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.


2 Responses to “Pachinko Boards & Ferris Wheels”

  1. 2011 August 17 at 5:00 am

    Hey Jay – a nice surprise to get an email telling me you had written something on your blog. I am really sorry about the Indiana State Fair – I know here in Oregon I am going to our State Fair at the end of the month and somehow it is such a uniting (? is that a word?) event . . . it feels very personal and is supposed to remind us of friendly, more rural times when life was closer to the earth and people were closer to each other. To have a tragedy like that happen – it just is so awful. 😦

    As I was reading your post I couldn’t help but wonder how much fuller an experience life would be if I had your kind of intelligence and grasp of things like the dice hitting the sides of the table and the scientific reasons behind certain things. Understanding “why” must make it that much more difficult, however, when you run up against something that just cannot be explained by observable phenomenon (well, it could if it were in a controlled environment, but . . . you know what I mean.)

    Anyway, lovely writing as usual and again I’m sorry – having been to Indiana (twice!) I felt especially saddened at this tragedy.

  2. 2011 August 17 at 11:15 am

    Hi Missy! Glad you liked it. I actually know someone who was at the concert, although she was far enough back that she wasn’t in any danger. She was badly shaken up, though, emotionally.

    I was motivated to write this when I saw how the comments on the local TV station’s FB page were immediately turning into accusations that state or state fair officials acted inappropriately in not starting an evacuation sooner. It’s crazy. The gust front was twelve miles in front of the storm itself, far enough that the rain hadn’t even started on the west side of Indy yet; and the wind gust was so localized that not a single structure other than the stage rigging was damaged. Like, say, the huge Ferris wheel half a mile away.

    Does knowing about things like that make the “WTF” moments harder to deal with? I think a solid background in science and math makes it easier to distinguish between those things that we can’t know and those that we can but don’t. But I also take comfort that the butterfly effect (what I described) doesn’t mean the universe is somehow random and purposeless: When Ed (Edward Lorenz was his name) put the exact same numbers in the model, he got the exact same results out.

    I do love the Lorenz story. If you want more info, you can look up his name, or “butterfly effect” (or, for that matter, “chaos theory”). I think you should give your intelligence more credit – you and I have just spent our study time in different arenas. You’re a pretty smart cookie. 🙂

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