38; Mikami, 1913: 45–58; Qian, 1985: 62–63; Ho, 1985: 125–127; Chen, 1987:
77–85; Li and Du, 1987). Algebra reached sophisticated methods in the solution
of higher-order equations between 1200 and Chu Shih-chieh’s work in 1303; fifty
years later textbooks had reverted to an elementary level of arithmetic (Ho, 1985:
106). In the 1500s those who still recorded the Sung “celestial element” algebra
were no longer able to understand it (Mikami, 1913: 110). For other instances of
loss of advanced work, see Ho (1985: 72, 77); Needham (1959: 31, 33); Mikami
(1913: 37–39).
- In India, Aryabhata I (late 400s c.e.) expounded two astronomical systems; shortly
thereafter Varahamihira (ca. 500 c.e.) described five systems, one based on Vedic
astrology and four on Greek models (DSB, 1981: 15:533–632). Chinese astronomy
was always divided among competing models. In the Han dynasty there was a
struggle between advocates of the kaitian (hemispherical dome) and huntian (ce-
lestial sphere) cosmologies; in addition, two other systems were known. The
huntian model became dominant in the astronomical bureaus of dynasties after
550 c.e., but there continued to be advocates of a rival model as late as the Sung.
During the T’ang dynasty, there were three different schools of Indian astronomers
employed at the imperial observatory, but without influence on Chinese astrono-
mers. In the Yuan and Ming dynasties, there were Arab astronomers in official
service, but Chinese astronomers ignored the Arab-Ptolemaic epicyclic planetary
theory (Needham, 1959: 171–436; Sivin, 1969; Ho, 1985: 82, 129, 161–168;
Mikami, 1913: 101–106).
- There is evidence of around five competing research groups in a scientific specialty
(Price, [1963] 1986: 130–133).
- Thus Boyle’s vacuum pump could not be successfully imitated by anyone who had
not physically used an earlier exemplar (Shapin and Shaffer, 1985: 229–230, 281).
Harry Collins (1974) emphasizes that tacit knowledge of how to do research must
be transmitted by a personal network of craft-like apprenticeship, since it cannot
be encoded in purely verbal instructions. Latour’s (1987) depiction of science as a
network of human plus non-human actors may well anthropomorphize the natural
world, but it has this much justification: research-front science includes an ongoing
network of scientists together with the genealogy of machines on which they are
parasites, and vice versa.
- Many examples are given in Braudel ([1967] 1973: 244–324) in which technologies
stagnated for hundreds of years, including during the European centuries of the
scientific revolution. And even where there were periods of technological innova-
tion, they did not spill over into lineages of scientific research technology unless
they were carried by intellectual networks. Thus the periods of innovation in
weaponry, shipping, and construction engineering at various times in the history
of Hellenistic Greece, the Islamic world, and medieval Christendom did not connect
to intellectuals or become rapid-discovery science. See references in Collins (1986:
77–116).
- The number of mathematicians treated in DSB (1981) active in each third of a
century is as follows:
Notes to Pages 534–538^ •^993
