For the takeoff of rapid-discovery science in Europe, there are two major
candidates for external conditions: early capitalism and the Reformation.
Capitalism gives an impetus to commercial mathematics.^24 But low-status
practitioners do not usually attract the attention of the core intellectual net-
work; and by itself, the contents of commercial arithmetic does not automat-
ically lead to the abstract puzzles of higher mathematics. Capitalism also gives
some impetus to new technology, and we have seen that some of this equip-
ment—most famously, mining pumps—was brought into the network of “me-
chanical philosophers” and made into a technology of discovery. We must
beware of crude technological determinism, and of projecting backwards the
relationship between technology, capitalism, and science, which became char-
acteristic only after the “second industrial revolution” following the 1880s. As
Weber ([1923] 1961: 129–136; Collins, 1986: 19–44) pointed out, the ration-
alized capitalism which generates self-sustaining growth depends on a mixture
of social ingredients. Background conditions must free up all the factors of
production (land, labor, capital) so that they can move on the market, under
the control of entrepreneurs, and protected by a legal system guaranteeing
private property and facilitating its transactions through organized financial
instruments. Sustained technological innovation typically occurs late in this
process; conversely, the first few centuries of the capitalist takeoff involved
rationalized procedures in agriculture typically without any new machinery at
all.^25 Capitalism in Europe during the 1500s and 1600s made available some
fragmentary developments of machinery that could be pressed into intellectual
service by the philosophical networks; but the impetus to speed up their
evolution as pieces of research equipment came from the side of the philosophi-
cal network with its dynamics of competition over the attention space.
Capitalism by itself did little to rearrange the intellectual networks. Of
greater importance as an external condition was the Reformation, or more
precisely, the struggle over church politics culminating in the Reformation and
Counterreformation. Let us avoid any reflection argument. Science does not
reflect the spirit of Protestantism, nor indeed of Catholicism or wearied secu-
larism either. The familiar arguments of Weber and Merton rely too heavily
on an episode rather late in the rearrangement of networks, the coincidence of
the British Invisible College with the Puritan Revolution; the Catholic side of
the network was older, and in many respects more central. Most important,
the late medieval church had been breaking apart for centuries. The papal bid
for theocratic power over Christian Europe had crested in the mid-1200s;
thereafter the consolidating national states, most prominently France and
Spain, had struggled to make the papacy the instrument of their national
power; other states, in response, withdrew into increasingly nationally organ-
ized churches. The conciliar movement of the early 1400s, in which Cusanus
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