Outrunning a decimal point

By Nicholas_T on Flickr

Now, we’re all polite people here. So let’s be polite and talk about the weather. No wait! Don’t go! I mean, let’s really talk about the weather.

Now, aside from the extremes, most weather can be dealt with. Rain? Raincoat. Sun? T-shirt. Snow? Stay inside, what are you even thinking about, jeez.

What’s difficult to deal with is the unpredictability. It’s sunny now, but next week? That’s tricky. And you know what the kicker is? You can’t know the weather that far in advance. There is a theoretical limit to that of about a month. Anything beyond a week is tricky, but no matter what you do, how good our computers get, however many weather stations we have, how much we shake our fists at the clouds, we can’t get past a month.

There was a man named Edward Lorenz who was doing some work in 1961 on weather prediction. He was using one of those newfangled computer things to run some models. He wanted to run one of these models again, but to save time he took the old printout and input the numbers from half way through the run – essentially just skipping to the bit he was interested in and starting from there. But what Lorenz noticed was that it gave him a different answer. The weather pattern changed. He checked again. Then it hit him, the computer operated to the sixth decimal place – so it used numbers like 0.864592. But the printout he used only printed out the first three digits – so his piece of paper would just have 0.864. Lorenz had put 0.864 instead of 0.864592, and gotten a massively different answer. But nobody at that time would have thought such a tiny difference would have such big consequences. Lorenz realised that he had stumbled onto something important.

It’s called a ‘sensitive dependence on initial conditions’, which means that very tiny changes in your setup can lead to very different long term results. It’s also known as the butterfly effect – the flap of a butterfly’s wing will change the air, and hence the initial conditions, enough so that a hurricane appears on the other side of the world that never would have been there otherwise.

Not all systems in the world are like this – but systems like the weather, a dripping tap, population growth, cloud formation, or a double-pendulum, all exhibit this strange property. Change one, tiny thing and no matter how tiny that change it will eventually lead to radically different outputs.

And this is the problem with the weather. Even if we had a magical device which could tell you the exact wind speed, direction, temperature and humidity, and spaced them out across every millimetre of the earth’s surface, the little numbers in our machine’s head couldn’t measure things accurately enough to predict with certainty what will happen. Even if they measured to a hundred decimal places, the hundred-and-first would still be enough to make it deviate from whatever we predicted. A thousand decimal places? The thousand-and-first is going to get you – maybe a little later than the hundred-and-first, but you can’t outrun it. If it’s a chaotic system, it’ll always win in the end. And, for the weather, with the best technology you could ever imagine, you’d find it hard to be accurate more than a month in advance before those extra decimal places started to make things different to what you predicted.

If, however, you are very smart, and manage to develop a device to predict that sort of thing, well, no-one would believe you. Of course, the next step is the casino, and after that – well, we all know who likes to hang around at casinos.

If you’re interested in this sort of thing – and I’ve only just brushed the very top surface of something which goes all the way down into the guts of the universe (as far as we can tell) – then I can recommend “Chaos: Making a New Science” by James Gleick

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