The Man Who Knew Infinity Quotes

They must be true because, if they were not true, no one would have the imagination to invent them.

Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.

But what Ramanujan wanted more, more than anything, was simply the freedom to do as he wished, to be left alone to think, to dream, to create, to lose himself in a world of his own making.

Don’t be so easy on yourself, it said.

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

His academic failure forced him to develop unconventionally, free of the social straightjacket that might have constrained his progress to well-worn paths.

A pure mathematician must leave to happier colleagues the great task of alleviating the sufferings of humanity.

My little brother's greatest fear was that the one person who meant so much to him would go away. He loved Lindsey and Grandma Lynn and Samuel and Hal, but my father kept him stepping lightly, son gingerly monitoring father every morning and every evening as if, without such vigilance, he would lose him. We stood- the dead child and the living- on either side of my father, both wanting the same thing. To have him to ourselves forver. To please us both was an impossibility. ... 'Please don't let Daddy die, Susie,' he whispered. 'I need him.' When I left my brother, I walked out past the gazebo and under the lights hanging down like berries, and I saw the brick paths branching out as I advanced. I walked until the bricks turned to flat stones and then to small, sharp rocks and then to nothing but churned earth for miles adn miles around me. I stood there. I had been in heaven long enough to know that something would be revealed. And as the light began to fade and the sky to turn a dark, sweet blue as it had on the night of my death, I saw something walking into view, so far away I could not at first make out if it was man or woman, child or adult. But as moonlight reached this figure I could make out a man and, frightened now, my breathing shallow, I raced just far enough to see. Was it my father? Was it what I had wanted all this time so deperately? 'Susie,' the man said as I approached and then stopped a few feet from where he stood. He raised his arms up toward me. 'Remember?' he said. I found myself small again, age six and in a living room in Illinois. Now, as I had done then, I placed my feet on top of his feet. 'Granddaddy,' I said. And because we were all alone and both in heaven, I was light enough to move as I had moved when I was six and in a living room in Illinois. Now, as I had done then, I placed my feet on top of his feet. 'Granddaddy,' I said. And because we were all alone and both in heaven, I was light enough to move as I had moved when I was six and he was fifty-six and my father had taken us to visit. We danced so slowly to a song that on Earth had always made my grandfather cry. 'Do you remember?' he asked. 'Barber!' 'Adagio for Strings,' he said. But as we danced and spun- none of the herky-jerky awkwardness of Earth- what I remembered was how I'd found him crying to this music and asked him why. 'Sometimes you cry,' Susie, even when someone you love has been gone a long time.' He had held me against him then, just briefly, and then I had run outside to play again with Lindsey in what seemed like my grandfather's huge backyard. We didn't speak any more that night, but we danced for hours in that timeless blue light. I knew as we danced that something was happening on Earth and in heaven. A shifting. The sort of slow-to-sudden movement that we'd read about in science class one year. Seismic, impossible, a rending and tearing of time and space. I pressed myself into my grandfather's chest and smelled the old-man smell of him, the mothball version of my own father, the blood on Earth, the sky in heaven. The kumquat, skunk, grade-A tobacco. When the music stopped, it cold have been forever since we'd begun. My grandfateher took a step back, and the light grew yellow at his back. 'I'm going,' he said. 'Where?' I asked. 'Don't worry, sweetheart. You're so close.' He turned and walked away, disappearing rapidly into spots and dust. Infinity.

In the West, there was an old debate as to whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. Ramanujan was squarely in the latter camp; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fit together. Each new theorem was one more piece of the Infinite unfathomed. So he wasn’t being silly, or sly, or cute when later he told a friend, “An equation for me has no meaning unless it expresses a thought of God.

impetuous

Ramanujan was not the first foreigner to retreat into his shell in a new country; indeed, his was the typical response, not the exceptional one. One later study of Asian and African students in Britain observed that a sense of exclusion “from the life of the community … constituted one of the most serious problems with which they were confronted … [and had] a serious psychological effect” upon them. Another study, this time of Indian students in particular, reported that while 83 percent of them saw friends more or less every day back in India, just 17 percent did while in England.

Ramanujan’s refrain was always the same—that his parents had made him marry, that now he needed a job, that he had no degree but that he’d been conducting mathematical researches on his own. And here … well, why didn’t the good sir just examine his notebooks. His notebooks were his sole credential in a society where, even more than in the West, credentials mattered; where academic degrees usually appeared on letterheads and were mentioned as part of any introduction; where, when they were not, you’d take care to slip them into the conversation. “Like regiments we have to carry our drums, and tambourinage is as essential a thing to the march of our careers as it is to the march of soldiers in the West,” Indian novelist and critic Nirad C. Chaudhuri has written of his countrymen’s bent for self-promotion. “In our society, a man is always what his designation makes him.” Ramanujan’s only designations were unemployed, and flunk-out. Without his B.A., one prominent mathematics professor told him straight out, he would simply never amount to anything.

The Riemann zeta function was a simple enough looking infinite series expressed in terms of a complex variable. Here, “complex” means not difficult or complicated, but refers to a variable of two distinct components, “real” and “imaginary,” which together could be thought to range over a two-dimensional plane. In 1860, Georg Friedrich Bernhard Riemann made six conjectures concerning the zeta function. By Ramanujan’s time, five had been proven. One, enshrined today as the Riemann hypothesis, had not

We might call this existential paradox the condition of individuality finitude. Man has a symbolic identity that brings him sharply out of nature. He is a symbolic self, a creature with a name, a life history. He is a creator with a mind that soars out to speculate about atoms and infinity, who can place himself imaginatively at a point in space and contemplate bemusedly his own planet. This immense expansion, this dexterity, this ethereality, this self-consciousness gives to man literally the status of a small god in nature, as the Renaissance thinkers knew. Yet, at the same time, as the Eastern sages also knew, man is a worm and food for worms. This is the paradox: he is out of nature and hopelessly in it; he is dual, up in the stars and yet housed in a heart-pumping, breath-gasping body that once belonged to a fish and still carries the gill-marks to prove it. His body is a material fleshy casing that is alien to him in many ways-the strangest and most repugnant way being that it aches and bleeds and will decay and die. Man is literally split in two: he has an awareness of his own splendid uniqueness in that he sticks out of nature with a towering majesty, and yet he goes back into the ground a few feet in order to blindly and dumbly rot and disappear forever. It is a terrifying dilemma to be in and to have to live with. The lower animals are, of course, spared this painful contradiction, as they lack a symbolic identity and the self-consciousness that goes with it. They merely act and move reflexively as they are driven by their instincts. If they pause at all, it is only a physical pause; inside they are anonymous, and even their faces have no name. They live in a world without time, pulsating, as it were, in a state of dumb being. This is what has made it so simple to shoot down whole herds of buffalo or elephants. The animals don't know that death is happening and continue grazing placidly while others drop alongside them. The knowledge of death is reflective and conceptual, and animals are spared it. They live and they disappear with the same thoughtlessness: a few minutes of fear, a few seconds of anguish, and it is over. But to live a whole lifetime with the fate of death haunting one's dreams and even the most sun-filled days-that's something else.

{From Luther Burbank's funeral. He was loved until he revealed he was an atheist, then he began to receive death threats. He tried to amiably answer them all, leading to his death} It is impossible to estimate the wealth he has created. It has been generously given to the world. Unlike inventors, in other fields, no patent rights were given him, nor did he seek a monopoly in what he created. Had that been the case, Luther Burbank would have been perhaps the world's richest man. But the world is richer because of him. In this he found joy that no amount of money could give. And so we meet him here today, not in death, but in the only immortal life we positively know--his good deeds, his kindly, simple, life of constructive work and loving service to the whole wide world. These things cannot die. They are cumulative, and the work he has done shall be as nothing to its continuation in the only immortality this brave, unselfish man ever sought, or asked to know. As great as were his contributions to the material wealth of this planet, the ages yet to come, that shall better understand him, will give first place in judging the importance of his work to what he has done for the betterment of human plants and the strength they shall gain, through his courage, to conquer the tares, the thistles and the weeds. Then no more shall we have a mythical God that smells of brimstone and fire; that confuses hate with love; a God that binds up the minds of little children, as other heathen bind up their feet--little children equally helpless to defend their precious right to think and choose and not be chained from the dawn of childhood to the dogmas of the dead. Luther Burbank will rank with the great leaders who have driven heathenish gods back into darkness, forever from this earth. In the orthodox threat of eternal punishment for sin--which he knew was often synonymous with yielding up all liberty and freedom--and in its promise of an immortality, often held out for the sacrifice of all that was dear to life, the right to think, the right to one's mind, the right to choose, he saw nothing but cowardice. He shrank from such ways of thought as a flower from the icy blasts of death. As shown by his work in life, contributing billions of wealth to humanity, with no more return than the maintenance of his own breadline, he was too humble, too unselfish, to be cajoled with dogmatic promises of rewards as a sort of heavenly bribe for righteous conduct here. He knew that the man who fearlessly stands for the right, regardless of the threat of punishment or the promise of reward, was the real man. Rather was he willing to accept eternal sleep, in returning to the elements from whence he came, for in his lexicon change was life. Here he was content to mingle as a part of the whole, as the raindrop from the sea performs its sacred service in watering the land to which it is assigned, that two blades may grow instead of one, and then, its mission ended, goes back to the ocean from whence it came. With such service, with such a life as gardener to the lilies of the field, in his return to the bosoms of infinity, he has not lost himself. There he has found himself, is a part of the cosmic sea of eternal force, eternal energy. And thus he lived and always will live. Thomas Edison, who believes very much as Burbank, once discussed with me immortality. He pointed to the electric light, his invention, saying: 'There lives Tom Edison.' So Luther Burbank lives. He lives forever in the myriad fields of strengthened grain, in the new forms of fruits and flowers, plants, vines, and trees, and above all, the newly watered gardens of the human mind, from whence shall spring human freedom that shall drive out false and brutal gods. The gods are toppling from their thrones. They go before the laughter and the joy of the new childhood of the race, unshackled and unafraid.

This was not merely the cellar maze crafted by Ronny Jessup, but also the labyrinth below Crete, where the Minotaur prowled and ate the flesh of those who dared enter its realm, but also Grendel’s far northern lair where Beowulf ventured, also the huge catacombs beneath the Mountains of Madness, where the Old Ones of Lovecraft’s story still waited to be called out of the depths of time or from another dimension, and this was as well the tunnel system under the terraforming atmosphere factories where brave Ripley had gone with a team of high-tech colonial marines on a bug hunt, to learn what happened to the colonists on the planet called LV-426. This was both reality and myth, concrete and symbol, the maze of homicidal desires and lust and hunger for power that spiraled to infinity within the deepest darkness of the human heart, male and female alike, here given dimension and immediacy. It was inhabited by a Grendel named Ulrich and a would-be hero who knew himself to be no hero at all, but only an imperfect man with something to prove to himself.

The P.I. states that if something x has happened in certain particular circumstances n times in the past, we are justified in believing that the same circumstances will produce x on the (n + 1)th occasion. The P.I. is wholly respectable and authoritative, and it seems like a well-lit exit out of the whole problem. Until, that is, it happens to strike you (as can occur only in very abstract moods or when there’s an unusual amount of time before the alarm goes off) that the P.I. is itself merely an abstraction from experience … and so now what exactly is it that justifies our confidence in the P.I.? This latest thought may or may not be accompanied by a concrete memory of several weeks spent on a relative’s farm in childhood (long story). There were four chickens in a wire coop off the garage, the brightest of whom was called Mr. Chicken. Every morning, the farm’s hired man’s appearance in the coop area with a certain burlap sack caused Mr. Chicken to get excited and start doing warmup-pecks at the ground, because he knew it was feeding time. It was always around the same time t every morning, and Mr. Chicken had figured out that t(man + sack) = food, and thus was confidently doing his warmup-pecks on that last Sunday morning when the hired man suddenly reached out and grabbed Mr. Chicken and in one smooth motion wrung his neck and put him in the burlap sack and bore him off to the kitchen. Memories like this tend to remain quite vivid, if you have any. But with the thrust, lying here, being that Mr. Chicken appears now actually to have been correct—according to the Principle of Induction—in expecting nothing but breakfast from that (n + 1)th appearance of man + sack at t. Something about the fact that Mr. Chicken not only didn’t suspect a thing but appears to have been wholly justified in not suspecting a thing—this seems concretely creepy and upsetting. Finding some higher-level justification for your confidence in the P.I. seems much more urgent when you realize that, without this justification, our own situation is basically indistinguishable from that of Mr. Chicken. But the conclusion, abstract as it is, seems inescapable: what justifies our confidence in the Principle of Induction is that it has always worked so well in the past, at least up to now. Meaning that our only real justification for the Principle of Induction is the Principle of Induction, which seems shaky and question-begging in the extreme. The only way out of the potentially bedridden-for-life paralysis of this last conclusion is to pursue further abstract side-inquiries into what exactly ‘justification’ means and whether it’s true that the only valid justifications for certain beliefs and principles are rational and noncircular. For instance, we know that in a certain number of cases every year cars suddenly veer across the centerline into oncoming traffic and crash head-on into people who were driving along not expecting to get killed; and thus we also know, on some level, that whatever confidence lets us drive on two-way roads is not 100% rationally justified by the laws of statistical probability. And yet ‘rational justification’ might not apply here. It might be more the fact that, if you cannot believe your car won’t suddenly get crashed into out of nowhere, you just can’t drive, and thus that your need/desire to be able to drive functions as a kind of ‘justification’ of your confidence.* It would be better not to then start analyzing the various putative ‘justifications’ for your need/desire to be able to drive a car—at some point you realize that the process of abstract justification can, at least in principle, go on forever. The ability to halt a line of abstract thinking once you see it has no end is part of what usually distinguishes sane, functional people—people who when the alarm finally goes off can hit the floor without trepidation and plunge into the concrete business of the real workaday world—from the unhinged.

Ramanujan had lost all his scholarships. He had failed in school. Even as a tutor of the subject he loved most, he'd been found wanting. He had nothing. And yet, viewed a little differently, he had everything. For now there was nothing to distract him from his notebooks- notebooks, crammed with theorems, that each day, each week, bulged wider.

Viewed one way, then, for at least five years between 1904 and 1909, Ramanujan floundered- mostly out of school, without a degree, without contact with other mathematicians. And yet, was the cup half-empty or half-full?

He received no guidance, no stimulation, no money beyond the few rupees he made from tutoring. But for all the economic deadweight he represented, his family apparently discouraged him little- not enough, in any case, to stop him.

Then, too, it seems certain, in light of future events, simple racism was a factor; Ramanujan, after all, was a black man.

The cards are stacked, against any original mind, and perhaps properly so.