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A blog written for those whose interests more or less match mine.

John Conway: A life in games

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Very interesting article in Quanta by Siobhan Roberts:

Gnawing on his left index finger with his chipped old British teeth, temporal veins bulging and brow pensively squinched beneath the day-before-yesterday’s hair, the mathematician John Horton Conway unapologetically whiles away his hours tinkering and thinkering — which is to say he’s ruminating, although he will insist he’s doing nothing, being lazy, playing games.

Based at Princeton University, though he found fame at Cambridge (as a student and professor from 1957 to 1987), Conway, 77, claims never to have worked a day in his life. Instead, he purports to have frittered away reams and reams of time playing. Yet he is Princeton’s John von Neumann Professor in Applied and Computational Mathematics (now emeritus). He’s a fellow of the Royal Society. And he is roundly praised as a genius. “The word ‘genius’ gets misused an awful lot,” said Persi Diaconis, a mathematician at Stanford University. “John Conway is a genius. And the thing about John is he’ll think about anything.… He has a real sense of whimsy. You can’t put him in a mathematical box.”

The hoity-toity Princeton bubble seems like an incongruously grand home base for someone so gamesome. The campus buildings are Gothic and festooned with ivy. It’s a milieu where the well-groomed preppy aesthetic never seems passé. By contrast, Conway is rumpled, with an otherworldly mien, somewhere between The Hobbit’s Bilbo Baggins and Gandalf. Conway can usually be found loitering in the mathematics department’s third-floor common room. The department is housed in the 13-story Fine Hall, the tallest tower in Princeton, with Sprint and AT&T cell towers on the rooftop. Inside, the professor-to-undergrad ratio is nearly 1-to-1. With a querying student often at his side, Conway settles either on a cluster of couches in the main room or a window alcove just outside the fray in the hallway, furnished with two armchairs facing a blackboard — a very edifying nook. From there Conway, borrowing some Shakespeare, addresses a familiar visitor with his Liverpudlian lilt:

Welcome! It’s a poor place but mine own!

Conway’s contributions to the mathematical canon include innumerable games. He is perhaps most famous for inventing the Game of Life in the late 1960s. The Scientific American columnist Martin Gardner called it “Conway’s most famous brainchild.” This is not Life the family board game, but Life the cellular automaton. A cellular automaton is a little machine with groups of cells that evolve from iteration to iteration in discrete rather than continuous time — in seconds, say, each tick of the clock advances the next iteration, and over time, behaving a bit like a transformer or a shape-shifter, the cells evolve into something, anything, everything else. Life is played on a grid, like tic-tac-toe, where its proliferating cells resemble skittering microorganisms viewed under a microscope.Conway_LifeRules

The Game of Life is not really a game, strictly speaking. Conway calls it a “no-player never-ending” game. The recording artist and composer Brian Eno once recalled that seeing an electronic Game of Life exhibit on display at the Exploratorium in San Francisco gave him a “shock to the intuition.” “The whole system is so transparent that there should be no surprises at all,” Eno said, “but in fact there are plenty: The complexity and ‘organic-ness’ of the evolution of the dot patterns completely beggars prediction.” And as suggested by the narrator in an episode of the television showStephen Hawking’s Grand Design, “It’s possible to imagine that something like the Game of Life, with only a few basic laws, might produce highly complex features, perhaps even intelligence. It might take a grid with many billions of squares, but that’s not surprising. We have many hundreds of billions of cells in our brains.”

Life was among the first cellular automata and remains perhaps the best known. It was coopted by Google for one of its Easter eggs: Type in “Conway’s Game of Life,” and alongside the search results ghostly light-blue cells will appear and gradually overrun the page. Practically speaking, the game nudged cellular automata and agent-based simulations into use in the complexity sciences, where they model the behavior of everything from ants to traffic to clouds to galaxies. Impractically speaking, it became a cult classic for those keen on wasting time. The spectacle of Life cells morphing on computer screens proved dangerously addictive for graduate students in math, physics and computer science, as well as for many people with jobs that provided access to idling mainframe computers. A U.S. military report estimated that the workplace hours lost clandestinely watching Life evolve on computer screens cost millions of dollars. Or so one Life legend has it. Another purports that when Life went viral in the early-to-mid-1970s, one-quarter of all the world’s computers were playing.

Yet when Conway’s vanity strikes, as it often does, and he opens the index of a new mathematics book, casually checking for his name, he gets peeved that more often than not his name is cited only in reference to the Game of Life. Aside from Life, his myriad contributions to the canon run broad and deep, though with such meandering interests he considers himself quite shallow. There’s his first serious love, geometry, and by extension symmetry. He proved himself by discovering what’s sometimes called Conway’s constellation — three sporadic groups among a family of such groups in the ocean of mathematical symmetry. The biggest of his groups, called the Conway group, is based on the Leech lattice, which represents a dense packing of spheres in 24-dimensional space where each sphere touches 196,560 other spheres. He also shed light on the largest of all the sporadic groups, the Monster group, in the “Monstrous Moonshine” conjectures, reported in a paper composed frenetically with his eccentric Cambridge colleague Simon Norton. And his greatest masterpiece, in his own opinion at least, is the discovery of a new type of numbers, aptly named “surreal” numbers. The surreals are a souped-up continuum of numbers, including all the reals — integers, fractions and irrationals such as Euler’s number (2.718281828459045235360287471352662 … ) — and then going above and beyond and below and within, gathering in all the infinites, all the infinitesimals, and amounting to the largest possible extension of the real-number line. In Gardner’s reliable assessment, the surreals are “infinite classes of weird numbers never before seen by man.” And they may turn out to explain everything from the incomprehensible infinitude of the cosmos to the infinitely tiny minutiae of the quantum.

But the truly amazing thing about the surreal numbers is how Conway found them: by playing and analyzing games. Like an Escher tessellation of birds morphing into fish — focus on the white and you see the birds, focus on the red and you see fish — Conway beheld a game, such as Go, and saw that it embedded or contained something else entirely, the numbers. And when he found these numbers, he walked around in a white-hot daydream for weeks. . .

Continue reading.

There’s a lot more.

Siobhan Roberts also wrote an article on John Conway in the Guardian: “John Horton Conway: the world’s most charismatic mathematician“.

Written by Leisureguy

28 August 2015 at 12:05 pm

Posted in Books, Education, Games, Math

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