The Marginalian
The Marginalian

Probability Theory Pioneer Mark Kac on the Unpredictability of Creativity and the Two Types of Geniuses

Probability Theory Pioneer Mark Kac on the Unpredictability of Creativity and the Two Types of Geniuses

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.”)

Mark Kac
Mark Kac

Kac writes:

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.

He points to the nuclear physicist Hans Bethe as an example of an “ordinary genius” and to Richard Feynman as a “magician.” (Kac’s distinction appears in James Gleick’s superb biography of Feynman and there is a high probability that it inspired the title of BBC’s documentary about the legendary physicist, No Ordinary Genius.) I would add Alan Turing to the “magicians” category, and of course Albert Einstein.

Illustration by Vladimir Radunsky for On a Beam of Light: A Story of Albert Einstein by Jennifer Berne

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.

A champion of nuance, Kac challenges Bertrand Russell’s famous assertion that “mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” Kac finds it to be a “dull and rather miserable picture of mathematics” and yet “not wholly wrong,” “just hopelessly incomplete and one-sided.” Instead, he considers what grants mathematics its richness as a mode of illuminating reality:

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.

It warrants noting that the altogether marvelous Enigmas of Chance is part of a series of scientists’ autobiographies funded by the Alfred P. Sloan Foundation, which has probably done more for science and its social life than any other entity in the past half-century. Complement it with this beautiful love letter to mathematics by the pioneering 19th-century English mathematician James Joseph Sylvester, the illustrated life of the eccentric mathematical genius Paul Erdos, and the great English mathematician John Horton Conway on tinkering, thinkering, and the art of being a professional nonunderstander.

BP

Nobel Laureate Doris Lessing on Breaking Free from the Prisons We Choose to Live Inside

Nobel Laureate Doris Lessing on Breaking Free from the Prisons We Choose to Live Inside

This is the history of the world: revolutionaries turning into tyrants, leaders who claim to stand with the masses turning the individuals within them on each other, stirring certainties and self-righteousness to distract from the uncomfortable unknowns, from the great open question of what makes us and keeps us human, and human together.

This is also the history of the world: artists — those lighthouses of the spirit — speaking truth to power, placing imagination ahead of ideology, the soul above the self, unselfing us into seeing each other, into remembering, as James Baldwin told Margaret Mead in their epochal conversation, that “we are still each other’s only hope.”

Born in Iran months after the end of the First World War and raised by farming parents in present-day Zimbabwe, Doris Lessing (October 22, 1919–November 17, 2013) was still a girl when she sensed something deeply wrong with the unquestioned colonial system of her world, with the oppression that was the axis of that world. By the time she was a young woman — a time when our urge to rebel against the broken system is fiery but we don’t yet have the tools to rebel intelligently, don’t yet know the right questions to ask in order to tell whether the answer we are holding up as an alternative is any better or worse — she rebelled by embracing Communism as “an interesting manifestation of popular will.” Working by that point as a telephone operator in England, she joined the Communist Party. “It was a conversion, apparently sudden, and total (though short-lived),” she would later recall. “Communism was in fact a germ or virus that had already been at work in me for a long time… because of my rejection of the repressive and unjust society of old white-dominated Africa.” It didn’t take her long to see the cracks in Communism. She left the party, discovered Sufism, grew fascinated with the nascent field of behavioral psychology and its revelatory, often disquieting findings about the inner workings of the mind, of its formidable powers to act and its immense vulnerabilities to being acted upon. But she found no ready-made answer to the problem of social harmony.

And so, in that way artists have of complaining by creating, she devoted her life — almost a century of life, a century of world wars and violent uprisings, of changes unimaginable to her parents — to asking the difficult, clarifying questions that help us better understand what makes us human, how we allow ourselves to dehumanize others, and what it takes to cohere, as individuals and as societies. At 87, she became the oldest person to receive the Nobel Prize, awarded her for writing that “with scepticism, fire and visionary power has subjected a divided civilisation to scrutiny.”

In 1985, months after I was born under Bulgaria’s Communist dictatorship, Doris Lessing delivered Canada’s esteemed annual Massey Lectures, later adapted into a series of short essays under the haunting title Prisons We Choose to Live Inside (public library) — a searching look at how it is that “we (the human race) are now in possession of a great deal of hard information about ourselves, but we do not use it to improve our institutions and therefore our lives,” lensed through a lucid faith that we have all the power, urgency, and dignity we need to choose otherwise, to use what we have learned about the worst of our nature to nurture and magnify the best of our nature, to figure out “how we behave so that we control the society and the society does not control us.”

One of Antoine de Saint Exupéry’s original watercolors for The Little Prince. (Morgan Library & Museum)

In a sentiment Rebecca Solnit would echo three decades later in her modern classic Hope in the Dark, Lessing writes:

This is a time when it is frightening to be alive, when it is hard to think of human beings as rational creatures. Everywhere we look we see brutality, stupidity, until it seems that there is nothing else to be seen but that — a descent into barbarism, everywhere, which we are unable to check. But I think that while it is true there is a general worsening, it is precisely because things are so frightening we become hypnotized, and do not notice — or if we notice, belittle — equally strong forces on the other side, the forces, in short, of reason, sanity and civilization.

To be realistic about our own nature, Lessing argues, requires attentiveness to both of these strands — the destructive and the creative. This is the cosmic mirror Maya Angelou held up to humanity in her stunning space-bound poem, urging us to “learn that we are neither devils nor divines.” An epoch before her, Bertrand Russell — also a Nobel laureate in Literature, though trained as a scientist — reckoned with our twin capacities to define them in elemental terms — “We construct when we increase the potential energy of the system in which we are interested, and we destroy when we diminish the potential energy.” — and in existential terms: “Construction and destruction alike satisfy the will to power, but construction is more difficult as a rule, and therefore gives more satisfaction to the person who can achieve it.”

Our sanity, Lessing observes, lies in “our capacity to be detached and unflattering about ourselves” — and in the understanding that our selves are not islanded in time but lineages of beliefs and tendencies with roots much longer than our lifetimes, not sovereign but contiguous with all the other selves that occupy the particular patch of spacetime we have been born into. It is vital, she insists, that we examine ourselves — our selves, and the constellation of selves that is our given society — from various elsewheres.

Art by Felicita Sala from A Velocity of Being: Letters to a Young Reader.

This is why we need writers — those professional observers, in Susan Sontag’s splendid definition, whose job it is to “pay attention to the world” and shine the light of that attention on every side of the kaleidoscope that is a given culture at a given time. A decade after Iris Murdoch wrote in her superb reckoning with the role of literature in democracy that “tyrants always fear art because tyrants want to mystify while art tends to clarify,” Lessing writes:

In totalitarian societies writers are distrusted for precisely this reason… Writers everywhere are aspects of each other, aspects of a function that has been evolved by society… Literature is one of the most useful ways we have of achieving this “other eye,” this detached manner of seeing ourselves; history is another.

Because we are the future of our own past, the posterity of our ancestors, looking back on history from our present vantage point offers fertile training ground for looking forward, for shaping the world of tomorrow. Lessing writes:

Anyone who reads history at all knows that the passionate and powerful convictions of one century usually seem absurd, extraordinary, to the next. There is no epoch in history that seems to us as it must have to the people who lived through it. What we live through, in any age, is the effect on us of mass emotions and of social conditions from which it is almost impossible to detach ourselves.

[…]

There is no such thing as my being in the right, my side being in the right, because within a generation or two, my present way of thinking is bound to be found perhaps faintly ludicrous, perhaps quite outmoded by new development — at the best, something that has been changed, all passion spent, into a small part of a great process, a development.

Doris Lessing, 1950s. (National Portrait Gallery, London)

In consonance with Carl Sagan’s admonition against “the sense that we have a monopoly on the truth” and with Joan Didion’s admonition against mistaking self-righteousness for morality, Lessing offers:

This business of seeing ourselves as in the right, others in the wrong; our cause as right, theirs as wrong; our ideas as correct, theirs as nonsense, if not as downright evil… Well, in our sober moments, our human moments, the times when we think, reflect, and allow our rational minds to dominate us, we all of us suspect that this “I am right, you are wrong” is, quite simply, nonsense. All history, development goes on through interaction and mutual influence, and even the most violent extremes of thought, of behaviour, become woven into the general texture of human life, as one strand of it. This process can be seen over and over again in history. In fact, it is as if what is real in human development — the main current of social evolution — cannot tolerate extremes, so it seeks to expel extremes and extremists, or to get rid of them by absorbing them into the general stream.

Looking back on the colonialist Zimbabwe of her childhood, on the “prejudiced, ugly, ignorant” attitudes of the ruling whites, she reflects:

These attitudes were assumed to be unchallengeable and unalterable, though the merest glance at history would have told them (and many of them were educated people) that it was inevitable their rule would pass, that their certitudes were temporary.

At the center of Lessing’s inquiry is the paradox of how seemingly sound-minded, kind-hearted people get enlisted in ideologies of oppression. Kierkegaard had written in the Golden Age of European revolutions — those idealistic but imperfect attempts to unify fractured feudal duchies into free nations, attempts that modeled the possibility of a United States of America — that “the evolution of the world tends to show the absolute importance of the category of the individual apart from the crowd,” that “truth always rests with the minority, and the minority is always stronger than the majority, because… the strength of a majority is illusory, formed by the gangs who have no opinion.” An epoch and a world order later, Lessing considers how regimes of terror take hold:

Nearly everyone in such situations behaves automatically. But there is always the minority who do not, and it seems to me that our future, the future of everybody, depends on this minority. And that we should be thinking of ways to educate our children to strengthen this minority and not, as we mostly do now, to revere the pack.

Art by Jeska Verstegen from Bear Is Never Alone by Marc Veerkamp

The mess we have made, she intimates, may be the most effective teaching tool we have — a living admonition against doing the same, a clarion call to rebel by doing otherwise:

Perhaps it is not too much to say that in these violent times the kindest, wisest wish we have for the young must be: “We hope that your period of immersion in group lunacy, group self-righteousness, will not coincide with some period of your country’s history when you can put your murderous and stupid ideas into practice. “If you are lucky, you will emerge much enlarged by your experience of what you are capable of in the way of bigotry and intolerance. You will understand absolutely how sane people, in periods of public insanity, can murder, destroy, lie, swear black is white.”

As for us, here in the roiling mess, our sole salvation lies in learning to “live our lives with minds free of violent and passionate commitment, but in a condition of intelligent doubt about ourselves and our lives, a state of quiet, tentative, dispassionate curiosity.” Lessing writes:

While all these boilings and upheavals go on, at the same time, parallel, continues this other revolution: the quiet revolution, based on sober and accurate observation of ourselves, our behaviour, our capacities… If we decided to use it, [we may] transform the world we live in. But it means making that deliberate step into objectivity and away from wild emotionalism, deliberately choosing to see ourselves as, perhaps, a visitor from another planet might see us.

Art by Diana Ejaita from Kamau & ZuZu Find a Way by poet Aracelis Girmay

This, in fact, was the conditional clause in Baldwin’s words to Mead — in order to be “each other’s only hope,” he said, we ought to be “as clear-headed about human beings as possible.” This, too, was Maya Angelou’s conditional optimism for humanity: “That is when, and only when, we come to it” — to that “Brave and Startling Truth,” balanced on the fulcrum of our conflicted capacities, “that we are the possible, we are the miraculous, the true wonder of this world.”

BP

Hermann Hesse on How to Read a Book and How to Read Yourself

Hermann Hesse on How to Read a Book and How to Read Yourself

Books show us what it is like to be another and at the same time return us to ourselves. We read to learn how to live — how to love and how to suffer, how to grieve and how to be glad. We read to clarify ourselves and to anneal our values. We read for the assurance that others have lived through what we are living through. “You think your pain and your heartbreak are unprecedented in the history of the world, but then you read,” James Baldwin reflected in his most personal interview.

And yet while books may give us a foothold for the disorientation of being and an antidote to our existential loneliness, the paradox of living is that no example, no parallel, no borrowed wisdom is a substitute for life itself. The story of our own lives is only ever written on the blank page of living, our store of wisdom only ever found in the deepening truth of our own experience.

In 1918 — more than a decade before he penned his magnificent essay on the timeless magic of books and three decades before he was awarded the Nobel Prize in Literature — Hermann Hesse (July 2, 1877–August 9, 1962), entering his forties, captured this paradox in a short poem of great simplicity and loveliness, found in the posthumous collection The Seasons of the Soul: The Poetic Guidance and Spiritual Wisdom of Herman Hesse (public library).

hesse_books

BOOKS
by Hermann Hesse

All the books of the world
will not bring you happiness,
but build a secret path
toward your heart.

What you need is in you:
the sun, the stars, the moon,
the illumination you were seeking
shines up from within you.

The quest for wisdom
made you comb the libraries.
Now every page speaks the truth
that flashes forth from you.

The young Proust had arrived at the same conclusion in his reflections on why we read, observing that “the end of a book’s wisdom appears to us as merely the start of our own” because “the essential book, the one true book… already exists in every one of us.”

Complement with Pythagoras on the purpose of life and the meaning of wisdom, Nick Cave on the importance of trusting yourself, and Rebecca Solnit on how books solace, empower, and transform us, then revisit Hesse on the courage to be yourself, the wisdom of the inner voice, and how to be more alive.

BP

James Baldwin on How Love (Finally) Finds You

James Baldwin on How Love (Finally) Finds You

Our language betrays our self-betrayals: We speak of finding love, as if it were an undiscovered eighth continent or a habitable world in another solar system, as if it got lost like the Little Red Riding Hood or the names of the women who painted the caves. Like the paradoxical notion of finding yourself, the notion of finding love pulsates with equal parts helplessness and hubris — a rueful recognition that something is missing from your life and a belief that it falls on you to do the looking, that if you only look hard enough and long enough, you will achieve the goal of finding it. But no one, not one person in the history of the heart, achieved love by striving.

From the vantage of love, it is you who are lost; it is love that finds you — and not the way you expected.

No one has articulated this more perfectly, more poignantly, than James Baldwin (August 2, 1924–December 1, 1987) in a conversation with his young filmmaker friend Sedat Pakay, quoted in Nicholas Boggs’s altogether excellent biography Baldwin: A Love Story (which also gave us the moving letter Baldwin received at the peak of his fame and his heartbreak from his childhood teacher).

James Baldwin at work

Having turned his entire life around to follow his improbable Turkish lover to Istanbul, Baldwin reflects:

I will never be able to deny for any reason at all is a certain power that I had to deal with, which has dealt with me, which is called love. And love comes in very strange packages. And I think everything depends in life on whether or not you are able to accept what comes to you. Because it never comes to you the way you think it will. It never comes to you the way you’re taught it will. It comes as it comes.

Never having imagined that love would make of the Harlem River an estuary to the Bosphorus, Baldwin finds himself reckoning with the broader meaning of it all:

Love takes off the masks that we fear we cannot live without and know we cannot live within. I use the word “love” here not merely in the personal sense but as a state of being, or a state of grace — not in the infantile American sense of being made happy but in the tough and universal sense of quest and daring and growth.

The trouble, of course, is that we can choose, without knowing we are choosing, to stay behind the mask, chose being sure over being seen, chose control — which is always the feeling of control, never the fact of control — over possibility. The notion of finding love suffers the same pitfall, for it presumes that the searcher is in control of the find. Elsewhere, Baldwin razes through the delusion:

People who believe that they are strong-willed and the masters of their destiny can only continue to believe this by becoming specialists in self-deception. Their decisions are not really decisions at all — a real decision makes one humble, one knows that it is at the mercy of more things than can be named — but elaborate systems of evasion, of illusion, designed to make themselves and the world appear to be what they and the world are not.

Ultimately, love asks of us the same thing life does — to meet it on its terms. Baldwin writes:

People can’t, unhappily, invent their mooring posts, their lovers and their friends, anymore than they can invent their parents. Life gives these and also takes them away and the great difficulty is to say Yes to life.

BP

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