SIR ISSAC NEWTON
Newton, Sir Isaac (1642-1727), English natural
philosopher, generally regarded as the most original and influential theorist in
the history of science. In addition to his invention of the infinitesimal
calculus and a new theory of light and color, Newton transformed the structure
of physical science with his three laws of motion and the law of universal
gravitation. As the keystone of the scientific revolution of the 17th century,
Newton's work combined the contributions of Copernicus, Kepler, Galileo,
Descartes, and others into a new and powerful synthesis. Three centuries later
the resulting structure - classical mechanics - continues to be a useful but no
less elegant monument to his genius.
Life & Character
Isaac Newton was born prematurely on
Christmas day 1642 (4 January 1643, New Style) in Woolsthorpe, a hamlet near
Grantham in Lincolnshire. The posthumous son of an illiterate yeoman (also named
Isaac), the fatherless infant was small enough at birth to fit 'into a
quartpot.' When he was barely three years old Newton's mother, Hanna (Ayscough),
placed her first born with his grandmother in order to remarry and raise a
second family with Barnabas Smith, a wealthy rector from nearby North Witham.
Much has been made of Newton's posthumous birth, his prolonged separation from
his mother, and his unrivaled hatred of his stepfather. Until Hanna returned to
Woolsthorpe in 1653 after the death of her second husband, Newton was denied his
mother's attention, a possible clue to his complex character. Newton's childhood
was anything but happy, and throughout his life he verged on emotional collapse,
occasionally falling into violent and vindictive attacks against friend and foe
alike.
With his mother's return to Woolsthorpe in 1653, Newton was taken from
school to fulfill his birthright as a farmer. Happily, he failed in this
calling, and returned to King's School at Grantham to prepare for entrance to
Trinity College, Cambridge. Numerous anecdotes survive from this period about
Newton's absent-mindedness as a fledging farmer and his lackluster performance
as a student. But the turning point in Newton's life came in June 1661 when he
left Woolsthorpe for Cambridge University. Here Newton entered a new world, one
he could eventually call his own.
Although Cambridge was an outstanding center of learning, the spirit of
the scientific revolution had yet to penetrate its ancient and somewhat ossified
curriculum. Little is known of Newton's formal studies as an undergraduate, but
he likely received large doses of Aristotle as well as other classical authors.
And by all appearances his academic performance was undistinguished. In 1664
Isaac Barrow, Lucasian Professor of Mathematics at Cambridge, examined Newton's
understanding of Euclid and found it sorely lacking. We now know that during his
undergraduate years Newton was deeply engrossed in private study, that he
privately mastered the works of René Descartes, Pierre Gassendi, Thomas Hobbes,
and other major figures of the scientific revolution. A series of extant
notebooks shows that by 1664 Newton had begun to master Descartes'
Géométrie and other forms of mathematics far in advance of Euclid's
Elements. Barrow, himself a gifted mathematician, had yet to appreciate
Newton's genius.
In 1665 Newton took his bachelor's degree at Cambridge without honors or
distinction. Since the university was closed for the next two years because of
plague, Newton returned to Woolsthorpe in midyear. There, in the following 18
months, he made a series of original contributions to science. As he later
recalled, 'All this was in the two plague years of 1665 and 1666, for in those
days I was in my prime of age for invention, and minded mathematics and
philosophy more than at any time since.' In mathematics Newton conceived his
'method of fluxions' (infinitesimal calculus), laid the foundations for his
theory of light and color, and achieved significant insight into the problem of
planetary motion, insights that eventually led to the publication of his
Principia (1687).
In April 1667, Newton returned to Cambridge and, against stiff odds, was
elected a minor fellow at Trinity. Success followed good fortune. In the next
year he became a senior fellow upon taking his master of arts degree, and in
1669, before he had reached his 27th birthday, he succeeded Isaac Barrow as
Lucasian Professor of Mathematics. The duties of this appointment offered Newton
the opportunity to organize the results of his earlier optical researches, and
in 1672, shortly after his election to the Royal Society, he communicated his
first public paper, a brilliant but no less controversial study on the nature of
color.
In the first of a series of bitter disputes, Newton locked horns with the
society's celebrated curator of experiments, the bright but brittle Robert
Hooke. The ensuing controversy, which continued until 1678, established a
pattern in Newton's behavior. After an initial skirmish, he quietly retreated.
Nonetheless, in 1675 Newton ventured another yet another paper, which again drew
lightning, this time charged with claims that he had plagiarized from Hooke. The
charges were entirely ungrounded. Twice burned, Newton
withdrew.
In 1678, Newton suffered a serious emotional breakdown, and in the
following year his mother died. Newton's response was to cut off contact with
others and engross himself in alchemical research. These studies, once an
embarrassment to Newton scholars, were not misguided musings but rigorous
investigations into the hidden forces of nature. Newton's alchemical studies
opened theoretical avenues not found in the mechanical philosophy, the world
view that sustained his early work. While the mechanical philosophy reduced all
phenomena to the impact of matter in motion, the alchemical tradition upheld the
possibility of attraction and repulsion at the particulate level. Newton's later
insights in celestial mechanics can be traced in part to his alchemical
interests. By combining action-at-a-distance and mathematics, Newton transformed
the mechanical philosophy by adding a mysterious but no less measurable
quantity, gravitational force.
In 1666, as tradition has it, Newton observed the fall of an apple in his
garden at Woolsthorpe, later recalling, 'In the same year I began to think of
gravity extending to the orb of the Moon.' Newton's memory was not accurate. In
fact, all evidence suggests that the concept of universal gravitation did not
spring full-blown from Newton's head in 1666 but was nearly 20 years in
gestation. Ironically, Robert Hooke helped give it life. In November 1679, Hooke
initiated an exchange of letters that bore on the question of planetary motion.
Although Newton hastily broke off the correspondence, Hooke's letters provided a
conceptual link between central attraction and a force falling off with the
square of distance. Sometime in early 1680, Newton appears to have quietly drawn
his own conclusions.
Meanwhile, in the coffeehouses of London, Hooke, Edmund Halley, and
Christopher Wren struggled unsuccessfully with the problem of planetary motion.
Finally, in August 1684, Halley paid a legendary visit to Newton in Cambridge,
hoping for an answer to his riddle: What type of curve does a planet describe
in its orbit around the sun, assuming an inverse square law of attraction? When
Halley posed the question, Newton's ready response was 'an ellipse.' When asked
how he knew it was an ellipse Newton replied that he had already calculated it.
Although Newton had privately answered one of the riddles of the universe--and
he alone possessed the mathematical ability to do so--he had characteristically
misplaced the calculation. After further discussion he promised to send Halley a
fresh calculation forthwith. In partial fulfillment of his promise Newton
produced his De Motu of 1684. From that seed, after nearly two years of
intense labor, the Philosophiae Naturalis Principia Mathematica appeared.
Arguably, it is the most important book published in the history of science. But
if the Principia was Newton's brainchild, Hooke and Halley were nothing
less than midwives.
Although the Principia was well received, its future was cast in
doubt before it appeared. Here again Hooke was center stage, this time claiming
(not without justification) that his letters of 1679-1680 earned him a role in
Newton's discovery. But to no effect. Newton was so furious with Hooke that he
threatened to suppress Book III of the Principia altogether, finally
denouncing science as 'an impertinently litigious lady.' Newton calmed down and
finally consented to publication. But instead of acknowledging Hooke's
contribution Newton systematically deleted every possible mention of Hooke's
name. Newton's hatred for Hooke was consumptive. Indeed, Newton later withheld
publication of his Opticks (1704) and virtually withdrew from the Royal
Society until Hooke's death in 1703.
After publishing the Principia, Newton became more involved in
public affairs. In 1689 he was elected to represent Cambridge in Parliament, and
during his stay in London he became acquainted with John Locke, the famous
philosopher, and Nicolas Fatio de Duillier, a brilliant young mathematician who
became an intimate friend. In 1693, however, Newton suffered a severe nervous
disorder, not unlike his breakdown of 1677-1678. The cause is open to
interpretation: overwork; the stress of controversy; the unexplained loss of
friendship with Fatio; or perhaps chronic mercury poisoning, the result of
nearly three decades of alchemical research. Each factor may have played a role.
We only know Locke and Samuel Pepys received strange and seemingly deranged
letters that prompted concern for Newton's 'discomposure in head, or mind, or
both.' Whatever the cause, shortly after his recovery Newton sought a new
position in London. In 1696, with the help of Charles Montague, a fellow of
Trinity and later earl of Halifax, Newton was appointed Warden and then Master
of the Mint. His new position proved 'most proper,' and he left Cambridge for
London without regret.
During his London years Newton enjoyed power and worldly success. His
position at the Mint assured a comfortable social and economic status, and he
was an active and able administrator. After the death of Hooke in 1703, Newton
was elected president of the Royal Society and was annually reelected until his
death. In 1704 he published his second major work, the Opticks, based
largely on work completed decades before. He was knighted in
1705.
Although his creative years had passed, Newton continued to exercise a
profound influence on the development of science. In effect, the Royal Society
was Newton's instrument, and he played it to his personal advantage. His tenure
as president has been described as tyrannical and autocratic, and his control
over the lives and careers of younger disciples was all but absolute. Newton
could not abide contradiction or controversy - his quarrels with Hooke provide
singular examples. But in later disputes, as president of the Royal Society,
Newton marshaled all the forces at his command. For example, he published
Flamsteed's astronomical observations - the labor of a lifetime - without the
author's permission; and in his priority dispute with Leibniz concerning the
calculus, Newton enlisted younger men to fight his war of words, while behind
the lines he secretly directed charge and countercharge. In the end, the actions
of the Society were little more than extensions of Newton's will, and until his
death he dominated the landscape of science without rival. He died in London on
March 20, 1727 (March 31, New Style).
Scientific Achievements
Mathematics - The origin of Newton's interest in
mathematics can be traced to his undergraduate days at Cambridge. Here Newton
became acquainted with a number of contemporary works, including an edition of
Descartes Géométrie, John Wallis' Arithmetica infinitorum, and
other works by prominent mathematicians. But between 1664 and his return to
Cambridge after the plague, Newton made fundamental contributions to analytic
geometry, algebra, and calculus. Specifically, he discovered the binomial
theorem, new methods for expansion of infinite series, and his 'direct and
inverse method of fluxions.' As the term implies, fluxional calculus is a method
for treating changing or flowing quantities. Hence, a 'fluxion' represents the
rate of change of a 'fluent'--a continuously changing or flowing quantity, such
as distance, area, or length. In essence, fluxions were the first words in a new
language of physics.
Newton's creative years in mathematics extended from 1664 to roughly the
spring of 1696. Although his predecessors had anticipated various elements of
the calculus, Newton generalized and integrated these insights while developing
new and more rigorous methods. The essential elements of his thought were
presented in three tracts, the first appearing in a privately circulated
treatise, De analysi (On Analysis),which went unpublished until
1711. In 1671, Newton developed a more complete account of his method of
infinitesimals, which appeared nine years after his death as Methodus
fluxionum et serierum infinitarum (The Method of Fluxions and Infinite
Series, 1736). In addition to these works, Newton wrote four smaller tracts,
two of which were appended to his Opticks of
1704.
Newton and
Leibniz. Next to
its brilliance, the most characteristic feature of Newton's mathematical career
was delayed publication. Newton's priority dispute with Leibniz is a celebrated
but unhappy example. Gottfried Wilhelm Leibniz, Newton's most capable adversary,
began publishing papers on calculus in 1684, almost 20 years after Newton's
discoveries commenced. The result of this temporal discrepancy was a bitter
dispute that raged for nearly two decades. The ordeal began with rumors that
Leibniz had borrowed ideas from Newton and rushed them into print. It ended with
charges of dishonesty and outright plagiarism. The Newton-Leibniz priority
dispute--which eventually extended into philosophical areas concerning the
nature of God and the universe--ultimately turned on the ambiguity of priority.
It is now generally agreed that Newton and Leibniz each developed the calculus
independently, and hence they are considered co-discoverers. But while Newton
was the first to conceive and develop his method of fluxions, Leibniz was the
first to publish his independent results.
Optics. Newton's optical research, like his mathematical investigations, began
during his undergraduate years at Cambridge. But unlike his mathematical work,
Newton's studies in optics quickly became public. Shortly after his election to
the Royal Society in 1671, Newton published his first paper in the
Philosophical Transactions of the Royal Society. This paper, and others that
followed, drew on his undergraduate researches as well as his Lucasian lectures
at Cambridge.
In 1665-1666, Newton performed a number of experiments on the composition
of light. Guided initially by the writings of Kepler and Descartes, Newton's
main discovery was that visible (white) light is heterogeneous--that is, white
light is composed of colors that can be considered primary. Through a brilliant
series of experiments, Newton demonstrated that prisms separate rather than
modify white light. Contrary to the theories of Aristotle and other ancients,
Newton held that white light is secondary and heterogeneous, while the separate
colors are primary and homogeneous. Of perhaps equal importance, Newton also
demonstrated that the colors of the spectrum, once thought to be qualities,
correspond to an observed and quantifiable 'degree of
Refrangibility.'
The Crucial
Experiment. Newton's most famous experiment, the experimentum crucis,
demonstrated his theory of the composition of light. Briefly, in a dark room
Newton allowed a narrow beam of sunlight to pass from a small hole in a window
shutter through a prism, thus breaking the white light into an oblong spectrum
on a board. Then, through a small aperture in the board, Newton selected a given
color (for example, red) to pass through yet another aperture to a second prism,
through which it was refracted onto a second board. What began as ordinary white
light was thus dispersed through two prisms.
Newton's 'crucial experiment' demonstrated that a selected color leaving
the first prism could not be separated further by the second prism. The selected
beam remained the same color, and its angle of refraction was constant
throughout. Newton concluded that white light is a 'Heterogeneous mixture of
differently refrangible Rays' and that colors of the spectrum cannot themselves
be individually modified, but are 'Original and connate
properties.'
Newton probably conducted a number of his prism experiments at Cambridge
before the plague forced him to return to Woolsthorpe. His Lucasian lectures,
later published in part as Optical Lectures (1728), supplement other
researches published in the Society's Transactions dating from February
1672.
The
Opticks. The
Opticks of 1704, which first appeared in English, is Newton's most
comprehensive and readily accessible work on light and color. In Newton's words,
the purpose of the Opticks was 'not to explain the Properties of Light by
Hypotheses, but to propose and prove them by Reason and Experiments.' Divided
into three books, the Opticks moves from definitions, axioms,
propositions, and theorems to proof by experiment. A subtle blend of
mathematical reasoning and careful observation, the Opticks became the
model for experimental physics in the 18th century.
The
Corpuscular Theory. But the Opticks contained more than experimental results. During
the 17th century it was widely held that light, like sound, consisted of a wave
or undulatory motion, and Newton's major critics in the field of optics--Robert
Hooke and Christiaan Huygens--were articulate spokesmen for this theory. But
Newton disagreed. Although his views evolved over time, Newton's theory of light
was essentially corpuscular, or particulate. In effect, since light (unlike
sound) travels in straight lines and casts a sharp shadow, Newton suggested that
light was composed of discrete particles moving in straight lines in the manner
of inertial bodies. Further, since experiment had shown that the properties of
the separate colors of light were constant and unchanging, so too, Newton
reasoned, was the stuff of light itself-- particles.
At various points in his career Newton in effect combined the particle
and wave theories of light. In his earliest dispute with Hooke and again in his
Opticks of 1717, Newton considered the possibility of an ethereal
substance--an all-pervasive elastic material more subtle than air--that would
provide a medium for the propagation of waves or vibrations. From the outset
Newton rejected the basic wave models of Hooke and Huygens, perhaps because they
overlooked the subtlety of periodicity.
The question of periodicity arose with the phenomenon known as 'Newton's
rings.' In book II of the Opticks, Newton describes a series of
experiments concerning the colors of thin films. His most remarkable observation
was that light passing through a convex lens pressed against a flat glass plate
produces concentric colored rings (Newton's rings) with alternating dark rings.
Newton attempted to explain this phenomenon by employing the particle theory in
conjunction with his hypothesis of 'fits of easy transmission [refraction] and
reflection.' After making careful measurements, Newton found that the thickness
of the film of air between the lens (of a given curvature) and the glass
corresponded to the spacing of the rings. If dark rings occurred at thicknesses
of 0, 2, 4, 6... , then the colored rings corresponded to an odd number
progression, 1, 3, 5, 7, .... Although Newton did not speculate on the cause of
this periodicity, his initial association of 'Newton's rings' with vibrations in
a medium suggests his willingness to modify but not abandon the particle
theory.
The Opticks was Newton's most widely read work. Following the
first edition, Latin versions appeared in 1706 and 1719, and second and third
English editions in 1717 and 1721. Perhaps the most provocative part of the
Opticks is the section known as the 'Queries,' which Newton placed at the
end of the book. Here he posed questions and ventured opinions on the nature of
light, matter, and the forces of nature.
Mechanics. Newton's research in dynamics falls into
three major periods: the plague years 1664-1666, the investigations of
1679-1680, following Hooke's correspondence, and the period 1684-1687, following
Halley's visit to Cambridge. The gradual evolution of Newton's thought over
these two decades illustrates the complexity of his achievement as well as the
prolonged character of scientific 'discovery.'
While the myth of Newton and the apple maybe true, the traditional
account of Newton and gravity is not. To be sure, Newton's early thoughts on
gravity began in Woolsthorpe, but at the time of his famous 'moon test' Newton
had yet to arrive at the concept of gravitational attraction. Early manuscripts
suggest that in the mid-1660's, Newton did not think in terms of the moon's
central attraction toward the earth but rather of the moon's centrifugal
tendency to recede. Under the influence of the mechanical philosophy, Newton had
yet to consider the possibility of action- at-a-distance; nor was he aware of
Kepler's first two planetary hypotheses. For historical, philosophical, and
mathematical reasons, Newton assumed the moon's centrifugal 'endeavour' to be
equal and opposite to some unknown mechanical constraint. For the same reasons,
he also assumed a circular orbit and an inverse square relation. The latter was
derived from Kepler's third hypothesis (the square of a planet's orbital period
is proportional to the cube of its mean distance from the sun), the formula for
centrifugal force (the centrifugal force on a revolving body is proportional to
the square of its velocity and inversely proportional to the radius of its
orbit), and the assumption of circular orbits.
The next step was to test the inverse square relation against empirical
data. To do this Newton, in effect, compared the restraint on the moon's
'endeavour' to recede with the observed rate of acceleration of falling objects
on earth. The problem was to obtain accurate data. Assuming Galileo's estimate
that the moon is 60 earth radii from the earth, the restraint on the moon should
have been 1/3600 (1/602) of the gravitational acceleration on earth.
But Newton's estimate of the size of the earth was too low, and his calculation
showed the effect on the moon to be about 1/4000 of that on earth. As Newton
later described it, the moon test answered 'pretty nearly.' But the figures for
the moon were not exact, and Newton abandoned the
problem.
In late 1679 and early 1680 an exchange of letters with Hooke renewed
Newton's interest. In November 1679, nearly 15 years after the moon test, Hooke
wrote Newton concerning a hypothesis presented in his Attempt to Prove the
Motion of the Earth (1674). Here Hooke proposed that planetary orbits result
from a tangential motion and 'an attractive motion towards the centrall body.'
In later letters Hooke further specified a central attracting force that fell
off with the square of distance. As a result of this exchange Newton rejected
his earlier notion of centrifugal tendencies in favor of central attraction.
Hooke's letters provided crucial insight. But in retrospect, if Hooke's
intuitive power seems unparalleled, it never approached Newton's mathematical
power in principle or in practice.
When Halley visited Cambridge in 1684, Newton had already demonstrated
the relation between an inverse square attraction and elliptical orbits. To
Halley's 'joy and amazement,' Newton apparently succeeded where he and others
failed. With this, Halley's role shifted, and he proceeded to guide Newton
toward publication. Halley personally financed the Principia and saw it
through the press to publication in July 1687.
The
Principia. Newton's masterpiece is divided into three
books. Book I of the Principia begins with eight definitions and three
axioms, the latter now known as Newton's laws of motion. No discussion of Newton
would be complete without them: (1) Every body continues in its state of rest,
or uniform motion in a straight line, unless it is compelled to change that
state by forces impressed on it (inertia). (2) The change in motion is
proportional to the motive force impressed and is made in the direction of the
straight line in which that force is impressed (F = ma). (3) To every action
there is always an opposed and equal reaction. Following these axioms, Newton
proceeds step by step with propositions, theorems, and
problems.
In Book II of the Principia, Newton treats the Motion of bodies
through resisting mediums as well as the motion of fluids themselves. Since Book
II was not part of Newton's initial outline, it has traditionally seemed
somewhat out of place. Nonetheless, it is noteworthy that near the end of Book
II (Section IX) Newton demonstrates that the vortices invoked by Descartes to
explain planetary motion could not be self-sustaining; nor was the vortex theory
consistent with Kepler's three planetary rules. The purpose of Book II then
becomes clear. After discrediting Descartes' system, Newton concludes: 'How
these motions are performed in free space without vortices, may be understood by
the first book; and I shall now more fully treat of it in the following
book.'
In Book III, subtitled the System of the World, Newton extended
his three laws of motion to the frame of the world, finally demonstrating 'that
there is a power of gravity tending to all bodies, proportional to the several
quantities of matter which they contain.' Newton's law of universal gravitation
states that F = G Mm/R2; that is, that all matter is mutually
attracted with a force (F) proportional to the product of their masses (Mm) and
inversely proportional to the square of distance (R2) between them. G is a
constant whose value depends on the units used for mass and distance. To
demonstrate the power of his theory, Newton used gravitational attraction to
explain the motion of the planets and their moons, the precession of equinoxes,
the action of the tides, and the motion of comets. In sum, Newton's universe
united heaven and earth with a single set of laws. It became the physical and
intellectual foundation of the modern world view.
Perhaps the most powerful and influential scientific treatise ever
published, the Principia appeared in two further editions during Newton's
lifetime, in 1713 and 1726.
Other Researches
Throughout his career Newton conducted research
in theology and history with the same passion that he pursued alchemy and
science. Although some historians have neglected Newton's nonscientific
writings, there is little doubt of his devotion to these subjects, as his
manuscripts amply attest. Newton's writings on theological and biblical subjects
alone amount to about 1.3 million words, the equivalent of 20 of today's
standard length books. Although these writings say little about Newtonian
science, they tell us a good deal about Isaac Newton.
Newton's final gesture before death was to refuse the sacrament, a
decision of some consequence in the 18th century. Although Newton was dutifully
raised in the Protestant tradition his mature views on theology were neither
Protestant, traditional, nor orthodox. In the privacy of his thoughts and
writings, Newton rejected a host of doctrines he considered mystical,
irrational, or superstitious. In a word, he was a
Unitarian.
Newton's research outside of science--in theology, prophecy, and
history--was a quest for coherence and unity. His passion was to unite knowledge
and belief, to reconcile the Book of Nature with the Book of Scripture. But for
all the elegance of his thought and the boldness of his quest, the riddle of
Isaac Newton remained. In the end, Newton is as much an enigma to us as he was,
no doubt, to himself.
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