Can artificial intelligence discover new laws of physics? Possibly. An article in Technology Review suggests that data from a swinging pendulum experiment allowed a neural network to discover some of the laws of motion [1]. More generally, the idea is that if we give AI systems lots of data about a physical system, or from experiments, they will discover the relationships and regularities within this data, and do so much more quickly than humans. But recent research also highlights the perils of trying to generate theories from experimental data. Some mathematicians and scientists gave a machine learning algorithm data from experiments with falling bodies. The algorithm didn’t do so well. An AI system, based on measurement data, would “yield an Aristotelian theory of gravitation” [2]. The reasons why have important lessons for the role of AI in science.
A brief history of throwing things off buildings
Aristotle believed that heavier objects fall faster than lighter ones, in direct proportion to their weight. This is wrong; the time it takes an object to fall is independent of its mass. The equation for the time taken t for an object to fall a distance d is t=√(2d/g), where g is the acceleration due to gravity.
In the popular version, it was Galileo (1564–1642) who discovered that Aristotle was wrong. In the version I was taught, it had never crossed anyone’s mind to check what Aristotle said, until Galileo chucked differently sized cannon balls off the (conveniently) leaning tower of Pisa. This is also wrong; people had been throwing objects off buildings and watching how they fell for a long time. John Philoponus rejected Aristotle’s theory on falling bodies in the 6th century, concluding that the weight of an object made little difference to how quickly it fell. Simon Stevin and Jan Cornets de Groot also threw objects off the church tower in Delft in 1586. It is disputed whether Galileo needed to throw things off the tower in Pisa at all, because so many people had done it for him.
People knew that Aristotle was wrong, and experiments suggested it. However, generating a new theory, and getting to the equations describing falling bodies is extraordinarily difficult, even when we have data. The credit for this, mostly, goes to Galileo.
Knowing what data to exclude
Imagine that you’re a 6th century person with an interest in falling bodies. You worry that Aristotle is wrong and you’re keen to discover what’s really going on. What do you do? Find the nearest tall building and throw things off it. But which things? It seems so obvious to us that the things we throw off should be similar in shape and differ in their weight. But why? Don’t we want a theory that explains how cannon balls, and feathers, and tunics, and shoes fall? It’s only obvious if we think weight is the important factor.
We do know how objects other than cannon balls fall. Feathers and tunics fall more slowly than balls of the same weight because of their greater air …
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