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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda
Hoping to firm up such notions, Wissner-Gross teamed up with Cameron Freer of the University of Hawaii at Manoa to propose a “causal path entropy.” This entropy is based not on the internal arrangements accessible to a system at any moment, but on the number of arrangements it could pass through on the way to possible future states. They then calculated a “causal entropic force” that pushes the system to evolve so as to increase this modified entropy. This hypothetical force is analogous to the pressure that a gas-filled compartment exerts on a piston separating it from a nearly evacuated compartment. In this example, the force arises because the piston’s motion increases the entropy of the filled compartment more than it reduces that of the nearly empty one.
In contrast with the usual entropy, no known fundamental law stipulates that this future-looking entropic force governs how a system evolves. But as a thought experiment, the researchers simulated the behavior of simple mechanical systems that included the force, and the effects were profound. For example, a particle wandering in a box did not explore the volume randomly but found its way to the center, where it was best positioned to move anywhere in the box. Another simulation tracked the motion of a rigid pendulum hanging from a pivot that could slide back and forth horizontally. The pendulum eventually moved into an inverted configuration, which is unstable without the modified entropic force. From this upside-down position, the researchers argue, the pendulum can most easily explore all other possible positions.
The researchers interpreted this and other behaviors as indications of a rudimentary adaptive intelligence, in that the systems moved toward configurations that maximized their ability to respond to further changes. Wissner-Gross acknowledges that “there’s no widely agreed-upon definition of what intelligence actually is,” but he says that social scientists have speculated that certain skills prospered during evolution because they allowed humans to exploit ecological opportunities. In that vein, the researchers connect the inverted pendulum’s mechanical “versatility” to the abilities that bipeds like us require in order to make the numerous on-the-fly adjustments needed to stay balanced while walking.