have the kind of widespread repeatability that is the social basis of certainty.
It was this takeoff in manipulating the machinery of mathematics that consti-
tuted the European mathematical revolution.
Overlaps among the Networks: World Comparison
How then did this revolution come about? Why did a genealogy of research
technologies build up, promoting rapid discovery, first in mathematics, then in
natural science? For a sociological answer, let us look at the networks.
The scientific-mathematical and philosophical networks overlap to a high
degree in the 1600s, so much so that they appear to be one revolution rather
than two. Of 6 major philosophers in that century, 5 are active scientists; 2
of them—Descartes and Leibniz—are mathematicians of the first rank. If we
go to the secondary philosophers of the 1600s, 3 of 14 are scientists, but
these 3 include another scientific star—Pascal—and two others, Gassendi and
Mersenne, who are at the center of the network of correspondence which
organizes the self-conscious movement that becomes in the next generation the
Royal Society and the Académie des Sciences.^14
European philosophy in the 1700s and 1800s continues to be linked to
science, although not to the same degree as in the Golden Century.^15 Major
philosophers in the West seem to have acquired some of their special creativity
from close connection to science, as the connection was much stronger than
among secondaries. Even philosophers known for their critiques of science—
such as Berkeley, Hume, and Rousseau—were in close contact with scientific
networks.
Although this connection reached its peak during the scientific revolution,
a connection between the networks of science and philosophy was long-stand-
ing in the West. In ancient Greece, the mathematical network was interwoven
with the philosophical one throughout their classical periods of creativity.^16 Of
the three earliest lineages of philosophers, all began with a reputed mathema-
tician: Thales, Pythagoras, and Leucippus. Not only the Pythagorean but the
Sophist network as well was full of mathematicians. It was in the milieu of the
latter that the first “mathematical revolution” took place; by the late 400s
b.c.e., the classic puzzles were being posed (trisecting an angle, squaring a
circle, tripling the volume of a cube), axiomatic proofs were afoot, geometric
results were collecting. Plato established his Academy by surrounding himself
with former Pythagoreans and other mathematical innovators.
Throughout the 300s b.c.e., the network of mathematicians and astrono-
mers in Figure 10.2 broadly overlaps with the philosophical network compris-
ing the interconnected schools of Plato, Eudoxus, and Aristotle; there is also
some scientific competition from the lineages of Democritus and of the Stoics.
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