In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.
But their work has ramifications far beyond the specific question of how those two infinities are related. It opens an unexpected link between the sizes of infinite sets and a parallel effort to map the complexity of mathematical theories.
It is here, among the clucking chickens, crowing roosters, and cooing doves, that Kabul’s oldest restaurant, Bacha Broot, has been serving delicious chainaki — traditional lamb stew — for over 70 years. Bacha Broot, named after the original owner who had peculiar facial hair, is from the Dari, meaning “boy with a mustache.”
While wars have raged on the restaurant’s doorstep, very little has changed inside. The claustrophobic stairs, the sparse interior, the tiny door easily missed in the maze-like bazaar; all in their original state. While modern fast food joints lure Afghanistan’s younger generations with pizza and burgers, Bacha Broot stays loyal to its recipe for success. The famous chainaki — lamb on the bone, split peas, and onions cooked for four hours in tiny teapots — has drawn customers for decades, during war and peace, good times and bad.
Draft No. 4 contains a carefully balanced ratio of directly instructive writing advice, behind-the-scenes views on McPhee’s greatest hits, and war stories from the golden age of post-WWII American magazine publishing. This is near the bullseye of what you’d hope for from an octogenarian doyen, and it’s a pleasure to read. Any writer or editor could learn something from McPhee, as many famous and successful ones already have. In the essay “Frame of Reference,” he advises against borrowing vividness from famous names: “If you say someone looks like Tom Cruise—and you let it go at at that—you are asking Tom Cruise to do your writing for you.” Any obscure reference tightens the writer’s audience, almost always for the worse. Though McPhee does end the section with the story of an elegant exception, a fittingly exceptional line of writing gifted to a few readers who would receive it.
There are only two kinds of writers in the world, according to John McPhee: the overtly insecure and the covertly insecure. His new book, “Draft. No. 4,” a collection of essays on craft, is a sunny tribute to the gloomy side of the writing life: the insecurity, dread, shame, envy, magical thinking, pointless rituals, financial instability, self-hatred — the whole “masochistic self-inflicted paralysis of a writer’s normal routine.” And then the queasy desire to do it all over again.
“Word by Word” is both memoir and exposé, an insider’s tour of the inner circles of the mysterious fortress that is Merriam-Webster. Stamper leads us through her own lexicographical bildungsroman, exploring how she fell in love with words and showing us how the dictionary works, and how it interacts with the world that it strives to reflect. Though Stamper takes great pains to paint herself as your garden-variety, genial nerd, she doesn’t fully dispel the reader of the wonderful myth that there are hyperverbal elves who live somewhere within the pages of the dictionary, scribbling at the language whenever we readers aren’t looking. Stamper paints etymologists as alchemists or magicians, mysterious figures who fill their cubicles with gravity-defying Jenga piles of Old German and Frisian dictionaries. Within lexicographical ranks, Stamper told me, there’s a reverence for expert grammarians that approaches the devotional. “It’s esoteric, Kabbalistic knowledge,” she said. “As you move up the layers towards enlightenment, you will learn more about conjunctive adverbs.”