Hosted from the Archives: The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Brad DeLong (2005) : The Unreasonable Effectiveness of Mathematics in the Natural Sciences: Chad Orzel provides the pointer to Helge Kraghe, who writes in Physics Web http://physicsweb.org/articles/world/13/12/8 about how quantum theory existed in the equations of physics half a decade before the human brain of any physicist understood it….

Max Planck comes up with an equation that works. In order to do so he has to make a "purely formal assumption." And it is only half a decade later that Einstein realizes that the little h that appears in Max Planck's equation is not a "purely formal assumption" or an "artefact" but instead tells us what is perhaps the most important thing about the guts of the universe.

For half a decade the first equation of quantum theory was there. But nobody knew how to read it.

It is this "what if we took this equation seriously?" factor that is, to my mind at least, the spookiest thing about the unreasonable effectiveness of mathematics in physics. Take the h in Max Planck's equation seriously, and you have the quantum principle--something that was not in Planck's brain when he wrote the equation down. Take seriously the symmetry in Maxwell's equations between the force generated when you move a magnet near a wire and the force and the force generated when you move a wire near a magnet, and you have Special Relativity--something that was not in Maxwell's brain when he wrote down the equation. Take Newton's gravitational force law's equivalence between inertial and gravitational mass seriously and you have General Relativity--something never in Newton's mind. And take the mathematical pathology at r = 2M in the Schwarzchild metric for the space-time metric around a point mass seriously, and you have black holes and event horizons.