I just downloaded a list of over 20,000 spectral lines from http://physics.nist.gov/cgi-bin/ASD/lines1.pl that have had their frequency painstakingly measured in laboratories around the world, and by capturing the patterns and regularities in these numbers, the Schrödinger equation can data-compress them down to just three numbers: the so-called fine-structure constant α ≈ 1/137.036, which gives the strength of electromagnetism, the number 1836.15, which is how many times heavier the proton is than the electron, and the orbital frequency of hydrogen.
