Using Math To Make Complex Systems Simple

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It's Mathematics Awareness Month, and this year's theme is Unraveling Complex Systems. Host Scott Simon talks to Weekend Edition Math Guy Keith Devlin about how math can be a guide to understanding everything from how financial markets work to how schools of fish interact.


Birds do it, bees do it - use math, I mean. When they fly in formation or create a colony, it's called a complex system. Now, that term applies to just about anything that requires a lot of interaction to make things run smoothly -power grids, the Internet, financial markets, the cells in your body, schools of fish, any average kindergarten - and math is the basis.

Unraveling Complex Systems is the theme of Mathematics Awareness Month. You might not have known it was Mathematics Awareness Month. That's an annual project of the Joint Policy Board for Mathematics. So, we've asked our math guy, Keith Devlin, to describe complex systems to us - simply, we hope. Keith joins us from Stanford. Keith, thanks for being with us.

KEITH DEVLIN: Good morning, Scott, and Happy Mathematics Awareness Month to you.

SIMON: You were the first person to say that to me, Keith.

DEVLIN: You know, I'm shocked, shocked, to hear that, Scott.

SIMON: And I predict it might have to last me the month too. But...

DEVLIN: It will.

SIMON: That being noted, are complex systems the same that another way of saying complicated?

DEVLIN: In a sense, yeah. I mean, complicated systems is really just a generic term in everyday language. The first complex systems really means when you've got a very large number of relatively simple systems which you can specify using mathematics interacting together and we call it a complex system because the complexity defies prediction. We're used to mathematics predicting things. You know, we know exactly when Haley's Comet is going to reappear in the sky; the Army knows exactly where a mortar shell is going to land when it sends one off.

That's using mathematics to predict with great precision what's going to happen. When you have these complex interacting systems, there's no way we can predict what's going to happen. We have to use mathematics in a different and a new way in order to apply to complex systems.

SIMON: And what's that way?

DEVLIN: It really comes down to computer modeling. We build computer models of these systems. The mathematics we use to build the models - there's a lot of mathematics used, there's a lot of probability theory, there's a lot of statistic, quite often there's differential equations, a lot of modern network theory. We put a whole bunch of mathematics together and we build computer models and then we simulate what's going to happen.

The simulation is never going to tell us what happens but by playing with that simulation - changing one thing, seeing what happens when one power station goes off on a grid, seeing what might happen when there's an earthquake - we can come not to predict what will happen but to have a much better overall holistic understanding of what's going to happen so we can actually design them to minimize the likelihood that things go wrong and also to prepare to do things when they do go wrong.

And one thing that we've learned from running these simulations over many years now is that things will go wrong and they'll go wrong in ways that no one has thought about before.

SIMON: And at the same time, Keith, the situation we've been seeing unfold in Japan suggest to a lot of people that maybe it's dangerous to have complex systems when the stakes are so high.

DEVLIN: They are indeed dangerous but we're in that world now. Some of the complex systems we have to live with - the Internet is certain. The airline network; it's true, there's an enormous complex in the airline network. You know, one or two planes go out and then a whole country can be affected by them.

But, you know, if we wanted to avoid those dangers, we'd have to say, well, we won't have airline networks, we won't have a power grid, we won't have the Internet, we won't have any kind of an economy. It's just the world we live in.

SIMON: Keith, are there complex systems out there we haven't been able to unravel, we don't understand?

DEVLIN: The honest answer, Scott, is we have not been able to unravel any complex system. And I think one of the things we've learned - if we didn't already suspect it or know it - was that complex systems are inherently non-unravenable. The best you can do is gain a holistic understanding by running simulations. And that's the world we live in and there's no other alternative to doing that I think.

SIMON: Keith Devlin, our Math Guy and Stanford University professor, thanks so much for being with us.

DEVLIN: My pleasure, Scott. Bye-bye.

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