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Alan Turing’s Little-Known Contributions to Biology and His Mesmerizing Hand-Drawn Diagrams of Dappling Patterns

What the Fibonacci fascinations of daisies have to do with Kandinsky and mid-century graphic design.

Alan Turing’s Little-Known Contributions to Biology and His Mesmerizing Hand-Drawn Diagrams of Dappling Patterns

Alan Turing (June 23, 1912–June 7, 1954) is celebrated as the godfather of modern computing, but what remains practically unknown is his seminal contribution to an obscure branch of biology: Turing dedicated a significant portion of his life to the study of morphogenesis — the biological process by which organisms take their shape. Fascinated by the presence of Fibonacci numbers in the leaf arrangements of plants and the color patterns of animals, he developed some of the earliest mathematical models of how biological shapes emerge — a pioneering effort to crack the algorithmic code of nature, correctly predicting the diffusion of chemical signals that determine the patterns of shape-development. All of this he did at a time before Cartwright, Watson, and Crick discovered the molecular structure of DNA — the dawn of molecular biology and biochemistry as we know them today.

As scholar Jonathan Swinton explains in Alan Turing: His Work and Impact (public library), this fascination began in Turing’s childhood. As a boy, he had been so entranced by daisies that his mother, railway engineer Sara Turing, once drew a sketch of little Alan gazing at the daisies instead of paying attention to his hockey game.

In his tragically curtailed lifetime, Turing published only one paper on the morphogenesis two years before his death. Some of his remaining work on the subject was published posthumously in the hefty third volume of his collected works and much remains tucked away in the archives of King’s College in Cambridge, with a portion available in the Turing Digital Archive.

Among the materials, donated in 1960 by Turing’s mother and later digitized by P.N. Furbank at the Archive, is a set of Turing’s hand-drawn, hand-colored morphogenesis diagrams — eerily beautiful visual explorations of dappling patterns, leaf arrangements, and daisy rings, somehow reminiscent of Kandinsky and mid-century graphic design.









Complement with an uncommon portrait of Turing, then revisit his contemporary Beatrix Potter’s little-known contributions to mycology.

HT Stefanie Posavec


The Gutsy Girl: A Modern Manifesto for Bravery, Perseverance, and Breaking the Tyranny of Perfection

A former firefighter and lifelong adventurer’s clarion call for the joy of adventure in a culture obsessed with risk-averse achievement.

The Gutsy Girl: A Modern Manifesto for Bravery, Perseverance, and Breaking the Tyranny of Perfection

In 1885, a young woman sent the editor of her hometown newspaper a brilliant response to a letter by a patronizing chauvinist, which the paper had published under the title “What Girls Are Good For.” The woman, known today as Nellie Bly, so impressed the editor that she was hired at the paper and went on to become a trailblazing journalist, circumnavigating the globe in 75 days with only a duffle bag and risking her life to write a seminal exposé of asylum abuse, which forever changed legal protections for the mentally ill. But Bly’s courage says as much about her triumphant character as it does about the tragedies of her culture — she is celebrated as a hero in large part because she defied and transcended the limiting gender norms of the Victorian era, which reserved courageous and adventurous feats for men, while raising women to be diffident, perfect, and perfectly pretty instead.

Writer Caroline Paul, one of the first women on San Francisco’s firefighting force and an experimental plane pilot, believes that not much has changed in the century since — that beneath the surface progress, our culture still nurses girls on “the insidious language of fear” and boys on that of bravery and resilience. She offers an intelligent and imaginative antidote in The Gutsy Girl: Escapades for Your Life of Epic Adventure (public library) — part memoir, part manifesto, part aspirational workbook, aimed at tween girls but speaking to the ageless, ungendered spirit of adventure in all of us, exploring what it means to be brave, to persevere, to break the tyranny of perfection, and to laugh at oneself while setting out to do the seemingly impossible.


Illustrated by Paul’s partner (and my frequent collaborator), artist and graphic journalist Wendy MacNaughton, the book features sidebar celebrations of diverse “girl heroes” of nearly every imaginable background, ranging from famous pioneers like Nellie Bly and astronaut Mae Jemison to little-known adventurers like canopy-climbing botanist Marie Antoine, prodigy rock-climber Ashima Shiraishi, and barnstorming pilot and parachutist Bessie “Queen Bess” Coleman.

A masterful memoirist who has previously written about what a lost cat taught her about finding human love and what it’s like to be a twin, Paul structures each chapter as a thrilling micro-memoir of a particular adventure from her own life — building a milk carton pirate ship as a teenager and sinking it triumphantly into the rapids, mastering a challenging type of paragliding as a young woman, climbing and nearly dying on the formidable mount Denali as an adult.


Let me make one thing clear: Throughout the book, Paul does a remarkably thoughtful job of pointing out the line between adventurousness and recklessness. Her brushes with disaster, rather than lionizing heedlessness, are the book’s greatest gift precisely because they decondition the notion that an adventure is the same thing as an achievement — that one must be perfect and error-proof in every way in order to live a daring and courageous life. Instead, by chronicling her many missteps along the running starts of her leaps, she assures the young reader over and over that owning up to mistakes isn’t an attrition of one’s courage but an essential building block of it. After all, the fear of humiliation is perhaps what undergirds all fear, and in our culture of stubborn self-righteousness, there are few things we resist more staunchly, to the detriment of our own growth, than looking foolish for being wrong. The courageous, Paul reminds us, trip and fall, often in public, but get right back up and leap again.

Indeed, the book is a lived and living testament to psychologist Carol Dweck’s seminal work on the “fixed” vs. “growth” mindsets — life-tested evidence that courage is the fruit not of perfection but of doggedness in the face of fallibility, fertilized by the choice (and it is a choice, Paul reminds us over and over) to get up and dust yourself off each time.

But Paul wasn’t always an adventurer. She reflects:

I had been a shy and fearful kid. Many things had scared me. Bigger kids. Second grade. The elderly woman across the street. Being called on in class. The book Where the Wild Things Are. Woods at dusk. The way the bones in my hand crisscrossed.

Being scared was a terrible feeling, like sinking in quicksand. My stomach would drop, my feet would feel heavy, my head would prickle. Fear was an all-body experience. For a shy kid like me it was overwhelming.

Let me pause here to note that Caroline Paul is one of the most extraordinary human beings I know — a modern-day Amazon, Shackleton, Amelia Earhart, and Hedy Lamarr rolled into one — and since she is also a brilliant writer, the self-deprecating humor permeating the book serves a deliberate purpose: to assure us that no one is born a modern-day Amazon, Shackleton, Amelia Earhart, and Hedy Lamarr rolled into one, but the determined can become it by taking on challenges, conceding the possibility of imperfection and embarrassment, and seeing those outcomes as part of the adventure rather than as failure at achievement.

That’s exactly what Paul does in the adventures she chronicles. It’s time, after all, to replace that woeful Victorian map of woman’s heart with a modern map of the gutsy girl spirit.


There is even a nod to Harvard social scientist Amy Cuddy’s pioneering work on power poses:


As a lover of clouds and their classification, I delighted in Paul’s foray into thermal flying — a particularly challenging yet poetic type of paragliding, in which paragliders do what birds do and ride the column-like streams of hot air, known as thermals, learning which clouds are allies and which mortal threat.


Cumulus clouds — those cotton-like fluff formations you see on sunny days — are formed when the hot air of the thermal cools and stops rising. They are thus helpful indicators that there is a thermal below. But the rub is that because the hot air cools as it rises, the paraglider must stop before reaching a bottom of the cloud — otherwise disaster might strike.

For Paul, a practiced paraglider but a novice at thermal flying, disaster did strike as she found herself so enraptured by soaring like the birds amid the misty air that she forgot this basic rule:

I realized what was happening, just as the cloud completely enveloped me.

It was called Cloud Suck. It happened when you thought you were flying below a cumulus cloud, but you were really below a building cumulonimbus. The difference between those two clouds doesn’t sound like a big deal. Cumulus means “heap” in Latin. But in Latin the word “nimbus” means “dark cloud.” In other words a cumulus cloud was just a heap of clouds, but a cumulonimbus cloud was one of those black, towering, anvil-shaped monsters that you associate with an incoming storm.

I was in a thundercloud.

I’d heard all the stories. Visibility goes from white to black. You’re rained on, hailed on, and lightning flashes on all sides. At some point you lose consciousness. Your wing begins to freeze. You are finally spat out and you’re probably dead. If you’re not, your wing has been ripped to shreds and you soon will be. One paraglider pilot, a European champion, had been cloud-sucked to thirty-two thousand feet — that’s where jetliners fly. This was recorded on her variometer, which froze there. She survived only because she gained consciousness on her descent, her paraglider miraculously intact, and guided herself to the ground.

Rapidly, Paul is sucked into the thunderous darkness, leaving her only seconds to decide — react, really — what to do. In a testament to legendary chemist Louis Pasteur’s famous proclamation that “chance favors the prepared mind,” she saves herself by calling on her mental library of practiced maneuvers and instinctively combining two tricks she had performed individually before. She writes:

I rocketed out of the bottom of that storm cloud, spinning and dropping like a downed war plane. Luck was with me, and my wing held. Skill was with me, too, as I gently transitioned out of the two maneuvers and leveled off. EEEeeeeeee went my exhaled breath. Ba BOOM, Ba BOOM went my heart. I glided for a while, calming down. I was both ashamed of my mistake, and exhilarated to be alive. Was there a lesson here? I had tried to learn something new, but I had almost killed myself doing it. Still, I hadn’t killed myself.

Suddenly it was clear to me: The best outdoor athletes are adventurous, but they aren’t reckless! They know their skill level, and their goals.

She recounts an exchange with her paragliding partners:

When we regrouped at the landing zone, Lars and Mike wanted to know how my flight had been. They’d lost sight of me, Lars said, after their own launches. “Oh, I’m getting the hang of it,” I said, shrugging with feigned nonchalance.

Lars looked happy. “Pretty great, right?!” he cried. Then his eyes widened, and his voice lowered. “Well, I don’t want to freak you out.” He leaned in closer. “But I saw this dude get cloud sucked. Cumulonimbus! He escaped, though.” Lars shook his head. “I don’t know who it was but man, that guy was brave, and jeez, was he stupid!”

It’s hard not to appreciate the tragicomedy of the exchange — Lars speaks for our culture at large, in which it is assumed that the adventurous feat, even if bordering on recklessness, is reserved for the dudes.


But Paul’s most instructive adventure, for it is the one most laced with larger psychological dimensions and philosophical lessons, took place in Denali — Alaska’s formidable mountain summit, where she and her friend Trish traveled to visit their friend Eric, working there as a park ranger. With humor foreboding peril, she paints the backdrop against which the drama was to unfold:

One day soon after we arrived, the forecast for the mountain said something unexpected: It was going to be clear and balmy for the next week. Where were the terrible blizzards? Where were the high winds? Where were the blood-stopping temperatures? Gone. Suddenly Denali, with none of its fierce weather, seemed tame.

It was as if a large tiger had abruptly sighed and said, forget this, I’m going to be a kitten for a while. And what do you do with a cute cuddly kitten? You tickle its tummy and play with its nose. So suddenly we were not sticking to our plan of remaining at base camp. We were pondering a two-day expedition to the next camp at fourteen thousand feet. We asked each other: What could possibly go wrong? We asked as if it was a question, but it wasn’t a question. It was a statement. The weather was fine, is what we meant, so nothing could possibly go wrong.

Everything went wrong.

The balmy weather had come with a dark side — melting snow, unveiling a mine field of cracks in the ice. After a few hours of easy skiing, the trio tied together with a hefty climbing rope (which Paul affectionately calls “the Hoister, the Puller-Upper, or the Thankyouthankyouthankyou”) so that if one of them fell the other two would hold the weight, Eric is suddenly inhaled by a crevasse — a cleave in the glacier, opening up a bottomless grotto below the ice.

Paul recounts the freeze-frame terror of the moment:

There was silence.

Silence, except for the sound that adrenaline must make as it floods the body. Silence, except for the clicking and clacking as my brain began to assess this new succession of facts. Eric, in crevasse. Trish and me, prone on snow. Ice axe, our savior.

Trish and I called to each other. Okay? Okay! Then we called for Eric.

No response.

Was he dead? Was he unconscious? We didn’t know. But this was no time to lie about, even if we were lying about because gravity and more than three hundred pounds of swinging, possibly dead, weight was pulling on us. If the hundred-pound sled that had followed Eric down hadn’t killed him, hypothermia would. Once the heat began to leach from Eric’s body, he would have only a little time. So we had work to do, and I was the one who had to do it. It was time to set up the Thankyouthankyouthankyou, so I scrabbled for the stakes I was carrying on my back, and I drove one into the snow with the ferocity of someone aiming for a vampire’s heart.

That single stake is to serve as the anchor, holding the entire weight of Eric and his sled. But, to Paul’s horror, the skate doesn’t hold in the melting snow. With the heavy humility that comes with recognizing one’s hubris only after the fact, she writes:

The very weather that had made us feel so safe was now conspiring against us. The warmth that had lulled us into believing everything was going to be fine had opened up crevasses and turned the snow soft and mushy. Denali had been a friendly kitten for a while. But it remained a wild tiger at heart, and we had made the mistake of forgetting that.

Scrambling for a new anchor, she grabs all four of her stakes and jabs them into the snow as deep as she can. Just then, she feels a teardrop on her face. There is, of course, no crying in the life of adventure — but there is always the weather. It has started to rain — one of the mountain’s famous summer blizzards, a deadly hazard threatening to melt the stakes loose. Paul, with the ice melting under her rapidly, frantically unburies the stakes and carves an even deeper hole for the anchor. The leverage system is at last in place and can begin hauling Eric up — as soon as Trish unclips herself from the rope.

This being a Rube Goldberg machine of disaster, Trish can’t unclip — pulled asunder in opposite directions by the rope stretched between the anchor and Eric, her carabiner is strained by too much pressure to release. The rain is now not only melting the snow, but soaking Eric — if alive at all, this puts him at severe risk of hypothermia. Paul decides to throw a knife to Trish so that she can cut the harness and release herself. Once again, tragedy and comedy conspire:

Trish was on the national champion Frisbee team. She knew how to throw. And she knew that I did not, because she had, on a few occasions at least, attempted to teach me to throw a Frisbee. The attempts had been a disaster. The Frisbee had careered off to one side repeatedly. Or it had dropped sadly to the ground in front of me. On one or two occasions it had even disappeared behind me.

But a knife is not a Frisbee. And I had seen enough movies to know that when a knife is tossed by the hero to someone in need, it lands exactly where it should. So I picked up the knife, and I centered myself. “Be the hero,” I whispered.

I inhaled a deep breath. I brought my arm back. Exhaling, I tossed the knife.

It landed fifteen feet wide, disappearing into the snow. “AAARRRGGHH,” I yelled in disbelief.

“AAAARRRGGHH,” Trish yelled, with the same vigor.

This was not a movie, it turned out. This was real life and in real life I remained a nincompoop who couldn’t throw a Frisbee or a knife.

Somehow, Trish manages to release herself. But just as she begins climbing toward Paul, she is swallowed by the snow — another crevasse. By a superhuman exertion, she manages to swing her legs up, pulls herself onto the edge, and rolls over to the side, trying to keep as still as possible on the feeble snow, with the crevasse gaping beneath her. There is still Eric to save. Paul recounts:

Both Trish and I were tied into the anchor I had set. But would the anchor hold with the falling weight of all three of us? I doubted it. But that scenario was unthinkable, so I did what all people do when they need to concentrate on the task at hand with a clear mind and steady hand. I un-thinked it.

Trish and I began to pull on the Thankyouthankyouthankyou. It was slow going. The rope bit into the soft and mushy snow, hampering our progress immensely. We pulled and pulled, the rope sank and sank, and little by little by little Eric and his sled began to rise. But it was too slow, and we knew it.

Then tiny dots appeared on the horizon. The dots snaked quickly toward us, enlarging into people. It was a team of climbers, descending the mountain!


Both relieved and mortified, Paul faces her saviors:

We were staring at two female mountaineers, genuine kick-ass gals, shining examples of superhero skill, and at that moment very disgusted with us. They threw us a withering look: You got yourself in this situation and you can’t get yourself out? With a yawn, and a slow, stern shake of her superhero head, one of the women guides unspooled a rope from her back. She commanded her ten clients to grip that rope with their hands. Then she clipped in.

Now this seemed a little unfair. No anchor in the soft mushy snow? No Thankyouthankyouthankyou? Just the twenty hands of ten eager climbers. But I swallowed my pride and watched as the kick-ass woman guide rappelled (a technique climbers use to descend a rope) into the crevasse, while her clients held fast. We waited. Five minutes later she jugged (a technique climbers use to ascend a rope) her way back up.

“He’s alive,” she said in the same tone of voice you might use to say Pass the Butter, or Two Plus Two Equals Four. And why not? As a kick-ass superhero mountaineer she had seen many things, it was clear, and being alive was the most normal of them. Then she added, “But there’s blood all down the walls. Let’s do this fast.” In the same Pass the Butter voice she commanded her clients to pull on the rope, now attached to Eric… The woman guides called their team to attention, then tilted their square chins at us and, in the tradition of superheroes everywhere, skied away with hardly a word.

Paul tampers the story with the necessary nuances of real life, where outcomes aren’t allotted to the binary model of tragic deaths and happy endings — Eric had sustained a concussion, a fractured vertebrae, and a head gash that would require eighty stitches, and his recovery was slow. But the experience had taught her invaluable lessons that transcend the realm of mountain-climbing and apply to everything from entrepreneurship to love — about the line between courage and cockiness, about how we lacerate ourselves on our own misguided expectations, about the price of pride and the cost of overconfidence.


In the remainder of The Gutsy Girl, Paul goes on to chronicle the thrills and takeaways of adventures ranging from kayaking the rough Adriatic Sea to her days as a working firefighter. Complement it with her very differently wonderful memoir for grownups, Lost Cat, then revisit psychologist Carol Dweck on the two basic mindsets that shape our lives.

Illustrations courtesy of Wendy MacNaughton / Bloomsbury


Gardening and the Secret of Happiness

“It came to me while picking beans, the secret of happiness.”

Gardening and the Secret of Happiness

“This is happiness,” Willa Cather’s fictional narrator gasps as he sinks into his grandmother’s garden, “to be dissolved into something complete and great.” A generation later, in a real-life counterpart, Virginia Woolf arrived at the greatest epiphany of her life — and to this day perhaps the finest definition of what it takes to be an artist — while contemplating the completeness and greatness abloom in the garden.

Nearly a century later, botanist and nature writer Robin Wall Kimmerer, who has written beautifully about the art of attentiveness to life at all scales, examines the revelations of the garden in Braiding Sweetgrass: Indigenous Wisdom, Scientific Knowledge and the Teachings of Plants (public library) — an unusual and richly rewarding book blending botany, Native American mythology, natural history, and philosophy.

In a particularly enchanting passage, Kimmerer, who fuses her scientific training with her Native American storytelling heritage, considers happiness as a sort of reciprocity between the Earth and the human spirit — a gladdening mutuality of affections and animacy:

It came to me while picking beans, the secret of happiness.

I was hunting among the spiraling vines that envelop my teepees of pole beans, lifting the dark-green leaves to find handfuls of pods, long and green, firm and furred with tender fuzz. I snapped them off where they hung in slender twosomes, bit into one, and tasted nothing but August, distilled into pure, crisp beaniness… By the time I finished searching through just one trellis, my basket was full. To go and empty it in the kitchen, I stepped between heavy squash vines and around tomato plants fallen under the weight of their fruit. They sprawled at the feet of the sunflowers, whose heads bowed with the weight of maturing seeds.

Illustration by Emily Hughes from Little Gardener

Mid-stride in the garden, Kimmerer notices the potato patch her daughters had left off harvesting that morning. She twines this communion with the land and the commitment of good parenthood in a beautiful meditation on what it means to care for, to be a steward of, to love — be it a child or Mother Earth:

They complain about garden chores, as kids are supposed to do, but once they start they get caught up in the softness of the dirt and the smell of the day and it is hours later when they come back into the house. Seeds for this basket of beans were poked into the ground by their fingers back in May. Seeing them plant and harvest makes me feel like a good mother, teaching them how to provide for themselves.


How do I show my girls I love them on a morning in June? I pick them wild strawberries. On a February afternoon we build snowmen and then sit by the fire. In March we make maple syrup. We pick violets in May and go swimming in July. On an August night we lay out blankets and watch meteor showers. In November, that great teacher the woodpile comes into our lives. That’s just the beginning. How do we show our children our love? Each in our own way by a shower of gifts and a heavy rain of lessons.

Maybe it was the smell of ripe tomatoes, or the oriole singing, or that certain slant of light on a yellow afternoon and the beans hanging thick around me. It just came to me in a wash of happiness that made me laugh out loud, startling the chickadees who were picking at the sunflowers, raining black and white hulls on the ground. I knew it with a certainty as warm and clear as the September sunshine. The land loves us back. She loves us with beans and tomatoes, with roasting ears and blackberries and birdsongs. By a shower of gifts and a heavy rain of lessons. She provides for us and teaches us to provide for ourselves. That’s what good mothers do.

I was reminded of this passage from the altogether bewitching Braiding Sweetgrass by a mention in Kimmerer’s terrific On Being conversation with Krista Tippett — listen and revel below:

[The] kind of deep attention that we pay as children is something that I cherish, that I think we all can cherish and reclaim — because attention is the doorway to gratitude, the doorway to wonder, the doorway to reciprocity. And it worries me greatly that today’s children can recognize 100 corporate logos and fewer than 10 plants. That means they’re not paying attention.

Complement with Mary Oliver — another patron saint of listening and of the Earth — on what it really means to pay attention, then revisit Kimmerer’s exquisite writings about the magic of moss and how naming confers dignity upon existence.


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