Charter Day panelist preview: math whiz Steven Strogatz

Register for Charter Day Weekend events
Charter Day: A Festival of Ideas and Imagination, part of Cornell’s sesquicentennial celebration, runs April 24-27. For event details and registration visit 150.cornell.edu/charterday.

Steven Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics, will speak at Charter Day: A Festival of Ideas and Imagination. His panel, “Six Degrees of Separation,” will be held Sunday, April 26, 1-2:15 p.m. at Bailey Hall.

What does “Six Degrees of Separation” mean?

It comes from the work of social psychologist Stanley Milgram. His “small world” experiment was to pick names out of the phone book in the middle of the country and get those people to send a packet by mail to a person in Boston. The rule was you can’t mail it to the person in Boston unless you know him. You were to send it to a friend of yours whom you think has more of a chance of knowing him than you do. The question was, would it ever get to the target? If so, how many steps would it take? That was a big question in 1967 … on average it turns out to be about six hops from anywhere to anywhere.

Steve Strogatz
Strogatz

Our event is about the breakthrough that came about from the work that my student Duncan Watts did with me when he was a grad student here. In the early ’90s, people were talking about six degrees of separation; this play [by the same name] came out, and then the movie, and soon after that, there was six degrees of Kevin Bacon. Around that time Duncan and I started to think, That’s an interesting math problem – how is it possible that a gigantic network could have this property that everybody is connected like that? We don’t know what the social network of the world looks like, but it must be constrained if it has this “small world” property.

Lots of things in the world are connected – for example, your brain is made of billions of brain cells. How does your brain operate as a giant network? If you think about the financial crisis, a few banks fail and then insurance companies start to fail, and you get propagation through the financial network. Or in the power grid, sometimes a power plant will go down, and then it starts to propagate as a blackout. Giant interconnected networks are all around us. And the more Duncan thought about it, the more he realized, this is THE problem of the modern world.

And that was the breakthrough – we said, let’s look at many different networks from a comparative point of view. How is the financial network like the brain, or like an ecosystem of species or like Stanley Milgram’s people sending letters? Is there a universal theory of networks?

That’s exciting stuff. Most people don’t think of math as very exciting.

People don’t see this as a creative or imaginative or human subject. People ask, why am I learning algebra or trigonometry, when am I gonna use that? The only honest answer is, you’re not going to need it.

But you could live your whole life without music, right? Music doesn’t help you do anything. And the humanities are not justified by what they help you to do. They enrich your life; they make your life better and more meaningful and more beautiful. And so I really ally myself with the humanities here. Mathematics is one of the great creative achievements of humanity, like art, like music.

The creative part of math is abstract. Abstraction is a very bold artistic statement. That this is what matters, and the other stuff doesn’t matter. Think of it as if we’re flying up in the sky, looking down and seeing an impressionistic view of the world. If you go up close, you’ll see that we’re missing a lot. But from a distance, we’re getting the picture nearly right. And that pointillist view of the world shows unifying principles. That’s the point of abstraction, that it lets you see the essence. This is why it’s beautiful to be a mathematician. I feel like it’s a completely thrilling subject.

The Charter Day celebrations are being called a Festival of Ideas and Imagination. Is there a particular idea that has inspired your imagination?

Art Winfree ’65 … He was my mentor. He’s really my inspiration. He said, “Choose something that grips you irrationally by the imagination or else nothing remarkable can happen.” That has been for me a lesson that I’ve tried to give to my students.

When Duncan Watts wanted to jump on the question of thinking about six degrees, even though we both knew that we didn’t know any sociology, we didn’t know the relevant branch of math … But the question gripped us both irrationally by the imagination.

We do these things because it’s beyond passion – it’s obsession. We are fascinated by this thing; it’s irrational, and we can’t help ourselves. If you want something remarkable to happen creatively, that’s what you need. Otherwise, it’ll all be pedestrian work. It’s interesting that genius is often at the edge of lunacy. I thought that was a great and inspiring idea. 

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Joe Schwartz