The Eureka machine and cliodynamics

Computers are incredibly fast, accurate, and stupid. Human beings are incredibly slow, inaccurate, and brilliant. Together they are powerful beyond imagination. (Einstein)

Michael Schmidt and Hod Lipson have apparently developed an automated search algorithm which discovers physical laws and conservation equations from scratch. The algorithm scrutinises the experimental data extracted from the motion capture of physical systems, and reproduces the classical laws which explain the data. Or, as The Guardian claimed, Schmidt and Lipson have developed a 'Eureka machine'.

In a technique Schmidt and Lipson refer to as 'symbolic regression', their algorithm searches the space of possible mathematical expressions until it finds analytical expressions which reproduce the empirical data. Starting from algebraic operations and simple analytical functions such as sine and cosine, the algorithm randomly re-combines previous equations and parameters, and tests each set of expressions for accuracy against the empirical data, until it reaches a desired level of accuracy. Schmidt and Lipson's algorithm was able to converge on the Hamiltonians, Lagrangians and force laws of classical physical systems, including non-linear systems.

As an aside, if it is true that civilization is a non-linear classical physical system, then Schmidt and Lipson's algorithm could perhaps be applied to the data generated by human history, to discover the fundamental laws of cliodynamics. The difficulties of extracting empirical data in this case, where there is only historical documentation rather than motion capture, are obviously not to be underestimated. Moreover, whilst Schmidt and Lipson are able to pre-specify what the state variables of their systems are - they direct their software to look at positions, velocities and accelerations - in the case of cliodynamics, a central difficulty is identifying what the state variables actually are.

Schmidt and Lipson's work raises a number of funamental issues for both the philosophy of science, and for physics. The fact that their algorithm converges on unique, self-consistent laws, seems to undermine the purported underdetermination of theory by data, a popular bone of contention in the philosophy of science.

It also looks like this work is the first serious step down a road which will considerably alter, and perhaps reduce the creative opportunities for physicists. There would still be, of course, the need to develop such algorithms, to prepare the input data, and to interpret the output. And it should also be emphasised that, from the perspective of mathematical physics, the primary creative task is the discovery of mathematical structures, not the discovery of the laws satisfied by the variables embedded in those structures. An algorithm which discovers the mathematical structures necessary to represent the physical world is a step beyond the work of Schmidt and Lipson. Nevertheless, whilst mathematical physicists might take this consolation, the long-term prospects may not be quite as rosy for their counterparts in theoretical physics.