Posts Tagged ‘thoughts

14
Aug
11

Pachinko Boards & Ferris Wheels

Back in the early 60s there was a guy at MIT – Ed was his name – who was using computers to model the weather. Computers in the 60s being what they were, Ed didn’t have a lot of the tools we take for granted in the 21st Century, like entire gigabytes of RAM. Or a hard drive to save your data. Or even a screen to look at. If he wanted to know what his program was doing, he had to include instructions to print the information.

So one night, he was in the middle of a complicated simulation, but needed to leave. So he told the program to print its current state, took the printout, and left. The next morning, he put those numbers back into the program… and something went wrong. The model the computer produced was nothing like the one it was working on the previous night.

Ed checked his program and checked it again, and couldn’t find any mistakes. Eventually, he came to a startling conclusion: his printout was at fault – sort of. See, the computer held numbers in memory out to six decimal places of precision, like 0.517228, but the code he’d written to print the program’s state rounded everything to three places, like 0.517. Such a minuscule difference… surely that couldn’t produce an entirely different result?

As it turns out, yes, it could.

An analogy: consider a pachinko board with no pegs in it, just a smooth board and a puck. Let the puck go, and it will slide down the board and land in a particular place; adjust the puck’s position only slightly, and the place it lands will only be slightly different.

Now put the pegs in, and repeat the experiment; now the tiniest change in the puck’s starting position can produce a markedly different path down the board.

This “sensitive dependence on initial conditions” is what Ed discovered with his weather model: a small change in the input can affect the result just as much as a big change.

Sensitive dependence on initial conditions – a key concept of chaos theory – is why your local meteorologist can’t predict the weather more than about a week ahead, and couches forecasts in terms of percentages – “a 30% chance of rain” and so on – because some weather patterns are more or less stable than others. (It’s also why the stickman at the craps table demands that you throw the dice hard enough to hit the opposite wall – all the creases in the side of the table introduce a level of chaos into the most controlled throw.)

When Ed told his co-workers what he’d found, one of them replied that if he was right, a single flap of a seagull’s wing could change all the weather on the planet forever.

Years later Ed would describe this mathematical reality with a similar image, although he used a butterfly instead of a bird, possibly thinking of a famous short story in which the death of a butterfly changed history. But the point is, weather is a chaotic system. It’s impossible to predict with absolute accuracy what will unfold. Who knows if a person sneezing at the top of a Ferris wheel could tip the balance and push a 50mph gust of wind up to 70mph?

Things I’m thinking about as I watch the news reports from the Indiana State Fair.

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