1 The Birth of Science - MSRI

334 11. The Age-Long Recovery
We can therefore conjecture that in his scientific source there was a quantitative
statement, expressed through an equality of ratios, linking the
force exerted by the sun with the spread of heat. It is possible that the
source stated that the force decreases with distance in the same ratio as
the intensity of light and heat, and thus in inverse proportion to the area
reached: the same idea later stated by Roger Bacon, Kepler and Boulliau.
The two-dimensional context of Vitruvius’ work matches particular well
Kepler’s treatment (which, as we have already seen, appears to almost
quote verbatim from Vitruvius in this matter of the force exerted by the
sun).
Of course, the interpretation we have suggested for Vitruvius’ passage
is only one possibility. Boulliau might have taken his ideas from some
other classical author or from medieval authors, such as Roger Bacon.
However, in the absence of ancient sources, direct or indirect, it is unlikely
that either he or Bacon would have examined the variation with distance
in a “force” whose meaning they did not know yet.
Misunderstanding for reflections on nature what were in fact attempts
to interpret ancient texts may have led astray many historians who have
sought to trace the development of ideas in the dawn of “modern science”.
11.8 The Rift Between Mathematics and Physics
The terminology of Renaissance scientists still followed the Greek model.
“Mathematics” meant the exact sciences as a whole. 149 When Copernicus
proudly wrote, in the dedicatory letter of the De revolutionibus, that “math- page 410
ematics is for mathematicians” (mathemata mathematicis scribuntur), he had
no doubt that his theory of the solar system was part of math.
As an example of what was still understood by the word in the early
seventeenth century, consider the second postulate in Simon Stevin’s On
the theory of ebb and flow (of tides):
[We postulate] that the earth is entirely covered with water, without
the wind or anything else hindering the ebb and flow. 150
148 This section contains material drawn from [Russo: Appunti].
149 In fact, the Renaissance’s extraordinary cultural unity caused the term to acquire an even wider
meaning for some authors. Fra Luca Pacioli, in the front page of his famous De divina proportione
(1509), addresses it to “every student of philosophy, perspective, painting, sculpture, architecture,
music and other mathematics”.
150 Simon Stevin, Van de spiegheling der ebbenvloet (Leiden, 1608), p. 179 = [Stevin: PW], p. 333. The
work is methodologically very interesting, but no more than middling in its technical content: it
lays out a simple static model for tides, based on lunar effects alone, and does not even discuss the
correlation between tides and phases of the moon.
Revision: 1.11 Date: 2003/01/06 07:48:20