We're not alone in the universe of free will

A fascination with children's games has led mathematician John Conway to a mathematical proof of the existence of free will.

Dr Conway, a British-born professor at America's Princeton University, became famous in the maths world in 1970 when he invented a whole new theory of numbers based on simple games.

Six months ago he and a colleague, Simon Kochen, made another breakthrough with a mathematical proof that, if even a single human being can decide freely whether or not to drop a pen on the ground, then every particle in the universe must be able to exercise similar free will.

"This has changed my view of the universe," Dr Conway said yesterday in Auckland, where he will give a public lecture on his new theory tomorrow night.

Touching a desk, he said: "Inside this table are zillions of independent particles. They are taking independent decisions on whether to 'drop the pen'."

Dr Conway, 67, has written books on how to win popular games such as "dots and boxes", where two players take turns to connect the dots and the winner is the one who completes the most full squares.

In a public lecture in Napier this month, he challenged a young man in the audience to play 10 games of dots and boxes with him and told him that if he won a single game he would be the winner.

"He didn't win any. I am the world's great expert on children's games and how to play them properly.

"I take some tiny thing which is very marginal and insist on understanding it with an intensity you won't believe, such as dots and boxes - I wanted to understand it no matter how unimportant it was."

He astonished even himself, 35 years ago, when he began to express the outcomes of games in numbers.

The British champion of the ancient Chinese game of Go happened to be in the maths department at Cambridge, where Dr Conway was then teaching. Dr Conway watched him playing for hours and observed that the final stages of a game resembled the sum of earlier stages.

He gave values of +1 to a position in the game where you could make one move and your opponent could make no moves, -1 to a position where your opponent could make one move but you were trapped with no feasible moves, and so on.

He realised that this created a set not just of "real numbers" such as 0.5 or 5000, but what came to be called "surreal numbers" such as infinity plus 1, which were logically possible but paradoxical because they implied you could have numbers bigger than "infinity" and smaller than the smallest possible fraction. "So there are infinitely many infinite numbers."

Games also inspired him to create the "Game of Life", an experiment in what happens when you let "cells" multiply or die based on three simple rules: a living cell with two or three neighbouring living cells stays alive; a cell with fewer than two or more than three living neighbours dies of "loneliness" or "overcrowding"; but a dead cell with exactly three neighbours becomes a living cell again.

But 35 years later, he now believes that our real lives are not, as in the Game of Life, totally predetermined by a few simple rules. He believes that he is free to decide whether or not to drop his pen on the ground.

He and Dr Kochen have taken three basic axioms about the universe, such as the constant speed of light, and concluded mathematically that, if even one person has free will, then all particles must have it too.

In essence, they have proved that there is no possible set of "spins" of the three particles that is consistent with all three axioms, so the only way the universe can exist as we observe it is if the spins of the particles are not predetermined.

On a large scale, the universe is still predictable. A crowd may move in a certain direction, overall. The movements of big objects such as the planets can still be predicted hundreds of years into the future.

"It's only a limited amount of free will these particles have. Nonetheless, that's where my free will comes from. I am made of particles. Somehow, their ability to take these decisions is amplified in my behaviour. So I believe the universe is a wilful place, full of free will."

* John Conway on the free-will theorem, 4pm tomorrow, MLT1, Maths & Physics Building, University of Auckland.

Free-will theorem

* The smallest particles inside an atom have a certain tendency to keep rotating, or "spin".

* Scientists have found that the spin of some particles may be determined by the spin of other particles which have been "entangled" with them.

* However, information about the spin of a particle cannot be communicated faster than the speed of light.

* On this basis, and if a human experimenter can make decisions independently of past events, then the spin of a particle also cannot be predetermined.