HISTORICAL BACKGROUND OF THE UNIFICATION OF OPTICS AND MECHANICS

• 420 B.C., Hippias (460-400 B.C., Pythagorean follower) is said to have discovered incommensurability of square root of 2 and to have given proof of this.. Circa 390 B.C., Pythagorean scholar and student of Hippias, Theatetus (described by Plato in "Dialogue" by that name), teaches about "incommensurability". Also taught by Theodorus of Cyrene. Circa 365 B.C., Eudoxus (c. 408-355 B.C.) -- considered with Archimedes (287-212 B.C.) as "greatest ancient mathematicians" -- taught in Plato's School that MAGNITUDE should only be defined GEOMETRICALLY and created a ratio of magnitudes and a proportion, which comprehended both commensurable and incommensurable ratios (anticipating the work of 18th and 19the century mathematicians). This led to 2000 years of domination of MATHEMATICS by GEOMETRY. And led Plato to argue that proclaiming arithmetic incommensurables implies that motion ("geometry set to time") cannot be arithmetized -- meaning no measures of speed, acceleration, force, etc. -- causing a 1900-year neglect of theoretical mechanics in Europe, postponing "The Industrial Revolution" and prolonging slavery.

• Research in the pre-Renaissancew period was left to Islamic scholars. The most important Islamic advance was to arithmetize motion and challenge the Aristotlean "Law of Falling Bodies". Peculiarly, Islamic arguments for arithmetizing motion derived from analogies in pharmacy (mechanics at the molar level) and optics. It appeared possible to change magnitudes in medicines and in light intensities, hence, it was extrapolated to motion.

• The theory of the propagation of light of Pierre de Fermat (1601-1665) required light to follow a path of least time. William Rowan Hamilton (1805-1865) took Lagrange's action property (in mechanics) and showed that the path a particle would take would be the path of least action. This correlation between the motion of waves (as light was undertood at the time) and the motion of particles hints to the wave-particle duality of modern quantics. Some argue that, if experiments had been sufficiently advanced, Hamilton might have developed quantum theory one century before Schrödinger.