Brain Pickings

Love and Math: Equations as an Equalizer for Humanity

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“Mathematics is the source of timeless profound knowledge, which goes to the heart of all matter and unites us across cultures, continents, and centuries.”

French polymath Henri Poincaré saw in mathematics a metaphor for how creativity works, while autistic savant Daniel Tammet believes that math expands our circle of empathy. So how can a field so diverse in its benefits and so rich in human value remain alienating to so many people who subscribe to the toxic cultural mythology that in order to appreciate its beauty, one needs a special kind of “mathematical mind”? That’s precisely what renowned mathematician Edward Frenkel sets out to debunk in Love and Math: The Heart of Hidden Reality (public library) — a quest to unravel the secrets of the “hidden parallel universe of beauty and elegance, intricately intertwined with ours,” premised on the idea that math is just as valuable a part of our cultural heritage as art, music, literature, and the rest of the humanities we so treasure.

Frenkel makes the same case for math that philosopher Judith Butler made for reading and the humanities, arguing for it as a powerful equalizer of humanity:

Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere — no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.

Math also helps lift our blinders and break the shackles of our own prejudices:

Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in the search for truth. Georg Cantor, creator of the theory of infinity, wrote: “The essence of mathematics lies in its freedom.” Mathematics teaches us to rigorously analyze reality, study the facts, follow them wherever they lead. It liberates us from dogmas and prejudice, nurtures the capacity for innovation.

BEAUTY OF MATHEMATICS by Yann Pineill & Nicolas Lefaucheux

To illustrate why our aversion to math is a product of our culture’s bias rather than of math’s intrinsic whimsy, Frenkel offers an analogy:

What if at school you had to take an “art class” in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it. You would probably say something like this: “Learning art at school was a waste of my time. If I ever need to have my fence painted, I’ll just hire people to do this for me.” Of course, this sounds ridiculous, but this is how math is taught, and so in the eyes of most of us it becomes the equivalent of watching paint dry. While the paintings of the great masters are readily available, the math of the great masters is locked away.

Countering these conventional attitudes toward math, Frenkel argues that it isn’t necessary to immerse yourself in the field for years of rigorous study in order to appreciate its far-reaching power and beauty:

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.

[…]

There is a common fallacy that one has to study mathematics for years to appreciate it. Some even think that most people have an innate learning disability when it comes to math. I disagree: most of us have heard of and have at least a rudimentary understanding of such concepts as the solar system, atoms and elementary particles, the double helix of DNA, and much more, without taking courses in physics and biology. And nobody is surprised that these sophisticated ideas are part of our culture, our collective consciousness. Likewise, everybody can grasp key mathematical concepts and ideas, if they are explained in the right way. . . .

The problem is: while the world at large is always talking about planets, atoms, and DNA, chances are no one has ever talked to you about the fascinating ideas of modern math, such as symmetry groups, novel numerical systems in which 2 and 2 isn’t always 4, and beautiful geometric shapes like Riemann surfaces. It’s like they keep showing you a little cat and telling you that this is what a tiger looks like. But actually the tiger is an entirely different animal. I’ll show it to you in all of its splendor, and you’ll be able to appreciate its “fearful symmetry,” as William Blake eloquently said.

Drawing from Soviet artist and mathematician Anatolii Fomenko’s 'Mathematical Impressions.' Click image for more.

And as if a mathematician quoting Blake weren’t already an embodiment that boldly counters our cultural stereotypes, Frenkel adds even more compelling evidence from his own journey: Born in Soviet Russia where mathematics had become “an outpost of freedom in the face of an oppressive regime,” discriminatory policies denied him entrance into Moscow State University. But already enamored with math, he secretly snuck into lectures and seminars, read books well into the night, and gave himself the education the system had attempted to bar him from. A young self-taught mathematician, he began publishing provocative papers, one of which was smuggled abroad and gained international acclaim. Soon, he was invited as a visiting professor at Harvard. He was only twenty-one.

The point of this biographical anecdote, of course, isn’t that Frenkel is brilliant, though he certainly is — it’s that the love math ignites in those willing to surrender to its siren call can stir hearts, move minds, and change lives. Frenkel puts it beautifully, returning to math’s equalizing quality:

Mathematics is the source of timeless profound knowledge, which goes to the heart of all matter and unites us across cultures, continents, and centuries. My dream is that all of us will be able to see, appreciate, and marvel at the magic beauty and exquisite harmony of these ideas, formulas, and equations, for this will give so much more meaning to our love for this world and for each other.

Love and Math goes on to explore the alchemy of that magic through its various facets, including one of the biggest ideas that ever came from mathematics — the Langlands Program, launched in the 1960s by Robert Langlands, the mathematician who currently occupies Einstein’s office at Princeton, and considered by many the Grand Unified Theory of mathematics. Complement it with Paul Lockhart’s exploration of the whimsy of math and Daniel Tammet on the poetry of numbers.

Thanks, Kirstin

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Charles Dickens’s Fan Letter to George Eliot

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“The exquisite truth and delicacy, both of the humour and the pathos of those stories, I have never seen the like of.”

To avoid the Victorian era’s biases against women writers, Mary Ann Evans (November 22, 1819–December 22, 1880) began writing under the male pseudonym George Eliot, which went on to become one of the most revered names in literary history. Her first big break came at the age of 37, in 1857, when “The Sad Fortunes of the Reverend Amos Barton” — the first installment in her Scenes of Clerical Life (free download) — was published in Blackwood’s Magazine, then in book form in early 1858. Eliot made sure it got into the hands of all the right people — in the first week of 1858, she mailed copies to some of the era’s most influential luminaries, including Dickens, Thackeray, Faraday, Ruskin, Tennyson, and Carlyle. It was met with overwhelming acclaim — all 1,500 printed copies sold out and early reviewers praised the writer as “strong in his knowledge of the human heart,” which sparked speculation about the author’s identity. Rumors attributed the work to Joseph Liggins, who tried to deny the allegations, in vain, then resigned to accepting the misattributed celebrity.

Portrait of George Eliot by Lisa Congdon for our Reconstructionists project. Click image for more.

But the most vibrant testament to Eliot’s talent came in a letter from none other than Charles Dickens himself, which he sent to Eliot’s publisher before her identity was revealed. Though he addressed it “Dear Sir,” Dickens — whom Eliot had met in 1852 and found “disappointing [and with] no benevolence in the face and I think little in the heart” — makes a point of his intuition that the writer, despite popular rumors, was a woman. The letter, found in George Eliot’s Life, as Related in her Letters and Journals (public library; public domain) — the altogether fascinating 1884 sort-of-biography edited by her husband, John Walter Cross — disarms Eliot’s first impressions of Dickens in the most direct and beautiful of ways. It is a pinnacle of praise, written with equal parts professional admiration, generosity of spirit, and the special kindness Dickens reserved for his kin:

January 18, 1858, London

My Dear Sir

I have been so strongly affected by the two first tales in the book you have had the kindness to send me through Messrs. Blackwood, that I hope you will excuse my writing to you to express my admiration of their extraordinary merit. The exquisite truth and delicacy, both of the humour and the pathos of those stories, I have never seen the like of; and they have impressed me in a manner that I should find it very difficult to describe to you, if I had the impertinence to try.

In addressing these few words of thankfulness, to the creator of the sad fortunes of Mr. Amos Barton, and the sad love-story of Mr. Gilfil, I am (I presume) bound to adopt the name that it pleases that excellent writer to assume. I can suggest no better one; but I should have been strongly disposed, if I had been left to my own devices, to address the said writer as a woman. I have observed what seem to me to be such womanly touches, in those moving fictions, that the assurance on the title-page is insufficient to satisfy me, even now. If they originated with no woman, I believe that no man ever before had the art of making himself, mentally, so like a woman, since the world began.

You will not suppose that I have any vulgar wish to fathom your secret. I mention the point as one of great interest to me — not of mere curiosity. If it should ever suit your convenience and inclination, to shew me the face of the man or woman who has written so charmingly, it will be a very memorable occasion to me. If otherwise, I shall always hold that impalpable personage in loving attachment and respect, and shall yield myself up to all future utterances from the same source, with a perfect confidence in their making me wiser and better.

Your obliged and faithful Servant, and admirer

CHARLES DICKENS.

For a heart-warmer in the same spirit, complement this with Isaac Asimov’s fan mail to young Carl Sagan, then see what George Eliot teaches us about happiness.

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To Live Long, Write for Children: RIP Charlotte Zolotow, 98

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Honoring one of the biggest hearts and most brilliant minds in children’s literature.

For those who hold children’s books dear, a little piece of the soul dies every time another beloved children’s book author or artist leaves us. It helps a little to know that the great Charlotte Zolotow (June 26, 1915–November 19, 2013) lived to be 98. (On a semi-serious aside: It seems that writing for children holds an especial promise of longevity, with many authors and illustrators outliving the average life expectancy of their homeland by years, often decades — Maurice Sendak lived to be 84, E. B. White 86, Ruth Krauss 92, Alice Provensen reportedly continues to draw well into her nineties, and Eric Carle just released his latest book at 84. There must be something uniquely soul-nourishing about the warmth and kindness that writing for children both requires and stimulates.)

Illustration by Maurice Sendak from Charlotte Zolotow's Mr. Rabbit and the Lovely Present (1962)

Although she authored and edited more than seventy books, Zolotow remains best-known for Mr. Rabbit and the Lovely Present, published in 1962 and illustrated by none other than Sendak. But the most influential relationship of her career was with the great Ursula Nordstrom, fairy godmother of modern children’s literature, who steered Zolotow’s collaboration with Sendak and with whom Zolotow worked closely for many years thereafter. From Leonard Marcus’s altogether fantastic Dear Genius: The Letters of Ursula Nordstrom (public library) — which also gave us Nordstrom’s witty, wise, and prescient 1953 letter on the state of publishing and the infinitely heartwarming story of how she cultivated young Sendak’s genius — comes the wonderful record of Zolotow’s formative relationship with Nordstrom.

Illustration by Maurice Sendak from Charlotte Zolotow's Mr. Rabbit and the Lovely Present (1962)

In August of 1961, when Mr. Rabbit and the Lovely Present was coming together, Nordstrom assured Sendak of Zolotow’s commitment to the project:

She is so glad you’re illustrating it, and so are we, that nothing can cloud our pleasure.

A few months later, on October 30, she sent a heartwarming letter to Zolotow herself:

Dear Charlotte—

Sendak’s pictures are so lovely for your (untitled) book! Utterly different from anything he’s ever done — with a timeless, classic quality: You’ll be happy, I know. The little girl is so lovely, and the rabbit is funny, a good combination, I think.

After thanking Zolotow for recommending a play Nordstrom had just seen and loved, and for Zolotow’s kind words about the only children’s book Nordstrom herself ever wrote, The Secret Language, she holds up a mirror of warm mutuality:

I can never tell you how grateful I am to you, dear friend and author. I’ve never had anyone — well, — be so generous and kind, certainly no AUTHOR — as you’ve been.

The longtime collaboration and lifelong friendship between the two began when Zolotow became Nordstrom’s editorial assistant at Harper & Row — a position that, under the influence of Nordstrom’s enormous generosity of spirit and creative bravery, no doubt helped Zolotow cultivate her own. In fact, she soon became Nordstrom’s right-hand-woman and was even the one to bring in Louise Fitzhugh’s hugely popular 1964 classic, Harriet the Spy, which queer women continue to celebrate for its trailblazing use of an apparently queer protagonist.

Harriet the Spy by Louise Fitzhugh (1964)

In a 2009 interview, Zolotow spoke of the interplay between being a writer and being an editor:

Being both a writer and editor affects different expressions of the same personality. Writers must shut out everyone else while they write. They must forget outside suggestions, or the temptation to follow suggestions separate from their own visions.

Editors must resist the desire to insert their own idea of how and where the story goes. They must resist the temptation to offer their own words as a solution when something is weak; instead they should alert the writer to this weakness, so that if the writer agrees, she may solve the problem in her own words and way.

When Nordstrom was ready to leave Harper, she bequeath her department to Zolotow. In a 1980 letter to another one of her authors, Mary Stolz, Nordstrom wrote:

I told Charlotte Zolotow many months ago that I wanted to slope off my job with Harper, and not be an editor any more. There are good things about it, always have been, but no more working with authors, dealing with contracts, worrying about the lack of reviews, or when there are bad ones, for “my” authors. Charlotte, as head of the department, is a brilliant and sensitive creative person. She will see that your work get the good attention I think you have always had from the dept.

Illustration by William Pène du Bois from William's Doll (1972)

And see to it she did — Zolotow went on to bring to life dozens of books for young readers, from her very first, The Park Book, published in 1944 and illustrated by H. A. Ray, to such delights as William’s Doll (1972) illustrated by William Pène du Bois and I Know a Lady (1984) illustrated by James Stevenson to her final book, The Beautiful Christmas Tree, published in 1999 and illustrated by the inimitable Yan Nascimbene, whom we also lost this year.

Illustration by Maurice Sendak from Charlotte Zolotow's Mr. Rabbit and the Lovely Present (1962)

Thank you for the many lovely presents, Charlotte.

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