Cornell University researchers have developed an algorithm that can identify regularities in the natural world that represent natural laws. The researchers tested the algorithm on simple mechanical systems and believe that it could be applied to more complex systems. They say it could be useful in analyzing the massive amounts of data generated by experiments that use electronic data collection.
The algorithm, which was created by Cornell professor Hod Lipson and computational biology graduate student Michael Schmidt (pictured), starts by taking the derivatives of every variable observed with respect to every other, creating a mathematical way of measuring how one quantity changes as another changes. The algorithm then creates equations at random from various constants and variables from the data that it tests against the known derivatives. Equations that come close to making accurate predictions are kept, altered slightly, and tested again. The process is repeated until the algorithm evolves a set of equations that accurately describe the behavior of the real system. The algorithm does not technically output equations, but instead finds "invariants," or mathematical expressions that remain true in every situation, from which humans can derive equations. Once the invariants are identified, all equations describing the system should be available.
The method was tested using a spring-loaded linear oscillator, a single pendulum, and a double pendulum. Using data on position and velocity over time and acceleration, the algorithm found energy laws, the law of conservation of movement, and Newton's second law of motion. The researchers say the algorithm found these laws without any prior knowledge of physics, kinematics, or geometry.
From Cornell University
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