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I am John Conway

For real

· maths,mathematicians,math

This great article on John Conway by Siobhan Roberts in Quanta Magazine makes a summary adaption of his biography Genius at Play.

I learned certain facts about the famous mathematician that made me question every question I've been made to have. This will make sense in a minute. Bear with me.

Conway's most famous contribution is a particular variety of cellular automaton, the Game of Life. A cellular automaton is a "no-player, never-ending game" playing out on a two-dimensional grid of cells, with cells evolving discretely in time according to a few simple rules. In the Game of Life, the life or death of cells depends on how many adjacent cells are alive : 2-3 live neighbors ensures survival at the next iteration, while more or fewer means death.

 

Watching the game unfolding feels like observing bacteria under the microscope. The resulting structures look very organic.

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.”

So did I in Numerical Physics class. One cannot help but recognize life itself: simple rules leading to complex outcomes. My favorite games have simple rules and complex outcomes, like Carcassone. I find games with complicated rules pathological.

Apart from the many applications of the Game of Life, Conway invented the Piano Problem:

What’s the largest object that can be maneuvered around a right-angle corner in a fixed-width corridor? (The lower bound for the object’s area is 2π + π2.)

I wish I had known this before moving that cumbersome brown couch into my last appartment. The great gentlemen to whom I ended up giving it found taking it out so laborious you'd think the appartment building was giving birth.

What was Conway like? Playful, and an inveterate game inventor. More on that later.

Conway can usually be found loitering in the mathematics department’s third-floor common room.

This is a type of figure frequently encountered in the student rooms of many math and physics departments. As a matter of fact, I did spend every minute I could in the physics student café, from my time as an undergrad to the end of my Ph.D. I had to. Spending more than an hour sitting at a desk made me so restless I wanted out of my own skin. I could have screamed. I had to be around people. I had to be discussing ridiculous theoretical topics.

 

Some astrophysics bores considered it a sign of maturity to eat lunch while talking solely about telescopes in a manner so terminally serious you would have thought they were talking about lawnmowers. Their mindset made me suffer. Not just the mindset itself, but the confidence they had for knowing they were backed up by society in their ridicule of those of us who needed to be silly about science a significant portion of the time to just be able to live. I hated the telescope-lawnmower guy.

"There are 10 half-hours in the working day, roughly speaking" - John Conway

Hear this: As a graduate research, my days lasted exactly that, 10 half-hours, or 5 hours. Not one minute more. I arrived at 10AM, took a one-hour lunch, and left at 4PM. You couldn't have made me stay longer. Five hours was what I had to give. This means John Conway validates my life choices, even if you don't.

Conway's favority activity was inventing games. One game in particular, Phutball, is a "two-player board game with stones governed by wickedly negative feedback". In the words of Conway himself:

"Every time you take your turn you get this horrible feeling in the pit of your stomach. Because every move is bad. Instead of selecting the move that is best, you select the move that is least bad.… You make any move and immediately feel you shouldn’t have done it, and you think to yourself, Oh God, what have I done?" - John Conway

Which makes Phutball, in fact, the real Game of Life.

Conway was also prone to

[...] spasmodic outbursts in which he leapt into the air, latched onto a pipe along the ceiling, and swung violently back and forth. This trapeze act hardly made Conway the department’s leading acrobat. He was outperformed by Frank Adams, an algebraic topologist and mountaineer who liked to climb under a table without touching the floor. Conway found Adams intimidating, a forbiddingly serious mathematician.

Take a moment here to reflect on this: Conway found intimidating another mathematician who liked to climb under a table without touching the floor. He also found him forbiddingly serious, no less.

This one gave me a shock of recognition: I too liked to suspend myself from the table without touching the floor as a four-year-old. I only stopped because I thought I had to, since I was entering kindergarten. The adults in my life were as boring as the telescope-lawnmower guy. To think I could have kept on into adulthood. Now tables are Scandinavian and flimsy and cannot support the weight of a suspended adult.

By 1968, he had not accomplished much. All he was doing, after all, was squatting in the common room playing games, inventing games and reinventing rules to games he found boring.

He still ended up contributing a lot. This is what happens when you don't play the actually stupid games, like expecting people who work for you to look busy for the sake of appearances.

Conway had an odd strategy when playing backgammon:

He wasn’t interested in winning at backgammon as much as he was interested in the possibilities of the game. He liked to play a flamboyant “back game,” falling intentionally behind with inexplicably loony plays. Opponents, witnessing such folly, would let their guard down and get careless, gradually losing ground. Then Conway would make his move. Usually this strategy backfired and he lost as expected. But every now and then, depending on the luck of the dice — the element of chance is key in backgammon, and consequently the game defies much mathematical analysis and any pretensions of a serious research agenda — Conway would successfully rush in from behind and pull off a spectacular win

This one also gave me a shock of recognition. Why? Because falling intentionally behind with inexplicably (even to me) loony plays is how I live my life.

 

Wait, is this the Game of Life?

Image source: https://datarepository.wolframcloud.com/resources/images/3b4/3b4df66a-3d94-4bcd-a133-e0b5d0ae2d00-io-3-o.en.gif

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