When Socrates was condemned to death ("for corrupting Athenian youth"), his pupil Plato sought Pythagorean sanctuary and learning. Repatriated, Plato renounced Pythagoreanism, canonizing Eleatic dogma historically. The motto of Plato's Academy -- "Let no one ignorant of geometry enter here!" -- implied "Geometry is incompatible with arithmetic." Platonists further argued. "Motion is geometry set to time." Hence, "Motion cannot be arithmetized!" Velocity, acceleration, force, momentum, energy, etc., seemed meaningless.

I call this the "AGstymie", since its argument of the incompatibility of arithmetic, "A", and geometry, "G", stymied the development of theoretical mechanics. (See below the "TOstymie", which the Platonists now maintain.)

But perhaps ancient applied mechanics was rudimentary. No! Quite the contrary!

Inheriting from the great Alexandrian Period -- which boasted robots and steam cars! -- imperial Roman engineers developed efficient windmills and water mills (For example, in the first century B.C., the Roman engineer Vitrivius described the undershot water wheel, later so useful in medieval and post- medieval Europe, as a machine rarely used.)

However, believing that theoretical extensions were impossible, no improvements replaced the vast slave power. (Compassion didn't end European slavery -- only disproof of cost-effectiveness.) We glean the efficiency of this machinery from The Medieval Machine, The Industrial Revolution of the Middle Ages, by J. Gimpel. To produce food, materials for clothing, etc., yet leave time for prayer and meditation, 12th century monks were permitted to read "pagan" Roman manuals about labor-saving devices. Soon thousands of windmills and water mills covered Europe and Britain.

This Mechanical Industrial Revolution waned with "The Black Death" (bubonic plague), peaking in 1348. In some regions, 50% of the population died in "The Black Death". Many regions lacked blacksmiths, coopers, wheelrights, other craftsmen.

Training had been oral. The Church now allowed more general reading of "pagan" books, initiating The Renaissance. (Tell this story to teen-agers who "want to work with their hands", and ask why they need reading skills!)

Thus did the Platonists delay the "Industrial Revolution" and prolong slavery!

Today, Platonism" is the dominant mathmetical philosophy in mathematics departments around the world.