to follow the conventions can repeat the chain of argument. Mathematics is
certain because it is repeatable and reliable, and these consist in the repeatabil-
ity of a chain of social conventions.The Objects of Rapid-Discovery Science
Social constructivism in the sociology of science is generally associated with
an anti-realist position as to the entities of science. Let us see to what extent
this is justified. The activity of natural science, if not the name, has existed in
intellectual networks in many parts of the world since ancient times. Through-
out most of history (as Chapter 10 has described) these networks were subject
to the law of small numbers, dividing into opposing positions within astron-
omy, medical physiology, even mathematics. The entities of science constituted
multiple and competing realities for the networks that conceived them. In the
European generations between 1500 and 1700, a branch of intellectual net-
works reorganized in such a way that science changed its character: it became
rapid-discovery science, which eventually acquired a high degree of consensus.
The network shifted attention toward a train of forward-moving discoveries.
Disputes became more short-lived, rarely lasting beyond a generation. The
division among opposing positions under the law of small numbers was trun-
cated into a temporary disagreement at the research front, which was repeat-
edly put behind as attention moved onward to the next round of discoveries.
What I have just described is on the level of the social reality of these
networks of scientists; it refers to the entities of science only insofar as they
are contents asserted, disputed, accepted, and passed along by the network.
The network of scientists at the time of the rapid-discovery revolution was
largely a branch of the long-standing philosophical network. Gradually split-
ting off from the philosophers, the scientific network became in its own sphere
a double network: on one side a network of intellectuals, chains of masters
and pupils; on the other side chains of research equipment, modified from one
generation to the next.
The genealogies of research technology are carried along by the human
network; it is living persons who modify lenses into telescopes and micro-
scopes, and thence into the laboratory equipment of optics and spectrography.
Both kinds of networks are parasitical on one another. The rapid movement
of research equipment from one modification to the next is the key to the mode
of rapid discovery in which scientists have so much confidence; they feel that
discoveries are there to be made along a certain angle of research because the
previous generation of equipment has turned up phenomena which are suitable
for the intellectual life of the human network. The favored part of the scientific
network is that part which has closest access to the previous generation of
870 •^ Meta-reflections