economy, remained separate from the samurai schools, and had no effect on
innovation in abstract mathematics (Dore, 1965).
- We see this in the surrounding conditions of several episodes of takeoff in intellec-
tual mathematics: Athens established a monetized retail market in the late 400s
b.c.e., and from 330 to 100 b.c.e. the international grain trade, centered on
Alexandria, broke out of the usual government-administered exchange into the
only competitive price-setting markets in antiquity (Polanyi, 1977: 238–251; Fin-
ley, 1973). Tokugawa Japan was a period of commercial capitalist boom; Italian
and German cities of the 1400s and 1500s were commercial and banking centers.
In the latter two cases we know explicitly that numeracy spread widely in the urban
population, and there were many commercial schools teaching practical mathe-
matics. Swetz (1987) and, in a Marxian version, Sohn-Rethel (1978) argue on the
basis of this correlation that capitalism produced the mathematical worldview.
- In Tokugawa Japan a rapidly expanding capitalist market, based on Weberian
structural conditions, had very little innovation in machinery but a great deal of
innovation in refinements of production for specialized market niches (Morris-
Suzuki, 1994).
- Rheticus in turn visited Cardano in 1545, and Cardano dedicated his great mathe-
matical work Ars Magna to Osiander. The work was published in Nuremberg by
the printer of De Revolutionibus (Blumenberg, 1987: 340). Cardano, in contact
with virtually every innovative network, was also a friend of Vesalius. Historical
sources on mathematicians of this period (DSB, 1981; Kline, 1972; Boyer, 1985;
Smith, 1951; Cardan, [1575] 1962).
- Michael Mahoney (personal communication) suggests that Copernicus’s new
model was worked out within the long-standing Ptolemaic tradition of astronomy,
eliminating some spheres and thereby better preserving Aristotle’s cosmology; thus
Copernicus belongs to a “reestablished classical tradition.” Copernicus differs from
Oresme in that he actually worked out the mathematics in detail; along the way,
as I noted earlier, he took part in developing new trigonometric tables to speed up
calculations.
- Brunelleschi and Alberti became concerned with the geometry of perspective in the
early 1400s, and Piero della Francesca treated the subject in a mathematical treatise
in 1478. The painters too were raising their status by connecting their manual craft
to an academic field; the result was to widen audiences and increase the focus of
attention all around.
- Notice that Descartes met Beeckman in 1618, before either of them did the work
that would make them famous: yet another case of a network forming a node
which promotes the later success of its members.
- The intention is plain despite continuities in terminology. The new science is
variously referred to as “natural” or “mechanical philosophy,” or sometimes
merely “philosophy” (e.g., Bacon De Dig. 1.3). As did others, Descartes (in
Principles) distinguished his “Philosophy” from “that which is taught in the
schools” (Descartes, [1644] 1983: xxvi).
- Here we see one of the weaknesses of the Burtt-Koyré thesis that the scientific
Notes to Pages 553–563^ •^997
