like the mild infinity of the natural numbers, 1, 2, 3, 4, etc., again like Aleph Zero. A good undergraduate math major should be able to prove it, but this is not the place. On the other hand, the so-called ethereal monads are something entirely different, according to Cantor. They have the power of Aleph One, the next transfinite number. They are infinitely more infinite: they are like the real numbers, if you will. If we think of spiritual entities as consisting of ethereal monads, then the souls of every body that ever lived or that will ever live in this universe, plus every one of their memorable or forgettable moments, plus every single thought, every glance, every possibility not pursued, all the roads not taken, all those things and many more may be forever preserved, and not a single possibility be lost. Yet that spiritual universe would not be crowded, all these possibilities being no more than a few specks in a vast page, infinitely more comfortable and thinly packed than five characters in a 200 gigabytes hard disk. Cantor's theory of transfinite numbers has the effect of freeing the mind to take difficult leaps, and so we should not be surprised that those theorems were associated with metaphysical speculation, that they elicited at first the same kind of opposition as metaphysics often did, an odium almost theologicum.
Dauben, Cantor's biographer, makes the point that such a theological frame of the great mathematician's mind may have been necessary in order to give him the determination and the energy to forge ahead in spite of strong criticism and attacks. This doesn't diminish the eccentricity of Cantor's attitude: a mixture of theological speculation with scientific work had been the rule during the Renaissance and throughout the 16th century, and was common even in the 17th (remember Leibniz' theological or Newton's alchemic and prophetic ventures), but it had ceased to be normal by the 19th century.
Robert Musil's account of how a mathematician thinks is, at least on the face of it, a total opposite of Cantor's. Musil had been a physicist, an engineer, a student of mathematics, before becoming a novelist. A mathematician's mind at work, according to Musil in The Man Without Qualities, is a bit more complex perhaps, but of essentially the same nature as the mind of a dog who tries to get through a narrow door with a stick in its mouth. Perhaps Musil would have agreed with those who take the computer as the model of all intellectual work. Isn't it odd that the novelist would hold such a pedestrian view of scientific creativity, while the scientist Cantor held a lofty, mystical one?
Cantor was born in St. Petersburg in 1845, of a pious family of Danish Lutherans of Jewish origins, and his strong attachment to, and intellectual and emotional dependence on, his father is reminiscent of Kierkegaard. Cantor remained all his life a fervent Christian. Musil, on the other hand, was born in Austria in 1880, of a family of freethinkers belonging to the Austrian haute bourgeoisie, and his relations with his parents were difficult, strained, and later cold. His household was a ménage à trois: the man who was probably his mother's lover lived with the family. Musil's mother was a rather volatile, hysterical woman, the very opposite of his father, who was a quiet, devoted engineer. This might go some way toward explaining Musil's mistrust of leaping high sentiment and his sympathy for the plodding gait of the scientist.
The mathematician came from a family that had produced illustrious musicians; he himself formed in his youth a string quartet. Musil, on the contrary, disliked and mistrusted music. There seemed to be something in that art (at least in the Wagnerian kind) akin to madness, as Clarissa and Walter, two of the characters in The Man Without Qualities, suggest. We are reminded of Schopenhauer's privileged placing of music as the only art in direct contact with the Will, bypassing the realm of Ideas. Was this bypassing of the realm of ideas what constituted madness for Musil? After rereading parts of his unfinished novel, I feel inclined to think so.
According to popular wisdom, mathematicians feel a special affinity for music. There is some truth in that, and I think I see why. While music does not signify, it is pregnant with emotional meaning. Math is at the other end: it is the most stable signification we know of, albeit to the contemporary mathematical mind emotionally infertile (it only grows one feeling: architectonic beauty.) But both, math and music, avoid the uncertain terrain in between, where all is dissemination, explosions of signifiers, and there is no place to draw a line and no fixed points. I have never seen a deconstructionist reading of either a musical score or a mathematical theorem.
But returning to the different accounts of Cantor and Musil about creation, there is also the wide gap between their generations, 35 years apart, and the reaction we have come to expect against the feelings and thoughts of one's immediate forebears. Here's part of Nietzsche's text on creativity and inspiration in Ecce Homo, an account which would have elicited Cantor's agreement, but which Musil explicitly rejected:
Has anyone at the end of the 19th century a distinct conception of what poets of strong ages called inspiration? If not, I will describe it. If one had the slightest residue of superstition left in one, one would be hardly able to set aside the idea that one is merely incarnation, merely mouthpiece, merely medium of overwhelming forces. The concept of revelation, in the sense that something suddenly, with unspeakable certainty and subtlety, becomes visible, audible, something that shakes and overturns one to the depths, simply describes the fact. One hears, one does not seek; one takes, one does not ask who gives; a thought flashes up like lightning, with necessity, unfalteringly formed - I have never had any choice. An ecstasy whose tremendous tension sometimes discharges itself in a flood of tears, while one's steps now involuntarily rush along, now involuntarily lag; a complete being outside of oneself with the distinct consciousness of a multitude of subtle shudders and trickles down to one's toes; a depth of happiness ... This is my experience of inspiration; I do not doubt that one has to go back thousands of years to find anyone who could say to me "it is mine also".
Thus, Nietzsche's not too modest account of his own creativity. Observe that he doesn't claim universality for his personal story: on the contrary, he pretends to uniqueness, almost. Nobody was more aware than he of the imperialistic tendencies of scientific reason, so we can interpret what he is saying as deliberately shielding his own creativity from any universal kind of law.In any case, it was Nietzsche's story, in great measure, that Musil reacted against in telling his own antimystical, deliberately unpoetic tale. There may be in the latter a positive element as well, for, just as whitefish mixed with pike is a good recipe for gefilte fish, a combination of tender poetic gifts with a semblance of scientific hard-headedness is an even better one for literary success. Witness Poe and Paul Valéry. And Proust too, at times, speaks of his novel as a scientific enterprise.
In 1778 Luigi Galvani observed that some frog legs, which happened to be hanging from an iron railing, contracted when an electric current was generated, by a lucky chance, nearby. In 1798 a dairymaid told Edward Jenner that she couldn't get smallpox because she had previously contracted cowpox: Jenner then realized that cowpox could be deliberately used to prevent smallpox. In 1828 Friedrich Wöhler was trying to create ammonium cyanate by combining cyanic acid and ammonia. The chemical product in his reaction turned out to be a four-sided prismatic crystal. Earlier, as a medical student, Wöhler had separated urea crystals from urine, so he was able to recognize them. Stories of lucky breaks happening to minds prepared to react, but not necessarily better prepared than Musil's dog to fit his stick through the door.
On the opposite side, we have the stories of mysterious inspirations as a source of discovery, stories of the Cantor or Nietzsche type: Descartes' famous dream, or Kekulé's of a snake biting its tail, inspiring his hitting upon the cyclic structure of the benzene molecule. Or Poincaré making his great breakthrough in the theory of the theta functions as he stepped into a Paris bus, illumined suddenly, as if by lightning.
Narratives of creation can be very different. So the question comes up: perhaps there might be some narration of creativity that encompasses or grounds all other accounts, which tells us what any true account must minimally contain in order to be consistent, or what shape it should take. Perhaps. But suppose we were offered such a story of creation, a kind of necessary & universal cosmogony, far more general than the Bible's or Hesiod's, telling us how any creative process must come to pass. I suspect that ipso facto a genius would arise whose account of his own creativity would directly oppose the one agreed upon. Could we say then, "Ah, but here's the exception that confirms the rule"? It wouldn't work too well in this case, for creativity deals with and thrives on exceptions, precisely. Creativity is the work of the spirit, which, at least so Hegel thought, is pure negativity. Picasso once said, "In order to make, one must make against." And so our supernarrative, no sooner born and still in diapers, would be trod on by some creative foot. If neurosis, which of all the works of the spirit is surely the most pedestrian and repetitive, has proved to be protean and quite irreducible to any supernarrative, why expect Mozart's or Euler's creativity to be simpler?
We can, as is often done, speak of creativity as either associativity, the bringing of things considered until then widely different together into a new, sparkling unit, or as dissociativity, the noticing of deep differences between things which we thought were the same. This kind of talk seems to explain something but in fact doesn't. When I saw for the first time the set theoretical definition of a relation as a subset of the set of pairs of elements of two sets, it seemed to me extraordinarily ingenious and illuminating. After some growing up though, I came to see it as essentially vacuous. Heidegger writes in Sein und Zeit about that very same definition: "One must note that in such formalizations the phenomena get leveled off so much that their real phenomenal content may be lost..."
Briefly then, a general theory of how the creative act happens is unlikely. The most we can hope for are personal stories. Yet, scientific reason has such an imperialist vocation, such a drive to explore and colonize what lands were heretofore beyond its pale, that now it wants to take a peek behind the curtain and look at itself being engendered. Not to mention the incalculable profits to be made if we could accelerate the process of scientific creation. So science, calling itself Cognitive, tries to peek at its primal scene. But now we are awake and know, or think we do, that Freudian theories are nothing but another story, after all.
Nothing but another story: is that, then, all we can grasp? The poet Charles Olson says that "a man becomes who he is in the process of discovering the narrative of his own existence; that the process of self-discovery is an act of narrative that is constitutive for the soul."
I add that the narrative of one's own existence grows from a soil of previous narratives, of the stories one has loved. Don Quixote says, very solemnly, somewhere in the second part of the great novel, "I know who I am." Now, that's quite a statement. Who in his right mind would dare to say as much? Yet, it is a perfectly reasonable thing for Don Quixote to say, for he has willed himself into a knight-errant, he has become a character of those knight-errantry stories which he knows by heart. He knows the narrative of his own existence inside out, and so he speaks truly, he does know who he is.
But Don Quixote is mad; shut off from reality, he lives in his own private world, and that's why he knows who he is. Nobody but a madman can be so certain of his own identity. And so my other story is not of madmen but of savages. In W. H. Hudson's novel Green Mansions, there is a tribe of Indians who live near the Orinoco River, in Venezuela. The oldest woman in that tribe was called Cla-Cla, and every night, after the men were in their hammocks, she would spin out her stories until the last listener was asleep. Later in the night, if any of the men, drunk perhaps, or dreaming of the hunt, woke up with a start and a grunt, off she would go again, taking up the thread of the tale where she had dropped it. And Hudson says that Cla-Cla was the only person in the whole tribe who knew the name her parents had bestowed on her at birth. The storyteller of the tribe was the only one who knew her true name. Self-knowledge, in the case of Don Quixote as well as of Cla-Cla, in the case of each of us, goes together with skillful story telling and loving story listening. "All men naturally desire knowledge," says Aristotle at the beginning of his Metaphysics. No: more likely all we desire naturally is a good night's sleep, and if at any moment we wake up with a grunt, there's old Cla-Cla ready to go on with her yarn.
A drawing of Nietzsche near the end of his life (1899), by Hans Olse.