1 The Birth of Science - MSRI

340 11. The Age-Long Recovery
of “phenomenon” changed in the same way. A rereading of the Dreyer
quote on page 76 will give a further example of how hard it became to
understand the ancient scientific method.
11.9 Ancient Science and Modern Science
At the base of modern science were Hellenistic science, on the one hand,
and on the other the study of and experimentation with technological
products having, in large measure, the same source. Yet modern science
attained fairly soon a state that appeared much more powerful than that
of its ancient counterpart. Why?
The exponential growth in scientific and technological knowledge and
industrial production that started in seventeenth-century Europe — and at
no other time or place in human history — hinged on many prerequisites,
as we saw in Section 9.7, not all of them easy to identify. One of them was
of course a sufficient mass of technological and scientific knowledge. This
initial mass, or cultural capital, was inherited from a distant civilization,
which (though lacking stock brokers and even a word for them) managed
to create many cultural instruments of lasting usefulness. Since the introduction
of writing, information can be preserved down the centuries and
millennia, and this means that superficially unexpected similarities can
coexist with profound differences between cultures.
What were the new factors that unchained the development seen in
modern times?
Taking mathematics first, consider the common claim that the positional
number system gave a decisive advantage to modern over ancient science.
But this system was borrowed from the Arabs, who inherited it from the
Indians, who in turn learned it from Hellenistic mathematicians. While its
furthest origins go back to Old Babylon, it was reformulated and rational- page 417
ized in the time of, and largely thanks to, Archimedes and Apollonius; in
Hellenistic times it was systematically used (especially in base sixty) for
trigonometrical and astronomical calculations — namely, those problems
that could not be solved with ruler and compass.
Thus the question becomes: How did solutions with ruler and compass,
which in Antiquity were considered simpler, get replaced by numerical
calculations in the modern age?
In reality, numerical calculations got a significant lead over geometric
methods only after the advent of printed tables of logarithms, in 1614.
The speedup represented by these computational aids meant that instead
of solving algebraic problems with ruler and compass, it became more
convenient to turn even geometric problems into algebraic ones, inverting
Revision: 1.11 Date: 2003/01/06 07:48:20