# Analysis

Tannenbaum and Stillman successfully convey a sense of Newton’s cleverness at practical invention, and they sketch in the salient features of his magnificent accomplishments in mathematics, the theory of gravitation, and optics. Newton’s inventiveness first appeared when he was boarding with the Clarkes. He spent hours observing the construction of a nearby windmill and then astonished the Clarkes with a model that he had carved, complete with a fan that was powered by a mouse running on a tiny treadmill. He frightened the villagers by flying kites containing lighted candles, and he delighted the Clarkes by carving a four-foot-high clepsydra, or water clock, which they could point to with great pride. The inventor’s crowning achievement came years later when he built the first reflecting, as opposed to refracting, telescope.

This biography explores Newton’s two greatest achievements, the invention of
the method of fluxions (or differential calculus, as it is commonly known) and
the formulation of the laws of gravity, which had their origin in his private
studies during his student days. In Newton’s day, comets were still mysterious
phenomena, and even Newton could not predict their paths with only Euclidean
geometry and René Descartes’ algebra. Thus was born a new system of
mathematics, fluxions, from the Latin *fluxus*, meaning “change.” At
about the same time the German mathematician-philosopher Gottfried Wilhelm
Leibniz developed a similar method, which he called calculus. For years, a
bitter controversy raged over who should receive credit for the invention.
Modern scientists use two refinements of Newton’s and Leibniz’s mathematics:
From the positions of an object at given times, they calculate its velocity by
means of differential calculus, and when changes in an object’s velocity are
known, they can determine its position through integral calculus.

Tannenbaum and Stillman explain how Newton spent much of 1665 in Woolsthorpe
in retreat from an epidemic of plague and, while there, how he pondered the
mysteries of the positions of the planets, wondering what kept these whirling
bodies in their places. Johannes Kepler had said they were governed by their
souls, and Descartes had argued that space was full of tiny particles called
vortices that formed a medium in which the planets floated. It was at this time
that Newton is supposed to have asked why an apple fell down at his feet rather
than zooming off in another direction. Whatever the truth of that familiar
story, Newton intuited a mutual attraction that kept the universe from falling
apart, and he expressed his insight in the statement that the force of gravity
is inversely proportional to the square of the distance between two objects.
The authors show how these thoughts all bore monumental fruit in 1684 when
Newton submitted, subject to the insistence of his friend and astronomer Edmund
Halley, a paper that became what is often considered the greatest scientific
work ever written: *Philosophiae Naturalis Principia Mathematica* (1687;
the mathematical principles of natural philosophy).

While he was still a Fellow at Trinity College, Newton experimented with a prism. He discovered that white light passing through a prism created a spectrum but that individual colors in the spectrum produced only themselves. Eventually, he advanced his studies by building a successful reflecting telescope, and in 1672 he reported his theory of light and color to the Royal Society. His theory that light was made up of tiny bundles called corpuscles caused a tremendous row with fellow scientist Robert Hooke. Hooke had argued that light traveled as waves, and this controversy continued until the twentieth century.

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