THE AGE OF MYTHS AND SPECULATIONS
And God said, Let there be light, and there was light.
--Genesis 1:3
For thousands of years men have looked up into the star-filled night
sky and have wondered about the nature of the "fixed" stars as opposed
to that of the five planets wandering among the constellations of the
zodiac. The daily course of the sun, its brilliance and heat, and the
passing of the seasons are among the central problems that have
concerned every human society. Undoubtedly, the appearance of a comet or
a shooting star, the passing phenomena of clouds and rain and
lightning, the Milky Way, the changing phases of the moon and the
eclipses--all of these must have caused quite a sense of wonder and been
the source of endless discussions.
Faced with this confusing
multiplicity of brute facts, beyond their physical power to control, our
ancestors sought to master these unrelated phenomena symbolically by
picturing the universe in terms of objects familiar to them so as to
make clear the unfamiliar and the unexplained. The cosmologies that
these men set up thus inevitably reflect the physical and intellectual
environment in which they lived.Physical
cosmology arose in the Greek colonies of the eastern Mediterranean and
of southern Italy during the sixth century B.C. It flourished in Athens
during the next two centuries, whence it passed on to Alexandria, which
became the center of Hellenistic culture for several centuries.
Unfortunately, although that golden age saw great advances in
observational astronomy and mathematics, physics did not keep pace with
these sciences. Thus, lacking a firm theoretical base and constrained by
metaphysical dogma, physical cosmology stagnated at the dawn of the
Christian era until resurrected in the Renaissance. This period, which
was essentially the transition of the medieval to the modern order, saw
the beginning of a great burst of critical speculation about nature and
with it the emergence of two most promising ideas--the demotion of the
earth from its position as the center of motion of the universe, and the
existence of an infinite universe populated with an infinity of worlds.
The times were not ripe for the general acceptance of these ideas,
however, since it was not until late into the seventeenth century that
the new science of dynamics and the law of gravitation made the age-old
geocentric universe obsolete.
ANCIENT EGYPT AND THE MIDDLE EAST
In the many stories recorded in texts of the third and second millennia
B.C. in Egypt, Mesopotamia, and neighboring countries, the tales of
creation are presented as a series of births and cosmic battles among
the gods. The mother country is always represented as the center, the
earth being a flat disk surrounded by a rim of mountains and floating on
an ocean.
The Egyptians believed that in the beginning a
primordial abysmal ocean, deified as Nun, filled the universe like a
cosmic egg. Just as the Nile floodwaters receded, leaving behind fertile
lands, so a primeval hill rose out of Nun. In a Heliopolitan text on
papyrus from the fifth dynasty (c. 2500-2350 B.C.), Atun--a predynastic
sun-god, later identified with the sun-god Ra--arose out of the abyss.
He created a son, Shu--god of wind or air--and a daughter,
Tefnut--goddess of lifegiving dew. Shu and Tefnut begot the twins Geb
and Nut. Nut was the sky-goddess. She was sometimes pictured as an
elongated woman bending over the earth-god Geb and separated from him by
her father Shu. To the Egyptians, the sky was a
heavenly Nile, along which the barque of the sun-god Ra sailed from east
to west each day. (The sun was occasionally thrown into an eclipse when
his barque was attacked by a great serpent.) Below, the earth-god Geb
was lying prone in the center of a circular ocean, the Nile flowing
through the fertile lands of Egypt and into the subterranean abode of
the dead through which the night-barque of the sun-god Ra sailed. It was
also believed that the sky-goddess Nut swallowed the sun each evening
but that it was reborn from her lions each monring. Then, as the sun
rose in the sky, she would swallow the stars and give birth to them
again at sunset.
The theory that the shape of the universe
resulted from the forceful separation of heaven from earth by a third
party was also adopted in Mesopotamia.
It is recorded in the great Babylonian epic called, from its opening sentence,
Enuma Elish,
"When above . . . ." The composition of its earliest known version goes
back to the middle of the second millennium B.C., but we know that it
had its roots in an ancient Sumerian story of about 3000 B.C. It seems
that Enlil, the city-god of Nippur, was the original hero of the epic
and that he was merely replaced by Marduk, the city-god of Babylon, when
the later version was composed. This epic was extremely popular since,
later on, an Assyrian version of the first millennium B.C. substituted
the name of Ashur, the national god of the Assyrians, for that of
Marduk. It is recorded on seven clay tablets.
Enuma Elish presents
the earliest stage of the universe as one of watery chaos. This chaos
was closely modeled on the Iraqi seashore, with large pools of sweet
water mingling freely with the salty waters of the Persian Gulf, and
with low banks of clouds hanging over the horizon. It consisted of Apsu
(the sweetwater ocean), his wife Tiamat (the saltwater ocean), and their
son Mummu (the cloud banks and mist rising from the two bodies of
water). The myth of creation relates how the primordial forces of chaos
bore the other gods of the Mesopotamian pantheon who, in turn, created
the earth and the heaven. One of these gods was Ea. To make a long story
short, after overcoming Apsu and Mummu, the god Ea fathered Marduk, who
possessed outstanding qualities and so was chosen by the gods to fight
the remaining evil forces of chaos. After an epic combat, Marduk pierced
Tiamat's heart with an arrow and smashed her skull with his mace. Then
he completed creation, making half of her dead body into the sky and
placing the other half beneath the earth. After his victory, Marduk put
the universe in order and organized the calendar. Thus, on the sky he
had fashioned he set up the constellations to determine, by their rising
and setting, the years, the months, and the days. On both sides of the
sky, where the sun comes out in the morning and leaves in the evening,
he built gates and secured them with strong locks. Marduk also made the
moon shine forth and entrusted the night to her. (It is to be regretted
that the only extant clay tablet dealing with the creation and
organization of the heavenly bodies breaks off at the point where it
reports some detailed orders to the moon.) Then, according to the last
two tablets, Marduk decided to create man and to impose upon him the
service which the defeated forces of chaos had to render to the gods.
It has long been recognized that
Enuma Elish contains
several points that invite comparison with the biblical account of
creation which was compiled by the Priestly school during the fifth
century B.C. Indeed,
Enuma Elish and Genesis (1:1-2:3) both refer
to a watery chaos, which was separated into heaven and earth. However,
in Genesis it is the Spirit of God which hovers over the waters and
divides the light from the darkness; thus, as is fitting to a
monotheistic religion, He alone created the heavens and the earth. Both
texts also refer to the existence of light and to the alternation of day
and night before the creation of the celestial luminaries. And in both
texts the succession of creative acts virtually follows in the same
order, culminating in the creation of mankind. At this juncture it is
worth noting that the Koran, which was written during the first half of
the seventh century A.D., also presents an elaborate account of creation
that shows quite evident biblical traces. Thus, in sura 21:30 we learn
that "the heavens and the earth used to be one entity, and then (God)
parted them"; whereas in sura 71:15-16 we are told that "God created
seven heavens in layers" and that "He placed the moon therein as a light
and the sun as a lamp." The creation of the heavens and the earth in
six days, which is mentioned in sura 7:54, also finds its counterpart in
Genesis.
IONIA: THE EASTERN GREEK SCHOOL
Before the sixth century B.C. and the time of rationalism heralded by
Ionian philosophers, Greek cosmologies were dependent on traditions that
came from more ancient civilizations. The first records containing the
early Greek ideas are due to Homer and Hesiod. Homer's two epics, the
Iliad and
Odyssey,
are mainly devoted to the Trojan war and to the return of Ulysses in
his homeland. Hesiod, the father of Greek didactic poetry, probably
flourished during the eighth century B.C. His poem
Theogony tells
of the generations of the gods and attempts in mythical terms to
provide an account of the events that brought the world into being. His
other poem
Works and Days resembles a modern almanac in that it
correlates the agricultural work to be done with the rising or setting
of certain stars. Both HOMER and HESIOD agree upon the fact that the
earth is a circular disk surrounded by the river Oceanus. Over the flat
earth is the vault of heaven; below the earth is Tartarus, the realm of
the underworld. The vault of heaven remains forever fixed; the sun, the
moon, and the stars move round under it, rising from Oceanus in the east
and plunging into it again in the west. We are not told what happens to
the heavenly bodies between their setting and rising. They cannot pass
under the earth, however, because Tartarus is never lit up by the sun.
Possibly they float round Oceanus, past the north, to the points where
they rise again in the east.
The great achievement of the
Ionian philosophers--Thales, Anaximander, and Anaximenes--was that of
dissipating the haze of myth from the origins of the world. The three of
them flourished during the sixth century B.C. in Miletus --a rich Greek
city on the Aegean, near the mouth of the Maeander River. Tradition
tells that Thales (c. 624-547 B.C.) was a man of great versatility:
successful businessman, statesman, engineer, mathematician, and
astronomer. Anaximander (c. 611-547 B.C.), who was the successor and
probably pupil of Thales, was the first to have developed anything like a
cosmological system; he was also the first among the Greeks who
ventured to draw a map of the inhabited earth. It seems almost certain
that Anaximenes (c. 585-528 B.C.), the younger contemporary of
Anaximander, was the first to distinguish the planets from the "fixed"
stars in respect of their irregular movements; he also extended
Anaximander's ideas on cosmology.
THALES thought the earth to
be a circular or cylindrical disk that floated on the cosmic ocean, like
a log or a cork, and was surrounded by its waters. So far as we can
judge of his views of the universe, he would appear to have regarded
water as the world's fundamental element. In this conception, therefore,
far above the solid earth floating on a mass of water stands the vault
of heaven, which is also bounded by the primeval waters. As a matter of
fact, the significance of this cosmology does not lie so much in the
primacy of water as in the attempt to search for causes within nature
itself rather than in supernatural events.
ANAXIMANDER offered a
much more detailed picture of the world. He maintained that the earth
was in the center of all things, suspended freely and without support,
whereas Thales regarded it as resting on water. Anaximander's earth had
the shape of a cylinder, round like a stone pillar, its height being
one-third of its diameter. Still more original was his conception of the
sun, moon, and stars, and of their motions. Indeed, these celestial
bodies were not thought to be objects but holes in rotating hoops filled
with fire.
To be specific, Anaximander's stars are compressed
portions of air, in the shape of rotating hoops filled with fire, that
emit visible flames from small openings, thereby producing what we see
as the stars. The hoops belonging to the sun, the moon, and the stars
were probably assumed to be concentric with the earth. The sun is thus a
rotating hoop full of fire, which lets its fire shine out through an
opening like the tube of a blowpipe. The moon sometimes appears as
waxing, sometimes as waning, to an extent corresponding to the opening
or closing of the passages in its hoop. The eclipses of the sun and the
moon occur when the openings in their hoops are shut up. For some
philosophical reason, however, the radius of the solar hoop is
twenty-seven times as large as the earth, whereas that of the lunar hoop
is eighteen times as large as the earth. Surprisingly, the hoops from
which the stars and planets shine are
nearer to the earth than
that of the moon. Despite some obvious shortcomings, this cosmological
system represents a definite improvement over previous ones since,
instead of moving laterally round the earth, the heavenly bodies
describe circles passing
under the earth, which is freely suspended in space.
For ANAXIMENES the earth is still flat but, instead of resting on
nothing, it is supported by air. The sun, the moon, and the planets are
all made of fire, and they ride on the air because of their breadth. The
sun derives its heat from its rapid motion, whereas the stars, which
are also composed of fire, fail to give warmth because they are too far
off. It is also assumed that the stars are fastened on a crystal sphere,
like nails or studs. Obviously, a definite improvement on Anaximander's
system is the relegation of the stars to a more distant region than
that in which the sun moves. And, as we know, the rigidity of the sphere
of the fixed stars remained the fundamental postulate of all astronomy
up to the beginning of modern science.
Highly speculative
theories about the nature of the heavenly bodies were also proposed by
Xenophanes (c. 570-478 B.C.) of Colophon and Heraclitus (c. 540-480
B.C.) of Ephesus. XENOPHANES was more a poet and satirist than a natural
philosopher. According to him, the stars (including the comets and
shooting stars) are made of clouds set on fire; they are extinguished
each day and are kindled at night like coals, and these happenings
constitute their setting and rising, respectively. The sun and the moon
are also made of clouds set on fire. On the contrary, HERACLITUS assumes
that the stars are bowls turned with their concave sides toward us,
which collect bright exhalations arising from the earth and from the
sea, thus producing flames. The sun and the moon are also bowl shaped,
like the stars, and are thus similarly lit up.
SOUTHERN ITALY: THE WESTERN GREEK SCHOOL
Much more remarkable developments were to follow in the great colonies
of southern Italy. The dominant figure is undoubtedly Pythagoras, who
gave his name to an order of scientific and religious thinkers. He was
an Ionian, born at Samos about 572 B.C. The important part of his career
began about the year 530 B.C. with his migration to Crotona, a Dorian
colony in southern Italy. Political reaction against his brotherhood
brought about his retirement to Metapontum, on the Gulf of Taranto,
where he died at the turn of the fifth century B.C.
PARMENIDES
of Elea, who was a contemporary of Heraclitus, is said to have been the
first to assert that the earth is spherical in shape and lies in the
center of the universe. There is, however, an alternative tradition
stating that it was PYTHAGORAS who first held that the universe, the
earth, and the other heavenly bodies are spherical in shape, that the
earth is at rest at the center, and that the sphere of the fixed stars
has a daily rotation from east to west about an axis passing through the
center of the earth. Pythagoras and his immediate successors left no
written exposition of their doctrines. Thus, although it is most likely
that Pythagoras arrived at geocentrism and the rotundity of the earth
from mathematical considerations, Parmenides--who was closely connected
with the Pythagoreans--may have been the first to state the doctrine
publicly.
It is improbable, however, that Pythagoras himself
was responsible for the astronomical system known as Pythagorean, which
reduces the earth to the status of a planet like the others. This
cosmology is often attributed to PHILOLAUS of Crotona, who flourished in
the latter half of the fifth century B.C.
The Pythagorean
system may be described briefly as follows. The universe is spherical in
shape and finite in size. At its center is the central fire, in which
is located the governing principle--the force that moves the celestial
bodies, including the earth, on their circular paths. The outer boundary
of the sphere is an envelope of fire, which is called Olympus; below
this is the universe. In the universe there revolve in circles round the
central fire the following bodies. Nearest to the central fire revolves
a body called the counterearth, which always accompanies the earth, the
earth's orbit coming next to that of the counterearth; next to the
earth, reckoning in order from the central fire outward, come the moon,
the sun, the five planets, and last of all, outside the orbits of the
planets, the sphere of the fixed stars.
Philolaus explained
that the Greeks had never seen the central fire nor the counterearth
because the earth turned so as always to place their country away from
those objects. Such a situation implies that the earth is rotating
around its axis in the same time as it takes the earth to complete a
revolution around the central fire. Obviously, this was a giant step
forward since it provided a simple explanation for the apparent daily
motion of all celestial objects. What evidence motivated Philolaus to
include a counterearth is not clear, however, but it could have been
invented for the purpose of explaining the frequency of eclipses of the
moon. Arguably, it could have been added to bring the number of
celestial objects up to ten, the perfect number according to the
Pythagoreans.
It is worth noting that the sun is not a body
with light of its own in this cosmological model. Instead, the sun is
made of a substance comparable to
glass that concentrates rays of
fire from elsewhere and transmits them to us. It is not stated,
however, whether these rays of fire come from Olympus or from the
central fire. A similar conception for the nature of the sun has been
attributed also to EMPEDOCLES (c. 490-430 B.C.) of Acragas in Sicily.
More importantly, Empedocles advocated the idea that there are four
primary substances--fire, air, water, and earth--out of which all the
structures in the world are made by their combination in different
proportions.
THE ATHENIAN PERIOD
During the
first half of the fifth century B.C., both the Ionian and the Italian
schools of natural philosophy were progressively overshadowed by Athens,
which became for two centuries the intellectual center of the Greek
world. The Ionian ANAXAGORAS seems to have been the first natural
philosopher to move to Athens. He was born in Clazomenae, near modern
Izmir, about 500 B.C. He came to Athens about the year 464 B.C., where
he enjoyed the friendship of the statesman Pericles (490-429 B.C.).
However, when Pericles became unpopular during the late 430s B.C.,
shortly before the outbreak of the Peloponnesian war, he was attacked
through his friends; and so Anaxagoras was prosecuted on a charge of
impiety for holding that the sun is a red-hot mass and the moon like
earth. According to one account of the events, Pericles managed to save
him, but Anaxagoras was forced to leave Athens. Eventually, he withdrew
to Lampsacus in Asia Minor, near modern Gallipoli, where he died about
428 B.C. This is an early case of persecution of scientific ideas
opposed to current views.
His greatest achievement was the
discovery of the fact that the moon does not shine by its own light but
is illuminated by the sun. As a result, he was able to give the correct
explanation of eclipses. He thus held that the eclipses of the moon were
caused by its falling within the shadow of the earth, which then comes
between the sun and the moon, while the eclipses of the sun were due to
the interposition of the moon. Whether he reached the true explanation
of the phases of the moon is much more doubtful, however.
Anaxagoras also developed a cosmological system according to which the
formation of the world began as a huge vortex set up by a
deus ex machina in
the primordial chaos. From the violence of this whirling motion, which
is still visible on the sky, he was able to explain the formation of the
earth and, thence, of the heavenly bodies. In his view, therefore, the
initial vortex caused the heavy earth to collect at the center of the
world while the surrounding ether tore stones away from the earth and
kindled them into planets and stars revolving around us. Obviously, this
is an indefinitely expanding universe since there is no spatial limit
set to the expansion of the ripples from the initial vortex.
Parenthetically note that another cosmogony initiated by a vortex was
suggested by his contemporary LEUCIPPUS of Miletus, with an infinity of
atoms taking
the place of Anaxagoras' initial mixed mass in which "all things were
together." There is also the difference that material and space are
supposed to be limitless so that there would be an unlimited number of
worlds similar to our own world-system in the universe.
Apart
from these remarkable innovations, Anaxagoras did not improve much upon
the earlier Ionian theories. Following Anaximenes, he thus assumed that
the earth was flat and supported by air; and that the sun, the moon, and
all the stars were stones on fire. However, he also held the view that
the moon was of earthy nature and had in it plains, mountains, and
ravines. According to Anaxagoras, the sun was "rather larger than the
Peloponnese."
At this juncture it is worth noting that
Anaxagoras also put forward a very original hypothesis to explain the
Milky Way. As we have seen, he thought the sun to be
smaller than
the earth. Hence, when the sun in its revolution passes under the earth
during the night, the shadow cast by the earth extends without limit.
Since the stars within this shadow are not illuminated by the sun, it
follows that we can see them shining; those stars, on the other hand,
that are outside this shadow are overpowered by the rays of the sun,
which shines on them even during the night, so that we cannot see them.
According to Anaxagoras, the Milky Way is the reflection of the light of
those stars that the sun cannot see when it is passing below the earth.
Although this conjecture can be easily disproved by observation, it was
supported by DEMOCRITUS (c. 460-370 B.C.) of Abdera. As far as we know,
Democritus seems to have been the first to appreciate the true
character of the Milky Way as a multitude of faint stars so close
together that it has the appearance of a continuous body of light.
Important for subsequent astronomical developments were the Athenian
Plato (c. 427-347 B.C.) and his pupil Aristotle (384-322 B.C.), who was
born at Stagira, a Greek colonial town on the Aegean near modern
Salonika. Although Plato is primarily known as a philosophical writer,
he himself probably felt that the foundation of the Academy in about 387
B.C. was his chief work. Aristotle entered the Academy in about 367
B.C. and worked there for twenty years by the side of Plato. After
acting for some years as tutor to the young Alexander (356-323 B.C.) in
Macedonia, he returned to Athens to found his own institute of higher
education, the Lyceum, which came to be known as the Peripatetic School
from the path in his garden where he walked and talked with his pupils.
The importance of PLATO, so far as the development of astronomy is
concerned, is to be sought in his appreciation of the role of
mathematics in making intelligible the motions of the heavenly bodies.
Tradition tells that the motto "Let none who has not learned geometry
enter here" was inscribed over the entrance of the Academy. Following in
this the Pythagoreans, the apparently irregular motions of the planets
had, in his opinion, to be accounted for in terms of combinations of
uniform circular motions only. This was to become the main task of
astronomers from his time to the dawn of the seventeenth century--a
stretch of two thousand years.
EUDOXUS (c. 408-355 B.C.) of
Cnidus, who came to Athens at the age of twenty-three where he heard
Plato and the sophists, is one of the key figures in the history of
Greek astronomy. His most influential contribution was his cosmological
model based on concentric spheres centered on the earth, which is itself
a sphere at rest. Thus, each heavenly body is attached to the surface
of an imaginary invisible sphere which is rotating uniformly around a
fixed direction. Each sphere is itself attached to a larger sphere
rotating around another axis. The secondary spheres could be succeeded,
in turn, by a set of interlocking spheres according to the observed
positions of each heavenly body. In this representation, twenty-seven
spheres in all were considered sufficient: three each for the sun and
moon, four for each of the five planets, and one for the fixed stars.
Further improvements were made by CALLIPPUS (c. 370-300 B.C.) of
Cyzicus, who added further imaginary spheres to the model, making use of
thirty-four concentric spheres in all.
Of great interest also
is the work of ARISTOTLE, since his picture of the universe was to
become the orthodox view of cosmology in the universities of western
Europe from the thirteenth to the seventeenth century.
In his astronomy, Aristotle builds upon the mathematical results of
Eudoxus and Callippus in their use of concentric spheres centered on the
earth. However, what were for these astronomers mere mathematical
devices of representation are regarded byhim as physical entities. The
heavenly bodies must also be thought of as composed of a distinctive
ethereal substance, different from the objects found below the sphere of
the moon. The latter alone are made of varying combinations of earth,
water, air, and fire. Beyond the moon's orbit, both the visible heavenly
bodies and their invisible spheres are therefore composed of a fifth
element, a special
ether, the movement of which is always circular. Finally, beyond all these spheres is the outermost heaven, the
primum movens, that communicates its motion to the whole system. Aristotle's world is of finite extent and has neither beginning nor end.
If so, then, by what mechanism do the sun, stars, and planets shine? This problem is also discussed in Aristotle's treatise
De caelo (On the heavens), where it is argued that the warmth and light that proceed from the heavenly bodies are caused by
friction set
up by their motion. According toAristotle, therefore, the heavenly
bodies are not themselves fiery, as was suggested by the Ionian
philosophers. Rather, they shine because they are carried on moving
spheres, so that the substance underneath the sphere of each of them is
necessarily heated by its motion, and particularly in that part where
the body is attached to its sphere. In his treatise
Meteorologica,
Aristotle further argues that the sun's motion alone is sufficient to
produce heat in the place where we live because it moves swiftly and is
not so far off as the stars. In his own terms: "For a motion that is to
have this effect must be rapid and near, and that of the stars is rapid
but distant, while that of the moon is near but slow, whereas the sun's
motion combines both conditions in a sufficient degree."
Another brilliant pupil of Plato was HERACLIDES PONTICUS (c. 388-315
B.C.) of Heraclea on the Black Sea (present-day Eregli, Turkey). His
great advance in astronomy was his suggestion that the earth is in the
center of the universe and rotates around an axis while the sphere of
the fixed stars is at rest. This is clearly at variance with the views
held by Aristotle. Heraclides has often been credited also with the
claim that Venus and Mercury circle round the sun like satellites, but
recent studies have revealed this interpretation of ancient texts to be
without rational basis. Actually, the first clear evidence for such a
hypothesis in relation to the motion of the inner planets is found in
the works of THEON of Smyrna, who flourished in the early part of the
second century A.D.
Throughout antiquity, natural
philosophers were also divided on many other aspects of Aristotelian
cosmology, such as the finitude of the universe and the continuity of
matter. Indeed, although the Athenian philosopher EPICURUS (341-270
B.C.) of Samos was especially celebrated for his ethical teaching, he
contributed to cosmology by holding the views that the universe has no
limit and that "nothing can arise out of nothing and nothing can be
reduced to nothing." Following the doctrines of Leucippus and Democritus
regarding the atoms and the void, he also taught that the number of
these irreducible particles of matter and the extent of empty space are
infinite. According to Epicurus, the universe therefore consists of
numberless worlds strewn throughout an infinite void, with all matter
composed of atoms and regulated by natural laws. His most eminent Roman
advocate was the poet and philosopher LUCRETIUS (c. 95-55 B.C.), whose
poem
De rerum natura (On the nature of things) is the fullest
statement extant of the atomist theory. However, about the same time
Epicurus established his cosmology, another system of philosophy was
founded by ZENO (c. 320-250 B.C.) of Citium in Cyprus, who came to
Athens and set up a school in a roofed colonnade called a
stoa.
The Stoics were also ready to accept that space by its nature is
edgeless; however, they argued for a rival cosmological system
consisting of a finite starry universe surrounded by a void of infinite
extent which is regularly drawn into it and then exhaled. The void is
actually needed to provide a region in which the universe, as a living
creature, continually breathes in and out in its entirety. Specifically,
the Stoics regarded the physical world as a dynamical continuum, made
coherent by the all-pervading
pneuma, a mixture of air and fire,
which imparts to matter its structure and all physical qualities.
Through its inherent tensions the pneuma was also thought to constitute a
kind of elastic medium for the propagation of physical action in the
universe as a whole. The Epicurean and Stoic systems--that is, atomism
and continuum theory--greatly influenced the Scientific Revolution of
the seventeenth century.
THE ALEXANDRIAN PERIOD
While Aristotle was teaching in Athens, his former pupil Alexander of
Macedonia was carving out a large military empire that brought Greek
science into direct contact with the older sources of culture in the
East. When Alexander died in 323 B.C., his empire broke down, and Egypt
was seized by Ptolemy, one of his generals. Alexandria, which was
founded byAlexander in 332 B.C., became the capital of Egypt during the
reigns of Ptolemy and his successors. The Ptolemies were patrons of
learning; they founded the Museum, temple of the Muses, which contained a
large library and an observatory, and the city soon became the center
of Greek scientific thought.
Among the earlier members of the
Alexandrian school was ARISTARCHUS (c. 310-230 B.C.) of Samos, who was
the first to put forward the heliocentric hypothesis. Although his
original text is no longer extant, his most important witness is
ARCHIMEDES (287-212 B.C.) of Syracuse, who made explicit mention
ofAristarchus' contribution in his treatise
Arenarius, noting
that "his hypotheses are that the fixed stars and the sun remain
unmoved, that the earth revolves about the sun in the circumference of a
circle, the sun lying in the middle of the orbit." On this ground the
Stoic philosopher CLEANTHES (c. 301-232 B.C.) declared that it was the
duty of Greeks to indict Aristarchus on the charge of impiety for
putting in motion the hearth of the universe.
About a century
later, the heliocentric hypothesis was also rejected by the greatest of
observational astronomers of antiquity, HIPPARCHUS (c. 190-120 B.C.) of
Nicaea in Asia Minor. The reasons that weighed with Hipparchus were
presumably the facts that a system in which the sun was the exact center
did not seem to account for the variations of distance and the
irregularities of planetary motion; that the theory of epicycles did
apparently suffice to describe the phenomena; and that the latter could
be reconciled with the commonly held view according to which the earth
was immobile.
When Hipparchus came to examine suitable
kinematic patterns for the planets, he had before him the techniques of
the eccentric circle and epicycle. The simple device that was found
satisfactory in the case of the sun was the use of an
eccentric,
that is, a circular orbit whose center does not coincide with the
position of the observer on the earth. However, a more enduring solution
was broached by a pure mathematician, APOLLONIUS (c. 240-170 B.C.) of
Perga, who lived for some time in Alexandria. In this approach each
planet moves uniformly on a small circle, called the
epicycle,
whose center moves on a larger circle, called the deferent. The
epicyclic view largely prevailed through the mediation of Claudius
Ptolemaeus, commonly known as PTOLEMY, who flourished in Alexandria
about the middle of the second century A.D. (He was not related to the
ruling dynasty of the Ptolemies.) His great treatise, later known as the
Almagest,
7 largely refines upon the work of his
predecessors, notably Hipparchus, and brings to a systematic culmination
all the efforts of Greek astronomy. The
Almagest also contains a
catalog giving the ecliptical coordinates and magnitudes of 1,022
stars, based in part on the lost catalog by Hipparchus. In a later book,
Hypotheses of the Planets, Ptolemy attempted to produce a
physical system that would fulfill the requirements of both the
mathematical theory expounded in the
Almagest and his philosophy of nature.
8 The
basic idea was to assume that the planets were carried around by a
sequence of nested eccentric shells (of an invisible ethereal
substance), within each of which the epicycles would revolve. This
geocentric and epicyclic representation of the world remained virtually
unchanged until the Renaissance.
Another important advance in
astronomy was made when Aristarchus attempted to measure the relative
distances of the sun and moon from the earth, and their sizes relative
to each other. He knew that the light of the moon was reflected from the
sun. Accordingly, if in figure 1.3 the points
O,
S, and
M denote,
respectively, the observer and the centers of the sun and moon, the
moon appears to the observer half full when the angle
OMS is a right angle. When this is the case, the observer can measure the angle
MOS. With a knowledge of the angles at the points
M and
O, the relative lengths of the sides
OS and
OM can be obtained, thus giving at once the relative distances of the sun and moon from the observer.
Aristarchus made the angle
MOS about
87°. Lacking the tools provided by trigonometry, he used purely
geometrical reasoning to estimate that the distance to the sun was from
18 to 20 times that of the moon, whereas the correct value is about 390.
Aristarchus further estimated that the apparent sizes of the sun and
moon were about equal, and correctly inferred that the relative sizes of
these bodies were in proportion to their distances. By a method based
on eclipse observations, which was afterward developed by Hipparchus, he
also found that the diameter of the moon was about one-third that of
the earth, a result not far from true. Thus, in spite of large
observational errors, Aristarchus was nevertheless able to show
convincingly that, while the moon is smaller than the earth, the sun is
much larger.
To ERATOSTHENES (c. 276-194 B.C.) of Cyrene, who
was librarian of the Museum at Alexandria, we owe one of the first
scientific estimates of the earth's radius. He knew that at noon at the
summer solstice the sun threw no shadow at Syene (near modern Aswan),
while at the same hour at Alexandria the angular distance of the sun
from the zenith was about 7°. Now, if in figure 1.4 the point
S denotes the sun, the points
A and
B Alexandria and Syene, respectively, the point
O the center of the earth, and
AZ the direction of the zenith, the angle
SAZ is almost equal to the angle
SOZ owing to the great distance of the sun, so that the arc
AB is
to the circumference of the earth in the proportion of 7°to 360°. The
distance between Alexandria and Syene being about 5,000 stadia,
Eratosthenes estimated the earth's circumference to be about 250,000
stadia. If the value of the stadium used was the common Olympic stadium,
or 157.5 meters, then his evaluation of the earth's radius is about one
percent in error. This good agreement with modern values is perhaps
fortuitous, however, since both the angle (7°) and the distance (5,000
stadia) have obviously been rounded.
Hipparchus improved on
Aristarchus' method and made a satisfactory estimate of the distance of
the moon by observing the angular diameter of the earth's shadow at the
distance of the moon during an eclipse. In figure 1.5, which represents a
plane section of the shadow cone, one can readily see the simple
relation that exists between the angles
a,
b,
c, and
d. In the triangle moon-earth-sun, one has
a +
b =
c +
d,
that is, the sun's parallax plus the moon's parallax is equal to the
sun's angular radius plus the semidiameter of the earth's shadow. Since
the sun's parallax is much smaller than the moon's parallax, the latter
is therefore almost equal to the sum of the apparent semidiameters of
the sun and the shadow. Thus, letting
a = 0', Hipparchus found
that the distance of the moon was 59 times the earth's radius. However,
assuming a solar parallax of 7', the smallest perceptible parallax, he
found that distance to be 67 1/3 times the earth's radius
.
Although these evaluations were made during the third and second
centuries B.C., they look surprisingly modern in the sense that they are
neither a mere speculation nor an accumulation of brute facts. Indeed,
the three natural philosophers--Aristarchus, Eratosthenes, and
Hipparchus--assumed a reasonable physical model and then, from simple
measurements only, they were able to deduce some information about the
relative sizes and distances of the earth, moon, and sun. The importance
of their work lies not so much in the numerical figures they obtained,
but in the facts that the relevant questions were asked and that they
were formulated correctly. Such an approach, which was also favored by
the Sicilian polymath Archimedes, lies at the core of modern science; it
is unfortunate that it did not survive the Hellenistic period and had
to be rediscovered at the end of the Middle Ages.
Of great
historical importance also is the work of the Christian philosopher
Johannes PHILOPONUS, who taught in Alexandria in the first half of the
sixth century A.D. and was one of the last great commentators of
Aristotle. His conception of the laws of motion, opposed to that of
Aristotle, is particularly interesting. According to the latter, a body
can move only if a mover exercises upon it an action at every instant of
the motion; if left alone, it will not continue to move. The fact that
missiles--such as stones and arrows--go on moving for some time after
having been projected was assumed to be due to the contact with the
surrounding air, to which the mover had imparted some of its moving
power. Philoponus' innovation was to suggest instead that the
continuance of the motion of a projectile was due to the action of a
certain immaterial force--later called the "impetus"--which was
communicated to the projectile by the mover. This new idea about forced
motion had a considerable impact on physical doctrine in the Middle
Ages--both in the Muslim world and in the Latin West--and played an
important part in the gradual disintegration of Aristotelian orthodoxy.
However, of greatest importance are Philoponus' cosmological views,
based on the Judeo-Christian doctrine of creation. Thus admitting that
the world was created by God from nothing and will be destroyed, he
vehemently attacked Aristotle's assumption that the celestial region
beyond the moon was immutable.
In particular, he advocated the idea that
the sun and the stars did not consist of ether but were made of the
same stuff as the earth. He also claimed that the difference among stars
in magnitude, color, and brightness was to be found in the composition
of the matter of which the stars were constituted, being sources of fire
of the same kind as terrestrial fires. Moreover, he declared that all
matter in the universe is nothing but tri-dimensional extension, in
which respect there is no difference between any of the celestial and
the terrestrial bodies. Philoponus' cosmological views found no echo in
his time, however, and about eleven centuries had to pass until
observation showed that creation and decay were by no means confined--as
was commonly believed--to the earth and its immediate surroundings.
FROM THE DARK AGE TO THE RENAISSANCE
With the decline and fall of the Roman Empire, ancient philosophies
gave place to a new religious, philosophical, and social
movement--Christianity. Most of the early Fathers of the Church had
little sympathy for anything that emanated from the heathen Greek and
Roman world. For many centuries, therefore, anything that could not be
reconciled with the Holy Scriptures was rejected with horror and scorn.
Thus the earth became flat again; the heaven was no longer a sphere but a
tent or tabernacle; and the sun did not pass under the earth during the
night, but traveled laterally round its northern parts as if hidden by a
wall. It was also widely believed that the sun, moon, and stars were
moved in their orbits by angels, who had to carry on this work until the
last day. Although this type of cosmology continued to flourish during
the Middle Ages, some writers did study the works of the Greek
philosophers, and they were not afraid to accept some of the teaching of
antiquity. One of the most eminent figures of the transition period
between Antiquity and the Middle Ages, Anicius BOETHIUS (c. 480-524), is
often called "The Last Roman." He translated several Greek scientific
works into Latin, the only language common to the learned West. Boethius
translated Ptolemy's
Almagest into Latin, but this Latin
translation was lost shortly after. As a result, astronomers of the
early Middle Ages in the Latin West were ignorant of the epicycle
theories of the planets.
11 The scientific heritage of that
period was fully displayed by the encyclopedist ISIDORUS HISPALENSIS (c.
560-636), archbishop of Seville, who repeatedly referred to the
spherical shape of the earth in his writings, although they otherwise
contain passages that may be reconciled only with belief in a flat
earth.
Another important step forward was made by an English
monk, the Venerable BEDE (673-735), who stoutly maintained that the
earth is a sphere and cited as proof the fact that stars visible in one
latitude are invisible in another; borrowing heavily from the Latin
author PLINY the Elder (23-79), he also gave a detailed account of the
nonuniform apparent motions of the planets circling round it. From about
the ninth century geocentrism and the rotundity of the earth may be
considered to have been acceptable again in the Christian West. In the
early Middle Ages, from the eighth to the twelfth century, the
geoheliocentric system attributed to Heraclides also enjoyed a
widespread popularity propagated by several Latin authors--such as
Martianus CAPELLA, who wrote a compendium of science and philosophy in
the first half of the fifth century. Let us also mention the work of
Johannes Scotus ERIGENA (c. 810-877), an Irish-born philosopher active
in France in the 850s and 860s, who referred to "Jupiter, Mars, Venus,
and Mercury, which ceaselessly pursue their orbits around the sun (
qui circa solem volvuntur)."
Historians have disagreed about whether Erigena meant to claim that
these four planets move on heliocentric orbits, or merely that they
differ from chilly Saturn in that they are near the sun, are much akin
to it, and traverse the same region of the heavens that it does. It is
unfortunate that in the original manuscript Erigena's famous passage was
not accompanied by a graph
.
Meanwhile, carrying
the banner of Islam, Arabic tribes were suddenly fused into a powerful
nation during the seventh century. War and conquest were rapidly
followed by intense intellectual activity in Syria and then in Iraq. The
rise of the Abbasid caliphate (750-1258) inaugurated the greatest
period of Islamic rule, and Baghdad became the center of a brilliant
civilization which spread over the entire Muslim world. Old Indian and
Greek books were translated into Arabic during the eighth and ninth
centuries. Ptolemy's
Almagest was translated into Arabic for the
caliph al-Ma'mun (c. 786-833) in the late 820s, while large
observatories were being built in Baghdad and Damascus. AL-BATTANI (c.
858-929), perhaps the greatest Islamic astronomer, tested many of
Ptolemy's results, brought important ameliorations to them, and
published improved tables of the sun and the moon. From the same time
AL-SUfi (903-986) is chiefly known for his catalog of stellar
magnitudes. This work was particularly valuable since its author
carefully recorded the magnitudes "as they were seen by his own eyes,"
whereas other star catalogs of that period had simply borrowed all the
magnitudes from the
Almagest.
The next astronomical
center of that time and region was at Cairo, where Ibn YUNUS (c.
950-1009) published a set of astronomical and mathematical tables, the
Hakemite Tables,
which remained the standard ones for about two centuries. Another
important observatory was built at Maragha in northwest Iran by the
Mongol prince Hulagu Khan (c. 1217-1265), a grandson of Genghis Khan
(1162-1227). Its main contribution was a volume of new astronomical
tables published under the direction of Nasir al-Din AL-TUSI (1201-1274)
in 1271, and known as the
Ilkhanic Tables. But the most
productive observatory in western Asia was that of the Muslim ruler and
scholar ULUGHBEK (1394-1449), a grandson of the Mongol conqueror Timur
(1336-1405). Working at Samarkand with his assistants, Ulughbek made a
star catalog from observations with a 40-meter sextant fixed on the
meridian and other precision instruments. This was probably the first
substantially independent catalog of stellar positions made since the
time of Hipparchus sixteen centuries before. He also published fresh
tables of the planets, and did his own amazingly accurate calculations
of the length of the year. Unfortunately, Ulughbek was the victim of a
cultural and religious backlash: He was murdered at the instigation of
his own son, and the Samarkand observatory was reduced to ruins by the
beginning of the sixteenth century, although his astronomical work was
saved and published to posthumous acclaim in Western Europe
.
During the tenth century, astronomy and other branches of knowledge
also made some progress in Muslim Spain and the opposite coast of
Africa. A great library and an academy were founded at Cordoba about
970, and similar establishments sprang up in Toledo, Seville, and
Morocco. Thence, the fame of Arabic astronomy began slowly to spread
through Spain into other parts of western Europe. Toledo, despite its
reconquest by Christendom in 1085, long remained an important center of
Arab and Hebrew culture, where a true spirit of collaboration lingered
on among Jewish, Christian, and Moorish scholars. The most important
work produced by these astronomers was the volume of astronomical tables
known as the
Toledan Tables (1080), of which translations and
adaptations were widely distributed in Europe. Western knowledge of
astronomy was very much increased by the activity of Alfonso X
(1221-1284), "the Wise," king of Castile and León. He collected at
Toledo a body of scholars, mostly Jews, who calculated a set of new
astronomical tables for predicting positions of planetary bodies. These
Alfonsine Tables (1272)
spread rapidly through Europe and were in use for about three
centuries, up to the middle of the sixteenth century. To Alfonso is also
due the publication of a vast encyclopedia of astronomical knowledge
compiled by a similar group from Arab sources.
One of the last
significant astronomers of Muslim Spain was al-Bitruji, known to the
Latins as ALPETRAGIUS (died 1204). Philosophically, he objected to
Ptolemy's planetary system on the grounds that it violated Aristotle's
physical principles. He therefore advocated an alternative model for
planetary motion that was based on concentric spheres rotating about
inclined axes. This work, which was translated into Latin in 1217,
remained influential for several centuries. In fact, at the beginning of
the twelfth century, a great wave of translations from Arabic to Latin
had already begun, partly of originalArabic books, partly ofArabic
translations of Greek books. The physical works of Aristotle, among
which
De caelo is by far the most important, and Ptolemy's books
thus became available to western scholars. The influence of Aristotle
over medieval thought soon became almost supreme, and by the end of the
thirteenth century most of his cosmological views, or supposed views,
were firmly established in the Latin West, with Church approval. With
the notable exception of Robert GROSSETESTE (c. 1175-1253), chancellor
of Oxford University, and a few others who denied the existence of
Aristotle's fifth element, it was therefore widely accepted that the
four elements--earth, water, air, and fire--filled the sublunar region
of the sky, while the celestial region from the moon outward was
composed exclusively of an extraordinary substance, a special ether or
fifth element. The earth was of course resting at the center of the
universe, which was spherical in shape and of finite extent (see figure
1.6). Not unexpectedly, beyond the general assertion that rotating
heavenly spheres move the stars and planets, opinion among medieval
thinkers as to the final causes of these rotations varied widely. Of
particular interest is the
Guide for the Perplexed, in which the
Jewish philosopher Moses MAIMONIDES (1135-1204) embraces different
patterns of interpretation of heavenly phenomena. His cosmology is
basically Aristotelian, and he held that rotating spheres moved the
planets by mechanical transmission of motion through contact. Movement
of the spheres proceeded from another causation: Elaborating on the
thought of his Muslim predecessors, Maimonides identified the separate
intelligences of Aristotelianism moving the heavenly spheres with the
angels of Scripture. These views influenced the Dominican theologian
Thomas AQUINAS (1227-1274) and, through him, the whole thought of Latin
Christendom. In fact, such terms as "moving intelligences" or "angels of
the spheres" were still familiar to all in the sixteenth and
seventeenth centuries.
Thirteenth-century astronomy in western
Europe was concerned mainly with a debate as to the relative merits of
two rival planetary systems. The first was derived from the works of
Aristotle and Alpetragius, where it was assumed that the planets were
carried around on concentric spheres. In the second system, derived
ultimately from Ptolemy's book
Hypotheses of the Planets, the
planets were assumed to be carried around by a system of material
eccentric and epicyclic spheres, whose centers did not coincide with the
earth's center. The Ptolemaic system was quickly recognized as being
the best geometric device for "saving the astronomical appearances." The
practical astronomers, who inevitably demanded quantitative results,
thus had no choice but to retain the eccentrics and epicycles of
Ptolemaic astronomy, even though they could not be easily reconciled
with the principles of the only adequate system of physics known--that
of Aristotle. By the end of the thirteenth century the system of
concentric spheres had been largely discarded, and scholastic
philosophers increasingly came to assume the existence of material
eccentrics and epicycles. Special consideration among the medieval
astronomers may be given to the Provençal Jew Levi ben Gerson, also
known as GERSONIDES (1288-1344), who was the first to criticize the
faulty methodology of medieval science. Specifically, he measured the
changes in the apparent brightnesses of the planets with the goal of
refuting the Ptolemaic system. (He developed specific instruments for
this purpose, essentially pinholes and the camera obscura.) Since the
results of his observations did not fit Ptolemy's planetary models,
Gersonides therefore concluded that the epicyclic hypothesis must be
rejected as contrary to the phenomena. He also rejected the model
suggested by Alpetragius, who had objected to epicycles for Aristotelian
reasons, but was unable to devise a better one. Gersonides' contention
was that "no argument can nullify the reality that is perceived by the
senses; for true opinion must follow reality, but reality need not
conform to opinion"--certainly not the usual position in the scholastic
age.During the fourteenth and fifteenth centuries, even
more radical developments may have been suggested by ancient Greek
speculations, in particular the earth's daily rotation and the
semiheliocentric system in which Venus and Mercury revolve around the
sun while the sun itself revolves around the earth. The concept of
geocentrism remained unchallenged until the 1510s, when the Polish
astronomer Nicolaus COPERNICUS (1473-1543) revived Aristarchus'
heliocentric hypothesis.
Although few considered the problem
during the Middle Ages, prior to the seventeenth century scholars were
divided on the nature of the light emanating from the fixed stars and
the planets.Of particular interest is the work of the
Cairo astronomer and optician Ibn al-Haytham, known in the West
asALHAZEN (965-1038), who pointed out that the stars and planets, unlike
the moon, always exhibited the bright shape of a complete circle
regardless of their positions with respect to the sun, and regardless of
the observer's location. (The phases of Venus had not yet been
observed.) He therefore concluded that the stars and planets were
selfluminous, and that the moon was unique among heavenly bodies in
being the only one that borrowed its light from the sun.
16 The
Persian physician and philosopher Ibn Sina, known to the Latins as
AVICENNA (980-1037), did also concede that the moon received its light
from the sun and that the stars and planets were self-luminous. Ibn
Rushd, also known as AVERROËS (1126-1198) and perhaps the most
influential Muslim philosopher in Spain, agreed that the moon had its
light from the sun, but argued for the sun as the sole source of light
for allstars and planets; the Franciscan friar Roger BACON (c.
1220-1292) in Oxford was of the same opinion. Subsequently, the
Dominican friar ALBERTUS MAGNUS (c. 1200-1280), also known as Albert of
Cologne, and the scholastic philosopher ALBERT OF SAXONY (c. 1316-1390)
developed various arguments in defense of the idea that the sun
illuminated the planets. Among other problems, they had to explain how
the planets could appear visibly different and yet receive their light
from the same source. Albert of Saxony coped with this problem by
assuming that the solar light can penetrate the diaphanous planetary
matter, each planet differing in its ability to absorb light. This was a
most popular explanation of planetary light: the planets were visible
to us because they were partly transparent and, hence, could be filled
more or less completely with the sun's light. The Norman polymath Nicole
ORESME (c. 1325-1382), a scholar in Paris and later bishop of Lisieux,
thought that the self-luminosity option was more probable.
Interest in the light source of the stars became manifest in the late
sixteenth century, but again scholars were hardly of one mind. Some were
convinced that the fixed stars received their light from the sun
because they were not so far off that the sun's light could not reach
them. Others believed that the solar light was not the only source of
stellar brightness but that each star might have a small amount of light
within itself. Thomas DIGGES (1545/46-1595) and Giordano BRUNO
(1548-1600) were the first natural philosophers to break with these
traditional views by interpreting the fixed stars as suns, and hence as
self-luminous bodies. In 1576 Digges published an English version of
Copernicus'
De revolutionibus orbium coelestium (1543), adding to
his translation the assertion that the heliocentric universe should be
conceived as infinite, with the fixed stars located at varying distances
throughout infinite space. Thus Digges clearly perceived that, the
moment the displacement of the earth was conceded, there was no longer
any necessity for picturing the stars as attached to a celestial sphere
at a finite distance from the earth. Contrary to Digges, Bruno was a
mystic, and his own speculations had their roots in some earlier
suggestion by the Rhinelander theologian Nicolaus CUSANUS (1401-1464),
who had been led to a belief that the universe has neither center nor
circumference; that it is not infinite, yet it cannot be conceived as
finite, since there are no limits within which it is enclosed; and that
the earth, which cannot be the center of the universe, must in some way
be in motion, as are all other bodies in space, with a velocity that is
not absolute but relative to the observer. Actually, it was this
doctrine of relativity, in space and in motion, that served as the
background for Bruno's conception of an infinite universe and
innumerable worlds.The essential conclusions of Bruno's
work are that not only does the earth move round the sun but the sun
itself moves; that our planetary system is not the center of the
universe, and that the latter is of infinite size and the worlds therein
without number; and that the stars are at large but varying distances
from the sun and are themselves centers of planetary systems. These
assertions, which were published in England in 1584, marked the change
from medieval to modern scientific thought. Betrayed and arrested in
Venice, Bruno was transferred to Rome in 1593 and remained in prison for
seven years. Then, after a long trial, he was burned at the stake in
Rome for his writings which, in addition to containing religious and
political heresies, supported the new Copernican system and opposed the
traditional Aristotelian cosmology.
THE EMERGENCE OF MODERN ASTRONOMY
About the end of the sixteenth century and the beginning of the
seventeenth century were made the first decided advances since antiquity
in observational astronomy. In this field the leading names are those
of Tycho BRAHE (1546-1601) and Galileo GALILEI (1564-1642), the former
relying upon the naked eye for his measurements, the latter on his
recently built refracting telescope.
In 1572 Tycho observed a
new star and, failing to detect parallax in his observations, he
correctly deduced that it was located well beyond the planets. The
star's eighteen-month life span left a considerable impact since it cast
serious doubt on the existence of an eternally unalterable celestial
region. His observations of a brilliant comet in 1577 also convinced
Tycho that its parallax placed it well beyond the sublunar region where
comets were supposed to be confined. This was another severe blow to the
medieval belief that the celestial region beyond the moon's orbit was
immutable. However, because his observations did not disclose a stellar
parallax, Tycho rejected the Copernican theory of the earth's
revolution. He proposed as a compromise that the sun revolved around a
stationary earth, while all the planets--Mercury, Venus, Mars, Jupiter,
and Saturn--went around the sun.
Galileo's first contribution
to astronomical discovery was made in 1604, when a new star appeared in
Ophiuchus, and was shown by him to be without parallax, a result
confirming Tycho's conclusions that changes take place in the celestial
region beyond the planets. With his telescopic observations made in the
1610s, Galileo added to this a picture of celestial bodies that
exhibited surface irregularities: the moon, whose mountains and valleys
made it akin to the earth; and the sun, whose spots continually changed
in shape and then disappeared while others again succeeded them. The
discovery of sunspots is of particular importance because it caused
irremediable damage to the Aristotelian principle of stability and
incorruptibility of the heavens beyond the moon. Of the new discoveries,
Galileo's telescopic observations of the phases of Venus and of the
satellites of Jupiter were perhaps the most dramatic events in
transforming heliocentrism from a convenient hypothesis for
mathematicians into a most plausible physical description of our
planetary system. This was a deadly blow to the traditional geocentric
and anthropocentric universe.
In 1616 the Copernican doctrines
were thus declared "false and absurd, formally heretical and contrary to
Scripture" and Galileo was admonished to abandon these opinions. In
1632 Galileo published his epoch-making treatise
Dialogo sopra i due massimi sistemi del mondo (Dialogue
on the two chief world systems), that is, the Ptolemaic and the
Copernican (see figure 1.7). Although the book came out bearing both the
Roman and the Florentine imprimaturs, it was soon suspended and its
sale prohibited on the ground that it was a compelling and unabashed
plea for the heliocentric system.
In 1633 Galileo was
condemned by the Roman Inquisition for believing and holding that the
Copernican doctrines were true and, in punishment, was required to
"abjure, curse, and detest the aforesaid errors" and forced to spend the
last eight years of his life under house arrest. While confined to his
villa at Arcetri, near Florence, he published in 1638 his
Discorsi e dimostrazioni matematiche interno a due nuove scienze (Dialogue
on two new sciences), in which he summarized the results of his early
work with falling bodies and projectiles and presented his penetrating
views on the principles of mechanics. This important work, which was not
published in Italy but in Holland, paved the way for Newtonian
mechanics.
Copernicus' heliocentric theory made continued
support for the medieval geocentric cosmology untenable for the majority
of astronomers, if not for the majority of scholastic philosophers. Yet
Copernicus was a conservative because he did not venture to abandon the
use of patterns of circular motion and indeed continued to make use of
epicycles in describing planetary trajectories. The great contribution
of Johannes KEPLER (1571-1630) was to improve the theory of planetary
motion by replacing circles and epicycles by
ellipses (see figure
1.8). He himself was not an observer, but he had great faith in the
accuracy of the observations of his teacher, Tycho, which he had
inherited at the time of Tycho's death. Although Kepler had strong
mystical leanings, so that a large portion of his work is now
unreadable, his claim to immortal fame rests upon his discovery of the
following empirical laws of planetary motion:
- Each planet describes an ellipse, with the sun being at one focus.
- The
speed of each moving planet changes with distance from the sun, so that
the straight line joining each planet to the sun sweeps out equal areas
in any two equal intervals of time.
- The squares of the
periods of revolution of any two planets (including the earth) about the
sun are in the same ratio as the cubes of their mean distances from the
sun.
(The "mean distance" in the third law is half
the major axis of the ellipse.) Kepler announced his third law in 1619,
ten years after he had given the first two. Not unexpectedly, his books
were promptly banned and placed on the Roman
Index of Prohibited Books.
Although the geocentric system continued to command widespread support
throughout the seventeenth century, heliocentrism with its Keplerian
modifications was cautiously gaining acceptance. Attempts were thus made
to find out what causes the planets to move on their elliptic orbits
with the sun occupying one of the focal points. The solution proposed by
the French philosopher René DESCARTES (1596-1650) in 1644 was eagerly
accepted.It assumes that all space is filled with a fluid,
or ether, the parts of which act on each other and generate a whole
spectrum of vortices of different size, velocity, and density. There is
an immense vortex around each star and, in particular, around the sun,
which carries in its circular motion the earth and the other planets.
Each of these planets is located, in turn, in a smaller vortex by which
gravitational attraction is produced. Descartes made no attempt to
reconcile his theory with Kepler's laws. In fact, it was unsupported by
any experimental evidence and did not explain a single phenomenon
satisfactorily. Yet "Cartesianism" became extremely fashionable,
especially in France, and its vogue undoubtedly contributed to the
overthrow of the Aristotelian system.
Descartes' vortex theory
required one motion to be the cause of another and explained the mutual
attraction of the sun and the planets in terms of actual bodily motions.
As early as the 1660s, however, Isaac NEWTON (1642-1727) rejected
Descartes' hypothesis of material vortices as the cause of gravitation.
According to him, gravity is the power of attraction that one body
exercises upon another without the first being in motion or coming in
contact with the second. Although this approach raises the problem of
action at a distance, which Newton properly acknowledged, it has the
merit of fitting the observed phenomena.What Newton brought to the subject is to be found in the simplicity that his
laws of motion combined with the principle of
gravitational attraction were
able to introduce into the description of planetary orbits and ordinary
terrestrial phenomena. Newton's unique achievement was to prove that
the force that causes a stone to fall on earth is also that which keeps
the planets in their orbits. This is expressed in Pope's famous epigram:
Nature and Nature's laws lay hid in Night,
God said, Let Newton be, and all was light,
which celebrates the illumination of nature by Newton's mechanical approach to the physical world.
When, in 1687, Newton published his epoch-making treatise
Philosophiae naturalis principia mathematica,
or "Mathematical Principles of Natural Philosophy" (figure 1.9), the
medieval geocentric world had become utterly irrelevant because it no
longer represented a viable alternative to a world in which
gravitational attraction forces each planet to move along an ellipse. In
other words, Newton's theory of gravitation made physical sense of
heliocentrism while providing a simple, natural derivation of Kepler's
empirical laws from first principles alone. The law of gravity is
basically simple: it merely states that
two bodies attract each other
with a force that is proportional to the product of their masses and
inversely proportional to the square of the distance between them.
The success of the theory was all the more evident that the general
solution of the two-body problem was found to be a conic (i.e., a
circle, an ellipse, a parabola, or a hyperbola), in perfect agreement
with the observed trajectories of different comets. Yet, as was noted by
Newton: "Hitherto we have explained the phenomena of the heavens and of
our sea by the power of gravity, but have not assigned the cause of
this power." Pointing out that he had made no unreasonable hypothesis,
he further concluded: "And to us it is enough that gravity does really
exist, and act according to the laws which we have explained, and
abundantly serves to account for all the motions of the celestial
bodies, and of our sea." Newton's theory is of great philosophical
importance because it is the first successful attempt to explain the
universe and its processes without reference to gods or animistic
conceptions.
By the time geocentrism and terrestrial immobility
had lost all credibility, it was widely accepted that the fixed stars
were self-luminous bodies, the sun being one among the multitude of
stars. However, because no stellar parallax could be detected from the
earth's orbital motion round the sun, enormous arbitrary distances had
to be assumed between the sun and the fixed stars. The problem was
discussed by the Dutch polymath Christiaan HUYGENS (1629-1695) in his
treatise
Cosmotheoros; his efforts at measuring the distance of
Sirius are particularly noteworthy. (The work was published posthumously
in 1698.) Lacking any information about the global properties of stars,
he assumed that his test star, Sirius, was exactly similar to the sun.
If so, then, he correctly deduced that its distance from us should be as
much greater than that of the sun as its apparent diameter was less
than the diameter of the solar disk. In practice, to compare the sun and
Sirius, he gradually lessened the sun's diameter in his telescope,
closing one end of his twelve-foot tube with a plate that had a variable
hole in its middle. Reducing the hole's diameter till the sun appeared
of the same brightness as Sirius, he found that he had to make its
diameter but the 27,664th part of the diameter of the observed solar
disk. In our modern notation, he evaluated the distance of Sirius at
about 27,664 AU whereas its distance is actually close to 546,000 AU.
(Here AU denotes the astronomical unit, that is, the mean sun-earth
distance.) Although we know that Huygens' evaluation was vitiated by an
inadequate assumption about the global properties of Sirius, this
observational work should not be ignored, because it is quite
illustrative of the spirit and methods of the Scientific Revolution that
changed our views of the universe.
