1 The Birth of Science - MSRI

6.9 Where Do the Clichés about “Ancient Science” Come From? 177
One other source of the myth that Hellenistic science had no applications
was the introduction of new computational tools in the modern age. page 225
In the three centuries that preceded the invention of digital computers,
calculations were perfomed using:
– arithmetic operations on numbers written in decimal notation;
– numerical tables of logarithms and of certain other (e.g., trigonometric)
functions;
– operations of analysis, such as differentiation and integration, on functions
expressible in terms of “elementary functions” (which is to say
those whose values had been tabulated).
The ancient geometric methods, which from the beginning of the modern
age had started to become less useful given the systematic use of positional
notation, were definitely surpassed as computational tools at least
as early as 1614, when the first tables of logarithms were published. By
contrast, Euclidean mathematics remained a peerless model of rigor until
1872, when a rigorous theory of real numbers was founded (cf. page 41).
Between these two dates, mathematicians used Euclidean geometry as a
framework and prime example of the hypothetico-deductive method, and
decimal numbers and tables of logarithms for the calculations needed in
the solution of concrete problems. Also, certain ancient problems inherited
unsolved from Hellenistic mathematicians, including the trisection of the
angle, the doubling of the cube and the even more famous quadrature of
the circle, continued to fascinate, and the demand that they be solved with
ruler and compass, in spite of having lost its original motivation, 92 was accepted
as a “rule of the game” that characterized what became known as
the classical problems. 93
It was this, then, that nourished the belief that “classical mathematics” page 226
was good only for theory, and so strengthened the prejudices in this direction
that had arisen from the loss of records on ancient technology and
from the fact that Hellenistic mathematics was part of “Greek thought”, a
term usually targeting primarily the literary and philosophical works of
the classical period.
92 See the discussion on page 35.
93 In the nineteenth century these three problems were proved to be unsolvable with ruler and
compass. Note that all three had some practical interest. The trisection of the angle was probably
suggested by the need to draw divisions corresponding to the hours in sundials (compare [Neugebauer:
ESA], p. 265). The quadrature of the circle was tied to the need to compute trigonometric
functions, essential in topography and astronomy. The extraction of cube roots was useful, for example,
in the design of catapults (see page 97).
Revision: 1.7 Date: 2002/09/14 23:17:37