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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
1 occurrence of Tonelli, Giorgio
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1 occurrence of Tonelli, Giorgio
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I. INTRODUCTION

The last forty years of the nineteenth century were
among the most remarkable in the history of science,
for this was a period of amazing scientific achievements
and contradictions; on the one hand classical physics
and astronomy were enjoying some of their greatest
successes during this period, but at the same time
observational and experimental data, which were ulti-
mately to overthrow the classical laws of physics, were
slowly being collected. Until the year 1860 physics and
astronomy were dominated by Newton's concepts of
space and time and by his laws of mechanics and
gravitation; these seemed sufficient to explain observa
tions ranging all the way from the motion of the planets
to the behavior of the tides on the earth. The great
eighteenth- and nineteenth-century mathematicians
such as Euler, Laplace, Lagrange, Hamilton, and
Gauss had cast the Newtonian laws into beautiful and
magnificent mathematical forms which had their
greatest applications to celestial mechanics. Astrono-
mers happily used these techniques to show how excel-
lent was the agreement between observation and the-
ory. The two domains of physics that still lay outside
the Newtonian laws—electromagnetism and optics—
were also soon to be incorporated into a satisfying
theoretical structure. In the year 1865, James Clerk
Maxwell published his famous papers on his electro-
magnetic theory of light, which gave a precise and
beautiful mathematical formulation of Faraday's ex-
perimental discoveries, unified electricity, magnetism,
and optics, and opened up the whole field of electro-
magnetic technology.

Thus, at the end of the first decade of the last forty
years of the nineteenth century, everything seemed to
fall neatly into place in the world of science. To the
scientists of that period, the universe appeared to be
a well ordered arrangement of celestial bodies moving
about in an infinite expanse of absolute space, and with
all the events in the universe occurring in a unique
and absolute sequence in time. There was no question
at that time as to the correctness of this Newtonian
universe based on the concepts of absolute space and
time; only the observational and experimental details
were lacking to make the picture complete, and
everyone was confident that, with improved technol-
ogy, these details would be obtained in time.

This absolute concept of the universe and of the laws
of nature was very satisfying to the late nine-
teenth-century man, who saw in the orderly and abso-
lute scheme of things the demonstration of the Divine
Omnipotence which he worshipped and which gave
him the reason for his existence; moreover, the infini-
tude of space and time required by the Newtonian
universe was also required by the concept of an in-
finitely powerful deity, as described by Alexander
Pope:

He sees with equal eye as God of all
A hero perish or a sparrow fall;
Atoms or systems into ruin hurl'd;
And now a bubble burst, and now a world.

(An Essay on Man III. 87-90)