Isaac
Newton
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Sir
Isaac Newton PRS MP (25 December 1642 – 20 March 1727) was an English physicist
and mathematician who is widely regarded as one of the most influential
scientists of all time and as a key figure in the scientific revolution. His
book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles
of Natural Philosophy"), first published in 1687, laid the foundations for
most of classical mechanics. Newton also made seminal contributions to optics
and shares credit with Gottfried Leibniz for the invention of the infinitesimal
calculus.
Newton's
Principia formulated the laws of motion and universal gravitation that
dominated scientists' view of the physical universe for the next three
centuries. It also demonstrated that the motion of objects on the Earth and
that of celestial bodies could be described by the same principles. By deriving
Kepler's laws of planetary motion from his mathematical description of gravity,
Newton removed the last doubts about the validity of the heliocentric model of
the cosmos.
Newton
built the first practical reflecting telescope and developed a theory of colour
based on the observation that a prism decomposes white light into the many
colours of the visible spectrum. He also formulated an empirical law of cooling
and studied the speed of sound. In addition to his work on the calculus, as a
mathematician Newton contributed to the study of power series, generalised the
binomial theorem to non-integer exponents, and developed Newton's method for
approximating the roots of a function.
Newton
was a fellow of Trinity College and the second Lucasian Professor of
Mathematics at the University of Cambridge. He was a devout but unorthodox
Christian and, unusually for a member of the Cambridge faculty, he refused to
take holy orders in the Church of England, perhaps because he privately
rejected the doctrine of trinitarianism. In addition to his work on the
mathematical sciences, Newton also dedicated much of his time to the study of
alchemy and biblical chronology, but most of his work in those areas remained
unpublished until long after his death. In his later life, Newton became
president of the Royal Society. He also served the British government as Warden
and Master of the Royal Mint.
Life
Early
life
Main
article: Early life of Isaac Newton
Isaac
Newton was born (according to the Julian calendar in use in England at the
time) on Christmas Day, 25 December 1642, (NS 4 January 1643.[1]) at
Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of
Lincolnshire. He was born three months after the death of his father, a
prosperous farmer also named Isaac Newton. Born prematurely, he was a small
child; his mother Hannah Ayscough reportedly said that he could have fit inside
a quart mug (≈ 1.1 litres). When Newton was three, his mother remarried and
went to live with her new husband, the Reverend Barnabus Smith, leaving her son
in the care of his maternal grandmother, Margery Ayscough. The young Isaac
disliked his stepfather and maintained some enmity towards his mother for
marrying him, as revealed by this entry in a list of sins committed up to the
age of 19: "Threatening my father and mother Smith to burn them and the
house over them."[8] Although it was claimed that he was once engaged,[9]
Newton never married.
From
the age of about twelve until he was seventeen, Newton was educated at The
King's School, Grantham. He was removed from school, and by October 1659, he
was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by
now for a second time, attempted to make a farmer of him. He hated farming.[10]
Henry Stokes, master at the King's School, persuaded his mother to send him
back to school so that he might complete his education. Motivated partly by a
desire for revenge against a schoolyard bully, he became the top-ranked
student.[11] The Cambridge psychologist Simon Baron-Cohen considers it
"fairly certain" that Newton had Asperger syndrome.[12]
In
June 1661, he was admitted to Trinity College, Cambridge as a sizar – a sort of
work-study role.[13] At that time, the college's teachings were based on those
of Aristotle, whom Newton supplemented with modern philosophers, such as
Descartes, and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he
discovered the generalised binomial theorem and began to develop a mathematical
theory that later became infinitesimal calculus. Soon after Newton had obtained
his degree in August 1665, the university temporarily closed as a precaution
against the Great Plague. Although he had been undistinguished as a Cambridge
student,[14] Newton's private studies at his home in Woolsthorpe over the
subsequent two years saw the development of his theories on calculus,[15]
optics and the law of gravitation. In 1667, he returned to Cambridge as a
fellow of Trinity.[16] Fellows were required to become ordained priests,
something Newton desired to avoid due to his unorthodox views. Luckily for
Newton, there was no specific deadline for ordination, and it could be
postponed indefinitely. The problem became more severe later when Newton was
elected for the prestigious Lucasian Chair. For such a significant appointment,
ordaining normally could not be dodged. Nevertheless, Newton managed to avoid
it by means of a special permission from Charles II (see "Middle years"
section below).
Middle
years
Mathematics
Newton's
work has been said "to distinctly advance every branch of mathematics then
studied".[17] His work on the subject usually referred to as fluxions or
calculus, seen in a manuscript of October 1666, is now published among Newton's
mathematical papers.[18] The author of the manuscript De analysi per
aequationes numero terminorum infinitas, sent by Isaac Barrow to John Collins
in June 1669, was identified by Barrow in a letter sent to Collins in August of
that year as:[19]
Mr
Newton, a fellow of our College, and very young ... but of an extraordinary
genius and proficiency in these things.
Newton
later became involved in a dispute with Leibniz over priority in the
development of infinitesimal calculus (the Leibniz–Newton calculus
controversy). Most modern historians believe that Newton and Leibniz developed
infinitesimal calculus independently, although with very different notations.
Occasionally it has been suggested that Newton published almost nothing about
it until 1693, and did not give a full account until 1704, while Leibniz began
publishing a full account of his methods in 1684. (Leibniz's notation and
"differential Method", nowadays recognised as much more convenient
notations, were adopted by continental European mathematicians, and after 1820
or so, also by British mathematicians.) Such a suggestion, however, fails to notice
the content of calculus which critics of Newton's time and modern times have
pointed out in Book 1 of Newton's Principia itself (published 1687) and in its
forerunner manuscripts, such as De motu corporum in gyrum ("On the motion
of bodies in orbit"), of 1684. The Principia is not written in the
language of calculus either as we know it or as Newton's (later) 'dot' notation
would write it. But his work extensively uses an infinitesimal calculus in
geometric form, based on limiting values of the ratios of vanishing small
quantities: in the Principia itself Newton gave demonstration of this under the
name of 'the method of first and last ratios'[20] and explained why he put his
expositions in this form,[21] remarking also that 'hereby the same thing is
performed as by the method of indivisibles'.
Because
of this, the Principia has been called "a book dense with the theory and
application of the infinitesimal calculus" in modern times[22] and
"lequel est presque tout de ce calcul" ('nearly all of it is of this
calculus') in Newton's time.[23] His use of methods involving "one or more
orders of the infinitesimally small" is present in his De motu corporum in
gyrum of 1684[24] and in his papers on motion "during the two decades
preceding 1684".[25]
Newton
had been reluctant to publish his calculus because he feared controversy and
criticism.[26] He was close to the Swiss mathematician Nicolas Fatio de
Duillier. In 1691, Duillier started to write a new version of Newton's
Principia, and corresponded with Leibniz.[27] In 1693 the relationship between
Duillier and Newton deteriorated, and the book was never completed.
Starting
in 1699, other members of the Royal Society (of which Newton was a member)
accused Leibniz of plagiarism, and the dispute broke out in full force in 1711.
The Royal Society proclaimed in a study that it was Newton who was the true
discoverer and labelled Leibniz a fraud. This study was cast into doubt when it
was later found that Newton himself wrote the study's concluding remarks on
Leibniz. Thus began the bitter controversy which marred the lives of both
Newton and Leibniz until the latter's death in 1716.[28]
Newton
is generally credited with the generalised binomial theorem, valid for any
exponent. He discovered Newton's identities, Newton's method, classified cubic
plane curves (polynomials of degree three in two variables), made substantial
contributions to the theory of finite differences, and was the first to use
fractional indices and to employ coordinate geometry to derive solutions to
Diophantine equations. He approximated partial sums of the harmonic series by
logarithms (a precursor to Euler's summation formula), and was the first to use
power series with confidence and to revert power series. Newton's work on
infinite series was inspired by Simon Stevin's decimals.[29]
He
was appointed Lucasian Professor of Mathematics in 1669 on Barrow's
recommendation. In that day, any fellow of Cambridge or Oxford was required to
become an ordained Anglican priest. However, the terms of the Lucasian professorship
required that the holder not be active in the church (presumably so as to have
more time for science). Newton argued that this should exempt him from the
ordination requirement, and Charles II, whose permission was needed, accepted
this argument. Thus a conflict between Newton's religious views and Anglican
orthodoxy was averted.[30]
Optics
From
1670 to 1672, Newton lectured on optics.[32] During this period he investigated
the refraction of light, demonstrating that a prism could decompose white light
into a spectrum of colours, and that a lens and a second prism could recompose
the multicoloured spectrum into white light.[33] Modern scholarship has
revealed that Newton's analysis and resynthesis of white light owes a debt to
corpuscular alchemy.[34]
He
also showed that the coloured light does not change its properties by
separating out a coloured beam and shining it on various objects. Newton noted
that regardless of whether it was reflected or scattered or transmitted, it
stayed the same colour. Thus, he observed that colour is the result of objects
interacting with already-coloured light rather than objects generating the
colour themselves. This is known as Newton's theory of colour.[35]
From
this work, he concluded that the lens of any refracting telescope would suffer
from the dispersion of light into colours (chromatic aberration). As a proof of
the concept, he constructed a telescope using a mirror as the objective to
bypass that problem.[36][37] Building the design, the first known functional
reflecting telescope, today known as a Newtonian telescope,[37] involved
solving the problem of a suitable mirror material and shaping technique. Newton
ground his own mirrors out of a custom composition of highly reflective
speculum metal, using Newton's rings to judge the quality of the optics for his
telescopes. In late 1668[38] he was able to produce this first reflecting
telescope. In 1671, the Royal Society asked for a demonstration of his
reflecting telescope.[39] Their interest encouraged him to publish his notes On
Colour, which he later expanded into his Opticks. When Robert Hooke criticised
some of Newton's ideas, Newton was so offended that he withdrew from public
debate. Newton and Hooke had brief exchanges in 1679–80, when Hooke, appointed
to manage the Royal Society's correspondence, opened up a correspondence
intended to elicit contributions from Newton to Royal Society transactions,[40]
which had the effect of stimulating Newton to work out a proof that the
elliptical form of planetary orbits would result from a centripetal force
inversely proportional to the square of the radius vector (see Newton's law of
universal gravitation – History and De motu corporum in gyrum). But the two men
remained generally on poor terms until Hooke's death.[41]
Newton
argued that light is composed of particles or corpuscles, which were refracted
by accelerating into a denser medium. He verged on soundlike waves to explain
the repeated pattern of reflection and transmission by thin films (Opticks
Bk.II, Props. 12), but still retained his theory of 'fits' that disposed
corpuscles to be reflected or transmitted (Props.13). Later physicists instead
favoured a purely wavelike explanation of light to account for the interference
patterns, and the general phenomenon of diffraction. Today's quantum mechanics,
photons and the idea of wave–particle duality bear only a minor resemblance to
Newton's understanding of light.
In
his Hypothesis of Light of 1675, Newton posited the existence of the ether to
transmit forces between particles. The contact with the theosophist Henry More,
revived his interest in alchemy. He replaced the ether with occult forces based
on Hermetic ideas of attraction and repulsion between particles. John Maynard
Keynes, who acquired many of Newton's writings on alchemy, stated that
"Newton was not the first of the age of reason: He was the last of the
magicians."[42] Newton's interest in alchemy cannot be isolated from his
contributions to science.[5] This was at a time when there was no clear distinction
between alchemy and science. Had he not relied on the occult idea of action at
a distance, across a vacuum, he might not have developed his theory of gravity.
(See also Isaac Newton's occult studies.)
In
1704, Newton published Opticks, in which he expounded his corpuscular theory of
light. He considered light to be made up of extremely subtle corpuscles, that
ordinary matter was made of grosser corpuscles and speculated that through a
kind of alchemical transmutation "Are not gross Bodies and Light
convertible into one another, ...and may not Bodies receive much of their
Activity from the Particles of Light which enter their Composition?"[43]
Newton also constructed a primitive form of a frictional electrostatic
generator, using a glass globe (Optics, 8th Query).
In
an article entitled "Newton, prisms, and the 'opticks' of tunable
lasers[44] it is indicated that Newton in his book Opticks was the first to
show a diagram using a prism as a beam expander. In the same book he describes,
via diagrams, the use of multiple-prism arrays. Some 278 years after Newton's
discussion, multiple-prism beam expanders became central to the development of
narrow-linewidth tunable lasers. Also, the use of these prismatic beam
expanders led to the multiple-prism dispersion theory.[44]
Mechanics
and gravitation
In
1679, Newton returned to his work on (celestial) mechanics, i.e., gravitation
and its effect on the orbits of planets, with reference to Kepler's laws of
planetary motion. This followed stimulation by a brief exchange of letters in
1679–80 with Hooke, who had been appointed to manage the Royal Society's
correspondence, and who opened a correspondence intended to elicit
contributions from Newton to Royal Society transactions.[40] Newton's
reawakening interest in astronomical matters received further stimulus by the
appearance of a comet in the winter of 1680–1681, on which he corresponded with
John Flamsteed.[45] After the exchanges with Hooke, Newton worked out a proof
that the elliptical form of planetary orbits would result from a centripetal
force inversely proportional to the square of the radius vector (see Newton's
law of universal gravitation – History and De motu corporum in gyrum). Newton
communicated his results to Edmond Halley and to the Royal Society in De motu
corporum in gyrum, a tract written on about 9 sheets which was copied into the
Royal Society's Register Book in December 1684.[46] This tract contained the
nucleus that Newton developed and expanded to form the Principia.
The
Principia was published on 5 July 1687 with encouragement and financial help
from Edmond Halley. In this work, Newton stated the three universal laws of
motion that enabled many of the advances of the Industrial Revolution which
soon followed and were not to be improved upon for more than 200 years, and are
still the underpinnings of the non-relativistic technologies of the modern
world. He used the Latin word gravitas (weight) for the effect that would
become known as gravity, and defined the law of universal gravitation.
In
the same work, Newton presented a calculus-like method of geometrical analysis
by 'first and last ratios', gave the first analytical determination (based on
Boyle's law) of the speed of sound in air, inferred the oblateness of the
spheroidal figure of the Earth, accounted for the precession of the equinoxes
as a result of the Moon's gravitational attraction on the Earth's oblateness,
initiated the gravitational study of the irregularities in the motion of the
moon, provided a theory for the determination of the orbits of comets, and much
more.
Newton
made clear his heliocentric view of the solar system – developed in a somewhat
modern way, because already in the mid-1680s he recognised the "deviation
of the Sun" from the centre of gravity of the solar system.[47] For
Newton, it was not precisely the centre of the Sun or any other body that could
be considered at rest, but rather "the common centre of gravity of the
Earth, the Sun and all the Planets is to be esteem'd the Centre of the
World", and this centre of gravity "either is at rest or moves uniformly
forward in a right line" (Newton adopted the "at rest"
alternative in view of common consent that the centre, wherever it was, was at
rest).[48]
Newton's
postulate of an invisible force able to act over vast distances led to him
being criticised for introducing "occult agencies" into science.[49]
Later, in the second edition of the Principia (1713), Newton firmly rejected
such criticisms in a concluding General Scholium, writing that it was enough
that the phenomena implied a gravitational attraction, as they did; but they
did not so far indicate its cause, and it was both unnecessary and improper to
frame hypotheses of things that were not implied by the phenomena. (Here Newton
used what became his famous expression "hypotheses non fingo"[50]).
With
the Principia, Newton became internationally recognised.[51] He acquired a
circle of admirers, including the Swiss-born mathematician Nicolas Fatio de
Duillier, with whom he formed an intense relationship. This abruptly ended in
1693, and at the same time Newton suffered a nervous breakdown.[52]
Classification
of cubics
Besides
the work of Newton and others on calculus, the first important demonstration of
the power of analytic geometry was Newton's classification of cubic curves in
the Euclidean plane in the late 1600s. He divided them into four types,
satisfying different equations, and in 1717 Stirling, probably with Newton's
help, proved that every cubic was one of these four. Newton also claimed that
the four types could be obtained by plane projection from one of them, and this
was proved in 1731.[53]
In
the 1690s, Newton wrote a number of religious tracts dealing with the literal
interpretation of the Bible. Henry More's belief in the Universe and rejection
of Cartesian dualism may have influenced Newton's religious ideas. A manuscript
he sent to John Locke in which he disputed the existence of the Trinity
remained unpublished until 1785, more than half a century after his
death.[54][55] Later works – The Chronology of Ancient Kingdoms Amended (1728)
and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John
(1733) – were published after his death. He also devoted a great deal of time
to alchemy (see above).
Newton
was also a member of the Parliament of England for Cambridge University in
1689–90 and 1701–2, but according to some accounts his only comments were to
complain about a cold draught in the chamber and request that the window be
closed.[56][57][58]
Newton
moved to London to take up the post of warden of the Royal Mint in 1696, a
position that he had obtained through the patronage of Charles Montagu, 1st
Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's
great recoining, somewhat treading on the toes of Lord Lucas, Governor of the
Tower (and securing the job of deputy comptroller of the temporary Chester
branch for Edmond Halley). Newton became perhaps the best-known Master of the
Mint upon the death of Thomas Neale in 1699, a position Newton held for the
last 30 years of his life.[59][60] These appointments were intended as
sinecures, but Newton took them seriously, retiring from his Cambridge duties
in 1701, and exercising his power to reform the currency and punish clippers
and counterfeiters. As Master of the Mint in 1717 in the "Law of Queen
Anne" Newton moved the Pound Sterling de facto from the silver standard to
the gold standard by setting the bimetallic relationship between gold coins and
the silver penny in favour of gold. This caused silver sterling coin to be
melted and shipped out of Britain. Newton was made President of the Royal
Society in 1703 and an associate of the French Académie des Sciences. In his
position at the Royal Society, Newton made an enemy of John Flamsteed, the
Astronomer Royal, by prematurely publishing Flamsteed's Historia Coelestis
Britannica, which Newton had used in his studies.[61]
In
April 1705, Queen Anne knighted Newton during a royal visit to Trinity College,
Cambridge. The knighthood is likely to have been motivated by political
considerations connected with the Parliamentary election in May 1705, rather
than any recognition of Newton's scientific work or services as Master of the
Mint.[63] Newton was the second scientist to be knighted, after Sir Francis
Bacon.
Towards
the end of his life, Newton took up residence at Cranbury Park, near Winchester
with his niece and her husband, until his death in 1727.[64] His half-niece,
Catherine Barton Conduitt,[65] served as his hostess in social affairs at his
house on Jermyn Street in London; he was her "very loving Uncle,"[66]
according to his letter to her when she was recovering from smallpox.
Newton
died in his sleep in London on 20 March 1727 (OS 20 March 1726; NS 31 March
1727)[1] and was buried in Westminster Abbey. A bachelor, he had divested much
of his estate to relatives during his last years, and died intestate. After his
death, Newton's hair was examined and found to contain mercury, probably
resulting from his alchemical pursuits. Mercury poisoning could explain
Newton's eccentricity in late life.[67]
After
death
Fame
The
mathematician Joseph-Louis Lagrange often said that Newton was the greatest
genius who ever lived, and once added that Newton was also "the most
fortunate, for we cannot find more than once a system of the world to
establish."[68] English poet Alexander Pope was moved by Newton's
accomplishments to write the famous epitaph:
Nature
and nature's laws lay hid in night;
God
said "Let Newton be" and all was light.
Newton
himself had been rather more modest of his own achievements, famously writing
in a letter to Robert Hooke in February 1676:
If
I have seen further it is by standing on the shoulders of giants.[69]
Two
writers think that the above quote, written at a time when Newton and Hooke
were in dispute over optical discoveries, was an oblique attack on Hooke (said
to have been short and hunchbacked), rather than – or in addition to – a
statement of modesty.[70][71] On the other hand, the widely known proverb about
standing on the shoulders of giants published among others by 17th-century poet
George Herbert (a former orator of the University of Cambridge and fellow of
Trinity College) in his Jacula Prudentum (1651), had as its main point that
"a dwarf on a giant's shoulders sees farther of the two", and so its
effect as an analogy would place Newton himself rather than Hooke as the
'dwarf'.
In
a later memoir, Newton wrote:
I
do not know what I may appear to the world, but to myself I seem to have been
only like a boy playing on the sea-shore, and diverting myself in now and then
finding a smoother pebble or a prettier shell than ordinary, whilst the great
ocean of truth lay all undiscovered before me.[72]
Albert
Einstein kept a picture of Newton on his study wall alongside ones of Michael
Faraday and James Clerk Maxwell.[73] Newton remains influential to today's
scientists, as demonstrated by a 2005 survey of members of Britain's Royal
Society (formerly headed by Newton) asking who had the greater effect on the
history of science, Newton or Einstein. Royal Society scientists deemed Newton
to have made the greater overall contribution.[74] In 1999, an opinion poll of
100 of today's leading physicists voted Einstein the "greatest physicist
ever;" with Newton the runner-up, while a parallel survey of rank-and-file
physicists by the site PhysicsWeb gave the top spot to Newton.[75]
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v
t e
Main
article: Newton's laws of motion
In
the Principia, Newton gives the famous three laws of motion, stated here in
modern form.
Newton's
First Law (also known as the Law of Inertia) states that an object at rest
tends to stay at rest and that an object in uniform motion tends to stay in uniform
motion unless acted upon by a net external force. The meaning of this law is
the existence of reference frames (called inertial frames) where objects not
acted upon by forces move in uniform motion (in particular, they may be at
rest).
Newton's
Second Law states that an applied force, , on an object equals the rate of
change of its momentum, , with time. Mathematically, this is expressed as
Since
the law applies only to systems of constant mass,[124] m can be brought out of
the derivative operator. By substitution using the definition of acceleration,
the equation can be written in the iconic form
The
first and second laws represent a break with the physics of Aristotle, in which
it was believed that a force was necessary in order to maintain motion. They
state that a force is only needed in order to change an object's state of
motion. The SI unit of force is the newton, named in Newton's honour.
Newton's
Third Law states that for every action there is an equal and opposite reaction.
This means that any force exerted onto an object has a counterpart force that
is exerted in the opposite direction back onto the first object. A common
example is of two ice skaters pushing against each other and sliding apart in
opposite directions. Another example is the recoil of a firearm, in which the
force propelling the bullet is exerted equally back onto the gun and is felt by
the shooter. Since the objects in question do not necessarily have the same
mass, the resulting acceleration of the two objects can be different (as in the
case of firearm recoil).
Unlike
Aristotle's, Newton's physics is meant to be universal. For example, the second
law applies both to a planet and to a falling stone.
The
vector nature of the second law addresses the geometrical relationship between
the direction of the force and the manner in which the object's momentum
changes. Before Newton, it had typically been assumed that a planet orbiting
the Sun would need a forward force to keep it moving. Newton showed instead
that all that was needed was an inward attraction from the Sun. Even many
decades after the publication of the Principia, this counterintuitive idea was
not universally accepted, and many scientists preferred Descartes' theory of
vortices.[125]
