peak generations coincide; the outburst of Neo-Confucianism came in the years
1030–1100, and the culminating systems of Chu Hsi and Lu Chiu-yüan were
produced 1170–1200. The celestial element algebra, however, began to develop
after 1100 away from the court circles of the Neo-Confucians, and the star
mathematicians were active in the period 1240–1300.
If there is a connection, it is a conflictual one, based on struggles over the
external base. The early Neo-Confucians were the conservative faction in a
period of administrative crisis when rival reforms of the examination system
were alternatively implemented and reversed. Then came full-scale state break-
down; during the disruption of official bureaucracy, the celestial element alge-
bra was created by private teachers and out-of-office officials during the alien
Jürchen monarchy of north China after 1126, culminating during the Mongol
conquest (1220–1280). The efflorescence of mathematical schools at this time
had overtones of a popular religious movement; the mathematics itself was
more abstract than practical; conditions of life during the military conquests
were violent and unsettled; and the terminology and titles of the books imply
miraculously new and secret methods. The movement is obscure and in need
of greater study. The breakdown of the segregated governmental bureaus for
practical mathematics seems to be a key; when they were reestablished, the
new algebra died. In 1313 Neo-Confucianism became the official basis for the
examination system; soon after, the ability to understand the celestial element
method died out in China.^23
In India the separation between science and philosophy was even more
complete. Chronologies for India are weak and biographical data meager. For
what it is worth, there are no recorded contacts between philosophical and
mathematical networks, and no individuals overlap both activities (DSB, 1981;
Smith, 1951; Pingree, 1981). Indian science and mathematics were especially
fragmentary, full of disagreeing systems. Mathematics and astronomy imported
from China and Greece and contact with the Arabs combined with bits of
indigenous science in a jumble of texts which the Arab traveler al-Biruni (ca.
1030) in his India described as “a mixture of pearl shells and sour dates...
both kinds of things are equal in their eyes.” Organizationally, the mathema-
ticians, astronomers, and medical doctors were based in private familistic
lineages and guilds, never part of the sustained argument provided by philo-
sophical networks. Public networks of argument did exist in India; its philo-
sophical lineages reached high levels of abstract development. Only mathemat-
ics and science were not carried along with it.
why do philosophical networks promote science?
The philosophical networks represent the central attention space of the com-
munity of intellectuals, where arguments of widest consequence are carried
Cross-Breeding Networks and Rapid-Discovery Science • 551