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 was "Let no one ignorant of geometry enter here!".

The incommensurability of the diagonal of a square with a side was thought to imply that "Geometry is incompatible with arithmetic." Since Platonists further argued that"Motion is geometry set to time", it was concluded that "Motion cannot be arithmetized!" (Velocity, acceleration, force, momentum, energy, etc., seemed meaningless.) Hence, the "AGstymie", since its argument of the incompatibility of arithmetic, "A", and geometry, "G", stymied the development of theoretical mechanics.

For, ancient applied mechanics was not rudimentary. 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, but rarely used in Roman times.)

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. Good reason, the Greco-Roman-Hebraic heritage of the West was one of slavery. That "thou-shalt-not" Book, The Bible nowhere says, "Thou shalt not enslave!" So, the Mathematical Establishment stood aside until evidence of the lack of cost-effectiveness ended widespread slavery -- still existent in "pockets" today.)

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. (The Black Death was caused by widespread killing of cats, which had controlled rats with their contagious fleas.) 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. However, the gravest charge against Galileo (1564-1642) was not his support of the argument of Johann Kepler (1571-1620) that the earth revolves around the sun, but rather that Galileo was a "Pythagorean" in promoting a "law of falling bodies".

Thus did the Platonists delay the "Industrial Revolution" and prolong slavery! (Today, Platonism is the dominant mathmetical philosophy in mathematics departments around the world.)