I have spoken of machines, but not only of machines having brains of brass and sinews of iron. When human atoms are knit into an organization in which they are used, not in their full right as responsible human beings, but as cogs and levers and rods, it matters little that their raw material is flesh and blood. What is used as an element in a machine, is in fact an element in the machine. Whether we entrust our fate to machines of metal, or to those machines of flesh and blood which are bureaus and vast laboratories and armies and corporations, we shall never receive the right answers unless we ask the right questions.
I would like then to ask this: what is it, in our behavior, that we can call specifically human? That is special to us as a living species? And what is it that, at least up to now, we can consign as merely machine behavior, or, by extension, insect behavior, or reflex behavior? And I would include, in this, the kind of pseudo-human behavior exhibited by what were once living men—creatures who have, in ways I wish to discuss next, become instruments, means, rather than ends, and hence to me analogs of machines in the bad sense, in the sense that although biological life continues and metabolism goes on, the soul—for lack of a better term—is no longer there or at least no longer active. And such does exist in our world—it always did, but the production of such inauthentic human activity has become a science of government and such-like agencies, now. The reduction of humans to mere use—men made into machines, serving a purpose which, although “good” in an abstract sense has, for its accomplishment, employed what I regard as the greatest evil imaginable: the placing on what was a free man who laughed and cried and made mistakes and wandered off into foolishness and play a restriction that limits him, despite what he may imagine, to the fulfilling of an aim outside of his own personal—however puny—destiny. As if, so to speak, history has made him into its instrument.
Oh, tell me, who was it first announced, who was it first proclaimed, that man only does nasty things because he does not know his own interests; and that if he were enlightened, if his eyes were opened to his real normal interests, man would at once cease to do nasty things, would at once become good and noble because, being enlightened and understanding his real advantage, he would see his own advantage in the good and nothing else, and we all know that not one man can, consciously, act against his own interests, consequently, so to say, through necessity, he would begin doing good? Oh, the babe! Oh, the pure, innocent child!
What is to be done with the millions of facts that bear witness that men, CONSCIOUSLY, that is fully understanding their real interests, have left them in the background and have rushed headlong on another path, to meet peril and danger, compelled to this course by nobody and by nothing, but, as it were, simply disliking the beaten track, and have obstinately, wilfully, struck out another difficult, absurd way, seeking it almost in the darkness. So, I suppose, this obstinacy and perversity were pleasanter to them than any advantage... Advantage! What is advantage? And will you take it upon yourself to define with perfect accuracy in what the advantage of man consists? And what if it so happens that a man’s advantage, SOMETIMES, not only may, but even must, consist in his desiring in certain cases what is harmful to himself and not advantageous. And if so, if there can be such a case, the whole principle falls into dust. What do you think—are there such cases? You laugh; laugh away, gentlemen, but only answer me: have man’s advantages been reckoned up with perfect certainty? Are there not some which not only have not been included but cannot possibly be included under any classification? You see, you gentlemen have, to the best of my knowledge, taken your whole register of human advantages from the averages of statistical figures and politico-economical formulas. Your advantages are prosperity, wealth, freedom, peace—and so on, and so on. So that the man who should, for instance, go openly and knowingly in opposition to all that list would to your thinking, and indeed mine, too, of course, be an obscurantist or an absolute madman: would not he? But, you know, this is what is surprising: why does it so happen that all these statisticians, sages and lovers of humanity, when they reckon up human advantages invariably leave out one? They don’t even take it into their reckoning in the form in which it should be taken, and the whole reckoning depends upon that. It would be no greater matter, they would simply have to take it, this advantage, and add it to the list. But the trouble is, that this strange advantage does not fall under any classification and is not in place in any list…
You tell me again that an enlightened and developed man, such, in short, as the future man will be, cannot consciously desire anything disadvantageous to himself, that that can be proved mathematically. I thoroughly agree, it can—by mathematics. But I repeat for the hundredth time, there is one case, one only, when man may consciously, purposely, desire what is injurious to himself, what is stupid, very stupid—simply in order to have the right to desire for himself even what is very stupid and not to be bound by an obligation to desire only what is sensible.
Shower upon him every earthly blessing, drown him in a sea of happiness, so that nothing but bubbles of bliss can be seen on the surface; give him economic prosperity, such that he should have nothing else to do but sleep, eat cakes and busy himself with the continuation of his species, and even then out of sheer ingratitude, sheer spite, man would play you some nasty trick. He would even risk his cakes and would deliberately desire the most fatal rubbish, the most uneconomical absurdity, simply to introduce into all this positive good sense his fatal fantastic element. It is just his fantastic dreams, his vulgar folly that he will desire to retain, simply in order to prove to himself—as though that were so necessary—that men still are men and not the keys of a piano, which the laws of nature threaten to control so completely that soon one will be able to desire nothing but by the calendar.
And that is not all: even if man really were nothing but a piano-key, even if this were proved to him by natural science and mathematics, even then he would not become reasonable, but would purposely do something perverse out of simple ingratitude, simply to gain his point. And if he does not find means he will contrive destruction and chaos, will contrive sufferings of all sorts, only to gain his point! He will launch a curse upon the world, and as only man can curse (it is his privilege, the primary distinction between him and other animals), may be by his curse alone he will attain his object—that is, convince himself that he is a man and not a piano-key! If you say that all this, too, can be calculated and tabulated—chaos and darkness and curses, so that the mere possibility of calculating it all beforehand would stop it all, and reason would reassert itself, then man would purposely go mad in order to be rid of reason and gain his point! I believe in it, I answer for it, for the whole work of man really seems to consist in nothing but proving to himself every minute that he is a man and not a piano-key!
Cannot you see that it is we that are dying, and that down here the only thing that really lives is the Machine? We created the Machine, to do our will, but we cannot make it do our will now. It has robbed us of the sense of space and of the sense of touch, it has blurred every human relation and narrowed down love to a carnal act, it has paralysed our bodies and our wills, and now it compels us to worship it. The Machine develops—but not on our lines. The Machine proceeds—but not to our goal. We only exist as the blood corpuscles that course through its arteries, and if it could work without us, it would let us die. Oh, I have no remedy—or, at least, only one—to tell men again and again that I have seen the hills of Wessex as Ælfrid saw them when he overthrew the Danes.
. . . The Machine appeared
In the distance, singing to itself
Of money. Its song was the web
They were caught in, men and women
Together. The villages were as flies
To be sucked empty.
God secreted
A tear. Enough, enough,
He commanded, but the Machine
Looked at him and went on singing.
The Machine is not simply a vast, soulless mechanism for accruing material wealth. It is, in some deadly fashion, a sacral object in itself.
Communities never exert themselves to the utmost, still less curtail the individual life, except for what they regard as a great religious end. Where such efforts and sacrifices seem to be made for purely economic advantages, it will turn out that this secular purpose has itself become a god, a sacred libidinous object.
This is what Mumford calls ‘the myth of the Machine’. Sometimes, in our age, we call it growth. Sometimes we call it progress. Sometimes we don’t need words, for no words can ever circumscribe a deity. But a deity it is—and throughout human history, from Egypt to Babylon, Sumeria to Rome, whenever the Machine falls, we work to build it up again, because at some level we need to hear the story that it tells us about ourselves.
This Machine was, by its very nature, absolutely irresistible—and yet, provided one did not oppose it, ultimately beneficent. That magical spell still enthralls both the controllers and the mass victims of the Machine today.
Conquest and expansion are the essence of the Machine. If it could be said to have an ideology, it would be the breaking of bounds, the destruction of limits, the homogenization of everything in its pursuit of its continued growth. The end result of this is the flattening of the world—cultures, ecosystems, landscapes, traditions: any forms of resistance which limit the scope of its kingdom.
What sphinx of cement and aluminum bashed open their skulls and ate up their brains and imagination? Moloch! Moloch! Nightmare of Moloch! Moloch the loveless! Moloch the heavy judger of men! Moloch whose mind is pure machinery! Moloch whose blood is endless oil and stone! Moloch whose soul is electricity and banks! Moloch whose fingers are ten armies! Moloch whose factories wheeze and belch in the fog! Moloch who entered my soul early! Wake up in Moloch!
Know this—there is, in the end, only one form of resistance which is not utterly futile, one rebellion which the Machine simply cannot regulate or tolerate, and that is sleep, for to sleep is to dream, and the Dream is everything which the Machine despises and abhors: inaccessible and irrepressible, chaotic and idiosyncratic, ambiguous and mysterious.
Hurons believe that our souls have other desires, which are, as it were, inborn and concealed, and that our soul makes these natural desires known by means of dreams, which are its language. Accordingly, when these desires are accomplished, it is satisfied; but, on the contrary, if it be not granted what it desires, it becomes angry, and not only does not give its body the good and the happiness that it wished to procure for it, but often it also revolts against the body, causing various diseases, and even death.
Among Iroquoian-speaking peoples in the sixteenth and seventeenth centuries it was considered extremely important literally to realize one’s dreams. Many European observers marvelled at how Indians would be willing to travel for days to bring back some object, trophy, crystal or even an animal like a dog that they had dreamed of acquiring. Anyone who dreamed about a neighbour or relative’s possession (a kettle, ornament, mask and so on) could normally demand it.
It was considered the responsibility of others to realize a fellow community member’s dream: even if one dreamed of appropriating a neighbour’s possession, it could only be refused at the risk of endangering the dreamer’s health. To do so was considered beyond awkward; almost socially impossible. Even if one did it would cause outraged gossip, and very possibly bloody revenge: if somebody was thought to have died because somebody else refused to grant a soul wish, his or her relatives might retaliate physically, or by supernatural means.
Any member of an Iroquoian society given an order would have fiercely resisted it as a threat to their personal autonomy—but the one exception to this norm was, precisely, dreams. One Huron-Wendat chief gave away his prized European cat, which he had carried by canoe all the way from Quebec, to a woman who dreamed she could only be cured by owning it. Dreams were treated as if they were commands, delivered either by one’s own soul or possibly, in the case of a particularly vivid or portentous dream, by some greater spirit. The spirit might be the Creator or some other spirit, perhaps entirely unknown.
Dreamers could become prophets—if only, usually, for a relatively brief period of time. During that time, however, their orders had to be obeyed. (Needless to say, there were few more terrible crimes than to falsify a dream.)
Plenty Coups was born into the Crow (Apsáalooke) tribe in about 1848 at The-Cliffs-That-Have-No-Name (possibly near Billings, Montana), to his father Medicine-Bird and his mother Otter-woman. He was given the birth name Chíilaphuchissaaleesh, or “Buffalo Bull Facing The Wind”.
During the first decades of Plenty Coups’ life, he led the life of a Crow warrior, which involved warring with other major tribes such as the Sioux and Cheyenne over territory, hunting rights, prestige, and the other parts of the traditional warrior way of life.
In accordance with tradition, as a young man his birth name was changed: his grandfather prophesied that he would become chief of the Crow Tribe, live a very long life, and accomplish many great deeds, thus christening him Alaxchiiaahush, meaning “many achievements”. Plenty Coups is the English translation of his name, coming from the word coup, or act of bravery. Over the course of his life, he would live up to his name and his grandfather’s prediction.
Early in his life, Plenty Coups started having prophetic dreams and visions. Many seemed so far-fetched that no one believed them, but when they started coming true, his fellow tribe members began to revere him and listened to him carefully.
After the death of his beloved older brother when he was nine years old, he had a vision in which one of the Little People of the Pryor Mountains told him to develop his senses and wits, and that if he used them well, he would become a chief. As he later said:
I had a will and I would use it, make it work for me, as the Dwarf-chief had advised. I became very happy, lying there looking up into the sky. My heart began to sing like a bird, and I went back to the village, needing no man to tell me the meaning of my dream. I took a sweat-bath and rested in my father’s lodge. I knew myself now."
In 1804, the Lewis and Clark Expedition stayed for a time with a band of Wičhíyena Sioux on the Vermillion River in modern-day South Dakota. On August 25, Meriwether Lewis, William Clark, and 10 other men traveled about 9 miles (14 km) north of the river’s junction with the Missouri River to see the “mountain of the Little People”. Lewis wrote in his journal that the Little People were “deavals” with very large heads, about 18 inches (46 cm) high, and very alert to any intrusions into their territory. The Sioux said that the devils carried sharp arrows which could strike at a very long distance, and that they killed anyone who approached their mound. The Little People so terrified the local population, Lewis reported, that the Maha (Omaha), Ottoes (Otoe), and Sioux would not go near the place. The Lakota people who came to live near the “Spirit Mound” after the Wičhíyena Sioux have a story no more than 250 years old which describes how a band of 350 warriors came near the mound late at night and were nearly wiped out by the ferocious Little People (the survivors were crippled for life).
Crow folklore differs slightly from that of other tribes in describing the Little People of the Pryor Mountains as having large heads, nearly fourteen inches tall, and incredibly strong but short arms and legs; and little or no neck. In the story of “Lost Boy”, the Crow told of a Little Person who killed a full-grown bull elk and carried it off just by tossing the elk’s head over its shoulder. The Crow expression, “strong as a dwarf,” references the incredible strength of these Little People.
When he was nine years old, Plenty Coups’ older brother (who was a great warrior and quite handsome, and whom Plenty Coups loved deeply) was killed by raiding Lakotas. Although the tribe was preparing to move out, Plenty Coups fasted for four days, used the sweat lodge, rubbed his body with sage and cedar to remove any smell, and then went into the nearby hills where he had a vision. In his vision, the chief of the Little People took him into a spirit-world lodge, where Plenty Coups saw representations of nature (the wind, the stars, thunder, the moon, bad storms, etc.). The dwarf chief demanded that Plenty Coups count coup, but since Plenty Coups was just nine years of age he knew that he had no great deeds to count. Nonetheless, the chief of the Little People recounted two great deeds to the spirits gathered in the lodge, and said that Plenty Coups would not only accomplish these deeds but many others as well. When he was 11 years old, Plenty Coups had a second vision involving the Little People, one that changed the fate of his entire tribe. Plenty Coups’ family had moved to be with other bands of Crow lodging in the Beartooth Mountains. All the young men were challenged to go into the hills to seek visions, and Plenty Coups did so. Plenty Coups walked for two days (fasting as he went) and entered the Crazy Mountains, but had no vision. He returned a few days later with three friends, fasted, and took sweat-baths. He decided to cut off the tip of his left index finger as an offering to the spirits. That night, he dreamt of the chief of the Little People again. The chief introduced Plenty Coups to a buffalo that turned into a man with buffalo-like features, who led him underground and down a tunnel or path toward the Pryor Mountains. For two days, he traveled underground among throngs of American bison. Finally, the buffalo-man showed Plenty Coups a vision of endless streams of bison coming out of a hole in the ground but disappearing. Then a second stream of bison—with different colors (even spots), tails, and sounds—came up out of the ground, and remained on the plains. Plenty Coups had a vision of himself as an old man lodged near the Medicine Rocks, and of a vast forest felled by a great wind, save for one tree. On that one, lone surviving tree was a chickadee, a humble member of the Crow people’s aviary pantheon, noted for its capacity to listen and adaptively change course.
Plenty Coups sought out the advice of his tribal elders in interpreting this dream. The elders said that it meant that the buffalo would soon disappear, to be replaced by white men’s cattle. To survive in the white man’s world, they would have to adapt from Crow virtues to Chickadee ones: from war virtues to other, more humble habits like listening, observing, and adapting to new situations, trading one sort of courage (martial) for another. They thought that the old Chickadee, who was no Crow, would have to be repurposed as a new icon of a new kind of courage and take the old Crow’s place.
Plenty Coups’ spirit guide became the chickadee, and he would carry a pair of chickadee legs in a medicine bag he used for protection and spiritual power. This vision would guide his actions (and that of the Crow People) for the remainder of his life.
Plenty Coups became a distinguished warrior in the Crow’s battles against their traditional enemies, the Sioux, Cheyenne, Arapaho, Blackfoot and Flathead tribes. In 1876, at age 28, he became chief of the Mountain Crows. As chief, he helped find Crow scouts for Generals Gibbon, Crook and Custer, and for the U.S. Army, during the Nez Perce war. He also quieted a threatened uprising among the Crow in 1887.
As Linderman wrote, “it was Plenty Coups who saw quite clearly that a readjustment of his people to meet the changing conditions was necessary. Gifted with the power of impressive speech and possessing a dignity of presence that readily won him any hearing, he more than once visited the Indian Department at Washington DC in the interest of his people—who were quick to recognize him as the outstanding Crow of his time. Giving advice to his people, he took care to follow it himself; Plenty Coups was one of the first Crow to begin cultivating the land, and he even opened a general merchandise store where his tribesmen might trade.”
Chief Plenty Coups was selected as sole representative of Native Americans for the dedication of the Tomb of the Unknown Soldier after World War I. He gave a short speech in his native tongue in honor of the soldier and the occasion. He placed his war bonnet and coup stick upon the tomb, which are preserved in a display case there.
When he died in 1932 at age 84, he was considered by his people to be the last of the great chiefs. The vision he had had when he was younger had come true: Bison were almost wholly replaced by cattle. White society and government dominated and had completely changed America. Through diplomacy, foresight and strong leadership, Plenty Coups was able to preserve the Crow Nation land, people and culture much better than most other Native American tribes.
Between 1958 and 1973, Alexander Grothendieck towered over mathematics like a veritable colossus. Even though he was able to solve three of the four Weil conjectures, the greatest mathematical enigmas of his time, Grothendieck was not interested in deciphering famous problems or reaching seemingly unthinkable results; his desire was to achieve an absolute understanding of the foundations of mathematics. To do so, he constructed intricate theoretical architectures around the simplest of questions, encircling them with a vast array of new concepts. Under the soft, continuous pressure of Grothendieck’s reasoning, solutions seemed to reveal themselves of their own free will, welling up to the surface, and opening, as he once said, “like a nutshell that had spent months submerged in water”.
His was the power of unbridled abstraction. He championed an approach that was based on wild generalizations, zooming further and further out and then focusing sharply, as any dilemma became clear when one viewed it from a sufficient distance. Numbers, angles, curves and equations did not interest him, nor did any other mathematical object in particular: all that he cared for was the relationship between them. “He had an extraordinary sensitivity to the harmony of things,” one of his disciples, Luc Illusie, recalled.
Space was his lifelong obsession. One of his greatest strokes of genius was expanding the notion of the point. Beneath his gaze, the humble dot was no longer a dimensionless position; it swelled with a complex inner structure. Where others had seen a simple locus without depth, size or breadth, Grothendieck saw an entire universe.
He was physically imposing, tall, thin and athletic, with a square jaw, broad shoulders and a large, bull nose. The corners of his thick lips curved upwards, giving him a mischievous look, as though he were privy to a secret that everyone else did not even suspect. When he began to lose his hair, he shaved his head, a perfect oval.
A talented boxer, fanatical about Beethoven’s final quartets and Bach, he loved nature and venerated “the humble and long-lived olive tree, full of sun and life”, but above all the things of this world, including mathematics, he had a devotion to writing that bordered on the fanatical. He wrote with such fervour that, in certain parts of his manuscripts, the pencil tip would pierce the page straight through. When calculating, he wrote his equations in his notebook and then retraced them over and over, until each symbol was so thick it was no longer intelligible, in thrall to the physical pleasure he felt by scratching graphite on paper.
Unifying mathematics is a dream that only the most ambitious minds have pursued. Descartes was among the first to show that geometric forms can be described through equations. Whoever writes x² + y² = 1 is describing a perfect circle. Every possible solution to this basic equation represents a circle drawn on a plane. But if one considers not only real numbers and the Cartesian plane, but also the bizarre spaces of complex numbers, there appears a series of circles of various sizes that move as if they were living creatures, growing and evolving in time. Part of Grothendieck’s brilliance was to recognize that there was something grander hidden behind every algebraic equation. He called this something a scheme. Each individual solution to an equation, each shape, was nothing but a shadow, an illusory projection that flashed forth from the general scheme, “like the contours of a rocky coast illuminated at night by the rotating lamp of a lighthouse”.
Grothendieck was capable of creating an entire mathematical universe fit for a single equation. His topoi, for example, were seemingly infinite spaces that defied the limits of the imagination. Grothendieck compared them to “the bed of a river so vast and so deep that all the horses from all the kings of this world, and from all possible worlds, could drink from its waters together”. To think in such terms demanded a completely novel conception of space, as radical as the change brought forth by Albert Einstein, fifty years before.
He was capable of sleeping at will, as many hours as he needed, then dedicating the whole of his energy to his work. He could begin working out an idea in the morning and not move from his desk until dawn the next day, squinting under the light of an old kerosene lamp. “It was fascinating to work with a genius,” his friend Yves Ladegaillerie remembers. “I don’t care for that word, but for Grothendieck there is no other. It was fascinating but also terrifying, because this was a man who simply did not resemble other human beings.”
“My first impression on hearing him lecture was that he had been transported to our planet from an alien civilization in some distant solar system in order to speed up our intellectual evolution,” a professor from the University of California at Santa Cruz said of him. Despite how radical they were, the mathematical landscapes Grothendieck conjured up gave no impression of artificiality. To the trained eyes of a mathematician, they revealed themselves as seemingly natural environments, for Grothendieck did not impose his will on things, preferring to let them grow and develop by themselves. The results had an organic beauty, as though each idea had budded and borne fruit following its own vital impulse.
“What stimulates me is not ambition or the thirst for power. It is the acute perception of something immense and yet very delicate at the same time.” Grothendieck continued to push past the limits of abstraction. No sooner had he conquered new territory than he was preparing to expand its frontiers. The pinnacle of his investigations was the concept of motive; a ray of light capable of illuminating every conceivable incarnation of a mathematical object. “The heart of the heart” he called this strange entity located at the crux of the mathematical universe, of which we know nothing save its faintest glimmers.
Even his closest and most loyal collaborators believed he had gone too far. Grothendieck wanted to hold the sun in the palm of his hand, uncover the secret root that could bind together countless theories that bore no apparent relation to one another. They told him his goal was unattainable, and that his project sounded more like the pipe dreams of an amateur than a legitimate programme for scientific exploration. Grothendieck did not listen.
At the tail end of the Sixties, he travelled for two months to Romania, Algeria and Vietnam to give a series of seminars. One of the colleges at which he taught in Vietnam was later bombed by American troops; two professors and dozens of students died. When he returned to France, he was a changed man. Influenced by the clamour of the May 1968 protests all around him, he called on more than a hundred students during a masterclass at the University of Paris in Orsay to renounce “the vile and dangerous practice of mathematics” in light of the hazards humanity was facing. It was not politicians who would destroy the planet, he told them, but scientists like them who were “marching like sleepwalkers towards the apocalypse”.
From that day forward, he refused to participate in any maths conference that would not allow him to devote equal time to ecology and pacifism. During his talks, he gave away apples and figs grown in his garden and warned about the destructive power of science: “The atoms that tore Hiroshima and Nagasaki apart were split not by the greasy fingers of a general, but by a group of physicists armed with a fistful of equations.” Grothendieck could not stop fretting over the possible effects that his own ideas could have on the world. What new horrors would spring forth from the total comprehension that he sought? What would mankind do if it could reach the heart of the heart?
In 1970, at the high point of his renown, creativity and influence, he resigned from the Institut des Hautes Études Scientifiques (IHÉS) after learning it accepted funds from the French Ministry of Defence. In the following years, he abandoned his family, disavowed his friends, repudiated his colleagues, and fled the rest of the world.
. . . The machine appeared
In the distance, singing to itself
Of money. Its song was the web
They were caught in, men and women
Together. The villages were as flies
To be sucked empty.
God secreted
A tear. Enough, enough,
He commanded, but the machine
Looked at him and went on singing.
“The Great Turning Point” was the term Grothendieck used to describe the change in the direction of his life during his forties. All at once, he found himself swept up by the spirit of the age: he became obsessed by ecology, the military-industrial complex and nuclear proliferation. To his wife’s despair, he founded a commune at home, where vagabonds, professors, hippies, pacifists, thieves, nuns and prostitutes dwelt side by side.
He became intolerant of all the comforts of bourgeois life; he tore up the carpets from the floors of his house, considering them superfluous adornments, and began to make his own clothing; sandals from recycled tires, trousers sewn from old burlap sacks. He only felt at ease among the poor, the young and the marginalized.
Although in general he was caring and kind, he could suffer sudden outbreaks of violence. During a pacifist protest in Avignon, he ran towards the containment barrier and knocked out two policemen who were attempting to impede the march, before being beaten to a pulp by dozens of officers who dragged him unconscious to the police station. At home, his wife heard him rant and rave while locked alone in his study, long monologues in German which degenerated into screams so loud that they shook the windows, followed by episodes of mutism that could last for days.
“Doing mathematics is like making love,” wrote Grothendieck, whose sexual impulses rivalled his spiritual inclinations. Throughout his life he seduced both men and women. He had three children with his wife, Mireille Dufour, and two more outside his marriage.
Sex is our deepest form of consciousness. It is utterly non-ideal, non-mental. It is pure blood-consciousness. It is the consciousness of the night, when the soul is almost asleep.
He was convinced that the environment had its own consciousness and that it was his duty to protect it. He would gather even the smallest shoots that grew between the cracks in the pavement outside his house to replant and care for them.
He began fasting once a week, then twice, and sometimes he would stop eating completely. Self-mortification became second nature to him. During a trip to Canada, he refused to wear shoes and walked through the snow in his sandals, like some Middle Eastern prophet spreading his gospel through a frozen desert. After a severe motorcycle accident, he declined anaesthesia, and agreed only to acupuncture during his surgery, as he had grown almost indifferent to physical pain.
In 1973, the commune he had founded as a place open to all descended into pure lawlessness. First, the police came to arrest two Japanese monks from the Order of the Marvellous Lotus Sutra who had overstayed their visas, and charged Grothendieck with harbouring illegal aliens. That same week, a girl he often spent the night with tried to hang herself with the curtains in his room. When he returned with her from the hospital, Grothendieck found the members of the commune dancing around an enormous bonfire they had built in the middle of the courtyard, feeding it with pages from his manuscripts. Grothendieck disbanded the community and retired to Villecun, a village of just a dozen tiny cottages.
In Villecun he lived without electricity or drinking water in a flea-infested cabin, but he was happier than he had ever been. For five years, in almost total isolation, he devoted himself to manual labour, undertaking no major projects. His children did not visit him, he had no lovers, and he ignored all his neighbours with the exception of a twelve-year-old girl he helped with her arithmetic homework.
In Villecun, he focused his immense analytical powers on his own mind. The result was a change even more radical than the one that had drawn him away from mathematical research, a complete metamorphosis that he tried to encapsulate in a cryptic list tracing out the stations of his spiritual journey, which had taken him further and further away from common sense.
May 1933: longing for death
27-30 December 1933: birth of the wolf
summer (?) 1936: the Gravedigger
March 1944: existence of God the creator
June-Dec. 1957: call and betrayal
1970: the stripping away— entry into the mission
1-7 Apr. 1974: moment of truth, entry into the spiritual path
July-Aug. 1974: insufficiency of the Law. I leave the paternal Universe
June-July 1976: awakening of the Ying
15-16 Nov. 1976: collapse of the image, discovery of meditation
18 Nov. 1976: re-encounter with my soul, entry of the Dreamer
March 1979: discovery of the wolf
August 1980: meeting with the Dreamer—recovery of childhood
Feb. 1984-May 1986: Reaping and Sowing
*NB 25.22.1986: first erotico-mystic dreams
28 Dec. 1986: death and rebirth
1-2. Jan, 1987: mystico “erotic abduction”
27 Dec. 1986-21 March 1987: metaphysical dreams, intelligence of dreams
8.1, 24.1, 26.2, 15.3 (1987): prophetic dreams
28.3.1987: nostalgia for God
30.4.1987: The Key to Dreams
The manuscript La Clef des Songes (The Key to Dreams) begins with the following words, written on April 30, 1987:
The first dream in my life which I examined and whose message I heard, immediately and profoundly transformed the course of my life. This moment was experienced, truly, as a profound renewal, as a rebirth. In hindsight I would now say that it was the moment of meeting again with my “soul”, from which I had lived apart since the days, lost in oblivion, of my earliest childhood. Up until that moment I had been living in ignorance of the fact that I even possessed a “soul”, that inside me there was another self, silent and nearly invisible, yet alive and vigorous—someone quite different to the one inside me who always took center stage, the only one whom I saw and with whom I continued to identify myself for better or worse: “the Boss”, the “me”. The one that I knew only too well, ad nauseam. But this day was a day of reunion with the other, thought to be dead and buried “for a whole lifetime”, along with the child inside me.
When reading these lines, one would like to know why Grothendieck experienced this dream so powerfully and why it changed his entire spiritual life, but in typical Grothendieck fashion he does not say a word about it. The reader is left with a sort of twofold impression. He feels invited to participate in Grothendieck’s thoughts—apparently there is something that Grothendieck wants to communicate—but then entry is denied to him.
Before we go into the content and style of La Clef des Songes, let us make a few remarks on its genesis and scope. This meditation is a typescript of some seven chapters and 345 pages, written in Les Aumettes between April 30, 1987 and September 13, 1987. The full title is La Clef des Songes—ou Dialogue avec le bon Dieu (The Key of Dreams—or Conversation with the good Lord). Added to this text are the Notes pour la Clef des Songes, which comprises 691 pages written between June 3, 1987 and early April 1988. According to a provisional table of contents, La Clef des Songes was to consist of twelve chapters, but only seven are extant. Currently no one knows if the other five chapters were never written, or were written and but subsequently destroyed, or whether they still exist somewhere.
The dates also show that the work progressed with incredible speed. Grothendieck wrote one thousand pages in eleven months. As he says himself, he needed on average two to three hours per page. He says repeatedly that the writing of La Clef des Songes took much effort and labor, far more than Récoltes et Semailles (Reaping and Sowing). Grothendieck used the same writing technique as in Récoltes et Semailles: in each of the numerous sections of varying length, he treated one subject or theme. In general he left these sections unchanged, but if he thought it was necessary to take up the subject again, in order to modify or complete it, he did this by adding new sections, or else via remarks or footnotes. In this manner a rather confusing text emerged, although it is all in all more structured than Récoltes et Semailles.
Many people who knew Grothendieck relate that he was “always” very interested in his dreams. But they only became a central component of his spirituality after “The Great Turning Point” in 1970, and especially after 1980. From this time onward they became a constantly recurring theme in his correspondence. He writes for example to his German friends:
Since the end of July [1980] I am above all examining my dreams. An overwhelming source of riches is lavished upon me, which until now I foolishly ignored with few exceptions. In each dream there is sense and humor and strength—and if it appears senseless, absurd and even idiotic that is only because of the tremendous inertia in me, which resists the dream’s playfully ingenuous message. But now I want to be a more attentive pupil of the Dreamer. Whether attentive and alert or not—in any case I am now already a pupil, and I am never bored.
He wrote in a very similar manner seven years later to his friends Felix and Matilde Carrasquer:
[...] and the work, of interpreting their [the dreams’] meaning is the most delicate and the most difficult, but also the most fascinating, that I have ever undertaken in my life—and also the most fruitful. Above all, it is the intensity of this work which has caused me to neglect my correspondence for months and months.
A few years after he had begun his work on dreams, Grothendieck apparently believed that his meditations on the phenomenon of dreaming were sufficiently mature for him to be able to present them to the interested reader in book form. In the first sections he often addresses the reader directly, for example in the following manner:
This book, which I am beginning to write this very day, addresses itself primarily to the very rare (if there are any others apart from myself) people who dare to explore the depths of certain dreams. To those who dare to believe in their dreams and in the messages which they carry. If you are one of these, then I would wish that this book be an encouragement to you, in case it is needful, to have faith in your dreams. And also to have faith (as I had faith) in your aptitude to hear their message. [...]
If this book can help you at all, it will not have been written in vain.
The first chapters of the meditation can be understood as the development of a “theory of dreams”. This is evidently not a scientific theory in any manner, but even viewed from an esoteric or spiritual angle, most people would find it impossible to share Grothendieck’s way of thinking and ideas. In spite of this, his vision is coherent in its own way. This author considers it to be not so much a description of some kind of “reality”, but rather as a sort of strange but fascinating metaphysical poetry.
What if you slept?
And what if, in your sleep, you dreamed?
And what if, in your dream, you went to heaven
And there plucked a strange and beautiful flower?
And what if, when you awoke,
You had the flower in your hand?
Ah, what then?
Strange! that you should not have suspected years ago—centuries, ages, eons, ago!—for you have existed, companionless, through all the eternities. Strange, indeed, that you should not have suspected that your universe and its contents were only dreams, visions, fiction! Strange, because they are so frankly and hysterically insane—like all dreams: a God who could make good children as easily as bad, yet preferred to make bad ones; who could have made every one of them happy, yet never made a single happy one; who made them prize their bitter life, yet stingily cut it short; who gave his angels eternal happiness unearned, yet required his other children to earn it; who gave his angels painless lives, yet cursed his other children with biting miseries and maladies of mind and body; who mouths justice and invented hell—mouths mercy and invented hell—mouths Golden Rules, and forgiveness multiplied by seventy times seven, and invented hell; who mouths morals to other people and has none himself; who frowns upon crimes, yet commits them all; who created man without invitation, then tries to shuffle the responsibility for man’s acts upon man, instead of honorably placing it where it belongs, upon himself; and finally, with altogether divine obtuseness, invites this poor, abused slave to worship him!
You perceive, now, that these things are all impossible except in a dream. You perceive that they are pure and puerile insanities, the silly creations of a mad mind—in a word, that they are a dream, and you the maker of it. The dream-marks are all present; you should have recognized them earlier.
After the introductory paragraphs, Grothendieck begins with the statement that self-awareness [connaissance de soi] is the most important and decisive element in a spiritual life.
Without self-awareness, there is neither understanding of the other nor of the world of men, nor the work of God in man. Over and over again I have found, in myself or my friends and acquaintances, and even in what we call “spiritual works” (including some of the most famous ones): without self-awareness the image that we create of the world and the other is nothing but the blind and idle workings of our cravings, our hopes, our fears, our frustrations, our voluntary ignorance, and our flights and abdications and our repressed urge to violence…
The opening chapter expresses the meaning and the importance of dreams and the Grothendieck’s empirical conviction that dreams are sent by an outside force, called “le Rêveur” (“the Dreamer”), who knows each of us intimately and sends dreams in order for each of us to know himself fully. Although all dreams are messages, he signals the existence of particularly powerful ones which should act as a call, and warns against the inertia (fear of change) which prevents the dreamer from the meaning contained in it.
Grothendieck mentions in the text that he came to this essential insight—that dreams are sent from an outside power—for the first time in August 1982, six years after he had recognized the importance of dreams.) Grothendieck understood quite well that his “theory of dreams” placed him in opposition to other views:
If I have learned such things about dreams which one cannot find in books, that is because I have come to them in a spirit of innocence, like a little child. And I have no doubt that if you do the same you will not only learn about yourself, but also about dreams and the Dreamer, things that are not in this book, nor in any other.
Grothendieck then goes on to analyze the nature of the “Dreamer”, and comes to the conclusion that God exists and that he is the Dreamer: the title of the second chapter is “Dieu est le Rȇveur”. God send dreams to humans so that they may understand themselves and find the way to true life. Presumably Grothendieck saw this as the central message of his text, and he recognized the need to explain these thoughts:
I was about to explain the meaning of the “main idea” [pensée maîtresse]: “God is the Dreamer,” to a reader who has not had any direct experience with God, one for whom “God” is perhaps nothing but a word, empty of meaning, or even a “superstition” from a “pre-logical” epoch, which has long since come to an end (thank God!) ever since the triumphant upsurge of rational thought and Science. I have friends of long date who plug their ears with sorrowful faces when they hear words like “God”, “soul”, or even “spirit”. I do not know if they will read my testimony, but I am also writing for them, in the hope, who knows? [...]
In several letters to friends and acquaintances from this time Grothendieck expressed the view that this discovery, namely that God is the Dreamer, was the most important discovery of his life.
Grothendieck then goes on to deal with the question as to how he himself found his way to God and to faith in God. For biographical purposes, this chapter, entitled, “Le Voyage à Memphis (1): L’Errance” is the most important one (The text contains three more chapters under the heading “Voyage à Memphis”. Typical of Grothendieck, he gives no explanation of what or where this Memphis is). There is no other text where Grothendieck expresses himself in such detail about his own life and that of his parents. He describes his parents as convinced non-believers and atheists, and speaks of his childhood in an irreligious environment. In doing so he doubtless wanted to make clear that, considering his past, it was far from obvious that he would find the “way to God”, that this in fact required an impetus from the outside, namely from God himself.
Grothendieck promises an account of several dreams and their interpretations (which are unfortunately not given in the present text). He expresses his empirical, primary knowledge of the identification of God with the Dreamer, and asserts that each individual has his own Dreamer, but they are all one and the same of infinite knowledge. However, he says that such a thing cannot be proved (gently mocking those who gave logical proofs of the existence of God) but only known first-hand by revelation and experience. He also briefly describes the prophetic contents of his dreams (a cataclysm for humanity within his lifetime, leading to a spiritual renewal of the remaining portion of humanity) and asserts that the realisation of these events is obviously the only ‘proof’ which can be offered to the doubting.
In chapter IV (Aspects d’une mission: un chant de liberté), Grothendieck discusses the meaning of the mission entrusted to each of us, and in particular his own; he rejects the idea of one’s mission being that of carrying a grand message to humanity such as many Gurus do, and explains that in fact that each of us is entrusted with the mission of witnessing to his own personal experience of self-knowledge, in the hope of leading, by example, others to the same process (and not to simple quotation of someone else’s experience). Later in the chapter, he turns to the powerful role of Eros in creativity and warns against the attempt to sublimate it. Creativity is evoked as a fundamental quality of humanity, which is crushed in almost every individual by the power of fear.
Grothendieck is convinced that each person has a “mission” and that the most important part of this mission consists in finding the way to oneself in order to recognize one’s true self. He discusses the meaning of the mission entrusted to each of us, and in particular his own; he rejects the idea of one’s mission being that of carrying a grand message to humanity such as many gurus do, and explains that in fact that each of us is entrusted with the mission of witnessing to his own personal experience of self-knowledge, in the hope of leading, by example, others to the same process (and not to simple quotation of someone else’s experience). Only in this way can a person’s creative forces be set free, forces which are repressed by social pressures in all sorts of ways, but above all by inner inertia, and never come to fruition.
Let each one turn his gaze inward and regard himself with awe and wonder, with mystery and reverence; let each one work his own influence, his own havoc, his own miracles.
Grothendieck evaluates every person with regard to how far they have come on the path to a true spiritual life. With respect to this he also discusses the spiritual aspects of pursuing mathematics. Although it is a small digression, it is worth noting a remark about mathematics which he made in a footnote to this chapter. In the text he had discussed the existence of a creative intelligence (God) which has created all things, the universe and also the laws which regulate the universe. In the footnote he added:
One must however make an exception here for the laws of mathematics. These laws can be discovered by man, but they are created neither by man nor even by God. The fact that two plus two equals four is not a decree of God, in the sense that He would be free to change this into two plus two equals three or five. I feel the mathematical laws as being part of the nature of God himself—a minuscule part, certainly, in some ways the most superficial, but the only one which is accessible to reason alone. This is why it is possible to be a great mathematician while being in a state of extreme spiritual decay.
Finally Grothendieck speaks of the manifold distortions of humanity, which go hand in hand with a loss of spirituality, and which can be seen for example in the fact that the feeling for “beauty” has been lost to a great extent in all domains. (In this context the herd [troupeau] is a frequently repeated word.)
Near the end of the fifth chapter (p. 212), we find the following passage:
And never as much as in these last few days have I had this strange and sometimes disorienting impression that the “control” over the writing of this book is slipping away from me in some mysterious way...Both in its content and in its spirit, this book bears absolutely no resemblance to what I had in mind when I started writing it.
The section (quite humorous or at least ironic in parts) describes the heart of Grothendieck’s vision of renewal; recognising the existence of enormous, powerful egotic forces defending what he calls the Image (or the Idol) of oneself erected by the ego and maintained at the price of an extraordinary amount of fiction, absurdity and gigantic resistance to simple observation. Grothendieck points out that people are generally not even remotely aware of these forces and resistances, much less vigilant about spotting and overcoming them. This, to him, is the key necessity for the development of an authentic spirituality (or ability to hear the voice of God). The ego is described as an inextricable skein of reflexes and greeds; the first step in freeing oneself from its power is the simple realisation that the soul is distinct from the ego. The second step is the realisation of what he calls one’s own blinkers, inveterate reactions of the psyche whose purpose is to blind the person to anything contradicting the Image.
Yet, as extraordinary as Grothendieck’s achievements are, he traced his creative capacity to something rather humble: the naive, avid curiosity of a child. “Discovery is the privilege of the child,” he wrote in Récoltes et Semailles (page 1), “the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.” For the work of discovery and creation, Grothendieck saw intellectual endowment and technical power as secondary to the child’s simple thirst to know and understand. This child is inside each of us, though it may be marginalized, neglected, or drowned out.
In our probing of things in the Universe (mathematical or otherwise), we dispose of a crucial rehabilitating power: innocence. By this I mean the original innocence which we have all received at birth and which rests within us, often the target of our scorn and of our deepest fears. It alone unites the humility and audacity which allow us to penetrate into the heart of things, while also allowing these things to penetrate into us and impregnate us with their meaning. This power does not only come as a privilege for the extraordinarily “gifted”, those with an exceptional intellectual power allowing them to absorb and manipulate, with ease and dexterity, an impressing quantity of known facts, ideas, and techniques. Such gifts are admittedly precious, and susceptible to generate the envy of those who were not so gifted at birth as I was. Yet, it is not those gifts, nor even the most burning of ambitions, accompanied with a relentless will, which allow us to cross the “invisible and imperious circles” which enclose our Universe. Only innocence can cross them, without noticing or even caring to, during the times where we find ourselves alone and listening to the voice of things, intensely absorbed in child’s play…
Youth, of course, has always tended toward this; in fact this is really a definition of youth. But right now it is so urgent, if, as I think, we are merging by degrees into homogeneity with our mechanical constructs, step by step, month by month, until a time will perhaps come when a writer, for example, will not stop writing because someone unplugged his electric typewriter but because some unplugged him. But there are kids now who cannot be unplugged because no electric cord links them to any external power source. Their hearts beat with an interior, private meaning. Their energy doesn’t come from a pacemaker; it comes from a stubborn, almost absurdly perverse, refusal to be “shucked,” that is, to be taken in by the slogans, the ideology—in fact by any and all ideology itself, of whatever sort—that would reduce them to instruments of abstract causes, however “good.”
Back in California, where I come from, I have been living with such kids, participating, to the extent I can, in their emerging world. I would like to tell you about their world because—if we are lucky—something of that world, those values, that way of life, will shape the future of our total society, our utopia or anti-utopia of the future. It is my hope—and I’d like to communicate it to you in the tremendous spirit of optimism that I feel so urgently and strongly—that our collective tomorrow exists in embryonic form in the heads, or rather in the hearts, of these kids who right now, at their young ages, are politically and sociologically powerless, unable even, by our Californian laws, to buy a bottle of beer or a cigarette, to vote, to in any way shape, be consulted about, or bring into existence the official laws that govern their and our society.
I think, really, this is what I’m saying: if you’re interested in the world of tomorrow, you might learn something by watching a 16- or 17-year-old kid go about his natural peregrinations, his normal day—or, as we say in the San Francisco Bay Area, ‘cruising around town to check out the action.’ This is what I’ve found. These kids that I’ve known, lived with, and still know in California are what I believe in, more than anything else I’ve ever encountered, and what I’d give my life for—my full measure of devotion in this war we’re fighting to maintain and augment what is human about us, the core of ourselves, the source of our destiny. Our flight must be not only to the stars but into the nature of our own beings. Because it is not merely where we go, to Alpha Centauri or Betelgeuse, but what we are as we make our pilgrimages there. Our natures will travel with us. Ad astra, but per hominem. We must never lose sight of that.
Sudden surprises, by the way—and this thought may be, in itself, a sudden surprise to you—are a sort of antidote to paranoia...or, to be accurate, to live in such a way as to encounter sudden surprises quite often or even now and then is an indication that you are not paranoid. Because to the paranoid, nothing is a surprise; everything happens exactly as he expected, and sometimes even more so. It all fits into his system. Maybe all systems—that is, any theoretical, verbal, symbolic, or semantic formulation that attempts to act as an all-encompassing, all-explaining hypothesis of what the universe is about—are manifestations of paranoia. We should be content with the mysterious, the meaningless, the contradictory, the hostile, and most of all, the unexplainably warm and giving—a so-called inanimate environment, in other words, that is very much like a person, like the behavior of one intricate, subtle, half-veiled, deep, perplexing, and loving human being to another. To be feared a little, too, sometimes. And perpetually misunderstood. About which we can neither know nor be sure; we must only trust and make guesses toward. Not being what you thought, not doing right by you, not being just, but then sustaining you as by momentary caprice, but then abandoning you, or at least seeming to. What it is actually up to we may never know. But at least this is better, is it not, than to possess the self-defeating, life-defeating spurious certitude of the paranoid—expressed, by a friend of mine, humorously, I guess, like this: “Doctor, someone is putting something in my food to make me paranoid.”
But no android—and you will recall and realize that by this term I am summing up that which is not human—no android would think to do what a bright-eyed little girl I know did. Something a little bizarre, certainly ethically questionable in several ways, at least in any traditional sense, but to me truly human, in that it shows a spirit of merry defiance, of spirited, although not spiritual, bravery and individuality.
One day, while driving along in her car, she found herself following a truck carrying cases of Coca-Cola bottles, case after case, stacks of them. And when the truck parked, she parked behind it and loaded the back of her own car with cases, as many cases of bottles of Coca-Cola as she could get in. So, for weeks afterward, she and her friends had all the Coca-Cola they could drink, free—and then, when the bottles were empty, she carried them to the store and turned them in for the deposit refund.
To that I say: God bless her. May she live forever. And the Coca-Cola company, the phone companies, the TV networks, and all the rest of them—may they be gone long ago. Metal and stone and wire and thread never did live. But she and her friends—they are the Fire, the Dream, the little song we sing.
Further posts in this series:
This is a great essay. I consumed it first in its audio form while going about my day. When I was able to later find time to sit and read it on the page, I realized just how bizarrely brilliant its structure is. I hope to emulate it in my own written meditations.
Its content, though, more than its form, is what will bring me back to it. Thank you for the reminders. The record and study of dreams has been a steady practice of mine for decades (with gaps), and I hadn't realized how significant this was for Grothendieck as well. My early published research was in a field adjacent to algebraic geometry – although by now one can reasonably claim that all fields of modern mathematics are adjacent to one another due to the sheer scale of cross-pollination the internet has enabled. While it has been years since I exited academic circles, reading this essay was a serendipitous and encouraging reminder that one should persevere in their communion with mathematical creativity, for its own sake, as a way to nourish the soul.
Will check back in as I gradually make my way through your other posts.
Post script: what are your sources for La Clef des Songes? Are you translating from one of the French typescripts online?
Great essay!
It's funny, I remember being a child - maybe around 8 - and asking my mum 'what if we are all just God's dream?'.
I can't remember what she said, but I think I was on to something. It's strange that the only people who can reach such insights are children and those who have re-discovered the child's mind.