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Standing on the Shoulders of Giants: The Story Behind Newton’s Famous Metaphor for How Knowledge Progresses

How hubris and humility conspired in illuminating the nature of creativity.

Standing on the Shoulders of Giants: The Story Behind Newton’s Famous Metaphor for How Knowledge Progresses

“Newton was so right about so many things,” cosmologist Janna Levin wrote in her magnificent meditation on madness and genius, “that it seems ungenerous to dwell on where he was wrong.” And yet in his day, even his most revolutionary rightness — especially his revolutionary rightness — was met with ungenerous opposition by his smaller-spirited peers. Chief among them was the English polymath Robert Hooke, whose famous rivalry with Newton resulted in humanity’s finest metaphor for how knowledge grows.

Science writer extraordinaire James Gleick, in his biographical masterwork Isaac Newton (public library), calls Hooke “Newton’s most enthusiastic antagonist,” his “goad, nemesis, tormentor, and victim.” Hooke, generally known for his curmudgeonly temperament and cynical disposition, reserved an especially caustic contempt for Newton, whose youthful genius aggrieved Hooke and aggravated his vain ego.


Where Hooke presented his ideas with unabashed hubris, Newton delivered his with humility — even if it was at times a false humility, for he too was a man animated by great ambition and in possession of a robust ego, it still stemmed from a hard realism about the fact that knowledge progresses not toward the definitive but toward the infinite.

Where Hooke bombastically proclaimed in his treatise on microscopes that “there is nothing so small, as to escape our inquiry,” Newton reported his own experiments on microscopy with the grounding caveat that the future would bring new instruments capable of magnifying four thousand times more powerfully, eventually making even the atom visible. Hooke, of course, was wrong and Newton right — something evidenced by our still-evolving understanding of matter five centuries later.

Newton’s humility sprang from an early and formative understanding of how knowledge builds upon itself, incrementally improving upon existing ideas until the cumulative adds up to the revolutionary. From a young age, he kept a commonplace book — a gift from his father, in which he copied passages from the books he read and supplemented them with extensive notes of his own, thus transmuting existing knowledge into original ideas. He named it his “Waste Book” — a testament to usefulness of useless knowledge and the combinatorial nature of creativity, or what his twentieth-century counterpart, Albert Einstein, would come to call “combinatory play.” This ability to originate by way of connection became the basic infrastructure of Newton’s mind — his singular superpower of perception.

Gleick writes:

When he observed the world it was as if he had an extra sense organ for peering into the frame or skeleton or wheels hidden beneath the surface of things. He sensed the understructure. His sight was enhanced, that is, by the geometry and calculus he had internalized. He made associations between seemingly disparate physical phenomena and across vast differences in scale. When he saw a tennis ball veer across the court at Cambridge, he also glimpsed invisible eddies in the air and linked them to eddies he had watched as a child in the rock-filled stream at Woolsthorpe. When one day he observed an air-pump at Christ’s College, creating a near vacuum in a jar of glass, he also saw what could not be seen, an invisible negative: that the reflection on the inside of the glass did not appear to change in any way. No one’s eyes are that sharp… He communed night and day with forms, forces, and spirits, some real and some imagined.

Hooke was different. The friction between the two men began even before Newton was elected a Fellow of the Royal Society in 1672. The previous year, the Society, where Hooke was curator of experiments, asked for a demonstration of the reflecting telescope Newton had invented three years earlier — known today as a Newtonian telescope, this then-revolutionary optical device for astronomical observation was significantly smaller than the refracting telescope that preceded it and used two mirrors instead of a lens to form an image by reflecting light. The invention led Newton to develop an entire theory of colors (which would later inspire Goethe’s theory of color and emotion).

Hooke immediately pounced on Newton’s ideas, dismissing them as mere “hypothesis” — a term Newton found particularly offensive. Hooke also boasted in private correspondence with members of the Royal Society that he had invented an even smaller and more powerful telescope himself three years before Newton, but hadn’t bothered to actually build it on account of the Great Plague that ravaged London at the time.

'Robert Hooke' at home by Rita Greer
‘Robert Hooke’ at home by Rita Greer

Fifteen months after he was elected to the Royal Society, Newton decided to withdraw from public debate — the incessant obstructionism by Hooke and other critics, who still remained merely epistolary bullies he was yet to meet in person, had started to wear down his sanity. Gleick writes:

He had discovered a great truth of nature. He had proved it and been disputed. He had tried to show how science is grounded in concrete practice rather than grand theories. In chasing a shadow, he felt, he had sacrificed his tranquillity.

But the private rivalry persisted. In 1675, Hooke alleged to have discovered what we now know as diffraction — the way light bends around a sharp edge. At the time, the nature of light was a mystery — some, like Descartes, considered it a particle, while others, like Hooke, thought it the product of motion. Because if an obstacle like an edge could stand in light’s path and bend it, diffraction supported the motion model, implying that light is a wave rather than a particle. (Today, we know that light can be both a particle and a wave, depending on how we measure it.)

“Beams of Light Through Glass” by pioneering photographer Berenice Abbott from her 1958 creative collaboration with MIT, Physical Sciences Study Project

This development excited Newton but, his mind by now an enormous commonplace book of knowledge, he recalled having read about diffraction experiments by a French Jesuit theologist, who built upon earlier ideas by a Bolognese mathematician — long before Hooke claimed the invention. He similarly challenged Hooke’s claims to originality in other aspects of the properties of light, urging the Royal Society to “cast out what [Hooke] has borrowed from Des Cartes or others.”

This recognition of the incremental, combinatorial character of knowledge came naturally to Newton, but even though the invention of the Gutenberg press two centuries earlier embodied it perfectly, it was still radical at the time. Gleick writes:

The idea of knowledge as cumulative — a ladder, or a tower of stones, rising higher and higher — existed only as one possibility among many. For several hundred years, scholars of scholarship had considered that they might be like dwarves seeing farther by standing on the shoulders of giants, but they tended to believe more in rediscovery than in progress.

This notion was particularly infuriating to Hooke, who saw any connection of his ideas to earlier ones not as a natural function of how science progresses but as an affront to his originality. He hungered to be seen as a giant — not as a dwarf who stood on the shoulders of giants — but hid his egomaniacal impulses behind the pretense of deference. He assured Newton that he was uninterested in a feud, that their experiments “aim both at the same thing which is the Discovery of truth” and as “two hard-to-yield contenders,” they should be able to “both endure to hear objections.”

And so, in their epistolary sparring, Newton’s famous metaphor was born — between pats of politesse, he delivered his legendary slap. Calling Hooke a “true Philosophical spirit,” he invited him to sort out their differences in private correspondence rather the public debate. In a letter penned on February 5, 1675, Newton wrote:

What’s done before many witnesses is seldome without some further concern than that for truth: but what passes between friends in private usually deserves the name of consultation rather than contest, & so I hope it will prove between you & me.


What Des-Cartes did was a good step. You have added much several ways, & especially in taking the colours of thin plates into philosophical consideration. If I have seen further it is by standing on the sholders of Giants.

Isaac Newton's famous letter to Robert Hooke, February 5, 1675 (Historical Society of Pennsylvania)
Isaac Newton’s famous letter to Robert Hooke, February 5, 1675 (Historical Society of Pennsylvania)

Hooke, who as far as it is known never replied, maintained an antagonistic attitude toward Newton for the remainder of his life. However vast his intellect may have been, he revealed himself as far from a giant, for it is the mark of a small spirit to hide behind one-directional criticism while fleeing from intelligent two-way discourse.

As for the metaphor itself, it too is a meta-testament to Newton’s point — although he popularized it and immortalized it in his iconic language, it originated at least five centuries earlier and underwent several transmutations, including a famous one in Robert Burton’s 1621 masterpiece The Anatomy to Melancholy.

Gleick considers how Newton’s famous proclamation frames his paradoxical life and immensely far-reaching legacy:

Isaac Newton said he had seen farther by standing on the shoulders of giants, but he did not believe it. He was born into a world of darkness, obscurity, and magic; led a strangely pure and obsessive life, lacking parents, lovers, and friends; quarreled bitterly with great men who crossed his path; veered at least once to the brink of madness; cloaked his work in secrecy; and yet discovered more of the essential core of human knowledge than anyone before or after. He was chief architect of the modern world. He answered the ancient philosophical riddles of light and motion, and he effectively discovered gravity. He showed how to predict the courses of heavenly bodies and so established our place in the cosmos. He made knowledge a thing of substance: quantitative and exact. He established principles, and they are called his laws.

Solitude was the essential part of his genius. As a youth he assimilated or rediscovered most of the mathematics known to humankind and then invented the calculus — the machinery by which the modern world understands change and flow — but kept this treasure to himself. He embraced his isolation through his productive years, devoting himself to the most secret of sciences, alchemy. He feared the light of exposure, shrank from criticism and controversy, and seldom published his work at all. Striving to decipher the riddles of the universe, he emulated the complex secrecy in which he saw them encoded…

“I don’t know what I may seem to the world,” he said before he died, “but, as to myself, I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”

Gleick’s Isaac Newton (public library) remains not only one of the finest biographies ever written, but a foundational text for anyone seeking to understand how the modern world as we know it came into view. Complement it with Hegel on knowledge and the true task of the human mind.


Sylvia Plath on Privilege, Free Will, and What Makes Us Who We Are

“I: how firm a letter; how reassuring the three strokes: one vertical, proud and assertive, and then the two short horizontal lines in quick, smug succession.”

One of our our basic human biases is the tendency to take credit for our successes as a function of our personal excellence and to attribute out failures to external circumstances. Privilege is problematic precisely because it leads the privileged to believe that their advantages in life are entirely earned and the disadvantages of the less fortunate entirely merited, when in reality powerful cultural currents can carry us in either direction based on cultural, political, and economic forces wholly external to our character, ability, and personal worth. But when all of our external conditions are stripped away, be they fortuitous or wretched, who are we in our innermost personhood? What erects the geometry of the “I”?

That’s what young Sylvia Plath (October 27, 1932–February 11, 1963) addresses in a characteristically poignant and exquisitely self-aware passage from The Unabridged Journals of Sylvia Plath (public library) — the same terrific volume that gave us the precocious poet on finding nonreligious divinity in nature, her exuberant celebration of curiosity, and her thoughts on life, death, hope and happiness.

In a journal entry from the autumn of 1950, eighteen-year-old Plath considers free will, the blinders of privilege, and what makes us who we are. She writes:

What do I know of sorrow? No one I love has ever died or been tortured. I have never wanted for food to eat, or a place to sleep. I have been gifted with five senses and an attractive exterior. So I can philosophize from my snug little cushioned seat. So I am going to one of the most outstanding colleges in America; I am living with two thousand of the most outstanding girls in the United States. What have I to complain about? Nothing much. The main way I can add to my self-respect is by saying that I’m on scholarship, and if I hadn’t exercised my free will and studied through high school I never would be here. But when you come right down to it, how much of that was free will? How much was the capacity to think that I got from my parents, the home urge to study and do well academically, the necessity to find an alternative for the social world of boys and girls to which I was forbidden acceptance? And does not my desire to write come from a tendency toward introversion begun when I was small, brought up as I was in the fairy-tale world of Mary Poppins and Winnie-the-Pooh? Did not that set me apart from most of my school mates? — the fact that I got all A’s and was “different” from the rough-and-tumble Conways — how I am not quite sure, but “different” as the animal with the touch of human hands about him when he returns to the herd. All this may be a subtle way of egoistically separating myself from the common herd, but take it for what it’s worth.

Illustration by Olivier Tallec from Louis I, King of the Sheep

A year earlier, Plath had written in a letter to her mother: “I want to be free — free to know people and their backgrounds — free to move to different parts of the world so I may learn that there are other morals and standards besides my own.” Now, it is with this empathetic curiosity and acute awareness of how different cultural backgrounds manifest different foregrounds of personhood that she returns to the question of free will in her journal:

As for free will, there is such a narrow crack of it for man to move in, crushed as he is from birth by environment, heredity, time and event and local convention. If I had been born of Italian parents in one of the caves in the hills I would be a prostitute at the age of 12 or so because I had to live (why?) and that was the only way open. If I was born into a wealthy New York family with pseudo-cultural leanings, I would have had my coming-out party along with the rest of them, and be equipped with fur coats, social contacts, and a blasé pout. How do I know? I don’t; I can only guess. I wouldn’t be I. But I am I now; and so many other millions are so irretrievably their own special variety of “I” that I can hardly bear to think of it. I: how firm a letter; how reassuring the three strokes: one vertical, proud and assertive, and then the two short horizontal lines in quick, smug succession. The pen scratches on the paper … I … I … I … I … I … I.

The Unabridged Journals of Sylvia Plath is a remarkable read in its entirety — a masterwork both of philosophy at its rawest and of prose at its most refined. Complement this particular passage with cosmologist Janna Levin on the perplexity of free will, C.S. Lewis on what it means to have a free will in a universe of fixed laws, and philosopher Rebecca Goldstein on the mystery of personal identity, then revisit Plath on the creative benefits of keeping a journal, her little-known children’s book illustrated by the great Quentin Blake, and her beautiful and heartbreaking reading of the poem “A Birthday Present.”


The Central Mystery of Quantum Mechanics, Animated

How a lineage of scientists pieced together the puzzle revealing the dual nature of the universe.

Ever since Heisenberg stood on the shoulders of giants to pave the way for quantum mechanics, this captivating branch of science and its central fact — that light can behave both as a particle and as a wave — has challenged us to grapple with the perplexing duality of the universe, inspiring everything from critical questions about the future of science to mind-bending meditations at the intersection of theology and astrophysics to philosophical children’s books.

That central mystery of quantum mechanics is what particle physicist Chad Orzel, author of the illuminating and intelligently entertaining How to Teach Quantum Physics to Your Dog (public library), explores in this animated primer from TED Ed.

Orzel writes in the book:

Classical physics is the physics of everyday objects — tennis balls and squeaky toys, stoves and ice cubes, magnets and electrical wiring… Modern physics describes the stranger world that we see when we go beyond the everyday… Modern physics is divided into two parts, each representing a radical departure from classical rules. One part, relativity, deals with objects that move very fast, or are in the presence of strong gravitational forces… The other part of modern physics is what I talk to my dog about.

He points out that quantum mechanics is woven into the very fabric of modern life:

Without an understanding of the quantum nature of the electron, it would be impossible to make the semiconductor chips that run our computers. Without an understanding of the quantum nature of light and atoms, it would be impossible to make the lasers we use to send messages over fiber-optic communication lines.

Quantum theory’s effect on science goes beyond the merely practical — it forces physicists to grapple with issues of philosophy. Quantum physics places limits on what we can know about the universe and the properties of objects in it. Quantum mechanics even changes our understanding of what it means to make a measurement. It requires a complete rethinking of the nature of reality at the most fundamental level.

Quantum mechanics describes an utterly bizarre world, where nothing is certain and objects don’t have definite properties until you measure them. It’s a world where distant objects are connected in strange ways, where there are entire universes with different histories right next to our own, and where “virtual particles” pop in and out of existence in otherwise empty space.

Quantum physics may sound like the stuff of fantasy fiction, but it’s science. The world described in quantum theory is our world, at a microscopic scale. The strange effects predicted by quantum physics are real, with real consequences and applications.

Those consequences and applications are what Orzel goes on to explore in the wholly fascinating How to Teach Quantum Physics to Your Dog. Complement it with Alice in Quantumland, an allegorical explanation of quantum mechanics inspired by Lewis Carroll, then revisit TED Ed’s stimulating animated primers on what makes a hero, how you know you exist, why playing music benefits your brain more than any other activity, how melancholy enhances creativity, why bees build perfect hexagons, and Plato’s parable for the nature of reality.


Oliver Jeffers on the Paradox of Ownership and the Allure of Duality

“We only own something because everybody agrees that we do.”

Oliver Jeffers is one of the most talented and thoughtful children’s book authors and artists of our time. Whether he is exploring love and loss in his unusual stories for young readers or the facts and fictions of memory in his fine art, undergirding his work is a deep fascination with duality and paradox.

In the foreword to the magnificent monograph Neither Here Nor There: The Art of Oliver Jeffers, Richard Seabrook remarks on this recurring theme, “the concept that something can mean one thing to one person, and something entirely different to another.” Nowhere does this come more vibrantly alive than in Jeffers’s This Moose Belongs to Me (public library) — a disarming story about a boy who believes he owns his pet moose Marcel, only to discover that so do other people, who call him by different names, while the moose himself doesn’t quite get the concept of being owned and is thus oblivious to the boy’s list of rules for being a good pet.

What emerges is an allegory for our rather human tendency to dig in our heels when things don’t go our way, forgetting Henry Miller’s timeless taunt — “And your way, is it really your way?” — and snapping into self-righteousness. When the moose doesn’t obey the rules of being a pet, the boy storms off “embarrassed and enraged” — another curious psychoemotional duality the richness of which Jeffers captures with great economy of words.

Sometimes the moose wasn’t a very good pet. He generally ignored Rule 7: going whichever way Wilfred wanted to go.

But the story is, above all, a parable about the nature of ownership as a mutually agreed upon figment and the comical sense of entitlement it engenders. What makes it especially enchanting is the conceptual meta-message — for the backgrounds of his illustrated vignettes, Jeffers reapporpriates classical landscape paintings by a mid-century Slovakian painter named Alexander Dzigurski, rendering the project a sort of posthumous collaboration and a creative mashup of which Montaigne would have approved.

Jeffers’s message is subtle but resounding: In art — as in science, as in all of human culture — the ideas we call our own are but the combinatorial product of countless borrowings from the intellectual “property” of others. Perhaps Mark Twain put it best in his supportive letter to Helen Keller when she was accused of plagiarism: “Substantially all ideas are second-hand, consciously and unconsciously drawn from a million outside sources.”

With another delightfully thoughtful touch, Jeffers reminds us that these borrowings can come not only from others but from ourselves — in one of the scenes, the lumberjack-bear protagonist of his previous book, The Great Paper Caper, makes a cameo against the backdrop of a borrowed landscape painting.

In his wholly wonderful Design Matters conversation with Debbie Millman, Jeffers tells the story of this moosely mashup and how he tracked down the grandson of the Slovakian painter for permissions, then reflects on the deeper elements of duality in his body of work. Transcribed highlights below — please enjoy:

On the conceptual confluences that sprouted This Moose Belongs to Me, which was essentially Arthur Koestler’s seminal bisociation theory of creativity in action:

I was reading, at that time, a history of Manhattan and I read about the sale of Manhattan to the Dutch. And the natives who were on the land were like, “Yeah, sure, you can buy it!” But nobody really owns land anyway, so they had to leave — and that was to the great confusion of the Dutch… There was an element of truth in that… We only own something because everybody agrees that we do.

I just thought this was a really interesting concept and applied it to owning a pet…

And then, when I was sketching the drawings … I knew that I wanted to use oil paintings… and I’d started off making all those oil paintings… At that point, I glanced over my studio and there were all of these old landscape paintings lined up for another project. And I’m thinking about this story, and the rules of how to be a good pet, and the moose doesn’t really get that he’s supposed to be a pet — and two things connected to each other. And I thought, “Well, if it is about ownership, then I should probably just reappropriate these paintings into this book… It seems conceptually a fit.”


The book ended up mostly being a collaboration between me and this long-ago dead guy.

On the roots of his obsession with duality and its particular manifestation in a collaboration with a doctor of quantum physics around the famed fact that light can appear to be both a particle and a wave, depending on how the question is asked and how the answer is measured:

There was a sense of duality I grew up with — [Belfast] was a split city, really. There was a lot of violence, but there was also a lot of happiness. And really, that being the backbone of the culture and the existence in which I grew up, and choosing to get past, I think it leaves its marks way down there.

But then, I fell in with this project with Professor Quantum Physics, and through that I discovered the actual theory of duality, which looks at light in particular — light when measured in particles becomes a particle and light when measured in waves becomes a wave. What I took from that was that it’s up to us, then, how we define it — we choose the equipment with which we measure, so therefore it’s up to us… That was what fascinated me — that we have the ability to look at anything and make it anything we want, to some degree.

That’s why I started making art about that sense of, “Can we look at things logically and emotionally, all at the same time?”

Subscribe to Design Matters here. For more of Jeffers’s magic, see Once Upon an Alphabet, which was among the best children’s books of 2014, and The Heart and the Bottle, a tender illustrated fable about what happens when we deny our difficult emotions.


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