Second hand water

Randall Munroe, over at xkcd, does some really funny cartoons, and is a physicist by training. Every week he answers a hypothetical question: this week it’s

How much of the Earth’s currently-existing water has ever been turned into a soft drink at some point in its history?

His answer, by the way, is “not much”. On the other hand, almost all of it has been drunk by a dinosaur.

One of the things I really like about these “what-if” answers is the way they demonstrate one of the important aspects of modelling: working out what’s significant and what’s not. And significance depends very much on what the purpose of the model is. Often, Munroe can make some really sweeping assumptions that are clearly not borne out in practice, but are equally clearly the right approximations to make for his purposes. And sometimes he says that he doesn’t know what assumption to make.

An example of a sweeping assumption comes in the answer to

How close would you have to be to a supernova to get a lethal dose of neutrino radiation?

where he assumes that you’re not going to get killed by being incinerated or vaporised. 

And in answering the question

When, if ever, will Facebook contain more profiles of dead people than of living ones?

the difficult assumption is whether Facebook is a flash in the pan, and stops adding new users, or whether it will become part of the infrastructure, and continue adding new users for ever (or at least for 50 or 60 years). There are also some sweeping demographic assumptions, of course.

(and while you’re at it, read the one on stirring tea)

I’m reminded of two things here. The first is doing mechanics problems in A-level maths: there was nothing difficult about the maths involved, the trick was all in recognising the type of problem. Was it a weightless, inelastic string, or a frictionless surface? It was all about building a really simple model.

The second is those Google interview questions we used to hear so much about, like how many golf balls fit in a school bus, or how many piano tuners there are in the world. The trick with these is to come up with a really simple model and then make reasonable guesses for the assumptions. And, of course, be aware of your model’s limitations.

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  1. Hmmm …

    One of my bugbears is the use (by actuaries) of the word “assumption” when they don’t really mean it. At least, not in the sense that it would normally be understood.

    When Munroe calculates how close one would need to be to a supernova in order to get a lethal does of neutrino radiation, his calculation doesn’t rely on an assumption that you’re not going to get killed by being incinerated or vaporised by the supernova. So it’s not an assumption for the purposes of his calculation. Munroe simply observes that, given the nature of a human body, it would have been incinerated or vaporised long before getting close enough for the radiation to be fatal. That’s really not an assumption at all.

    I am reminded of what Sundance said to Butch, when they were sitting atop a high rock, contemplating jumping into a river to escape from pursuing lawmen: there was no point Butch worrying about whether his lack of swimming skills would cause him to drown; the fall was going to kill him first. [On analysis, this example isn’t remotely relevant to the point I’m making. But it’s a nice scene from a great movie, and I’d already typed it out, so I thought I’d leave the reminiscence in.]

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