Preindustrial Europe: Science, the Economy, and Political Reorganization 293their attempts to solve an ever-growing list of prob-
lems. The problems arose mainly from the perception
that old, accepted answers, however logical and com-
forting they may have been, did not square with ob-
served reality. The answers, and the accumulation of
methods by which they were achieved, laid the
groundwork of modern science.
The Aristotelian tradition contributed a rigorous
concern for accurate observation and a logical method
for the construction of hypotheses. In the wake of Ock-
hamist criticism, many Aristotelians, especially in the
Italian universities, had turned their attention to the
physical sciences, often with impressive results. Their
tradition remained vital in some places until the eigh-
teenth century. Experimentalism, once the province of
medieval Franciscans and Joachimites, was revived and
popularized by Sir Francis Bacon (1561–1626), the lord
chancellor of England. Like his predecessors, he accom-
plished little because his hypotheses were faulty, but
the elegance of his prose inspired a host of followers.
His contemporary Galileo Galilei (1564–1642) used
experiment to greater effect, though many of his best
demonstrations were designed but never performed.
The humanist tradition contributed classical texts that
reintroduced half-forgotten ideas, including the physics
of Archimedes and the heliocentric theories of Eratos-
thenes and Aristarchus of Samos. It also encouraged
quantification by reviving the numerological theories of
Pythagoras.
The thinkers of the sixteenth and seventeenth cen-
turies were interested in nearly everything, but they
achieved their greatest breakthroughs in astronomy and
physics. The Copernican theory, though by no means
universally accepted, became their starting point.
Copernicus had brought the traditional cosmology into
question, but his system with its epicycles and circular
orbits remained mathematically complex and virtually
incomprehensible as a description of physical reality
(see illustration 16.1).
A more plausible model of the cosmos was devised
by Johannes Kepler (1571–1630), court astrologer to
the emperor Rudolph II. Kepler’s views were a fusion of
organic and mechanistic ideas. He believed that the
Earth had a soul, but as a follower of Pythagoras he
thought that the universe was organized on geometrical
principles. The Copernican epicycles offended his no-
tions of mathematical harmony. He wanted to believe in
circular orbits, but when he posited eccentric circles
that did not center on the Sun, he was left with a minute
discrepancy in his formulae. It was a terrible dilemma:
The circle may have been the perfect geometric figure,
but he could not accept a universe founded on imperfect
mathematics. In the end, he decided that planetary or-
bits had to be elliptical. This solution, which proved to
be correct, was not generally accepted until long after
his death, but Kepler did not mind. Like the number-
mystic he was, he went on searching for other, more
elusive cosmic harmonies that could be described in mu-
sical as well as mathematical terms.
Meanwhile, Galileo rejected the theory of elliptical
orbits but provided important evidence that the planets
rotated around the Sun. A professor at the University of
Padua, Galileo was perhaps the first thinker to use
something like the modern scientific method. He quar-
reled with the Aristotelians over their indifference to
mathematical proofs and denounced their teleological
obsession with final causes, but like them he was a care-
ful observer. Unlike them, he tried to verify his hy-
potheses through experiment. From the Platonists and
Pythagoreans, he adopted the view that the universe
followed mathematical laws and expressed his theoriesIllustration 16.1
The System of Epicycles as Used in Ptolemaic Cosmology.
Epicycles were needed to predict the position of the planets, es-
pecially in the case of eccentrics and retrograde motions. These
diagrams illustrate that the results were almost unimaginable.
Drawing (a) shows an epicycle (P) on an epicycle, on a circular
planetary orbit around the Earth (E). Drawing (b) shows the path
a planet would have to take through space if this system of com-
pound circles were taken literally. Copernicus and many of his
contemporaries were dissatisfied with the Ptolemaic theory.