Brain Pickings

Posts Tagged ‘culture’

16 APRIL, 2012

How 17 Equations Changed the World

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What Descartes has to do with C. P. Snow and the second law of thermodynamics.

When legendary theoretical physicist Stephen Hawking was setting out to release A Brief History of Time, one of the most influential science books in modern history, his publishers admonished him that every equation included would halve the book’s sales. Undeterred, he dared include E = mc², even though cutting it out would have allegedly sold another 10 million copies. The anecdote captures the extent of our culture’s distaste for, if not fear of, equations. And yet, argues mathematician Ian Stewart in In Pursuit of the Unknown: 17 Equations That Changed the World, equations have held remarkable power in facilitating humanity’s progress and, as such, call for rudimentary understanding as a form of our most basic literacy.

Stewart writes:

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us… This is the story of the ascent of humanity, told in 17 equations.

From how the Pythagorean theorem, which linked geometry and algebra, laid the groundwork of the best current theories of space, time, and gravity to how the Navier-Stokes equation applies to modeling climate change, Stewart delivers a scientist’s gift in a storyteller’s package to reveal how these seemingly esoteric equations are really the foundation for nearly everything we know and use today.

Greek stamp showing Pythagoras's theorem

But the case for why we should even care about equations — and mathematics, and science in general — goes back much further. In 1959, physicist and novelist C. P. Snow lamented — as Jonah Lehrer did half a century later — the tragic divergence of the sciences and humanities in his iconic lecture, The Two Cultures:

A good many times I have been presented at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: ‘Have you ever read a work of Shakespeare’s?’

Snow later added:

I now believe that if I had asked an even simpler question — such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, ‘Can you read?’ — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their Neolithic ancestors would have had.

It is no coincidence, then, that some of the most revolutionary of the breakthroughs Stewart outlines came from thinkers actively interested in both the sciences and the humanities. Take René Descartes, for instance, who is best remembered for his timeless soundbite, Cogito ergo sumI think, therefore I am. But Descartes’ interests, Stewart points out, extended beyond philosophy and into science and mathematics. In 1639, he observed a curious numerical pattern in regular solids — what was true of a cube was also true of a dodecahedron or an icosahedron, for all of which subtracting from the number of faces the number of edges and then adding the number of vertices equaled 2. (Try it: A cube has 6 faces, 12 edges, and 8 vertices, so 6 – 12 + 8 = 2.) But Descartes, perhaps enchanted by philosophy’s grander questions, saw the equation as a minor curiosity and never published it. Only centuries later mathematicians recognized it as monumentally important. It eventually resulted in Euler’s formula, which helps explain everything from how enzymes act on cellular DNA to why the motion of the celestial bodies can be chaotic.

So how did equations begin, anyway? Stewart explains:

An equation derives its power from a simple source. It tells us that two calculations, which appear different, have the same answer. The key symbol is the equals sign, =. The origins of most mathematical symbols are either lost in the mists of antiquity, or are so recent that there is no doubt where they came from. The equals sign is unusual because it dates back more than 450 years, yet we not only know who invented it, we even know why. The inventor was Robert Recorde, in 1557, in The Whetstone of Witte. He used two parallel lines (he used an obsolete word gemowe, meaning ‘twin’) to avoid tedious repetition of the words ‘is equal to’. He chose that symbol because ‘no two things can be more equal’. Recorde chose well. His symbol has remained in use for 450 years.

The original coinage appeared as follows:

To avoide the deiouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a paire of paralleles, or gemowe lines of one lengthe: =, bicause noe .2. thynges, can be moare equalle.

Far from being a mere math primer or trivia aid, In Pursuit of the Unknown is an essential piece of modern literacy, wrapped in an articulate argument for why this kind of knowledge should be precisely that.

Stewart concludes by turning his gaze towards the future, offering a kind of counter-vision to algo-utopians like Stephen Wolfram and making, instead, a case for the reliable humanity of the equation:

It is still entirely credible that we might soon find new laws of nature based on discrete, digital structures and systems. The future may consist of algorithms, not equations. But until that day dawns, if ever, our greatest insights into nature’s laws take the form of equations, and we should learn to understand them and appreciate them. Equations have a track record. They really have changed the world — and they will change it again.

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16 APRIL, 2012

The Geometry of God: The Striking Kaleidoscopic Patterns of European Cathedral Ceilings

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Photographer David Stephenson captures architectural triumphs at the intersection of art and mathematics.

If you’ve ever set foot in one of Europe’s Gothic or Romanesque cathedrals and looked up, you likely found yourself spellbound by the striking vaulted ceilings. If you haven’t, photographer David Stephenson allows you to do so vicariously with his Heavenly Vaults project — a series of magnificent kaleidoscopic photos that capture the singular blend of ethereal magic and patterned precision in these architectural triumphs at the intersection of art and mathematics, flattening the vaulted ceilings and distilling them to their essential shapes, recurring fractal-like patterns, and intricate detailing.

Many of these structures, particularly the Gothic cathedrals, were constructed in an era actively occupied with ordering the heavens and expressed in their mathematical nature was a microcosm model of the universe — perhaps a paradoxical proposition that rationality and logic could explain or convey the might of God to which these temples of worship aimed to attest.

Heavenly Vaults is a follow-up to Stephenson’s 2005 book, Visions of Heaven: The Dome in European Architecture. More of Stephenson’s stunning images can be seen on his site.

Visual News It’s Nice That

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13 APRIL, 2012

Magic Hours: Tom Bissell on the Secrets of Creators and Creation

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“To create anything… is to believe, if only momentarily, you are capable of magic.”

Creativity is a peculiar beast. Its nebulous nature and elusive allure don’t stop us from going after it with stubborn precision, tracing its history, dissecting its neuroscience, flowcharting our way to it and itemizing it into a 5-point plan, all in the hope that, if only we understood its inner workings enough and engineered the right conditions, it would bestow its gifts upon us.

But, as any creator would attest, there are factors at play well outside our control.

From McSweeney’s and Tom Bissell, one of the finest essayists writing today, comes Magic Hours: Essays on Creators and Creation — a collection of fourteen essays originally published in arbiters of literary culture such as The New Yorker, Believer, and Harper’s Magazine, spanning a decade of Bissell’s best writing and dissecting the creative process through such diverse subjects as Werner Herzog’s films, video game voiceovers, Iraq war documentaries, sitcoms, and David Foster Wallace.

In the first essay, entitled “Unflowered Aloes” and originally published in the Boston Review in 2000, a 25-year-old Bissell takes apart the myth that literature is destiny and demonstrates, through the works of Herman Melville, Emily Dickinson, and William Faulkner that luck — or what the Jewish call Schlimazeltov — might be the most valuable bargaining chip in whether a creative work survives and goes on to become a cultural icon.

Take Melville’s Moby-Dick, for instance. The first true American novel was a literary flop when it was first published in 1851, sliding out of print some 36 years with a scant total of 3,180 copies sold and sending Melville into a depression from which he never quite recovered. When Oxford University Press attempted to resuscitate the novel in 1907, they asked Joseph Conrad to write the introduction, but he dismissed it as “a rather strained rhapsody with whaling for its subject and not a single sincere line in the 3 volumes of it.” Then, one day in 1916, the influential critic Carl Van Doren stumbled upon a dusty copy of Moby-Dick in a used bookstore and was inspired to write an essay about it, calling Melville’s work “one of the greatest sea romances in the whole literature of the world.” D. H. Lawrence happened to read the essay and, through a few more clicks of the Rube Goldberg serendipity machine at play, it made its way, extolled, into E. M. Foster’s Aspects of the Novel in 1927. Thus, Bissell reminds us, “Melville’s greatest work, as we today know it, was born 76 years after its initial publication.”

Emily Dickinson and William Faulkner suffered a similar fate, their works mere seashells washed ashore the island of literary recognition by the capricious currents of the vast and all-engulfing ocean of chance. Bissell concludes the essay, which is titled after a plant that may live as long as 100 years and might never flower at all, with an observation that could be very glib or very optimistic, depending on how you look at it:

What faith, then, can the poet or novelist place in his or her work’s survival? Is literary destiny simply yet another god that failed? Although I know what I now believe, I hope I am wrong. Nevertheless, I cannot help but imagine that literature is an airplane, and we are passengers on it. One might assume that behind the flimsy accordion door sit pilots of skill and accomplishment. But the cockpit is empty. It was always been empty. The controls are abandoned. They have always been abandoned. One needs only to touch them to know how mutable our course.

But in this discomfiting awareness lies perhaps the self-selective secret of literature’s creators. In another essay, “Grief and the Outsider” (2003), Bissell observes:

Literature is always written by outsiders… by a person inclined not towards connecting with those around him or her but retreating into a world of nerdily private dream… To write is to fail, more or less, constantly.

This, then, begs the question — a question Bissell asks, and answers, in “Writing about Writing about Writing” (Believer, 2004):

Can writing be taught?… Of course writing can be taught… All human activity is taught. The only thing any human being is born to do is survive, and even in this we all need several years of initial guidance.

Harder to judge is the possibility of teaching a beginning writer how to be receptive to the very real emotional demands of creating literature. To write serious work is to reflexively grasp abstruse matters such as moral gravity, spiritual generosity, and the ability to know when one is boring the reader senseless, all of which are founded upon a distinct type of aptitude that has little apparent relation to more measurable forms of intelligence. Plenty of incredibly smart people cannot write to save their lives. Obviously, writerly intelligence is closely moored to the mature notion of intellect (unlike math or music, the adolescent prodigy is virtually unknown to literature) because writing is based on a gradual development of psychological perception, which takes time and experience. Writing can be taught, then, yes—but only to those who are teachable.

The essay goes on to discuss — to critique, to revere, to ponder, but mostly to critique — such classic writings about writing as Anne Lamott’s Bird by Bird, Stephen King’s On Writing, and even Snoopy’s Guide to the Writing Life, distilling them into astute observation of what we intuitively know to be true but rarely dare let ourselves believe:

Writers who fail are not pathetic; they are people who have attempted to do something incredibly difficult and found they cannot. Human longing exists in every person, along every frequency of accomplishment. It is the delusions endemic to bad writers and bad writing that need to be destroyed. Here are a few: Writing well will get you girls, or boys, or both. Writing well will make you happy. Fame and wealth are good writing’s expected rewards. Writing for a living is somehow nobler than what most people do. What needs to be reinforced is the idea that good writing — solid, honest, entertaining, beautiful good writing — is simultaneously the reward, the challenge, and the goal.

The most heartening insight in Magic Hours, however, comes at the very beginning. As if to immunize the reader with an antidote to some of the grimmer observations that follow, Bissell offers in the author’s note preceding the essays:

To create anything — whether a short story or a magazine profile or a film or a sitcom — is to believe, if only momentarily, you are capable of magic. These essays are about that magic — which is sometimes perilous, sometimes infectious, sometimes fragile, sometimes failed, sometimes infuriating, sometimes triumphant, and sometimes tragic. I went up there. I wrote. I tried to see.

In creation — as in love — it seems timing is if not everything, then at least very much indeed. Yet without integrity and dedication even the most impeccable of timing would be devoid of magic.

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