“…and when two people have loved each other see how it is like a scar between their bodies, stronger, darker, and proud…”
By Maria Popova
In the autumn of 1664, when the black plague shrouded the world in a deadly pandemic and universities sent their students home for a quarantine the end of which no one could foresee, a young man besotted with mathematics, motion, and light returned to his illiterate mother’s orchard, where he watched an apple fall. A revolution of understanding rose in its shadow — he fathomed the mechanics of a mystery that had enchanted humanity for epochs: how bodies can act on other bodies, attracting one another impalpably and invisibly across space and separation, as if by magic.
Religions had called it grace. Science, with the young Newton at its helm, called it gravity.
We have since discovered three other presently irreducible fundamental forces winding the clockwork of reality, with gravity the weakest of the four, 1038 times weaker than the strongest, and yet the most immediate, the most embodied, the most readily graspable by our creaturely intuitions. The unfathomed thing once explained as magic is now a commonplace of common sense, woven into our elemental understanding of the world and, in consequence, woven into our metaphors — those handles on the door of understanding.
Art from Sun and Moon — a collection of Indian celestial myths illustrated by tribal artists.
It is on gravity’s metaphor we lean when we speak of the binding force of love — the attraction that draws ensouled bodies to one another, as if by magic. But for all the progress science has made in the epochs since Newton, along the long procession of history in which the brilliant and the brokenhearted have walked hand in hand, this binding force is still a mystery, still something closer to grace, perhaps the only form of grace that is real.
This might always remain so — as the stardust-residue of ideas that was once Carl Sagan reminds us, “the universe will always be much richer than our ability to understand it.” A vast part of me hopes it does remain so — some things are more important felt than known: felt fully and unconditionally, for they can only ever be understood incompletely and conjecturally. Rachel Carson, for all her devotion to the poetics of reality we call science, knew this when she insisted that it is not half so important to know as to feel. E.E. Cummings knew it when, in his impassioned case for the courage to be yourself, he observed that “whenever you think or you believe or you know, you’re a lot of other people: but the moment you feel, you’re nobody-but-yourself… the hardest battle which any human being can fight.”
Centuries after Newton and generations after Carson and Cummings, Jane Hirshfield — another philosopher-poet intimately attuned to the poetics of reality, an ordained Zen Buddhist who thinks deeply and writes splendidly about the living realities and lush metaphors of the natural world — addressed this in a poem that has saved me, and continues to save me, across many seasons of being. Originally published in her 1988 lifeline of a collection Of Gravity & Angels (public library) — a title evocative of the posthumous record of Simone Weil’s exquisite consciousness, Gravity and Grace — it is generously read here for us by the poet herself:
FOR WHAT BINDS US by Jane Hirshfield
There are names for what binds us:
strong forces, weak forces.
Look around, you can see them:
the skin that forms in a half-empty cup,
nails rusting into the places they join,
joints dovetailed on their own weight.
The way things stay so solidly
wherever they’ve been set down —
and gravity, scientists say, is weak.
And see how the flesh grows back
across a wound, with a great vehemence,
more strong
than the simple, untested surface before.
There’s a name for it on horses,
when it comes back darker and raised: proud flesh,
as all flesh,
is proud of its wounds, wears them
as honors given out after battle,
small triumphs pinned to the chest —
And when two people have loved each other
see how it is like a
scar between their bodies,
stronger, darker, and proud;
how the black cord makes of them a single fabric
that nothing can tear or mend.
“The distance between here and there is the answer to the wrong question.”
By Maria Popova
“What exists, exists so that it can be lost and become precious,” Lisel Mueller wrote in her stunning poem about what gives meaning to our mortal lives as she neared, but never quite reached, the triumph of having lived a century — a bittersweet triumph, for to live at all, however long or short, is an unbidden bargain to lose everything you hold precious: every love and every life, including your own. Loss is the price of life — a price we never chose to pay any more than we chose to be born, and yet a price not merely worth paying but beyond questions of worth and why.
One corollary is that, both in the evolutionary sense and in the existential, every loss reveals what we are made of. But every loss also reveals what it is made of, which is more loss: Each loss takes a piece of us — a piece soft and alive — and leaves in its place something cold and heavy; each subsequent loss becomes the magnet that draws out those old leaden pieces, pulls them out from the reliquary of scar tissue where we have been keeping them in order to live, makes them rip through our being afresh. And yet the shrapnel pieces that surface are smaller and softer-edged than when they first entered through the open wound of raw bereavement, smoothed and contracted by the ongoingness of life.
In this sense, grief if fractal, each new instance containing within itself a set of self-similar sub-griefs — miniatures of the same emotional structure, rendered smaller in salience by time and tenacity, those twin inevitabilities of aliveness.
The Mandelbrot set. (Illustration by Wolfgang Beyer.)
How the fractal nature of grief is both the key to understanding it and the doorway to moving through it is what mathematician Michael Frame explores in his unusual book Geometry of Grief: Reflections on Mathematics, Loss, and Life (public library). After twenty years of working with the visionary father of fractals and another twenty years of teaching fractal geometry at Yale, Frame draws on a lifetime of loss and a lifetime of delicate attention to the details of aliveness we call beauty to interleave memoir and mathematics in an uncommon tapestry of thought, twining Borges and quantum mechanics, evolutionary biology and Islamic art, music and multiverse theory.
Because every sound theorem rests upon precise formulation, Frame offers a basic definition:
Grief is a response to an irreversible loss… To generate grief rather than sadness, the thing lost must carry great emotional weight, and it must pull back the veil that covers a transcendent aspect of the world. Breathe out to push the fog away from a brilliant pinpoint of light.
This trifecta of irreversibility, emotional heft, and transcendence anchors Frame’s model of grief and his map for navigating the landscape of loss not as a journey of recovery but as one of readjustment — of reconstituting our model of the world within, which governs our entire experience of the world without. Because the two basic building blocks of our world-model — inner and outer — are attention and narrative, readjustment to life after loss requires deliberate wielding of both. Frame writes:
All moments of our lives are immensely rich, with many — perhaps infinitely many — variables we could notice.
We can view our lives as trajectories, parameterized by time, through story space.
We can never simultaneously view all of the possible variables; rather, we focus on a few variables at a time, restricting our attention to a low-dimensional subspace of story space.
Our trajectories through these subspaces are the stories we tell ourselves about our lives; they are how we make sense of our lives, but always they miss some elements of our experiences.
Irreversible loss appears as a discontinuity, a jump, in our path through story space.
By focusing on certain subspaces, by projecting our trajectories into these spaces, we can reduce the apparent magnitude of the jumps, and consequently find a way to confront the emotional loss and perhaps reduce its impact.
The most gladdening thing about grief parallels the most gladdening thing about science: However meticulous our projections and our models of reality may be, however triumphant in their conquest of knowledge, they are not only perennially incomplete but could be — and, throughout the history of our species, have often been — fundamentally wrong. Science, like life itself, rests upon the abstract art of otherwise — things could be other than what they appear to be, other than what we assume them to be: stranger, more slippery, more possible. Frame writes:
Geometry is a way to organize our models of the world, its shapes and dynamics. But isn’t this all contingent, balanced on a knife’s edge? Could our models have turned out very differently? If the fractal geometry of Mandelbrot had been discovered before the geometry of Euclid, would manufacture be the same? If you think the question is far-fetched, consider the iterated branching of our pulmonary, circulatory, and nervous systems, or the recursive folding of our DNA, or the large surface area and small volume of our lungs and our digestive tract. Evolution has discovered and uses fractal geometry. If people had looked more closely at the geometry of nature, rather than emulating the “celestial perfection” imposed by the church’s interpretation of the works of Euclid and Aristotle, our constructions could be very different now.
Solids from Kepler’s Harmony of the World, exploring the relationship between harmony and geometry. (Available as a print and as a face mask.)
To be fair, the rare few did look and did see different constructions of reality — the Hungarian teenager who, two hundred years ago, subverted Euclid and equipped Einstein with the building blocks of relativity; the sickly German mathematician who, four hundred years ago, subverted the celestial interpretations of the church to give us the revolutionary laws of planetary motion while defending his mother in a witchcraft trial.
Frame writes:
Unless there were only one geometry, only one story — only one world — we should not expect the same categories to grid our views of the universe… Could the world be different than we think? Is it different? Must it be only one thing, or can it be many? If we view the world in one way, does this forever bar us from all others?
Pointing to a resounding “no” in the many-worlds model of quantum mechanics — a model in which “every observation of every particle splits the universe into branches, one in which each measurement outcome occurs, and communication between these branches is impossible” — he adds:
Once they are recognized, these patterns cannot go unnoticed. They change forever how the image of the world unfolds in our minds, change forever the categories of the models we build.
This recognition-as-model-revision, Frame intimates, is also the way to view and live through grief — an exercise in continual dilation of perspective, so that life can be seen from more and more angles besides the acuteness of loss, noticing more and more of what is there, what remains and what grows in the wake of the lost; an exercise in remembering, again and again, that healing is subtle and unpredictable, unfolding in tiny, quiet, immeasurable increments that eventually add up to profound changes of measurable difference.
Returning to the consolation of fractals — the mathematical language composing chaos theory — Frame writes:
Small changes may not cause large differences, but small changes, invisible because of our inability to measure exactly, can mask our ability to predict whether, when, and where large differences can occur. Chaos is about the breakdown of our ability to forecast for more than a short time.
Beauty and grief are next-door neighbors, or maybe grief is beauty in a dark mirror… To see beauty is to glimpse something deeper; to grieve is to glimpse a loss whose consequences we will not unpack for years, and maybe never. The beauty of geometry likewise involves great emotional weight, irreversibly alters our perceptions, and is transcendent. For we don’t see all of geometry, only a hint, a shadow of something much deeper.
In one of the book’s tenderest moments, illustrating this sidewise gleam at the depths, Frame shares a short lyrical essay he composed after his mother’s death, in response to a creative prompt from a student compiling meditations on gravity:
Gravity holds my feet on the ground. Gravity keeps the earth traveling around the sun, the sun dancing around the galaxy, the galaxy threading through the Local Group, and on and on.
Gravity pulls rain out of the sky. And snowflakes. And leaves in autumn. And tears from my eyes when I knew you really are gone. Where did you go?
[…]
The distance between here and there is the answer to the wrong question.
[…]
I thought gravity pulled my mind into the past, stuck in memories. But now I know I can’t trust memories. Some are invented, all are edited. The whole web of who I am — what I’ve seen and done, what skills I’ve found — is nothing but fog.
Gravity pulls me to the future, bits of me falling off along the way. Each of us disappears into the mist of the possible. In our minds, time is gravity’s other side.
A subtle sylvan celebration of how our hurts and our healings shape the singular beauty of our character.
By Maria Popova
Few things salve sanity better than the awareness that there are infinitely many kinds of beautiful lives, and few places foster this awareness more readily than the forest — this cathedral of infinite possibility, pillared by trees of wildly different shapes and sizes that all began life as nearly identical seeds.
Among the many existential consolations of trees — these teachers in loss as a portal to revelation, these high priestesses of optimism, these virtuosi of improvisation, these emissaries of eternity — is how they self-sculpt their beauty and character from the monolith of challenge that is life. Once planted in its chance-granted location, each tree morphs the basic givens of its genome into a singular shape in response to the gauntlets of its environment: It boughs down low to elude the unforgiving wind, rises and bends to reach the sunlit corner of the umbral canopy, grows a wondrous sidewise trunk to go on living after lightning.
This endless, life-affirming dialogue between a tree’s predestined structure and its living shape is what the visionary Italian artist, designer, inventor, futurist, and visual philosopher Bruno Munari (October 24, 1907–September 30, 1998) explores in the spare, splendid 1978 gem Drawing a Tree (public library). Inspired by Leonardo da Vinci’s centuries-old diagrammatic study of tree growth, this unexampled masterpiece is a work of visual poetry and existential philosophy in the guise of a simple, elegant drawing guide to the art of trees rooted in their science.
At last winter is finished and, from the ground where a seed has dropped, a vertical green blade appears. The sun starts to make itself felt and the green shoots grow. It is a tree, but so small no one recognizes it yet. Little by little it grows tough. It begins to branch, buds germinate on its branches, other branches spring from the buds, other leaves from the branches, and so on. A few years later, that green blade will have become a fine trunk covered in boughs. Later still, it will have produced wide branches which will produce leaves, blossoms and fruit. In autumn it will spread its seeds around, and some will fall beneath it while others will be carried far away by the wind.
Almost everywhere a seed falls, a new tree will grow.
Writing while elsewhere in Europe a refugee was revolutionizing the mathematics of reality with the discovery of fractals — a new science that would come to explain everything from earthquakes to economics markets, most readily visible in nature in trees — Munari deduces a basic growth pattern all trees share: each branch splitting into newer branches, each slenderer than its progenitor.
If they grew in isolation, free from any environmental challenge, all trees would follow perfectly predictable fractal geometries — a pattern so simple anyone could draw it, yet an ideal form not found in nature. This is where the existential meets the scientific and the artistic. Munari observes:
To grow so exactly, a tree would have to live in a place where there was no wind and with the sun always high in the sky, with the rain always the same and with constant nourishment from the ground all the time. There would have to be no lightning flashes nor even any spar changes in temperature, no snow or frost, never too hot or dry.
Because no such idyllic conditions exist in reality, Munari draws the tree as versions of the pattern adapted to various challenges. (Yes. There are infinitely many kinds of beautiful lives.)
Delighting in the wildest subversions of the pattern — “there are the mad branches too, like in nearly all families” — Munari observes that even through them, you can still discern the fundamental form if you look attentively enough.
Drawing on the long human tradition of seeing ourselves in trees, Munari offers a tender reminder that trees — like us — take their shape and sculpt their individual character in the act of healing from hurt:
Here we are at the point where the sky turns dark and a real and proper storm comes, the tree waves frantically in the wind, as if it were afraid. A flash of lightning from the almost black sky hits the tree and disappears in a blaze of light. Through the heavy rain you can see a part of the tree on the ground, a big limb with its smaller branches. All you can hear is the sound of the heavy rain on the leaves.
The next year the tree is different, wounded. New branches still shoot out though, as if nothing has happened. This is how trees change shape: a flash of lightning, the weight of the snow on the branches, insects that gnaw at the wood… and the tree changes shape.
As he draws “some hurt and wounded trees,” Munari observes that you can still see the contours of their elemental structure through their scars and healing adaptations.
In an oak leaf’s “network of nerves,” he finds a miniature of the entire tree’s branching pattern. (This resemblance, of course, is what fractals explain — the leaf at the tip of the branch at the side of the trunk is just the finest extension of the fractal structure.)
Munari goes on to draw variations on the basic tree-growth pattern in different species, and variations on each species’ adaptation of the pattern in different specimens.
For a contemporary counterpart of existential-processing-disguised-as-drawing-lessons, dive into my friend Wendy MacNaughton’s wondrous DrawTogether project for human saplings.
“This life of yours which you are living is not merely a piece of the entire existence, but is in a certain sense the whole.”
By Maria Popova
To face the question of what makes us who we are with courage, lucidity, and fulness of feeling is to face, with all the restlessness and helplessness this stirs in the meaning-hungry soul, the elemental fact of our choicelessness in the conditions that lead to our existence.
That is what the Nobel-winning founding father of quantum mechanics Erwin Schrödinger (August 12, 1887–January 4, 1961) addresses in some exquisite passages from My View of the World (public library) — the slender, daring deathbed book containing two long essays penned on either side of his Nobel Prize, thirty-five years apart yet united by the unbroken thread of his uncommon mind unafraid of its own capacity for feeling, that vital capacity for living fully into the grandest open questions of existence.
Erwin Schrödinger, circa 1920s.
Schrödinger opens with one swift, awe-striking defense of what scientists dismiss as metaphysics — a realm of knowledge that lies beyond the current scientific tools and modes of truth-extraction, which history attests always reveals more about the limitations of the tools than about the limits of nature’s truths. (Lest we forget, even so pure a form of physics as the hummingbird’s flight was long considered a metaphysical phenomenon — that is, a yet-unsolved phenomenon explained as magic — until science fermented the technology of photography to capture the mechanics of the process.) Echoing Hannah Arendt’s daring indictment that ceasing to ask unanswerable question would mean relinquishing “not only the ability to produce those thought-things that we call works of art but also the capacity to ask all the answerable questions upon which every civilization is founded,” Schrödinger writes:
It is relatively easy to sweep away the whole of metaphysics, as Kant did. The slightest puff in its direction blows it away, and what was needed was not so much a powerful pair of lungs to provide the blast, as a powerful dose of courage to turn it against so timelessly venerable a house of cards.
But you must not think that what has then been achieved is the actual elimination of metaphysics from the empirical content of human knowledge. In fact, if we cut out all metaphysics it will be found to be vastly more difficult, indeed probably quite impossible, to give any intelligible account of even the most circumscribed area of specialisation within any specialised science you please. Metaphysics includes, amongst other things — to take just one quite crude example — the unquestioning acceptance of a more-than-physical — that is, transcendental — significance in a large number of thin sheets of wood-pulp covered with black marks such as are now before you… A real elimination of metaphysics means taking the soul out of both art and science, turning them into skeletons incapable of any further development.
Even as he made his reality-reconfiguring contributions to science and its search for fundamental truth, Schrödinger never relinquished his passionate curiosity about philosophy and the ongoing questions of meaning that kernel every truth in the flesh of consciousness. He was as drawn to Spinoza and Schopenhauer as he was to the ancient Eastern traditions, and especially in their untrammeled common ground of panpsychism — one of the oldest and most notoriously misunderstood theoretical models of consciousness in relation to the universe.
A century after the pioneering Canadian philosopher, psychiatrist, and nature-explorer Richard Maurice Bucke drew inspiration from Whitman to develop his theory of cosmic consciousness, and a century before the emerging science of counterfactuals threw its gauntlet at our fundamental assumptions about the nature of the universe, Schrödinger takes up the parallels between the discoveries of quantum physics and the core ideas of the Hindu philosophy of Vedanta. In what might best be described as an existentialist prose-poem, he invites you to imagine yourself seated on a mountain bench at sunset, beholding a transcendent display of nature:
Facing you, soaring up from the depths of the valley, is the mighty, glacier-tipped peak, its smooth snowfields and hard-edged rock-faces touched at this moment with soft rose-colour by the last rays of the departing sun, all marvellously sharp against the clear, pale, transparent blue of the sky.
According to our usual way of looking at it, everything that you are seeing has, apart from small changes, been there for thousands of years before you. After a while — not long — you will no longer exist, and the woods and rocks and sky will continue, unchanged, for thousands of years after you.
What is it that has called you so suddenly out of nothingness to enjoy for a brief while a spectacle which remains quite indifferent to you?
In a passage evocative of Whitman’s timeless lines from “Crossing Brooklyn Ferry” — “Others will enter the gates of the ferry and cross from shore to shore… Others will see the islands large and small… A hundred years hence, or ever so many hundred years hence, others will see them… I am with you, you men and women of a generation, or ever so many generations hence … Just as you feel when you look on the river and sky, so I felt… Just as any of you is one of a living crowd, I was one of a crowd… What is it then between us?” — Schrödinger answers:
The conditions for your existence are almost as old as the rocks. For thousands of years men have striven and suffered and begotten and women have brought forth in pain. A hundred years ago, perhaps, another man sat on this spot; like you he gazed with awe and yearning in his heart at the dying light of the glaciers. Like you he was begotten of man and born of woman. He felt pain and brief joy as you do. Was he someone else? Was it not you yourself? What is this Self of yours? What was the necessary condition for making the thing conceived this time into you, just you and not someone else? What clearly intelligible scientific meaning can this ‘someone else’ really have? If she who is now your mother had cohabited with someone else and had a son by him, and your father had done likewise, would you have come to be? Or were you living in them, and in your father’s father… thousands of years ago? And even if this is so, why are you not your brother, why is your brother not you, why are you not one of your distant cousins? What justifies you in obstinately discovering this difference — the difference between you and someone else — when objectively what is there is the same?
[…]
Inconceivable as it seems to ordinary reason, you — and all other conscious beings as such — are all in all. Hence this life of yours which you are living is not merely a piece of the entire existence, but is in a certain sense the whole.
Once we fathom this fundamental reality of interbeing, Schrödinger observes, it becomes impossible to wish anything for ourselves that we do not wish for everyone else or to harm anyone else without harming ourselves:
It is the vision of this truth (of which the individual is seldom conscious in his actions) which underlies all morally valuable activity.
A decade later, in a lovely testament to Schrödinger’s insistence on the indivisibility of science and art in addressing those grandest unanswered question, Iris Murdoch — one of the vastest minds and finest literary artists of her time, and of all time — captured this elemental truth in her case for art as “an occasion for unselfing,” observing:
The self, the place where we live, is a place of illusion. Goodness is connected with the attempt to see the unself… to pierce the veil of selfish consciousness and join the world as it really is.
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