Q&A with Eugenia Cheng

Eugenia Cheng is the author of the new book The Art of Logic in an Illogical World. She also has written Beyond Infinity and How to Bake Pi. She is the scientist in residence at the School of the Art Institute of Chicago, and an Honorary Fellow of the University of Sheffield. She lives in Chicago.

Q: In your new book, you write of today's argumentative world, "Is all hope lost? Are we doomed to take sides, be stuck in echo chambers, never again agree? No." Why do you feel that way?

A: I feel this way because I almost always feel able to understand and sympathise with people even when I completely disagree with them.

Often when I think about it very logically I can see that we are not fundamentally that different, it's just that small difference in fundamental beliefs develop into big differences in real life, a bit like someone braking on the highway causing a huge tailback hours later. It is hard to prevent the traffic jam but easier to stop someone braking unnecessarily.

Q: How do you define logic?

A: Logic is a process of rigorous deduction, where you start with some statements, and see what definitely has to be true as a result of those statements, not because of tradition, hope, statistics, or past evidence, but by something more inherent and unchanging.

Q: What do you see as the relationship between logic and emotion?

A: I see this relationship as unnecessarily adversarial. It is often thought that logic and emotions cannot coexist, that if you're emotional that shows you're not logical, and vice versa.

This gets thrown around in unhelpful arguments, often (but not always) between a man accusing a woman of being illogical, and the woman counter-accusing the man of being unfeeling.

However, I am highly emotional and also very logical - I am a professional mathematician after all. I think that if we pit logic and emotions in a battle then logic can't win.

But we don't need that battle. Logic and emotions can work together. I think we need logic to help us verify the rigour of our arguments, but we need emotions to understand other people and to persuade them of anything.

Q: Looking ahead, what role do you see for logic in what your title describes as "an illogical world"?

A: I think that logic plays a surprising role in helping us understand other people. If we find that someone holds a view with which we completely disagree, we can use careful logic to work our way backwards through their beliefs to find out where they come from.

We can then acknowledge the logic of their argument, from their point of view, using their fundamental beliefs, without agreeing with them. I think we can then use logic to examine our fundamental beliefs and theirs, and find ways to discover in what ways we think alike, instead of just thinking about how we differ.

Finding points of commonality will help us work towards a less divisive world, as we discover that most of us are really on a grey area between extremes, and that most of the issues in the world are not at all black and white.

Q: What are you working on now?

A: I am still teaching math to art students at the School of the Art Institute of Chicago and doing research in category theory, as well as writing the Everyday Math column for The Wall Street Journal, travelling around giving public talks and visiting schools, making art, playing the piano and starting research for my next book.

Q: Anything else we should know?

A: I am often asked how we can possibly change the minds of people who don't believe in truth, facts, logic or science. People tell me it is surely futile.

However, first of all I think our aim shouldn't be to change people's minds, but to understand why they think the things they do. Secondly, it is true that there are some very extreme people who will never be convinced about anything they don't already believe.

However, I think there are plenty of less extreme people, including those who believe in logic but want to get better at it, and those who are logical but have very different starting points from ours, and we can definitely reach greater understanding with them.

If we try to reach the whole world at once then it will indeed seem futile. But if we start by reaching the people nearest us, those people can help us reach the people a little further away, and so on.

Even if we don't persuade everyone to be logical and empathetic, if we can at least shift the weight further in that direction then I think the world will be a better place for us all.

--Interview with Deborah Kalb. Here's a previous Q&A with Eugenia Cheng.