Interview with Professor Ian Stewart for the Naked Scientists – listen here.

Ian – It’s a more difficult question than most people tend to think because we’ve been brought up with this idea as maths as the kind of universal truth. It’s somehow truer than anything else because it’s all perfectly logical and it follows from basic principles and so forth. Two plus two has to be equal to four, once you’ve decided what two, four, plus, and equals mean and there’s no real way round that. And all of that’s very true so I doubt you’d find aliens who don’t think that two plus two equals four, but you might find aliens who don’t really understand two, or plus, or equals.

In fact, Henri Poincare was one of the great French mathematicians at the end of the 19th century-beginning of the 20th century said “in the real world equals does not behave the way we think it does.” In mathematics, if A equals B, and B equals C, then A equals C. In the real world if we think A equals C actually they might be very slightly different but we can’t measure the difference. I suppose you could only measure things to within 1cm. If two things are ¾ cm apart, you think they’re in the same place. And if the second one is ¾ cm away from one of those, you think that’s in the same place as the other one. But then two of them could be 1½ cm apart from each other and you could tell they’re different. So, in the real world if A equals B and B equals C, then maybe A is different from C, and this is what Poincare said.

So mathematics is an idealisation of what’s out there and I think that different creatures from different environments with different ways of living, different concerns as to what’s important might set things up in a different way.

Tom – It almost sounds to me like you’re saying the maths we have on Earth has evolved from our environment on Earth and so the maths that aliens use would have evolved from their environment?

Ian – If you actually start thinking about it, what we consider to be absolutely fundamental mathematical concepts are very closely related to the kind of creatures we are, the kind of world we live in, and how we perceive that world. Our counting came from keeping track of discrete objects or events. If I’ve got a lot of sheep, I’m a farmer with a lot of sheep – say 15 sheep, it’s useful to know that I’ve got 15 sheep. I’ve got to be able to count up to 15. If one of them’s missing I will spot it. If you just say well you know I’ve got some sheep, it’s not too many, it’s not too few, and you lose one of your sheep you don’t realise it’s gone. A bit later you lose another sheep and still don’t realise it’s gone and suddenly you’re down to 2 or 3 sheep and you think something happened there. But most of it happened so long ago you can’t do anything about it.

So we count things. And counting the number of days in a month in the cycle of phases of the moon; that was very important to a lot of early civilisations. So the idea of going 1, 2, 3, 4 and so on is very basic to us, but creatures that lived in a completely different environment where there aren’t any discrete objects. I’m thinking of creatures that maybe float around in the atmosphere of a gas giant planet. They’re more like giant amoebas or something – they flow, everything flows. So you try to explain Pythagoras’s theorem to one of these creatures and say – take a triangle with corners at A, B, C, and it puts down A. Then you say now make another point B and it says OK I’ve got point B but A’s disappeared – it’s blown away on the gas on the wind.

There aren’t any rigid triangles. They might have real trouble with concepts like triangle. On the other hand, turbulent vortex flow is something they would think is absolutely trivial and straightforward. A child of whatever would understand, and we have really, really serious mathematical problems with it.

Tom – It sounds to me like maths is still maybe our best bet with communicating with aliens? I mean better than language or our culture surely in terms of what they might have a chance of understanding?

Ian – I think that’s probably right. I think to be a bit less imaginative about the possibilities and just say what’s actually likely. Maths has a kind of universality that communicating with language would be difficult. They don’t speak the language, they might not even hear sounds. Poetry probably isn’t a great idea; the works of Shakespeare would not particularly impress them. Music possibly, but think of listening to music from other human cultures. It’s very hard to get used to and no generation of parents understands the music that their kids like – teenagers are aliens. It’s fairly notorious musical tastes are very different.

If there are points of contact, it’s somewhere you can start from. Very likely aliens would not use base ten numbers. The might use some sort of number base because it’s quite a neat idea for encoding numbers. But we’ve got ten fingers, if you count thumbs and that’s probably where base ten comes from – there’s nothing special about ten. So an alien with seven tentacles might might work in base seven. But they would rapidly think oh, these guys are working in base one three, that’s one seven plus three – we call it ten, they call it thirteen. And we would rapidly say oh, they’re working in base seven and you can translate from on to the other very straightforwardly.

So differences in notation, differences in number base, differences in… We think triangles are basic; no they prefer rectangles, whatever. That wouldn’t be a barrier to communication, it would be something to puzzle out. If we’re on that level, there would be this great possibility that the aliens know some maths that we don’t,and we know some that they don’t. I’ll trade you the proof of Fermat’s last theorem if you can tell me how to prove the Riemann hypothesis. You could actually have interstellar trade in mathematical theorems.