Sufi illuminationism prominent at the time (DSB, 1981: 11:249). Their science
became buried by the scholasticism of the madrasas which dominated later
Islamic intellectual life. In both cases of abortive scientific advance, Christian
and Islamic, loss of focus by the entire philosophical network dissolved the
possibility of cumulatively building on high points of scientific creativity, or
even remembering it.
Consider now a case in which scientific and philosophical networks sus-
tained interaction, indeed bootstrapped themselves cumulatively to levels long
remembered by the generations which followed. In Greece from the very
beginning of philosophical activity, from 600 down to about 200 b.c.e., the
network of mathematicians is virtually identical with a major segment of the
philosophical network. What difference did this make for mathematics? As an
ordinary practical activity of reckoning or measurement, mathematics gener-
ally shows little tendency toward formulating abstract theorems or rapidly
innovating. It was the intellectual networks that seized on mathematics, inter-
preting it as a clue to a cosmology rivaling other cosmologies (Pythagoras), or
turning it into a challenge to solve paradoxical problems (the Sophists). It was
the philosophical network which made Greek mathematics competitive and
innovation-oriented as well as generalized and abstract. As results accumu-
lated, the philosophical schools most interested in orderly synthesis promoted
the axiomatic method of formal derivation; these networks, deriving from
Democritus, the Platonists, and Aristoteleans alike, led to Euclid, Eratosthenes,
and Archimedes. Astronomers, and in another branch medical practitioners,
became part of the central network and were spurred to generalize abstract
systems on the terrain of philosophical cosmologies. Greek science set the
model for generalized science because it no longer represented a range of
practical activities pursued in private by low-status occupations, but rather
signaled a competition in the philosophical attention space.
an east-west divergence in scientists’ and
philosophers’ networks
Compare a crucial episode in the network history of China. Chinese mathe-
matics differed from the Greek puzzle-solving contests, with their impetus
toward proofs and axiomatic systems of abstract principles. For the most part,
Chinese math was practical calculation related to surveying and astronomy;
abstract developments were little valued and often forgotten by the official
textbooks. The cause of this difference may be seen in the relationship among
the networks. In China the practical mathematicians and astronomers were
largely separate from the philosophers.^21 Initial development could have gone
a different way; during the late Warring States, philosophers such as Hui Shih
and Kung-sun Lung produced quasi-mathematical paradoxes reminiscent of
Cross-Breeding Networks and Rapid-Discovery Science • 549