One of the great difficulties when investigating intelligence to a physicist is a lack of equations, — after all, physicists simply love equations. That’s probably why Alex Wissner-Gross decided to come up with an equation describing intelligence. And that equation is F = T ∇ Sτ, where F is the force, T is temperature and S is the entropy field. The idea behind the equation is that intelligence is a force F that pulls into the direction of states with more freedom of action, where T represents sort of an amount of resources a given intelligent system possesses. Finally, Sτ is the freedom of action that can be reached within a given time horizon τ.
It’s not trivial to interpret this equation, but, long story short, F is the force that drives an intelligent system towards the best possible future, which, in this case, is such that leaves the biggest variety choices. Now an interesting question that one might ask about this equation is whether this force is physical or not. For instance, the two most famous force equations, Coulomb’s law F=qq’/4πε0r2 and Newton’s law of gravity F= GMm/r2 represent two fundamental forces — electrostatic force and the force of gravity. In similar fashion, according to Wissner-Gross, F in his equation represents a new force — the force of intelligence. To illustrate the physical effects of this force he came up with a following example. Imagine a group of aliens observing planet Earth from far far away. Suppose the aliens measure the number of asteroids that hit the planet Earth for some reason. Now, imagine that after many years humans develop enough to be able to deflect or detonate these asteroids. For the alien astronomers such bizarre detonation or deflection of asteroids would appear as an effect of some yet unknown force — the force of intelligence. Naturally, a force law that would describe the behaviour of a large intelligent system, such as the humanity, might be invaluable in economics, sociology, politics and other fields.
For a more detailed explanation of the equation and the concepts behind it, visit this link.