Evolution of Mathematics in Civilizational History

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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.

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In 1851, London became the capital of the world, but by 1889, the year of the Universal Exhibition, the French had caught up, and Paris, in the words of the cultural critic Walter Benjamin (1974) became the ‘intellectual capital’ of the nineteenth century. For this exhibition, the Eiffel Tower was created, and it was the first human structure to pass the Great Pyramid in height. Edison showed his moving pictures, and Satie heard Indonesian gamalan music for the first time, and was so impressed by its complex rhythms, that he eliminated mechanical time markings in his own compositions to strive to express a tonal durée. La durée also became the focus of Bergson’s philsosophy of time, as both Bergson and Proust worked to explore the new space of consciousness, particularly, time consciousness.

In the year 1889, the mathematician Poincaré single handedly invented complex dynamical systems and won the prize from the King of Denmark by proving that the solar system was not truly elliptical in Kepler’s sense, but was a chaotic system.

Florence, Venice, Antwerp, Amsterdam, and London had all been great trading metropoles, but late nineteenth-century Paris was something new under the sun. With its painters, poets, scientists, philosophers, and mathematicians, Paris was becoming the world’s first noetic polity. With many minds thinking about related ideas in an open and non-ideological fashion within a quite novel ecology of mind, Paris became an example of the parallel-processing of art and science that produced, not a religious ceremonial centre like ancient Hellenic Alexandria, but a noetic polity — one based not upon tribe, territory, or trade, but participation in shared states of consciousness. So let us once again satisfy the student’s of history’s love of dates by saying that 1889 is the year in which global music and planetary culture were born.

Cultural history tends to overlook the contribution of mathematicians like Poincaré, unless like Einstein they serve the invention of a new sort of bomb, but in the long view, the general, whose statue may be in the park, is an insignificant figure, and the mathematician or scientist who is not there is the unsung avatar of an age.

Music is an invisible architecture. Noise, therefore, is a medium of communication, indeed, the ground of our new electronic being; but silence is fearful and makes us feel as if we were suspended in a disturbing free-fall of consciousness. Satie prophetically understood this new relationship between music, noise, and information, and long before the music of Varèse and Stockhausen, or the information theory of Shannon, he incorporated the clatter of typewriters into his ballet, Parade. "

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


The Shift from Representation to Participation and the Chaos Dynamics of a New Planetary Culture

William Irwin Thompson:

"In this shift from representation to participation in a global medium of noise, one needs to recognize the paradoxically contradictory nature of a global ecology of mind composed of the distributive lattice of noetic polities. Representational space was constructed around a centre/periphery dimensionality; but participatory space is constructed around node/lattice circulations. Like a rocket with its small nose cone pointed to outer space, but all hell breaking loose in the other direction, the emergence of noetic polities is also characterized by a new dumbing-down in the mass-media. Queen Victoria and the neo-medievalism of Pugin, the Pre-Raphaelities, the Oxford Movement of Cardinal Newman, and the Arthurianism of Tennyson all served to camouflage the structure of Industrialization with the content of the Middle Ages. So now our new mathematical mentality of complex dynamical systems and our new global electronic technology are camouflaged with the mindlessness of comic book movies, rock music and pseudo ‘Country Music’, Clear Channel opinion radio, Creationism, and a general anti-scientific attitude. But just as the fire of the rocket and the navigation systems of the nose cone both serve to move the rocket away from Earth, so do the noetic polity and the new mass stupidity serve to take us away from the stability of the territorial nation-state into the chaos dynamics of a new planetary culture."

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