| Isaac Newton's Life
I INTRODUCTION
Newton, Sir Isaac (1642-1727), mathematician and physicist,
one of the foremost scientific intellects of all time. Born
at Woolsthorpe, near Grantham in Lincolnshire, where he
attended school, he entered Cambridge University in 1661;
he was elected a Fellow of Trinity College in 1667, and
Lucasian Professor of Mathematics in 1669. He remained at
the university, lecturing in most years, until 1696. Of
these Cambridge years, in which Newton was at the height
of his creative power, he singled out 1665-1666 (spent largely
in Lincolnshire because of plague in Cambridge) as "the
prime of my age for invention". During two to three
years of intense mental effort he prepared Philosophiae
Naturalis Principia Mathematica (Mathematical Principles
of Natural Philosophy) commonly known as the Principia,
although this was not published until 1687.
As a firm opponent of the attempt by King James II to make
the universities into Catholic institutions, Newton was
elected Member of Parliament for the University of Cambridge
to the Convention Parliament of 1689, and sat again in 1701-1702.
Meanwhile, in 1696 he had moved to London as Warden of the
Royal Mint. He became Master of the Mint in 1699, an office
he retained to his death. He was elected a Fellow of the
Royal Society of London in 1671, and in 1703 he became President,
being annually re-elected for the rest of his life. His
major work, Opticks, appeared the next year; he was knighted
in Cambridge in 1705.
As Newtonian science became increasingly accepted on the
Continent, and especially after a general peace was restored
in 1714, following the War of the Spanish Succession, Newton
became the most highly esteemed natural philosopher in Europe.
His last decades were passed in revising his major works,
polishing his studies of ancient history, and defending
himself against critics, as well as carrying out his official
duties. Newton was modest, diffident, and a man of simple
tastes. He was angered by criticism or opposition, and harboured
resentment; he was harsh towards enemies but generous to
friends. In government, and at the Royal Society, he proved
an able administrator. He never married and lived modestly,
but was buried with great pomp in Westminster Abbey.
Newton has been regarded for almost 300 years as the founding
examplar of modern physical science, his achievements in
experimental investigation being as innovative as those
in mathematical research. With equal, if not greater, energy
and originality he also plunged into chemistry, the early
history of Western civilization, and theology; among his
special studies was an investigation of the form and dimensions,
as described in the Bible, of Solomon's Temple in Jerusalem.
II OPTICS
In 1664, while still a student, Newton read recent work
on optics and light by the English physicists Robert Boyle
and Robert Hooke; he also studied both the mathematics and
the physics of the French philosopher and scientist René
Descartes. He investigated the refraction of light by a
glass prism; developing over a few years a series of increasingly
elaborate, refined, and exact experiments, Newton discovered
measurable, mathematical patterns in the phenomenon of colour.
He found white light to be a mixture of infinitely varied
coloured rays (manifest in the rainbow and the spectrum),
each ray definable by the angle through which it is refracted
on entering or leaving a given transparent medium. He correlated
this notion with his study of the interference colours of
thin films (for example, of oil on water, or soap bubbles),
using a simple technique of extreme acuity to measure the
thickness of such films. He held that light consisted of
streams of minute particles. From his experiments he could
infer the magnitudes of the transparent "corpuscles"
forming the surfaces of bodies, which, according to their
dimensions, so interacted with white light as to reflect,
selectively, the different observed colours of those surfaces.
The roots of these unconventional ideas were with Newton
by about 1668; when first expressed (tersely and partially)
in public in 1672 and 1675, they provoked hostile criticism,
mainly because colours were thought to be modified forms
of homogeneous white light. Doubts, and Newton's rejoinders,
were printed in the learned journals. Notably, the scepticism
of Christiaan Huygens and the failure of the French physicist
Edmé Mariotte to duplicate Newton's refraction experiments
in 1681 set scientists on the Continent against him for
a generation. The publication of Opticks, largely written
by 1692, was delayed by Newton until the critics were dead.
The book was still imperfect: the colours of diffraction
defeated Newton. Nevertheless, Opticks established itself,
from about 1715, as a model of the interweaving of theory
with quantitative experimentation.
III MATHEMATICS
In mathematics too, early brilliance appeared in Newton's
student notes. He may have learnt geometry at school, though
he always spoke of himself as self-taught; certainly he
advanced through studying the writings of his compatriots
William Oughtred and John Wallis, and of Descartes and the
Dutch school. Newton made contributions to all branches
of mathematics then studied, but is especially famous for
his solutions to the contemporary problems in analytical
geometry of drawing tangents to curves (differentiation)
and defining areas bounded by curves (integration). Not
only did Newton discover that these problems were inverse
to each other, but he discovered general methods of resolving
problems of curvature, embraced in his "method of fluxions"
and "inverse method of fluxions", respectively
equivalent to Leibniz's later differential and integral
calculus. Newton used the term "fluxion" (from
Latin meaning "flow") because he imagined a quantity
"flowing" from one magnitude to another. Fluxions
were expressed algebraically, as Leibniz's differentials
were, but Newton made extensive use also (especially in
the Principia) of analogous geometrical arguments. Late
in life, Newton expressed regret for the algebraic style
of recent mathematical progress, preferring the geometrical
method of the Classical Greeks, which he regarded as clearer
and more rigorous.
Newton's work on pure mathematics was virtually hidden from
all but his correspondents until 1704, when he published,
with Opticks, a tract on the quadrature of curves (integration)
and another on the classification of the cubic curves. His
Cambridge lectures, delivered from about 1673 to 1683, were
published in 1707.
The Calculus Priority Dispute
Newton had the essence of the methods of fluxions by 1666.
The first to become known, privately, to other mathematicians,
in 1668, was his method of integration by infinite series.
In Paris in 1675 Gottfried Wilhelm Leibniz independently
evolved the first ideas of his differential calculus, outlined
to Newton in 1677. Newton had already described some of
his mathematical discoveries to Leibniz, not including his
method of fluxions. In 1684 Leibniz published his first
paper on calculus; a small group of mathematicians took
up his ideas.
In the 1690s Newton's friends proclaimed the priority of
Newton's methods of fluxions. Supporters of Leibniz asserted
that he had communicated the differential method to Newton,
although Leibniz had claimed no such thing. Newtonians then
asserted, rightly, that Leibniz had seen papers of Newton's
during a London visit in 1676; in reality, Leibniz had taken
no notice of material on fluxions. A violent dispute sprang
up, part public, part private, extended by Leibniz to attacks
on Newton's theory of gravitation and his ideas about God
and creation; it was not ended even by Leibniz's death in
1716. The dispute delayed the reception of Newtonian science
on the Continent, and dissuaded British mathematicians from
sharing the researches of Continental colleagues for a century.
IV MECHANICS AND GRAVITATION
According to the well-known story, it was on seeing an apple
fall in his orchard at some time during 1665 or 1666 that
Newton conceived that the same force governed the motion
of the Moon and the apple. He calculated the force needed
to hold the Moon in its orbit, as compared with the force
pulling an object to the ground. He also calculated the
centripetal force needed to hold a stone in a sling, and
the relation between the length of a pendulum and the time
of its swing. These early explorations were not soon exploited
by Newton, though he studied astronomy and the problems
of planetary motion.
Correspondence with Hooke (1679-1680) redirected Newton
to the problem of the path of a body subjected to a centrally
directed force that varies as the inverse square of the
distance; he determined it to be an ellipse, so informing
Edmond Halley in August 1684. Halley's interest led Newton
to demonstrate the relationship afresh, to compose a brief
tract on mechanics, and finally to write the Principia.
Book I of the Principia states the foundations of the science
of mechanics, developing upon them the mathematics of orbital
motion round centres of force. Newton identified gravitation
as the fundamental force controlling the motions of the
celestial bodies. He never found its cause. To contemporaries
who found the idea of attractions across empty space unintelligible,
he conceded that they might prove to be caused by the impacts
of unseen particles.
Book II inaugurates the theory of fluids: Newton solves
problems of fluids in movement and of motion through fluids.
From the density of air he calculated the speed of sound
waves.
Book III shows the law of gravitation at work in the universe:
Newton demonstrates it from the revolutions of the six known
planets, including the Earth, and their satellites. However,
he could never quite perfect the difficult theory of the
Moon's motion. Comets were shown to obey the same law; in
later editions, Newton added conjectures on the possibility
of their return. He calculated the relative masses of heavenly
bodies from their gravitational forces, and the oblateness
of Earth and Jupiter, already observed. He explained tidal
ebb and flow and the precession of the equinoxes from the
forces exerted by the Sun and Moon. All this was done by
exact computation.
Newton's work in mechanics was accepted at once in Britain,
and universally after half a century. Since then it has
been ranked among humanity's greatest achievements in abstract
thought. It was extended and perfected by others, notably
Pierre Simon de Laplace, without changing its basis and
it survived into the late 19th century before it began to
show signs of failing. See Quantum Theory; Relativity.
V ALCHEMY AND CHEMISTRY
Newton left a mass of manuscripts on the subjects of alchemy
and chemistry, then closely related topics. Most of these
were extracts from books, bibliographies, dictionaries,
and so on, but a few are original. He began intensive experimentation
in 1669, continuing till he left Cambridge, seeking to unravel
the meaning that he hoped was hidden in alchemical obscurity
and mysticism. He sought understanding of the nature and
structure of all matter, formed from the "solid, massy,
hard, impenetrable, movable particles" that he believed
God had created. Most importantly in the "Queries"
appended to "Opticks" and in the essay "On
the Nature of Acids" (1710), Newton published an incomplete
theory of chemical force, concealing his exploration of
the alchemists, which became known a century after his death.
VI HISTORICAL AND CHRONOLOGICAL STUDIES
Newton owned more books on humanistic learning than on mathematics
and science; all his life he studied them deeply. His unpublished
"classical scholia"—explanatory notes intended
for use in a future edition of the Principia—reveal
his knowledge of pre-Socratic philosophy; he read the Fathers
of the Church even more deeply. Newton sought to reconcile
Greek mythology and record with the Bible, considered the
prime authority on the early history of mankind. In his
work on chronology he undertook to make Jewish and pagan
dates compatible, and to fix them absolutely from an astronomical
argument about the earliest constellation figures devised
by the Greeks. He put the fall of Troy at 904 BC, about
500 years later than other scholars; this was not well received.
VII RELIGIOUS CONVICTIONS AND PERSONALITY
Newton also wrote on Judaeo-Christian prophecy, whose decipherment
was essential, he thought, to the understanding of God.
His book on the subject, which was reprinted well into the
Victorian Age, represented lifelong study. Its message was
that Christianity went astray in the 4th century AD, when
the first Council of Nicaea propounded erroneous doctrines
of the nature of Christ. The full extent of Newton's unorthodoxy
was recognized only in the present century: but although
a critic of accepted Trinitarian dogmas and the Council
of Nicaea, he possessed a deep religious sense, venerated
the Bible and accepted its account of creation. In late
editions of his scientific works he expressed a strong sense
of God's providential role in nature.
VIII PUBLICATIONS
Newton published an edition of Geographia generalis by the
German geographer Varenius in 1672. His own letters on optics
appeared in print from 1672 to 1676. Then he published nothing
until the Principia (published in Latin in 1687; revised
in 1713 and 1726; and translated into English in 1729).
This was followed by Opticks in 1704; a revised edition
in Latin appeared in 1706. Posthumously published writings
include The Chronology of Ancient Kingdoms Amended (1728),
The System of the World (1728), the first draft of Book
III of the Principia, and Observations upon the Prophecies
of Daniel and the Apocalypse of St John (1733).
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