The Great Ones
PTOLEMY
Claudius Ptolemy was one of the most influential Greek astronomers and
geographers of his time. Born about 85 in Alexandria, Egypt, Ptolemy
propounded the geocentric theory that prevailed for 1400 years.
Ptolemy's two major works are the Almagest and the Geography. The Almagest is
the earliest of the two, and gives a detailed mathematical theory of the
motions of the Sun, Moon, and planets. What came to be known as the
Ptolemaic system predicted the positions of the planets accurately enough
for human naked-eye observations, codifying the geocentric view of the
time (although he most likely thought it useful for nothing more than a
method of calculating positions, rather than reality). Ptolemy's geometric
models utilized combinations of circles known as epicycles to make these
predictions within the framework of Aristotle's basic geocentric system.
The Almagest was not superseded until a century after Copernicus presented his
heliocentric theory in the "De revolutionibus" of 1543.
In addition, Ptolemy devised new geometrical proofs and theorems. He obtained,
using chords of a circle and an inscribed 360-gon, an approximation of the
constant now referred to as "pi", as well as an approximation of the square
root of 3. The Geography contains the first know projection of the spherical
earth onto a plane, and remained the principal work on the subject until the
time of Columbus. In fact, Columbus's erroneous decision to sail west for the
Indies may have been influenced by this projection, as it had Asia extending
much too far east.
COPERNICUS
Nicolaus Copernicus was a proponent of the view of an Earth in daily
motion about its axis and in yearly motion around a stationary sun.
Born in 1473, Copernicus was a subject of the King of Poland all his life,
but it is
possible that his native language was German (his writings are in Latin).
Though Copernicus' official employment was as a canon in the cathedral
chapter under his maternal uncle, the Bishop of Olsztyn (Allenstein) and,
later, of Frombork (Frauenberg), he also practiced medicine. During his
education of the medical practice, he studied the mathematical sciences, which
at the time were considered relevant to medicine (because physicians made
use of astrology).
It seems that during a visit to Rome around 1513, Copernicus wrote a short
account of what has since become known as the Copernican theory,
namely that the Sun (not the Earth) is at rest in the center of the
Universe. A full account of the theory was apparently slow to take a
satisfactory shape, and was not published until the very end of
Copernicus's life, under the title "On the revolutions of the heavenly
spheres" ("De revolutionibus orbium coelestium", Nuremberg, 1543).
Copernicus is said to have received a copy of the printed book for the
first time on his deathbed. (He died of a cerebral hemorrhage.)
Copernicus' heliostatic cosmology involved giving several distinct motions
to the Earth, and was consequently considered implausible by the vast majority
of his contemporaries, and by most astronomers and natural philosophers of
succeeding generations before the middle of the seventeenth century. It
was, in fact, less accurate than the Ptolemaic system in its prediction of
positions until Kepler's Laws were incorporated. Its notable defenders
included Johannes Kepler (1571 -1630) and Galileo Galilei (1564 - 1642).
Strong theoretical support for the Copernican theory was provided by
Newton's theory of universal gravitation (1687).
GALILEO
Galileo Galilei, born in Pisa (now Italy) in 1564, is chiefly remembered
for his work on free fall, his use of the
telescope and his employment of experimentation.
After a spell teaching mathematics privately and at the University of
Pisa, in 1592 Galileo was appointed
professor of mathematics at the
university of Padua (the university of
the Republic of Venice). There his duties were mainly to teach
Euclid's geometry and standard
(geocentric) astronomy to medical students, though he apparently discussed
more
unconventional forms of astronomy and natural philosophy in a
public lecture he gave in connection
with the appearance of a New Star (now known as 'Kepler's
supernova') in 1604. In a personal
letter written to Kepler (1571 - 1630) in 1598, Galileo had
stated that he was a Copernican, a realization he wouldn't publicly
acknowledge until later.
In the summer of 1609, Galileo heard about a spyglass that a
Dutchman had shown in Venice. From
these reports, and using his own technical skills as a
mathematician and as a workman, Galileo made
a series of telescopes whose optical performance was much better
than that of the Dutch instrument.
The astronomical discoveries he made with his telescopes were
described in a short book called
Message from the stars (Sidereus Nuncius) published in Venice in
May 1610. It caused a
sensation. Galileo claimed to have seen mountains on the Moon, to
have proved the Milky Way was
made up of tiny stars, and to have seen four small bodies
orbiting Jupiter. These last, with an eye on
getting a job in Florence, he promptly named 'the Medicean
stars'.
It worked. Soon afterwards, Galileo became 'Mathematician and
[Natural] Philosopher' to the
Grand Duke of Tuscany. In Florence he continued his work on
motion and on mechanics, and began
to get involved in disputes about Copernicanism. In 1613 he
discovered that, when seen in the
telescope, the planet Venus showed phases like those of the Moon,
and therefore must orbit the Sun
not the Earth. This did not enable one to decide between the
Copernican system, in which everything
goes round the Sun, and the Tychonic (Tycho Brahe) one in which
everything but the Earth (and
Moon) goes round the Sun which in turn goes round the Earth. Most
astronomers of the time in fact
favored the Tychonic system. However, Galileo showed a marked
tendency to use all his
discoveries as evidence for Copernicanism, and to do so with
great verbal as well as mathematical
skill. He seems to have made a lot of enemies by making his
opponents look fools. Moreover, not all
of them actually were fools.
There eventually followed some expression of interest by the
Inquisition. Prima facie, Copernicanism
was in contradiction with Scripture, and in 1616 Galileo was
given some kind of secret, but official,
warning that he was not to defend Copernicanism. Just what was
said on this occasion was to
become a subject for dispute when Galileo was accused of
departing from this undertaking in his
Dialogue concerning the two greatest world systems, published in
Florence in 1632. Galileo,
who was not in the best of health, was summoned to Rome, found to
be vehemently suspected of
heresy, and eventually condemned to house arrest, for life, at
his villa at Arcetri (above Florence).
He was also forbidden to publish. By the standards of the time he
had got off rather lightly.
Galileo's sight was failing, but he had devoted pupils and
amanuenses, and he found it possible to
write up his studies on motion and the strength of materials. The
book, Discourses on two new
sciences, was smuggled out of Italy and published in Leiden (in
the Netherlands) in 1638.
Galileo wrote most of his later works in the vernacular, probably
to distance himself from the
conventional learning of university teachers. However, his books
were translated into Latin for the
international market, and they proved to be immensely
influential.
NEWTON
Isaac Newton was born in 1643 in Woolsthorpe, Lincolnshire, England into a
family of farmers; his father died before he was born. Though his grammar
school reports described him as "idle" and "inattentive", an uncle decided
that he should be prepared for the university.
June 1661 he entered his uncle's old college, Trinity College, Cambridge,
with the intent of obtaining a law degree. Though the instruction was
dominated by the philosophy of Aristotle, it was here that he also
encountered the philosophies of Descartes, Gassendi, and Boyle, and the
new algebra and analytical geometry of Vihte, Descartes, and Wallis;
however, it was the mechanics of the Copernican astronomy of
Galileo that attracted him.
It wasn't until the summer of 1665, at less than 25 years of age, that
Newton's scientific genius emerged, when the plague prompted the
University to close during the summer and he had to return to
Lincolnshire. Newton began revolutionary advances in mathematics,
optics, physics, and astronomy, laying the foundation for differential
and integral calculus several years prior to its independent development
by Leibniz. Newton applied his so-called 'method of fluxions'- based on
his crucial insight that the integration of a
function is the inverse procedure to differentiating it- to solve
apparently unrelated
problems such as finding areas, tangents, the lengths of curves and the
maxima and minima of functions. Newton's De Methodis Serierum et Fluxionum
was written in 1671 but was not published until nine years after his
death, in 1736.
Barrow, the presiding Lucasian chairman at Cambridge, resigned in 1669,
recommending that Newton (still
only 27 years old) be
appointed in his place.
Newton's first work as Lucasian Professor was on optics. Convinced by
the chromatic aberration on the telescopic lens, Newton had reached
the unpopular conclusion that white light is not a simple entity,
contradicting every
scientist since Aristotle.
When he passed a thin beam of sunlight through a
glass
prism, Newton noted the
spectrum of colours that was formed, prompting him to argue that white
light is
really a mixture of many
different types of rays which are refracted at slightly different angles,
and that each different type of
ray produces a different spectral color. He constructed a reflecting
telescope after coming to the erroneous conclusion that telescopes using
refracting lenses would always suffer
chromatic aberration.
After being elected a fellow of the Royal Society in 1672, he published
his first scientific
paper on light and color;
Newton's paper was well received but Hooke and Huygens objected to
Newton's attempt to prove,
by experiment alone, that light consists of the motion of small particles
rather than waves.
In fact, Newton's relations with Hooke deteriorated so much that he
delayed the
publication of Opticks, his full account of optical
research, until 1704, a year after Hooke's death.
Opticks theorized about light and color and the three themes of (i)
investigations of the colours of thin sheets (ii) 'Newton's
rings' and (iii) diffraction of light. Interestingly enough, he had to use
a wave theory of light in conjunction with his corpuscular theory to
explain some of his observations.
Newton's greatest achievement was his work in physics and celestial
mechanics, which culminated in
the theory of universal gravitation. By 1666 Newton had early versions of
his three laws of motion.
He had also discovered the law giving the centrifugal force on a body
moving uniformly in a circular
path. However he did not have a correct understanding of the mechanics of
circular motion.
Newton's novel idea of 1666 was to imagine that the Earth's gravity
influenced the Moon, counter-
balancing its centrifugal force. From his law of centrifugal force and
Kepler's third law of planetary motion, Newton deduced the inverse- square
law.
Around 1684 Halley persuaded Newton to write a full treatment of his new
physics and
its application to
astronomy. Over a year later (1687) Newton published the Philosophiae
naturalis principia
mathematica or Principia as it is always known, recognized as the greatest
scientific book ever written.
Newton analysed the motion
of bodies in resisting and non resisting media under the action of
centripetal forces. The results were
applied to orbiting bodies, projectiles, pendulums, and free-fall near the
Earth. He further
demonstrated that the planets were attracted toward the Sun by a force
varying as the inverse square
of the distance and generalized that all heavenly bodies mutually attract
one another.
Further generalization led Newton to the law of universal gravitation:
all matter attracts all other matter with a force proportional to the
product of
their masses and inversely proportional to the square of the distance
between
them.
Newton explained a wide range of previously unrelated phenomena:- the
eccentric orbits of comets;
the tides and their variations; the precession of the Earth's axis; and
motion of the Moon as
perturbed by the gravity of the Sun.
After suffering a nervous breakdown in 1693, Newton retired from research
to take up a
government position in London becoming Warden of the Royal Mint (1696) and
Master(1699).
In 1703 he was elected president of the Royal Society and was re-elected
each year until his death.
He was knighted in 1708 by Queen Anne, the first scientist to be so
honored for his work.
HUBBLE
Edwin Hubble was a man who changed our view of the Universe. In 1929 he
showed that galaxies
are moving away from us with a speed proportional to their distance. The
explanation is simple, but
revolutionary: the Universe is expanding.
Hubble was born in Missouri in 1889. His family moved to Chicago in 1898,
where at High School
he was a promising, though not exceptional, pupil. He was more remarkable
for his athletic ability,
breaking the Illinois State high jump record. At university too he was an
accomplished sportsman
playing for the University of Chicago basketball team. He won a Rhodes
scholarship to Oxford
where he studied law. It was only some time after he returned to the US
that he decided his future
lay in astronomy.
In the early 1920's Hubble played a key role in establishing just what
galaxies are. It was known that
some spiral nebulae (fuzzy clouds of light on the night sky) contained
individual stars, but there was
no consensus as to whether these were relatively small collections of
stars within our own galaxy, the
'Milky Way' that stretches right across the sky, or whether these could be
separate galaxies, or
'island universes', as big as our own galaxy but much further away. In
1924 Hubble measured the
distance to the Andromeda nebula, a faint patch of light with about the
same apparent diameter as
the moon, and showed it was about a hundred thousand times as far away as
the nearest stars. It
had to be a separate galaxy, comparable in size our own Milky Way but much
further away.
Hubble was able to measure the distances to only a handful of other
galaxies, but he realised that as
a rough guide he could take their apparent brightness as an indication of
their distance. The speed
with which a galaxy was moving toward or away from us was relatively easy
to measure due to the
Doppler shift of their light. Just as a sound of a racing car becomes
lower as it speeds away from us,
so the light from a galaxy becomes redder. Though our ears can hear the
change of pitch of the
racing car engine our eyes can't detect the tiny red-shift of the light,
but with a sensitive spectrograph
Hubble could determine the redshift of light from distant galaxies.
The observational data available to Hubble by 1929 was sketchy, but
whether guided by inspired
instinct or outrageous good fortune, he correctly divined a straight line
fit between the data points
showing the redshift was proportional to the distance. Since then much
improved data has shown the
conclusion to be a sound one. Galaxies are receding from us, and one
another, as the Universe
expands. Within General Relativity, the theory of gravity proposed by
Albert Einstein in 1915, the
inescapable conclusion was that all the galaxies, and the whole Universe,
had originated in a Big
Bang, thousands of millions of years in the past. And so the modern
science of cosmology was born.
Hubble made his great discoveries on the best telescope in the world at
that time - the 100-inch
telescope on Mount Wilson in southern California. Today his name carried
by the best telescope we
have, not on Earth, but a satellite observatory orbiting our planet. The
Hubble Space Telescope is
continuing the work begun by Hubble himself to map our Universe, and
producing the most
remarkable images of distant galaxies ever seen.
STEPHEN HAWKING
Stephen Hawking's parents lived in London where his father was undertaking
research into
medicine. However, London was a dangerous place during World War II and
Stephen's mother was
sent to the safer town of Oxford where Stephen was born. The family were
soon back together
living in Highgate, north London, where Stephen began his schooling.
In 1950 Stephen's father moved to the Institute for Medical Research in
Mill Hill. The family moved
to St Albans so that the journey to Mill Hill was easier. Stephen attended
St Albans High School for
Girls (which took boys up to the age of 10). When he was older he attended
St Albans school but
his father wanted him to take the scholarship examination to go to
Westminster public school.
However Stephen was ill at the time of the examinations and remained at St
Albans school which he
had attended from the age of 11. Stephen writes in [2]:-
I got an education there that was as good as, if not better than,
that I would have
had at Westminster. I have never found that my lack of social graces
has been a
hindrance.
Hawking wanted to specialize in mathematics in his last couple of years at
school where his
mathematics teacher had inspired him to study the subject. However
Hawking's father was strongly
against the idea and Hawking was persuaded to make chemistry his main
school subject. Part of his
father's reasoning was that he wanted Hawking to go to University College,
Oxford, the College he
himself had attended, and that College had no mathematics fellow.
In March 1959 Hawking took the scholarship examinations with the aim of
studying natural sciences
at Oxford. He was awarded a scholarship, despite feeling that he had
performed badly, and at
University College he specialized in physics in his natural sciences
degree. He only just made a First
Class degree in 1962 and in [1] he explains how the attitude of the time
worked against him:-
The prevailing attitude at Oxford at that time was very anti-work.
You were
supposed to be brilliant without effort, or accept your limitations
and get a
fourth-class degree. To work hard to get a better class of degree was
regarded as
the mark of a grey man - the worst epithet in the Oxford vocabulary.
From Oxford, Hawking moved to Cambridge to take up research in general
relativity and
cosmology, a difficult area for someone with only a little mathematical
background. Hawking had
noticed that he was becoming rather clumsy during his last year at Oxford
and, when he returned
home for Christmas 1962 at the end of his first term at Cambridge, his
mother persuaded him to see
a doctor.
In early 1963 he spent two weeks having tests in hospital and motor
neuron disease (Lou Gehrig's
disease) was diagnosed. His condition deteriorated quickly and the doctors
predicted that he would
not live long enough to complete his doctorate. However Hawking writes:-
... although there was a cloud hanging over my future, I found to my
surprise that
I was enjoying life in the present more than I had before. I began to
make
progress with my research...
The reason that his research progressed was that he met a girl he wanted
to marry and realised he
had to complete his doctorate to get a job so:-
... I therefore started working for the first time in my life. To my
surprise I found I
liked it.
After completing his doctorate in 1966 Hawking was awarded a fellowship at
Gonville and Caius
College, Cambridge. At first his position was that of Research Fellow, but
later he became a
Professorial Fellow at Gonville and Caius College. In 1973 he left the
Institute of Astronomy and
joined to the Department of Applied Mathematics and Theoretical Physics at
Cambridge. He
became Professor of Gravitational Physics at Cambridge in 1977. In 1979
Hawking was appointed
Lucasian Professor of Mathematics at Cambridge. The man born 300 years to
the day after Galileo
died now held Newton's chair at Cambridge.
Between 1965 and 1970 Hawking worked on singularities in the theory of
general relativity devising
new mathematical techniques to study this area of cosmology. Much of his
work in this area was
done in collaboration with Roger Penrose who, at that time, was at
Birkbeck College, London.
From 1970 Hawking began to apply his previous ideas to the study of black
holes.
Continuing this work on black holes, Hawking discovered in 1970 a
remarkable property. Using
quantum theory and general relativity he was able to show that black holes
can emit radiation. His
success with proving this made him work from that time on combining the
theory of general relativity
with quantum theory. In 1971 Hawking investigated the creation of the
Universe and predicted that,
following the big bang, many objects as heavy as 10 tons but only the size
of a proton would be
created. These mini black holes have large gravitational attraction
governed by general relativity,
while the laws of quantum mechanics would apply to objects that small.
Another remarkable achievement of Hawking's using these techniques was his
no boundary proposal
made in 1983 with Jim Hartle of Santa Barbara. Hawking explains that this
would mean:-
... that both time and space are finite in extent, but they don't
have any boundary
or edge. ... there would be no singularities, and the laws of science
would hold
everywhere, including at the beginning of the universe.
In 1982 Hawking decided to write a popular book on cosmology. By 1984 he
had produced a first
draft of A Brief History of Time. However Hawking was to suffer a further
illness:-
I was in Geneva, at CERN, the big particle accelerator, in the summer
of 1985. ...
I caught pneumonia and was rushed to hospital. The hospital in Geneva
suggested to my wife that it was not worth keeping the life support
machine on.
But she was having none of that. I was flown back to Addenbrooke's
Hospital in
Cambridge, where a surgeon called Roger Grey carried out a
tracheotomy. That
operation saved my life but took away my voice.
Hawking was given a computer system to enable him to have an electronic
voice. It was with these
difficulties that he revised the draft of A Brief History of Time which
was published in 1988. The
book broke sales records in a way that it would have been hard to predict.
By May 1995 it had
been in The Sunday Times best-sellers list for 237 weeks breaking the
previous record of 184
weeks. This feat is recorded in the 1998 Guinness Book of Records. Also
recorded there is the fact
that the paperback edition was published on 6 April 1995 and reached
number one in the best
sellers in 3 days. By April 1993 there had been 40 hardback editions of A
Brief History of Time in
the United States and 39 hardback editions in the UK.
Of course Hawking has received, and continues to receive, a large number
of honors. He was
elected a Fellow of The Royal Society in 1974, being one of its youngest
fellows. He was awarded
the CBE in 1982, and was made a Companion of Honour in 1989. Hawking has
also received many
foreign awards and prizes and was elected a Member of the National Academy
of Sciences of the
United States.
In addition to his popular writing he has also published The Large Scale
Structure of Space-Time
(1973; co-authored with G F R Ellis), Superspace and Supergravity (1981),
The Very Early
Universe (1983), General Relativity: An Einstein Centenary Survey
(co-authored with W
Israel), and 300 Years of Gravity (co-authored with W Israel).
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