Evolution of Mathematics in Civilizational History

Discussion

William Irwin Thompson:

"With the rise of the city and the imperial ceremonial centre, the prehistoric Arithmetic Mentality begins to give way to the new powers of the Geometric Mentality.

The Arithmetic Mentality revolved around the Great Mother— the One who became many—and held the power of generation—of creatures and numbers. But to draft plans for ceremonial centres with monumental statuary and imposing fortresses required geometry. This process of transformation is recorded in the Babylonian Enuma Elish, which shows the male war god Marduk tearing apart the body of the Great Mother in order to build the city of Babylon, and it is shown in Aeschylus’s Oresteia, in which the warrior goddess Athena, born from the head of her father Zeus, revokes the power of maternal custom with its avenging furies to build the new power on the written text and the law courts of the city of Athens.

...

If we wish to pamper our need for dates, then let us take 1500 as a dividing point in the shift of mathematical mentalities from the Geometric and Algebraic to the Galilean Dynamical Mentality (Thompson, 2004).

The medieval Geometric Mentality is one in which motion is a fallen state, charging interest on loans is usura and sinful, and static humours are seen in Galenic medicine to affect the health of the body.

The new mentality is one in which motion is constitutive of value.

The movement of money with interest increases value, and the movement of trading ships — from the Chinese Ming Global Expansion in 1423 to Columbus in 1492 — expands the whole world picture. Kepler shifts Ptolemy’s worldpicture of perfect circles to less perfect ellipses, Harvey discovers the motion of the blood, Galileo computes the motion of falling bodies, and at the end of the shift from medievalism to modernism, Newton and Leibniz work out the new mathematics of calculus to describe the movement of the planets, and then everything really gets going, as the future, and not the past, becomes the locus of value when your ship comes in.

The Chinese eunuchs who administered the Ming Empire did not understand this new dynamical mentality, and tried to continue to rule the empire with a medieval Geometrical Mentality. The world was fixed and derived from the Emperor’s Mandate from Heaven, so all value derived from the past in a Confucian system of ancestor worship. Trade was tribute, and foreigners were suspect. The Muslim Admiral Xeng He was, therefore, a personal threat to the imperial court when he expanded its world picture. And so he was recalled, the records of his twenty years of costly world travel were burned, and the capital was shifted from coastal Nanking to inland Beijing. But meanwhile the Portuguese were sailing down the coast of Africa to Asia, and, on African currents, across to Brazil. And so the global projection of a new world civilization fell to the hands and minds of the Europeans and not the Chinese; and, at that time, China was the world’s most advanced civilization. The Europeans were then still a scruffy and unbathed smelly lot to both the Chinese and the Aztecs.

In the global projection of Western European civilization, three different societal structures were used in an attempt to control and manage the new world-space: the kingdom, the empire, and the newly emergent industrial nation-state. "

(http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.853&rep=rep1&type=pdf)