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Tuesday, November 21, 2017

Ideal Numbers Seek Their Lost Primes, by Kevin Hartnett, Quanta Magazine

Today mathematicians are actively engaged in the study of “class numbers” of number systems. In their crudest form, they’re a rating of how badly a number system fails the test of unique prime factorization, depending on which roots get mixed in: A number system that gets a “1” has unique prime factorization; a system that gets a “2” misses unique prime factorization by a little; a system that gets a “7” misses it by a lot more.

On their face, you’d expect class numbers to be randomly distributed — that class number 5 occurs with the same frequency as class number 6, or that half of all class numbers are even. That’s not the case, though, and current research in the subject aims to understand why. Today mathematicians are circling in on the structure that underlies class numbers and inching closer to establishing the truth about long-conjectured values. It’s an effort that has generated insights about how numbers behave that go far beyond a proof of any one problem.

My Mother Has Terminal Cancer, And I Can’t Seem To Stop Buying Sweaters, by Rachel Vorona Cote, Catapult

For my part, this grotesque approximation of normalcy has spawned several unremarkable byproducts: surges of impotent fury, tears—a greater quantity than usual, for a stoic I am not—and a neurotic reluctance to settle future plans. The one question that previously reared its malignant head every several months now grips my brain like a vise: “How long will my mother live?”

A more trivial effect of her cancer: Most of my shopping budget has now been allocated to sweaters. I’ve entertained brief flirtations with flannel button-downs and the rare cropped sweatshirt, but ultimately determined that they supply only pale imitations of a sweater’s particularly intimate snug. By the end of last summer, as CT scans and blood tests yielded increasingly dismal tidings, my partiality to knitwear intensified to a mania. Washington, DC heaved with stubborn, swampy humidity; I—with similar persistence—rummaged for merino wool and thermal cotton in the sale racks.

America Rediscovers Its Love Of The Front Porch, by Lynn Freehill-Maye, CityLab

The thing is, what Doyon and Glica are doing represents a generational rethinking of the front porch. Porch-building is on the rise across the country, up 23 percent on new homes from two decades ago. That fact excites city designers, and it may well be linked to the U.S. urban renaissance—but the classic American porch isn’t being used in quite the practical way it once was. Through Porchfests and beyond, the front steps are taking on a new life—one that’s stylish, sporadic, and often more image-conscious.

The Story Of Appalachia, With Plenty Of Villains, by Dwight Garner, New York Times

This is granular history, especially when it comes to dispossession. This book’s primary sentence is probably this one: “I am interested in how people get kicked off land and why we don’t talk about them.” Native Americans and African-Americans are considered at some length in this book, but Stoll’s primary focus is on poor whites.

He delivers a painstaking history of how public land became real estate, and how hundreds if not thousands of people were pushed aside by one or two barons. Steal a little and they throw you in jail, as the Bob Dylan lyric has it; steal a lot and they make you king.