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How Big Is Infinity? An Animated Explanation from TED

On the whimsy and limitations of mathematics.

Beloved novelist Umberto Eco believed that we use lists to make infinity comprehensible. Quantum computation pioneer David Deutsch teased apart the beginning and unboundedness of infinity. But what, exactly, is “infinity” and how big is it?

The fine folks at TED-Ed have teamed up with educator Dennis Wildfogel and animation studio Augenblick to explore the dimensions of infinity through this stimulatingly mind-bending lesson on legacies of mathematicians Georg Cantor, David Hilbet, Kurt Gödel, and Paul J. Cohen, exposing both the genius and limitations of mathematics.

For more on this fascinating subject, see George Gamow’s 1961 gem One Two Three . . . Infinity: Facts and Speculations of Science, which features more than 120 pen-and-ink illustrations by the author himself, such as this:

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Henry Miller on the Beautiful Osmosis of Giving and Receiving

“It’s only when we demand that we are hurt.”

In The Diary of Anaïs Nin, Vol. 3: 1939-1944 (public library) — which gave us her timeless and ever-timely meditations on self-publishing, what maturity really means, the difference between Paris and New York came — Nin shares a letter she received in the summer of 1942 from Henry Miller, with whom she’d been closely involved creatively, intellectually and, for a long time, romantically.

Miller, passionately articulate as ever, gets to the heart of the paradox of altruism and the beautiful osmosis of giving and receiving.

He writes:

By choosing to live above the ordinary level we create extraordinary problems for ourselves. The ultimate goal is to make this earth a paradise.

[…]

For me it is no problem to depend on others. I am always curious to see how far people will go, how big a test one can put them to.

Certainly there are humiliations involved, but aren’t these humiliations due rather to our limitations? Isn’t it merely our pride which suffers? It’s only when we demand that we are hurt. I, who have been helped so much by others, I ought to know something of the duties of the receiver. It’s so much easier to be on the giving side. To receive is much harder — one actually has to be more delicate, if I may say so. One has to help people to be more generous. By receiving from others, by letting them help you, you really aid them to become bigger, more generous, more magnanimous. You do them a service.

And then finally, no one likes to do either one or the other alone. We all try to give and take, to the best of our powers. It’s only because giving is so much associated with material things that receiving looks bad. It would be a terrible calamity for the world if we eliminated the beggar. The beggar is just as important in the scheme of things as the giver. If begging were ever eliminated God help us if there should no longer be a need to appeal to some other human being, to make him give of his riches. Of what good abundance then? Must we not become strong in order to help, rich in order to give and so on? How will these fundamental aspects of life ever change?

Complement with Amanda Palmer, many decades later, on the art of asking. More of Nin and Miller’s correspondence can be found in A Literate Passion: Letters of Anaïs Nin and Henry Miller, 1932-1953.

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Significant Objects: How Stories Confer Value Upon the Vacant

“It turns out that once you start increasing the emotional energy of inanimate objects, an unpredictable chain reaction is set off.”

“The universe is made of stories, not atoms,” poet Muriel Rukeyser famously remarked. Hardly anyone can back this bombastic proclamation with more empirical conviction than Rob Walker and Joshua Glenn. In 2009, the duo embarked upon a curious experiment: They would purchase cheap trinkets, ask some of today’s most exciting creative writers to invent stories about them, then post the stories and the objects on eBay to see whether the invented story enhanced the value of the object. Which it did: The tchotchkes, originally purchased for a total of $128.74, sold for a whopping total of $3,612.51 — a 2,700% markup. (The most highly valued pairing in the entire project, bought for $1.49 and sold for $197.50, was a globe paperweight with a moving handwritten story by the magnificent Debbie Millman, with proceeds benefiting 826 National.)

Significant Objects: 100 Extraordinary Stories About Ordinary Things (public library) tells the tale of this irreverent testament to the power of storytelling through a hundred of the best stories since the beginning of the project. The anthology features such celebrated authors as William Gibson (HAWK Ashtray, bought for $2.99, sold for $101), Jonathan Lethem (Missouri Shotglass, bought for $1, sold for $76), and Colson Whitehead (Mallet, bought for 33 cents, sold for $71).

And what better way to open than with some timeless wisdom from the inimitable Edward Gorey?

A reflection from the introduction:

Writers love a challenge like the one we posed them — i.e., making up a story inspired by an object they’ve never seen before. Our contributors met the challenge with wildly imaginative, deeply moving, and darkly ironic stories. They wrote letters, email solicitations, memoirs, operating instructions, public notices, diary entries, wine-tasting notes, and public ordinances. Some crafted rich character studies, others told tales through whipsaw dialogue or internal monologue. Some took bold experimental risks, while others opted for evocative minimalism or genre fiction.

It turns out that once you start increasing the emotional energy of inanimate objects, an unpredictable chain reaction is set off.

Part Sentimental Value, part MacGuffinism, Significant Objects reminds us of the storiness of our lived materiality — of the artifacts we imbue with meaning, with loves and losses, with hopes and desperations. At its heart is something essential and essentially human, which Brian Eno once articulated beautifully:

Nearly all of art history is about trying to identify the source of value in cultural objects. Color theories and dimension theories, golden means, all those sort of ideas, assume that some objects are intrinsically more beautiful and meaningful than others. New cultural thinking isn’t like that. It says that we confer value on things. We create the value in things. It’s the act of conferring that makes things valuable.”

Anaïs Nin put it even more dramatically when she wrote in her diary in 1943:

Stories are the only enchantment possible, for when we begin to see our suffering as a story, we are saved.

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