“Creative people live in two worlds. One is the ordinary world which they share with others and in which they are not in any special way set apart from their fellow men. The other is private and it is in this world that the creative acts take place.”
By Maria Popova
The great Polish-American mathematician Mark Kac (August 3, 1914–October 26, 1984) possessed one of the most dazzling minds of the twentieth century. In pioneering probability theory, he paved the way for a radical new conception of truth and ushered in the first generation of scientists trained to think probabilistically — a more accurate assessment of knowledge, making room for uncertainty, be it scientific or otherwise. This probabilistic mode of judgment is all the more necessary today as the growing complexity of the world is swirling us into exponentially increasing uncertainty, which we attempt to tame through artificial absolutism.
Mathematics literally saved Kac’s life. His student work earned him a post-doctoral fellowship to study abroad, so he left Poland for Johns Hopkins University in December of 1938. World War II broke out months later. His entire family, along with millions of other Jews, was killed by the Nazis.
Kac went on to lead a long and creatively fertile life — one he considered, despite this unfathomable share of misfortune, a tremendously fortunate one. “I must pay tribute to that powerful but capricious lady, Chance, who chose to bestow her beneficence on my personal life even though I spent much of my mathematical life trying to prove that she does not really exist,” he wrote with his characteristic mix of wit and wisdom in Enigmas of Chance: An Autobiography (public library) — a small, wonderful 1976 book I discovered via a passing mention in an interview with the trailblazing astronomer Vera Rubin. (Here is further proof of my longstanding conviction that literature is the original Internet — such citations, allusions, and cross-references between books are the wondrous “hyperlinks” connecting human knowledge throughout our “common record.”)
Creative people live in two worlds. One is the ordinary world which they share with others and in which they are not in any special way set apart from their fellow men. The other is private and it is in this world that the creative acts take place. It is a world with its own passions, elations and despairs, and it is here that, if one is as great as Einstein, one may even hear the voice of God. The two worlds are intimately and intricately connected. Jealousy, the desire for recognition and competitiveness, for example, are part of the ordinary world but they are among the forces which propel into the second. Similarly, dreams and triumphs in the second have a way of merging with less than lofty thoughts of rewards in the first.
With an eye to the particular challenge that autobiography presents to the creative person, he adds:
To create a coherent and truthful picture of life in the two disparate and yet interrelated worlds is a nearly impossible task.
In discussing his great heroes and influences, Kac delineates another dichotomy in creative culture — the bifurcation of brilliance by degree and by kind:
In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the “ordinary” and the “magicians.” An ordinary genius is a [person] that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works.
In the postscript, Kac considers what lends mathematics its enduring enchantment — what renders people besotted with it:
Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we can find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man’s curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man’s desire to probe the workings of his own mind.
The urge to understand and to create mathematics has always been remarkable, considering that those who have devoted their lives to the service of this aloof and elusive mistress could expect neither great material rewards nor widespread fame.
I am reminded of something Balthazaar van der Pol, a great Dutch scientist and engineer who was also a fine musician, remarked to me about the music of Bach. “It is great,” he said, “because it is inevitable and yet surprising.” I have often thought about this lovely epigram in connection with mathematics… The inevitability is, in many cases, provided by logic alone, but the element of surprise must come from an insight outside the rigid confines of logic.
But perhaps the most useful and timelessly insightful take on the perennial puzzlement over the difference between talent and genius came the year after Thoreau’s birth from the great German philosopher Arthur Schopenhauer (February 22, 1788–September 21, 1860) in his 1818 masterwork The World as Will and Representation (public library).
Schopenhauer’s central premise is that talent achieves what others cannot achieve, whereas genius achieves what others cannot imagine. This vision of a different order, he argues, is what sets geniuses apart from mere mortals, and it arises from a superior capacity for contemplation that leads the genius to transcend the smallness of the ego and enter the infinite world of ideas. He writes:
Only through [such] pure contemplation … can Ideas be comprehended; and the nature of genius consists in pre-eminent capacity for such contemplation. Now, as this requires that a man* should entirely forget himself and the relations in which he stands, genius is simply the completest objectivity, i.e., the objective tendency of the mind, as opposed to the subjective, which is directed to one’s own self — in other words, to the will. Thus genius is the faculty of continuing in the state of pure perception, of losing oneself in perception, and of enlisting in this service the knowledge which originally existed only for the service of the will; that is to say, genius is the power of leaving one’s own interests, wishes, and aims entirely out of sight, thus of entirely renouncing one’s own personality for a time, so as to remain pure knowing subject, clear vision of the world; and this not merely at moments, but for a sufficient length of time, and with sufficient consciousness, to enable one to reproduce by deliberate art what has thus been apprehended.
But although a superior capacity to imagine is a centerpiece of genius, Schopenhauer cautions against mistaking the imagination for the entirety of genius:
Imagination has rightly been recognized as an essential element of genius; it has sometimes even been regarded as identical with it; but this is a mistake. As the objects of genius are the eternal Ideas, the permanent, essential forms of the world and all its phenomena, and as the knowledge of the Idea is necessarily knowledge through perception, is not abstract, the knowledge of the genius would be limited to the Ideas of the objects actually present to his person, and dependent upon the chain of circumstances that brought these objects to him, if his imagination did not extend his horizon far beyond the limits of his actual personal existence, and thus enable him to construct the whole out of the little that comes into his own actual apperception, and so to let almost all possible scenes of life pass before him in his own consciousness… The imagination then extends the intellectual horizon of the man of genius beyond the objects which actually present themselves to him, both as regards quality and quantity. Therefore extraordinary strength of imagination accompanies, and is indeed a necessary condition of genius. But the converse does not hold, for strength of imagination does not indicate genius; on the contrary, men who have no touch of genius may have much imagination.
But the curse of the extraordinary, Schopenhauer suggests, is a certain loneliness with which the person of genius walks through life, always slightly apart from the ordinary world in being slightly above it:
The common mortal, that manufacture of Nature which she produces by the thousand every day, is, as we have said, not capable, at least not continuously so, of observation that in every sense is wholly disinterested, as sensuous contemplation, strictly so called, is. He can turn his attention to things only so far as they have some relation to his will, however indirect it may be… The man of genius, on the other hand, whose excessive power of knowledge frees it at times from the service of will, dwells on the consideration of life itself, strives to comprehend the Idea of each thing, not its relations to other things; and in doing this he often forgets to consider his own path in life, and therefore for the most part pursues it awkwardly enough. While to the ordinary man his faculty of knowledge is a lamp to lighten his path, to the man of genius it is the sun which reveals the world… The man in whom genius lives and works is easily distinguished by his glance, which is both keen and steady, and bears the stamp of perception, of contemplation.
In the second volume of his treatise, Schopenhauer revisits the subject of talent versus genius through the lens of time — talent, he argues, speaks brilliantly to the moment and is of the moment, while genius speaks of the eternal and to eternity. He writes:
Mere men of talent always come at the right time; for, as they are roused by the spirit of their age and are called into being by its needs, they are only just capable of satisfying them. They therefore go hand in hand with the advancing culture of their contemporaries, or with the gradual advancement of a special science; for this they reap reward and approbation. But to the next generation their works are no longer enjoyable; they must be replaced by others; and these do not fail to appear.
The genius, on the other hand, lights on his age like a comet into the paths of the planets, to whose well-regulated and comprehensible arrangement its wholly eccentric course is foreign. Accordingly, he cannot go hand in hand with the regular course of the culture of the times as found; on the contrary, he casts his works far out on to the path in front (just as the emperor, giving himself up to death, flings his spear among the enemy), on which time has first to overtake them… Talent is able to achieve what is beyond other people’s capacity to achieve, yet not what is beyond their capacity of apprehension; therefore it at once finds its appreciators. The achievement of genius, on the other hand, transcends not only others’ capacity of achievement, but also their capacity of apprehension; therefore they do not become immediately aware of it. Talent is like the marksman who hits a target which others cannot reach; genius is like the marksman who hits a target … which others cannot even see.
“If I know what I shall find, I do not want to find it. Uncertainty is the salt of life.”
By Maria Popova
As a teenager, long before he became a pioneering biochemist, Erwin Chargaff (August 11, 1905–June 20, 2002) learned English from two women who ran a small school in his native Vienna. This fortuitous skill would later save his life. The year of his thirtieth birthday, Chargaff was offered a research position at Columbia University in New York, which he was able to take largely because he spoke English. “I was afraid of going to a country that was younger than most of Vienna’s toilets,” he would later recount. But there was something far more sinister to fear — the confluence of chance and choice that landed Chargaff in America spared him from the grim fate that befell his loved ones in Europe. His mother and sister — his only remaining family after his father’s untimely death — were among the millions of Jews killed by the Nazis.
As he witnessed from afar the inhumanity that made his homeland “tumble into the deepest abyss ever to engulf a civilized people,” Chargaff sought solace and meaning outside the human realm and immersed himself in science. He went on to discover base-pairing — a principle instrumental in identifying the double helix structure of DNA and thus a centerpiece of our understanding of genetics.
But Chargaff was also an extraordinary writer — not only an eloquent explainer and champion of science, but a lyrical memoirist and an incisive, erudite philosophical thinker. A master of what could best be described as biopoetics, he writes with infectious wonderment and tenderness about nature and human nature, about knowledge and mystery, about the electrifying joy of slicing through the darkness of being with the luminous saber of curiosity.
His 1978 autobiography, Heraclitean Fire: Sketches from a Life Before Nature (public library), is one of the finest books I’ve ever read, on par with Oliver Sacks’s On the Move. In reflecting on his own life, Chargaff speaks not only to what it means to be a scientist and how science in its highest form is done, but also to what it means to be human and what it takes to persevere on our most perennial quest — to understand reality and make sense of our place in it.
The discovery of this uncommonly wonderful book is a supreme testament to my longtime assertion, only half-facetious, that literature is the original Internet: A passing mention in an interview with trailblazing astronomer Vera Rubin in a forgotten book “hyperlinked” me to the autobiography of the great mathematician Mark Kac, in which he extols Chargaff’s as the gold standard for a scientist’s autobiography. The praise is more than merited, and anything said about the book here or anywhere is bound to belie its true splendor, which comes alive only with reading. The pages of this small, enormous book radiate layered and beautifully articulated wisdom on the many strands of life — psychology, philosophy, politics — absolutely inseparable, yet artificially segregated, from science.
From the fortunate and far-seeing platform of seven decades of life, Chargaff writes:
I came to biochemistry through chemistry; I came to chemistry … partly through the youthfully romantic notion that the natural sciences had something to do with nature. What I liked about chemistry was its clarity surrounded by darkness; what attracted me, slowly and hesitatingly, to biology was its darkness surrounded by the brightness of the givenness of nature, the holiness of life. And so I have always oscillated between the brightness of reality and the darkness of the unknowable. When Pascal speaks of God in hiding, Deus absconditius, we hear not only the profound existential thinker, but also the great searcher for the reality of the world. I consider this unquenchable resonance as the greatest gift that can be bestowed on a naturalist.
Nearly half a century before physicist Sean Carroll coined his beautiful notion of poetic naturalism, Chargaff considers the historical development of our quest to know reality:
It is clear that to meditate on the whole of nature, or even on the whole of living nature, is not a road that the natural sciences could long have traveled. This is the way of the poet, the philosopher, the seer. A division of labor had to take place. But the overfragmentation of the vision of nature — or actually its complete disappearance among the majority of scientists — has created a Humpty-Dumpty world that must become increasingly unmanageable as more and tinier pieces are broken off, “for closer inspection,” from the continuum of nature. The consequence of the excessive specialization, which often brings us news that nobody cares to hear, has been that in revisiting a field with which one had been very familiar, say, ten or twenty years earlier, one feels like an intruder in one’s own bathroom, with twenty-four grim experts sharing the tub.
In the same era that Buckminster Fuller made his case for the genius of generalists, Chargaff speaks to the immense yet endangered value of a robust and indiscriminate curiosity in grasping the big picture:
Without a firm center we flounder. The wonderful, inconceivably intricate tapestry is being taken apart strand by strand; each thread is being pulled out, torn up, and analyzed; and at the end even the memory of the design is lost and can no longer be recalled.
It is hoped that our road will lead to understanding; mostly it leads only to explanations. The difference between these two terms is also being forgotten… These are two very different things, for we understand very little about nature. Even the most exact of our exact sciences float above axiomatic abysses that cannot be explored. It is true, when one’s reason runs a fever, one believes, as in a dream, that this understanding can be grasped; but when one wakes up and the fever is gone, all one is left with are litanies of shallowness.
In our time, so-called laws of nature are being fabricated on the assembly line. But how often is the regularity of these “laws of nature” only the reflection of the regularity of the method employed in their formation! … Science is still faced with the age-old predicament, the lack of ultimate verification.
For a scientific concept to be formulated successfully, a concerted interaction of many requisites must occur. First of all, the right [person] must ask himself the right question. This may well be a random event that occurs much more often than we are aware… Less fortuitously, this [person] must find an audience, i.e., he must be able to publish and to find readers; and this may not have been so easy even in the bucolic days of the last century. But, most importantly, the times must be ripe for both question and answer.
If art represents the highest form of reality that man — or at least modern secular man — is capable of attaining, the many instances in which great creations were rejected initially, and often with incredible malice, show how reluctant we are to grasp reality. We accept only what has been predigested for us by the so-called tastemakers; but this is then a spurious reality.
Our understanding of the world is built up of innumerable layers. Each layer is worth exploring, as long as we do not forget that it is one of many. Knowing all there is to be known about one layer — a most unlikely event — would not teach us much about the rest. The integration of the enormous number of bits of information and the resulting vision of nature take place in our minds; but the human mind is easily deceived and confused, and the vision of nature changes every few generations. It is, in fact, the intensity of the vision that counts more heavily than its completeness or its correctness. I doubt that there is such a thing as a correct view of nature, unless the rules of the game are stated clearly. Undoubtedly, there will later be other games and other rules.
With a concerned eye toward the discouragement of curiosity-driven research by the institutions of modern science — a concern that has only swelled in urgency in the decades since — Chargaff writes:
When I look back on my early way in science, on the problems I studied, on the papers I published — and even more, perhaps, on those things that never got into print — I notice a freedom of movement, a lack of guild-imposed narrowness, whose existence in my youth I myself, as I write this, had almost forgotten. The world of science was open before us to a degree that has become inconceivable now, when pages and pages of application papers must justify the plan of investigating, “in depth,” the thirty-fifth foot of the centipede; and one is judged by a jury of one’s peers who are all centipedists or molecular podiatrists. I would say that most of the great scientists of the past could not have arisen, that, in fact, most sciences could not have been founded, if the present utility-drunk and goal-directed attitude had prevailed.
It would seem to me that man cannot live without mysteries. One could say, the great biologists worked in the very light of darkness.
What is success in science? Illuminated darkness is not light. We find ourselves in the cavern of limitless possibilities. Take a flashlight with you, and you may find you are only in a lumber room. If I know what I shall find, I do not want to find it. Uncertainty is the salt of life.
Chargaff reflects on how the allure of uncertainty animated his own foray into science:
What I remember of my beginnings is the truly lyrical shudder with which I contemplated nature. I am not sure that I even knew what I meant by nature. It was the blood and the bones of the universe, its dawn and dusk, flowering and decay, firmament and graveyard. The alterations of the spiritual and the material tides, the oscillations between future and past, the mysterious fates of everlasting stone and short-lived fly: they filled me with admiration and reverence. Nature, it seemed to me, was almost the entire non-I, the entire non-small-boy… A small boy begins by being unable to explain the explainable, but when he grows old he often looks away from what cannot be explained. I am grateful that fate has preserved me from this form of blindness. Surrounded by a surfeit of solved riddles, I am still struck by how little we understand.
I would not go so far as to claim that knowledge and wisdom are mutually exclusive; but they are far from being communicating vessels, and the level of one has no bearing on that of the other. More people have gained wisdom from unknowledge, which is not the same as ignorance, than from knowledge.
Returning to his formative years, he considers once again the different paths to wisdom, those different modes of illuminating reality:
Should I not have thought of becoming a painter or a poet? But I was entirely ungifted for the first and not courageous enough for the second… I was a monad searching for a destiny that did not exist… What I had at the time — and it has never left me — was a dream of reality that we could only touch tangentially, an awe of the numinous of nature whose power rested in its very unattainability. It was a feeling for the necessity of darkness in the life of man. In the Sistine Chapel, where Michelangelo depicts the creation of man, God’s finger and that of Adam are separated by a short space. That distance I called eternity; and there, I felt, I was sent to travel.
That this may be a voyage without a destination was no concern of mine … Only the road counted, not the goal… When I floated into science, a naive young man could still imagine that he was devoting himself to the study of nature… For me nature has still remained a synonym for the highest form of reality.
Radiating from his recollection is a sublime definition of what makes a scientist:
The feeling that there is always more than he can find, that he is only pulling shreds out of an unfathomable continuum, forms part of my definition of scientist.
It is the sense of mystery that, in my opinion, drives the true scientist; the same force, blindly seeing, deafly hearing, unconsciously remembering, that drives the larva into the butterfly. If he has not experienced, at least a few times in his life, this cold shudder down his spine, this confrontation with an immense, invisible face whose breath moves him to tears, he is not a scientist. The blacker the night, the brighter the light.
Heraclitean Fire is a book so magnificent as to make it almost criminal that commercial forces have swept it out of print. Perhaps a publisher who prioritizes cultural stewardship over such forces will take mercy on this forgotten treasure and bring it back to life.
How the precious scarcity of knowledge imbued one of humanity’s most beloved minds with “the pleasure of finding things out.”
By Maria Popova
In his taxonomy of the two types of geniuses, probability theory pioneer Mark Kac distinguishes between “ordinary geniuses” and “magicians,” pointing to Richard Feynman (May 11, 1918–February 15, 1988) as a rare example of the latter. One of the most celebrated minds of the past century, Feynman was a champion of scientific knowledge so effective and so beloved that he has generated an entire canon of personal mythology. And yet he held uncertainty at the center of his intellectual and creative life. The pursuit and stewardship of knowledge was his life’s work, but the ecstasy of not-knowing was the wellspring of his magic. “It is imperative,”he wrote, “to have uncertainty as a fundamental part of your inner nature.”
In chronicling Feynman’s childhood in Far Rockaway in the first half of the twentieth century, which unfolded in an era predating television and even the earliest visions of the web, Gleick does what makes him a biographer of such uncommon mastery — through the elements of his subject’s life, he constructs a diorama of an entire cultural epoch and stuns us into appreciating the imperceptible tectonic shifts that drifted us into the world we’ve come to take for granted. He writes:
Knowledge was rarer then. A secondhand magazine was an occasion. For a Far Rockaway teenager merely to find a mathematics textbook took will and enterprise. Each radio program, each telephone call, each lecture in a local synagogue, each movie at the new Gem theater on Mott Avenue carried the weight of something special. Each book Richard possessed burned itself into his memory.
Even with the radio era in full swing, one’s senses encountered nothing like the bombardment of images and sounds that television would bring—accelerated, flash-cut, disposable knowledge. For now, knowledge was scarce and therefore dear.
It’s easy to imagine how this mismatch between his intellectual voraciousness and the availability of knowledge would enamor young Ritty with “the pleasure of finding things out” — a phrase that grew to be so integral to Feynman’s identity that it became the title of his collected works.
It’s also suddenly easy, and somewhat alarming, to grasp how profoundly we are shaped by our formative environment and how much what we celebrate as genius is not just a function of personhood but of the confluence of person, place, and time. Can there be a comparable “pleasure of finding things out” in our era of informational morass, which burdens us with the deeply unpleasant task of sifting what is worth knowing from the deluge of what is knowable? When Feynman came of age, the cultural landscape was such that everything knowable was worth knowing — and worth going out of one’s way to know. Young Ritty and his friends “traded mathematical tidbits like baseball cards.”
It was the same for scientists. The currency of scientific information had not yet been devalued by excess. For a young student, that meant that the most timely questions were surprisingly close to hand. Feynman recognized early the special, distinctive feeling of being close to the edge of knowledge, where people do not know the answers.
This feeling, Gleick intimates, is also what led Feynman to consistently feel out the frontiers of competence by teaching himself a wide and wild array of skills, always romancing the intoxicating uncertainty of not-quite-knowing:
Democratically, as if he favored no skill above any other, he taught himself how to play drums, to give massages, to tell stories, to pick up women in bars, considering all these to be crafts with learnable rules.
He made islands of practical knowledge in the oceans of personal ignorance that remained: knowing nothing about drawing, he taught himself to make perfect freehand circles on the blackboard; knowing nothing about music, he bet his girlfriend that he could teach himself to play one piece, “The Flight of the Bumblebee,” and for once failed dismally; much later he learned to draw after all, after a fashion, specializing in sweetly romanticized female nudes and letting his friends know that a concomitant learned skill thrilled him even more — how to persuade a young woman to disrobe. In his entire life he could never quite teach himself to feel a difference between right and left, but his mother finally pointed out a mole on the back of his left hand, and even as an adult he checked the mole when he wanted to be sure. He taught himself how to hold a crowd with his not-jazz, not-ethnic improvisational drumming; and how to sustain a two-handed polyrhythm of not just the usual three against two and four against three but — astonishing to classically trained musicians — seven against six and thirteen against twelve. He taught himself how to write Chinese, a skill acquired specifically to annoy his sister and limited therefore to the characters for “elder brother also speaks.” … He taught himself how to discourage autograph seekers and refuse lecture invitations; how to hide from colleagues with administrative requests; how to force everything from his field of vision except for his research problem of the moment; how to hold off the special terrors of aging that shadow scientists; then how to live with cancer, and how to surrender to it.
After he died several colleagues tried to write his epitaph. One was Schwinger, in a certain time not just his colleague but his preeminent rival, who chose these words:
“An honest man, the outstanding intuitionist of our age, and a prime example of what may lie in store for anyone who dares to follow the beat of a different drum.” … When Feynman was gone, he had left behind — perhaps his chief legacy — a lesson in what it meant to know something in this most uncertain of centuries.