This is an adaptation of a radio episode from the NPR program Engines of Our Ingenuity. It was inspired by a recent article in Wired on the program Eureqa which "discovered" Newton's laws of motion. Why are Dynamical Systems' analysts not an endangered species? Tell us your thoughts - a summary may be posted in an upcoming issue. Send your feedback to the author Krešimir Josić.

Newton’s Laws of Motion embody some of humanity’s greatest insights. Each law describes a universal relation between the motion of an object and forces acting on it. These laws condense the result of millennia of human thought. It therefore came as a surprise when Michael Schmidt and Hod Lipson of Cornell announced that an algorithm named Eureqa rediscovered Newton’s Second Law on its own [1]. After only a few hours of computation, a machine concluded that force equals mass times acceleration.

They did this by a clever version of a genetic algorithm: They let the computer observe a swinging pendulum. The algorithm then attempted to guess the law that governed the pendulum’s motion. The first guesses were off the mark. But, some were less wrong than others. In a process similar to natural selection, the program slightly adjusted and combined the best guesses to create the next generation of potential laws. Those guesses that did not agree with the observations or were too complicated had no descendants – only the best ones reproduced. After refining its guesses over many thousands of generations, the program arrived at the same answer as Newton. For humans this would be a mind numbing process that would take generations to complete. It took only a few hours on their computer.

An algorithm was able to determine the Hamiltonian of the double pendulum.

Chris Anderson, the editor in chief of Wired Magazine, suggested recently that such developments herald the end of theory. Will theorists really become obsolete? It has indeed become easy to collect and store vast amounts of data. Anderson suggests that we can simply let clever algorithms sift through these mountains of observations. Computers can tease out relations and rules that would take humans centuries to uncover. Indeed data mining is already a big business: Just as an example, links between certain diseases and genes are being made this way. Will computers discover new physical laws? Or novel mathematical truths?

I don't think we are there yet, and I am not certain that we will ever arrive at the end of theory. Humans still form an essential part in any process of discovery. Machines are great at uncovering correlations. They can tell us that a variant of a gene increases the likelihood of diabetes. However, computers are not good at finding the mechanisms that are behind such links: Does the gene cause diabetes, or does it simply occur more frequently in people who are predisposed to diabetes?

Moreover, many statements are true, but only few are interesting or useful. Humans evaluate the output of machines. It is people who synthesize these facts into the theories and models that describe the world around us.

It is easy to be dazzled by the powers of our machines, and take for granted the powers of the humans that operate them. It was humans who decided what problem Eureqa should tackle. And it was humans who steered and fine tuned the algorithm, evaluated its output and decided which part was interesting and insightful. I am certain that they sifted through tons of output, and thought long and hard how to present their findings. This is the type of intelligence that computers do not yet possess, and perhaps never will. Newton’s Laws offered unprecedented insights into the nature of reality. And it is still only humans who can fully appreciate them.

[1] M. Schmidt and H. Lipson. Distilling free-form natural laws from experimental data. Science2009 vol. 324 (5923) p. 81. Available from the author’s website.

You can read more about Eureqa here. Eureqa is free to download and to use. It’s available here. Here is a video that explains what it does and how.