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So simple!* And yet Life, when the rules are applied over and over, ideally by a computer, yields endlessly varied patterns, including quasianimated clusters of cells known as “longboats,” “gliders,” “spaceships” and my favorite, “Speed Demonoids.” Otherwise, the cell dies or remains dead. A dead cell comes to life if three of its neighbors are alive, and a live cell stays alive if two or three of its neighbors are alive. *A given cell’s state depends on the state of its eight immediate neighbors.

The Game of Life is a two-dimensional cellular automaton with square cells that can be in one of two states, alive or dead (often represented by black or white). A cellular automaton is a grid of cells whose states depend on the states of neighboring cells, as determined by preset rules. The Times riff on Life got me thinking anew about old riddles. Scientific American’s legendary math columnist Martin Gardner introduced the Game of Life, sometimes just called Life, to the world in 1970 after receiving a letter about it from Conway. The Times focuses on the enduring influence of the Game of Life, a cellular automaton invented by Conway more than a half century ago. This encounter came back to me recently as I read a wonderful New York Times tribute to Conway, felled by COVID-19 last year at the age of 82. He, Conway informed me with a manic grin, is one of the world’s fastest day-of-the-week calculators. After a split second he blurted out, Tuesday! He tapped his keyboard, stared at the screen and exulted, Yes! Finally facing me, Conway explained that he belongs to a group of people who calculate the day of the week of any date, past or present, as quickly as possible. When I tentatively announced myself, he yelled without turning, What’s your birthday! Uh, June 23, I said. His office overflowed with books, journals, food wrappers and paper polyhedrons, many dangling from the ceiling. Hair tumbled down his back, his sagging pants exposed his ass-cleft.

the “ mathematical magician.” I met him in 1993 in Princeton while working on “ The Death of Proof.” When I poked my head into his office, Conway was sitting with his back to me staring at a computer.

Before I get to the serious stuff, a quick story about John Conway, a.k.a.

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