## Testing LaTeX

Test: $x^{2} = \int_{0}^{1} f(t) \, dt$.

Ever wanted to have a robot to do your research for you? If you are a scientist, you have almost certainly had this dream. Now it’s a real option: Eureqa, a program that distills scientific laws from raw data, is freely available to researchers.

The program was unveiled in April, when it used readouts of a double-pendulum to infer Newton’s second law of motion and the law of conservation of momentum. It could be an invaluable tool for revealing other, more complicated laws that have eluded humans. And scientists have been clamoring to get their hands on it.

“We tend to think of science as finding equations, like E=MC2, that are simple and elegant. But maybe some theories are complicated, and we can only find the simple ones,” said Hod Lipson of Cornell University’s Computational Synthesis Lab. “Those are unreachable right now. But the algorithms we’ve developed could let us reach them.”

Eureqa is descended from Lipson’s work on self-contemplating robots that figure out how to repair themselves. The same algorithms that guide the robots’ solution-finding computations have been customized for analyzing any type of data.

The program starts by searching within a dataset for numbers that seem connected to each other, then proposing a series of simple equations to describe the links. Those initial equations invariably fail, but some are slightly less wrong than others. The best are selected, tweaked, and again tested against the data. Eureqa repeats the cycle over and over, until it finds equations that work.

What took Newton years to calculate, Eureqa returned in a few hours on a decent desktop computer. Lipson and other researchers hope Eureqa can perform the same wizardry with data that now defies scientists, especially those working at the frontiers of biology, where genomes, proteins and cell signals have proven fantastically difficult to analyze. Their interactions appear to follow rules that traditional analytical methods can’t easily reveal.

“There’s a famous quote by Emerson Pugh: ‘If the human brain were so simple that we could understand it, we would be so simple that we couldn’t.’ I think that applies to all of biology,” said John Wikswo, a Vanderbilt University biophysicist who’s using the Eureqa engine in his own lab. “Biology is complicated beyond belief, too complicated for people to comprehend the solutions to its complexity. And the solution to this problem is the Eureqa project.”

Lipson made Eureqa available for download early in November, after being overwhelmed by requests from scientists who wanted him to analyze their data. In the meantime, he and Michael Schmidt, a Cornell University computational biologist responsible for much of Eureqa’s programming, continue to develop it.

An ongoing challenge is the tendency of Eureqa to return equations that fit data, but refer to variables that are not yet understood. Lipson likened this to what would happen if time-traveling scientists presented the laws of energy conservation to medieval mathematicians.

“Algebra was known. You could plug in the variable, and it would work. But the concept of energy wasn’t there. They didn’t have the vocabulary to understand it,” he said. “We’ve seen this in the lab. Eureqa finds a new relationship. It’s predictive, it’s elegant, it has to be true. But we have no idea what it means.”

Lipson and Schmidt are now devising “algorithms to explain what our algorithm is finding,” perhaps by relating unknown concepts to simpler, more familiar terms. “How do you explain something complicated to a child? That’s what it involves,” said Lipson. “It’s machine teaching, rather than machine learning.”

One set of incomprehensibly meaningful discoveries comes from Eureqa’s analysis of cellular readouts gathered by Gurol Suel, a University of Texas Southwestern molecular microbiologist who studies how cells divide and grow. But even if Eureqa can’t yet explain what it found, it’s still useful, said Suel.

“You can use this as a starting point for further investigations. It lets you think about new ideas of what’s going on in the cell, and generate new hypotheses about the properties of biological systems,” said Suel.

Sometimes Eureqa will require more data than it’s given before finding answers. In those cases, the program may be able to identify information gaps, and recommend experiments to fill them.

That functionality is included in the latest build of the program, and is being taken even further in a new Lipson-Wikswo project. They’re hooking a version of Eureqa directly to Wikswo’s experimental gadgetry.

“The program is going to adjust the valves, feeding different nutrients and toxins to the cells,” and it does this faster than any researcher, said Wikswo. “It comes up with the equations, plus the experiments needed to come up with the equations. It’s Eureqa on steroids.”

According to Wikswo, who studies the effects of cocaine on white blood cells, Eureqa can propose experiments that researchers would have difficulty imagining.

“In most of science, you try to keep everything constant except for one variable. You turn one knob at a time, and see how the system responds. That’s wonderful for linear systems,” he said. “But most biology is complex and non-linear. Emergent behaviors are very hard to understand unless you turn many knobs at a time, and we can’t figure out which knobs to turn. So we’re going to let Eureqa pick them.”

The Cornell team hasn’t counted downloads of their program, but it’s likely being used by researchers outside biology. As long as data fits on a spreadsheet, Eureqa can analyze it.

“In the past year, people have contacted us with some wild application ideas,” said Schmidt. “Everything from predicting the stock market to modeling the herding of cows.”

Images: 1) Hod Lipson running Eureqa in his office. 2) Diagrams of information flow through one of Lipson’s self-repairing robots (left) and Eureqa (right).