Chaos and the quest to understand human behaviour

Marcus du Sautoy, professor of mathematics at Oxford University, likes Pi – both the mathematical constant and the film of the same name.

His MRS Conference talk began with a clip from the movie, which follows a mathematician’s descent into insanity while trying to look for mathematical patterns in the Jewish Torah.

“Mathematicians are pattern searchers,” du Sautoy explains. “That’s where mathematicians and researchers have so much in common.”

Max Cohen, the protagonist of Pi, believes that “there are patterns everywhere in nature”, you just have to how to see them. But that way lies madness, as Cohen discovers.

In the era of big data, it’s tempting to go looking for those patterns that can help us understand and ultimately predict human behaviour. But du Sautoy’s talk was both a lesson and a warning about the danger of seeing patterns where none exist, and in thinking that all patterns are predictable.

The pattern behind prime numbers, for example, continues to elude the brightest minds in the field, du Sautoy said. There is no way of knowing where, in the sequence of numbers, a prime will occur. “They seem to have a very random behaviour, but they can’t be random,” du Sautoy said. “A prime is a prime.”

Elsewhere in maths there are instances where a pattern looks to have been established, fooling you into thinking that you can predict where it goes next, only for it to end up “somewhere unexpected”, du Sautoy said.

And yet randomness can be understood thanks to a branch of mathematics called chaos theory, which recognises that there are systems that are so delicate that small changes in variables can send them spiralling out of control.

“With chaos theory, it’s not necessarily true that you can’t make predictions,” says du Sautoy, “but it is important to know when you can and when you can’t.”

Earth’s weather system is a good example of this, he said. Five-day forecasts can be reasonably accurate, du Sautoy explained, but attempting to make predictions into the sixth, seventh or eighth day and beyond becomes nigh-on impossible, with too many possible variables to consider and too many possible outcomes.

All of which seems to apply to the study of human behaviour. If a researcher were to ask any one of us what we would buy if we went shopping tomorrow, or how we would vote if an election were held the next day, we – and thus they – might be able to predict our behaviour with some accuracy. But next week, next month, next year? Who’s to say.