Since ancient times, human beings have been enchanted by the immutable
relationship between the circumference of a circle and its diameter, no matter the circle’s size. Today, we have a symbolic form for that mathematical relationship: π — an ancient Greek letter conferred upon it by a Welsh mathematician in the first years of the eighteenth century, though it was the ancient Greeks themselves who first began thinking mathematically about the mysterious number. The longest number in nature and possibly the most powerful, π factors into our understanding of fractals and eclipses, of cosmology and thermodynamics, yet it remains ever elusive in its totality.
In the third century BCE, a millennium after Babylonian and Egyptian scholars tried to discern its exact value with fractions, Archimedes devised a geometrical approach that contoured its first few digits. Eight centuries later, ancient Chinese and Indian mathematicians approximated it to seven digits. The invention of calculus in the seventeenth century bloomed hundreds of digits, with Newton himself computing the first fifteen. Modern supercomputers can calculate with perfect precision 1.4 trillion digits. We need only the first thirty-two to compute the size of the known universe with a margin of error a single proton wide.
An irrational number — a number that cannot be expressed as a fraction, the ratio between two whole numbers — π unmoors our basic intuitions about reality with its disquieting whisper of an infinity beyond the grasp of reason. There are no known infinities in nature — as transient creatures suspended in space between the scale of atoms and the scale of stars, suspended in time between not yet and no more, we simply cannot conceive of infinity.
And yet the decimal point of π taunts us like the gun barrel of the unimaginable. If we ever reach the last digit of π, we will have known the universe.
Meanwhile, its assuring constancy goes hedging against our own transience, slaking our yearning for permanence in a cosmos governed by incessant change.
PI by Wisława Szymborska
The admirable number pi: three point one four one.
All the following digits are also initial, five nine two because it never ends.
It can’t be comprehended six five three five at a glance, eight nine by calculation, seven nine or imagination,
not even three two three eight by wit, that is, by comparison four six to anything else two six four three in the world.
The longest snake on earth calls it quits at about forty feet.
Likewise, snakes of myth and legend, though they may hold out a bit longer.
The pageant of digits comprising the number pi
doesn’t stop at the page’s edge.
It goes on across the table, through the air,
over a wall, a leaf, a bird’s nest, clouds, straight into the sky,
through all the bottomless, bloated heavens.
Oh how brief — a mouse tail, a pigtail — is the tail of a comet!
How feeble the star’s ray, bent by bumping up against space!
While here we have two three fifteen three hundred nineteen my phone number your shirt size the year
nineteen hundred and seventy-three the sixth floor
the number of inhabitants sixty-five cents
hip measurement two fingers a charade, a code,
in which we find hail to thee, blithe spirit, bird thou never wert
alongside ladies and gentlemen, no cause for alarm,
as well as heaven and earth shall pass away,
but not the number pi, oh no, nothing doing,
it keeps right on with its rather remarkable five,
its uncommonly fine eight,
its far from final seven,
nudging, always nudging a sluggish eternity
to continue.
We are accidents of biochemistry and chance, moving through the world waging wars and writing poems, spellbound by the seductive illusion of the self, every single one of our atoms traceable to some dead star.
In the interlude between the two World Wars, days after the stock market crash that sparked the Great Depression, the German-American poet and future Nazi sympathizer George Sylvester Viereck sat down with Albert Einstein (March 14, 1879–April 18, 1955) for what became his most extensive interview about life — reflections ranging from science to spirituality to the elemental questions of existence. It was published in the Saturday Evening Post on October 29, 1929 — a quarter century after Einstein’s theory of relativity reconfigured our basic understanding of reality with its revelation that space and time are the warp and weft threads of a single fabric, along the curvature of which everything we are and everything we know is gliding.
Albert Einstein by Lotte Jacobi. (University of New Hampshire Museum of Art.)
Considering the helplessness individual human beings feel before the immense geopolitical forces that had hurled the world into its first global war and the decisions individual political leaders were making — decisions already inclining the world toward a second — Einstein aims in his sensitive intellect at the fundamental reality of existence:
I am a determinist. As such, I do not believe in free will. The Jews believe in free will. They believe that man shapes his own life. I reject that doctrine philosophically. In that respect I am not a Jew… I believe with Schopenhauer: We can do what we wish, but we can only wish what we must. Practically, I am, nevertheless, compelled to act is if freedom of the will existed. If I wish to live in a civilized community, I must act as if man is a responsible being.
When asked about any personal responsibility for his own staggering achievements, he points a steadfast finger at the nonexistence of free will:
I claim credit for nothing. Everything is determined, the beginning as well as the end, by forces over which we have no control. It is determined for the insect as well as for the star. Human being, vegetables or cosmic dust, we all dance to an invisible tune, intoned in the distance by a mysterious player.
For Einstein, the most alive part of the mystery we live with — the mystery we are — is the imagination, that supreme redemption of human life from the prison of determinism. With an eye to his discovery of relativity, he reflects:
I believe in intuitions and inspirations. I sometimes feel that I am right. I do not know that I am. When two expeditions of scientists, funded by the Royal Academy, went forth to test my theory of relativity, I was convinced that their conclusions would totally tally with my hypothesis. I was not surprised when the eclipse of May 29, 1919, confirmed my intuitions. I would have been surprised if I had been wrong.
[…]
I am enough of an artist to draw freely from the imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.
In every life, there comes a time when we are razed to the bone of our resilience by losses beyond our control — lacerations of the heart that feel barely bearable, that leave us bereft of solid ground. What then?
“In art,” Kafka assured his teenage walking companion, “one must throw one’s life away in order to gain it.” As in art, so in life — so suggests the American Tibetan Buddhist nun and teacher Pema Chödrön. In When Things Fall Apart: Heart Advice for Difficult Times (public library), she draws on her own confrontation with personal crisis and on the ancient teachings of Tibetan Buddhism to offer gentle and incisive guidance to the enormity we stand to gain during those times when all seems to be lost. Half a century after Albert Camus asserted that “there is no love of life without despair of life,” Chödrön reframes those moments of acute despair as opportunities for befriending life by befriending ourselves in the deepest sense.
“Liminal Worlds” by Maria Popova. Available as a print.
Writing in that Buddhist way of wrapping in simple language the difficult and beautiful truths of existence, Chödrön examines the most elemental human response to the uncharted territory that comes with loss or any other species of unforeseen change:
Fear is a universal experience. Even the smallest insect feels it. We wade in the tidal pools and put our finger near the soft, open bodies of sea anemones and they close up. Everything spontaneously does that. It’s not a terrible thing that we feel fear when faced with the unknown. It is part of being alive, something we all share. We react against the possibility of loneliness, of death, of not having anything to hold on to. Fear is a natural reaction to moving closer to the truth.
If we commit ourselves to staying right where we are, then our experience becomes very vivid. Things become very clear when there is nowhere to escape.
This clarity, Chödrön argues, is a matter of becoming intimate with fear and rather than treating it as a problem to be solved, using it as a tool with which to dismantle all of our familiar structures of being, “a complete undoing of old ways of seeing, hearing, smelling, tasting, and thinking.” Noting that bravery is not the absence of fear but the intimacy with fear, she writes:
When we really begin to do this, we’re going to be continually humbled. There’s not going to be much room for the arrogance that holding on to ideals can bring. The arrogance that inevitably does arise is going to be continually shot down by our own courage to step forward a little further. The kinds of discoveries that are made through practice have nothing to do with believing in anything. They have much more to do with having the courage to die, the courage to die continually.
In essence, this is the hard work of befriending ourselves, which is our only mechanism for befriending life in its completeness. Out of that, Chödrön argues, arises our deepest strength:
Only to the extent that we expose ourselves over and over to annihilation can that which is indestructible be found in us.
[…]
Things falling apart is a kind of testing and also a kind of healing. We think that the point is to pass the test or to overcome the problem, but the truth is that things don’t really get solved. They come together and they fall apart. Then they come together again and fall apart again. It’s just like that. The healing comes from letting there be room for all of this to happen: room for grief, for relief, for misery, for joy.
“Broken/hearted” by Maria Popova. Available as a print.
Decades after Rollo May made his case for the constructiveness of despair, Chödrön considers the fundamental choice we have in facing our unsettlement — whether with aggressive aversion or with generative openness to possibility:
Life is a good teacher and a good friend. Things are always in transition, if we could only realize it. Nothing ever sums itself up in the way that we like to dream about. The off-center, in-between state is an ideal situation, a situation in which we don’t get caught and we can open our hearts and minds beyond limit. It’s a very tender, nonaggressive, open-ended state of affairs.
To stay with that shakiness — to stay with a broken heart, with a rumbling stomach, with the feeling of hopelessness and wanting to get revenge — that is the path of true awakening. Sticking with that uncertainty, getting the knack of relaxing in the midst of chaos, learning not to panic — this is the spiritual path. Getting the knack of catching ourselves, of gently and compassionately catching ourselves, is the path of the warrior. We catch ourselves one zillion times as once again, whether we like it or not, we harden into resentment, bitterness, righteous indignation — harden in any way, even into a sense of relief, a sense of inspiration.
Half a century after Alan Watts began introducing Eastern teachings into the West with his clarion call for presence as the antidote to anxiety, Chödrön points to the present moment — however uncertain, however difficult — as the sole seedbed of wakefulness to all of life:
This very moment is the perfect teacher, and it’s always with us.
[…]
We can be with what’s happening and not dissociate. Awakeness is found in our pleasure and our pain, our confusion and our wisdom, available in each moment of our weird, unfathomable, ordinary everyday lives.
Remaining present and intimate with the moment, she argues, requires mastering maitri — the Buddhist practice of loving-kindness toward oneself, that most difficult art of self-compassion. She contrasts maitri with the typical Western therapy and self-help method of handling crises:
What makes maitri such a different approach is that we are not trying to solve a problem. We are not striving to make pain go away or to become a better person. In fact, we are giving up control altogether and letting concepts and ideals fall apart. This starts with realizing that whatever occurs is neither the beginning nor the end. It is just the same kind of normal human experience that’s been happening to everyday people from the beginning of time. Thoughts, emotions, moods, and memories come and they go, and basic nowness is always here.
[…]
In the midst of all the heavy dialogue with ourselves, open space is always there.
Another Buddhist concept at odds with our Western coping mechanisms is the Tibetan expression ye tang che. Chödrön explains its connotations, evocative of Camus’s insistence on the vitalizing power of despair:
The ye part means “totally, completely,” and the rest of it means “exhausted.” Altogether, ye tang che means totally tired out. We might say “totally fed up.” It describes an experience of complete hopelessness, of completely giving up hope. This is an important point. This is the beginning of the beginning. Without giving up hope — that there’s somewhere better to be, that there’s someone better to be — we will never relax with where we are or who we are.
[…]
Suffering begins to dissolve when we can question the belief or the hope that there’s anywhere to hide.
Decades after Simone de Beauvoir’s proclamation about atheism and the ultimate frontier of hope, Chödrön points out that at the heart of Buddhism’s approach is not the escapism of religion but the realism of secular philosophy. And yet these crude demarcations fail to capture the subtlety of these teachings. She clarifies:
The difference between theism and nontheism is not whether one does or does not believe in God… Theism is a deep-seated conviction that there’s some hand to hold: if we just do the right things, someone will appreciate us and take care of us. It means thinking there’s always going to be a babysitter available when we need one. We all are inclined to abdicate our responsibilities and delegate our authority to something outside ourselves. Nontheism is relaxing with the ambiguity and uncertainty of the present moment without reaching for anything to protect ourselves.
[…]
Hopelessness is the basic ground. Otherwise, we’re going to make the journey with the hope of getting security… Begin the journey without hope of getting ground under your feet. Begin with hopelessness.
[…]
When inspiration has become hidden, when we feel ready to give up, this is the time when healing can be found in the tenderness of pain itself… In the midst of loneliness, in the midst of fear, in the middle of feeling misunderstood and rejected is the heartbeat of all things.
Only through such active self-compassion to our own darkness, Chödrön suggests, can we begin to offer authentic light to anybody else, to become a force of radiance in the world. She writes:
We don’t set out to save the world; we set out to wonder how other people are doing and to reflect on how our actions affect other people’s hearts.
“There is no place more intimate than the spirit alone,” the young May Sarton (May 3, 1912–July 16, 1995) wrote in her stunning ode to solitude — the solitude she came to know, over the course of her long and prolific life, as the seedbed of creativity.
Living alone can be deeply rewarding and deeply challenging. It is not for everyone. It is not for those who romanticize its offerings of freedom and focus, but excise its menacing visitations of loneliness and alienation. It is not for those who find silence shattering. It is especially not for those who hunger for another consciousness to validate their experience and redeem their reality. It is only for the whole.
In her elder years, living alone on the coast of Maine and savoring a renaissance of creative energy after a long depression, Sarton returns to the subject of what solitude is and is not on the pages of her boundlessly rewarding journal The House by the Sea (public library).
May Sarton
Looking back on her life, she writes:
Solitude, like a long love, deepens with time.
But what solitude brings to a person is shaped by what the person brings to solitude. One August day, life brings Sarton a prompt to consider the art of living alone and the necessary preconditions for making of solitude not a resignation but a rapture:
Yesterday I had a letter from a young woman who is living alone, a film maker of some reputation. She wants to do a film on people who live alone, and will come next week to talk about her plans. I gather she has some doubts about the solitary life. I told her that I feel it is not for the young (she is only thirty-three). I did not begin to live alone till I was forty-five, and had “lived” in the sense of passionate friendships and love affairs very richly for twenty-five years. I had a huge amount of life to think about and to digest, and, above all, I was a person by then and knew what I wanted of my life. The people we love are built into us. Every day I am suddenly aware of something someone taught me long ago — or just yesterday — of some certainty and self-awareness that grew out of conflict with someone I loved enough to try to encompass, however painful that effort may have been.
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“My business is circumference,” Emily Dickinson wrote in one of her most cryptic letters. 
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