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About 10,000 bce, wolves were probably domesticated. [added 02/01/03]
By 9000 bce, sheep were probably domesticated in the Middle
East.
About 7000 bce, there was probably an hallucinagenic mushroom,
or 'soma,' cult in the Tassili-n-Ajjer Plateau in the Sahara (McKenna 1992:98-137).
By 7000 bce, wheat was domesticated in Mesopotamia. The intoxicating effect of leaven on cereal dough and of warm
places on sweet fruits and honey was noticed before men could write.
By 6500 bce, goats were domesticated. "These herd animals only gradually revealed their full utility--sheep developing their woolly fleece over time during the Neolithic, and goats and cows awaiting the spread of lactose tolerance among adult humans and the invention of more digestible dairy products like yogurt and cheese" (O'Connell 2002:19). [added 02/01/03]
Between 6250 and 5400 bce at Çatal Hüyük, Turkey, maces, weapons used exclusively against human beings, were being assembled. Also, found were baked clay sling balls, likely a shepherd's weapon of choice (O'Connell 2002:25). [added 02/01/03]
About 5500 bce, there was a "sudden proliferation of walled communities" (O'Connell 2002:27). [added 02/01/03]
About 4800 bce, there is evidence of astronomical calendar stones
on the Nabta plateau, near the Sudanese border in Egypt. A parade
of six megaliths mark the position where Sirius, the bright
'Morning Star,' would have risen at the spring solstice. Nearby are
other aligned megaliths and a stone circle, perhaps from somewhat later.
About 4000 bce, horses
were being ridden on the Eurasian steppe
by the people of the Sredni Stog culture (Anthony et al. 1991:94-95).
About 4000 bce, light wooden plows were used in Mesopotamia.
Between 4000 and 3500 bce, copper smelting in minute quantities was introduced in Mesopotamia. [added 02/01/03]
Between 4000 and 3500 bce, copper smelting in minute quantities
was introduced in Mesopotamia.
By 3500 bce, irrigation was developed in Mesopotamia.
Between 3300 bce and 2850 bce, numerals appeared in Sumerian, Proto-Elamite,
and Egyptian hieroglyphics, and, somewhat later, the earliest known forms
of pictographic writing.
By 3200 bce, wheeled vehicles were used in Uruk.
From about 3200 bce, there exist Egyptian sailboat drawings, showing a mast with a single broad square sail hung from it. [added 02/01/03]
By 3000 bce, cotton was being grown in India.
About 3000 bce, draft oxen were pulling plows and potters
were using wheels in Mesopotamia.
About 2700 bce, cuneiform signs and numerals appeared on Sumerian
tablets, with a slanted double wedge between number symbols to indicate the absence of a number, or zero, in a specific place. .
About 2500 bce, the Stele of Vultures shows the Sumerian infantry in a phalanx: "all wearing helmets, advancing shoulder to shoulder behind a barrier of locked rectangular shields reinforced with bronze disks, and presenting a hedgehog of spears protruding from several rows back" (O'Connell 2002:32). [added 02/01/03]
About the middle of the third millenium, bronze enabled the dagger form to be stretched into swords. [added 02/01/03]
About 2400 bce, the short, composite bow was developed by mounted archers. Unstrung it curved forward and could pierce armor at 100 yards. [added 02/01/03]
About 2300 bce, Proto-Indian writing appeared in the Indus Valley.
Before 2000 bce, the Egyptians considered the souring
of wine comparable to the souring of milk.
In the first half of the second millenium bce, Assyro-Babylonian
cuneiform decimal notation gradually supplanted the Sumerian sexagesimal
system for representing numbers below 60. For representing higher
numbers the sexagesimal place-value principle with base 60 was invented
(Ifrah 1981:371-372).
In the seventeenth century bce, an Egyptian papyrus listed many diagnoses of head and neck injuries and their treatment and is the "first known document in which the brain's role in controlling limbs or organs at a considerable distance is established" (Changeux 1983:4; Breasted 1930). [added 02/01/03]
In the seventeenth century bce, the first use was made of phonetic
signs, derived from Eqyptian hieroglyphics, in the Serabit el Khadim inscriptions,
in the Sinai peninsula.
In the second millenium bce, in the Rig-Veda it was maintained
the Earth was a globe and in the Yajur-Veda that the Earth circled
the Sun.
By 1500 bce, Babylonian mathematicians understood "the determination
of the diagonal on the square from its side," that is to say, the 'Pythagorean
theorem' (Neugebauer 1957:36).
In the fourteenth century bce, the first known alphabetic writing,
in thirty cuneiform signs, appeared on Ugaritic tablets.
In the late twelfth century bce, modern alphabetic writing was prefigured
in the Phoenician alphabet.
Between 1200 and 1000 bce, iron smelting was introduced on an
industrial scale in Armenia.
About 1000 bce, mule breeders noticed that "a mare crossed
with a donkey yields a mule, whereas a stallion crossed with a donkey produces
a hinny, which has shorter ears, a thicker mane and tail, and stronger
legs than the mule. This made [modern] researchers aware that there
could be parent-specific effects in off-spring" (Pennisi 2001:1065).
About 850 bce, impaling rams jutted from the prows of Greek galleys. These galleys were propelled by ten oarsmen on each side. By the middle of the seventh century, Phoenician galleys, or triremes, employed crews of 200 and three levels of oarsmen (O'Connell 2002:99-104). [added 02/01/03]
About 800 bce, vowels were by the Greeks to consonants of Phoenician
origin.About 800 bce, vowels were by the Greeks to consonants of Phoenician
origin.
From 747 bce, a continuous record of solar and lunar eclipses
was kept in Mesopotamia.
In the early seventh century bce, gold coins were introduced in Lydia,
western Anatolia, as a standard of exchange.
About 600 bce, Thales of Miletus, arguing from the fact that
wherever there is life, there is moisture, speculated that the basic stuff
of nature is water, according to Aristotle.
About 560 bce, Anaximander, a monist of Miletus like Thales, said
that the primal substance, the substratum of the opposites, the originative
stuff, is the apeiron, which seems to have meant, at that time,
the spatially indefinite or unbounded (Kirk
et al. 1983:110).
About 530 bce, Pythagoras discovered the dependence of
musical intervals on the arithmetical ratios of the lengths of string at
the same tension, 2:1 giving an octave, 3:2 the fifth, and 4:3 the fourth.
He is also credited with a general formula for finding two square numbers
the sum of which is also a square, namely (if m is any odd number),
m2+{1/2(m2-1)}2={1/2(m2+1)}2. "The Pythagoreans and Plato [as well as the Renaissance Neo-Platonists]
noted that the conclusions they reached deductively agreed to a remarkable
extent with the results of observation and inductive inference. Unable
to account otherwise for this agreement, they were led to regard mathematics
as the study of ultimate, eternal reality, immanent in nature and the universe,
rather than as a branch of logic or a tool of science and technology" (Boyer
1949:1). Consequently, when the Pythagoreans developed the theory of geometric
magnitudes, by which they were able to compare two surfaces' ratio, they
were led, for lack of a system which could handle irrational numbers, to
the 'incommensurability problem': Applying the side of a square to the
diagonal, no common rational measure is discoverable.
About 510 bce, Almaeon of Crotona, a member of the Pythagorean
medical circle, located the seat of perception in the brain, or enkephalos,
and maintained that there were passages connecting the senses to the brain,
a position he was said to have arrived at by dissections of the optic nerve.
About 500 bce, Heraclitus of Ephesus maintained that permanence
was an illusion and the only possible real state was the process of becoming. He also said that to the
logos, all things are one, all opposites
are joined. Logos, a word which Anaximander also used,
seems to be a principle manifesting itself in the process or cohering of
things, and to occupy a place in Greek ideology similar to dharma
for Hindus or 'Wisdom' for Jews (Park 1990:10).
About 500 bce, Xenophanes examined fossils and speculated on
the evolution of the earth.
About 480 bce, Parmenides of Elea founded the Eleatic School where he taught that 'all is one,'
not an aggregation of units as
Pythagoras had said, and that to
arrive at a true statement, logical argument is necessary. Truth "is identical with the thought that recognizes it" (Lloyd 1963:327). Change
or movement and non-being, he held, are impossibilities since everything
is 'full' and 'nothing' is a contradiction which, as such, cannot exist. "Parmenides is said to have been the first to assert that the Earth
is spherical in shape...; there was, however, an alternative tradition
stating that it was Pythagoras" (Heath 1913:64).
[[Corollary to Parmenides' rejection of the existence of 'nothing' is the Greek number system which, like the later
Roman system, refused to use the Babylonian positional number system with
its marker for 'nothing.' Making no clear distinction between nature
and geometry, "mathematics, instead of being a science of possible relations,
was to [the Greeks] the study of situations thought to subsist in nature"
(Boyer 1949:25). Moreover, "almost everything in [Greek] philosophy
became subordinated to the problem of change.... All temporal changes
observed by the senses were mere permutations and combinations of 'eternal
principles,' [and] the historical sequence of events (which formed part
of the 'flux') lost all fundamental significance" (Toulmin and Goodfield
1965:40).]]
About 470 bce, Zeno
of Elea propounded forty paradoxes probably to point out inconsistencies in Pythagorean positions.
One of the most famous is this: The
fleeing and slower runner can never be overtaken by the faster, pursuer
because the faster must first reach the point where the slower is at a
that time, but by then the slower will be some distance ahead. Other paradoxes made the same or apposite points, but, in fact, mathematical
analysis shows that infinite aggregates and the nature of the continuum
are not self-contradictory but only counter to intuition.
About 450 bce, Empedocles
of Agrigento explained changes in quality or quantity of a thing as
movement by the basic particles of which the thing consisted, Fire, Earth,
Air, and Water. These elements mix and separate "under the guidance
of two opposing principles, Love, which draws them together, and Strife,
which drives them apart" (Park 1990:25).
About 450 bce, Anaxagoras of Athens taught that the moon shines
with the light of the sun and so was able to explain the eclipses.
About 440 bce, Leucippus of Miletus said that the world consisted in the
void and atoms, which are imperceptible individual particles that differ
only in size, shape, and position. That these particles were imperceptible
meant they met Parmenides' objection to the Pythagorean's geometric
points and, since they alone were unchanging, change could be explained
as mere sense impressions. "It is scarcely an exaggeration to say
that even in 1900 the only new idea to Leucippus's theory was
that each chemical element was identified with a separate atomic species"
(Park 1990:41).
About 440 bce, Protagoras of Abdera held that man is the measure
of all things by which he meant that we only know what we perceive, not
the thing perceived (Dictionary of Philosophy 1984:273).
About 440 bce, Oenopides of Chios probably created the first
three of what became Euclid's 'postulates' or assumptions.
What is postulated guarantees the existence of straight lines, circles,
and points of intersection. That they needed to be postulated is
because they require 'movement,' the possibility of which was challenged
by the Eleatics (Szabó 1978:276-279).
About 430 bce, Hippocrates
of Chios squared the lune, a major
step toward squaring the circle, probably using the theorem that circles
are to one another as the squares of their diameters.
Prior to about 425 bce, Herodotus wrote the first scientific
history; that is, he began by asking questions, rather than just telling
what he thinks he knows. Moreover, these questions were "about things
done by men at a determinate time in the past, [and the history itself
] exists in order to tell man what man is by telling him what man has done"
(Collingwood 1946:18).
About 420 bce, Democritus
of Abdera developed Leucippus's atomic theory: Atoms vibrate
when hitched together in solid bodies and exist in a space which is
infinite in extent and in which each star is a sun and has its own world.
He also
produced two major concepts
in the history of ideas concerning the brain--that thought was situated
there and, anticipating the nervous system, that psychic atoms constituted
the material basis of its communication with the rest of the body and the
world outside. Socrates, and hence the Platonic school, followed
Democritus in locating thought in the brain.
About 400 bce, Hippocrates of Cos, also locating thought,
pleasure, and pain in the brain, maintained that diseases have natural causes, and
observed that head injuries
led to impairments on the opposite side of the body. The 'Hippocratic method' of treatment of the sick was to keep the patient
in bed and let nature take its course.
About 400 bce, an arrow-shooting catapult was developed at Syracuse. Its main significance is that it "embodied the deliberate exploration of physical and mechanical principles to improve armaments" (O'Connell 2002:86) [added 02/01/03]
After about 380 bce, Plato said, in the Timaeus, that "as being is to becoming, so is truth
to belief" (Plato 1929:29c). In other words, we can only believe,
not know, on the basis of experience. Like, Parmenides, he
held being and truth, indeed the world, to be timeless and unchanging,
an ideal of which man can only hold the idea. This permitted him
a certain amount of flexibility: He was willing to accept objections to
his view of the universe, for example, if the new hypothesis would provide a rational explanation or 'save
the appearance' presented by the planets. In the Timaeus, he also held that the 'world soul' was constructed
according to mathematical principles, and, therefore, these principles
are already fixed in the individual. (Forms or ideas that have existence
independent of any particular mind came to be called archtypes.)
He scattered reflections on mathematical
issues throughout his dialogues; e.g., in the Meno, he illustrates
the difference between a class and its members by reference to the difference
between defining 'figure' and enumerating specific figures. References
to ratios and proportions are everywhere. The five regular polygons he ascribed to the four elements plus the
"decoration" of the universe (Plato 1929:55c), probably the animals of
the zodiac.
By the fourth century bce, Babylonian astronomers had learned enough
about the moon's motion that they could predict the occurence of lunar
eclipses.
About 370 bce, Eudoxus of Cnidus invented a model of twenty-seven
concentric spheres by which he was able to calculate the sun's annual motions
through the zodiac, the moon's motion including its wobble, and the planets'
retrograde motion. He used what came much later to be called the
'exhaustion method' for area determination. This method involved
inscribing polygons within circles, reducing the difference ad absurdum,
and was wholly geometric since there was at that time no knowledge of an
arithmatical continuum, at least among the Greeks.
By about 335 bce, Aristotle
had said that universals are abstractions
from particulars and that we "have knowledge of a scientific fact when
we can prove that it could not be otherwise." But "since observation
never shows whether this is the case," he established "reason rather observation
at the center of scientific effort" (Park 1990:32). A deductive argument
is "a 'demonstration' when the premises from which the reasoning starts
are true and primary.... Things are 'true' and 'primary' which are
believed on the strength not of anything else but themselves" (Aristotle
1928:100a-100b). Aristotle defined the syllogism as a formal argument
in which the conclusion necessarily follows from the premises, and said
that the four most common statements of this sort are 'all Subject
is Predicate,' 'no S is P,' 'some S
is P,' and 'some S is not P.' He also discerned four
sorts of 'cause.' The 'formal cause' is the design of a thing.
The 'material cause' is that of which it is made. The 'efficient
cause' is the maker. And the 'final cause' is the purpose of the
thing. Aristotle also insisted on the operational character of mathematics
and rejected any metaphysical character of number.
At the same time, Aristotle often states both his observations
and his reasons with rather too much conviction: "The shape of the heaven
is of necessity spherical; for that is the shape most appropriate to its
substance and also by nature primary" (Aristotle 1930:286b). "A heavenly
essence could not, according to [his] physics, manifest any but its own
'natural' movement, and its only natural movement [so his reason informed
him] was a uniform rotation around the center of the universe" (Duhem 1908:15). His name for the heavenly essence, the quintessence, is aiqhr, of which the Latin cognate is 'aether' (Although Aristotle is perhaps the earliest theorist of aiqhr, he was not the first to use the word, e.g., Heraclitus used it to mean heavenly fire.)
In fact, "in dealing with [any] concrete, physical problem, it is...always
necessary to take into account the world order, to consider the realm of
being to which a given body belongs by its nature.... It is only
in 'its' place that a being comes to its accomplishment and becomes truly
itself" (Koyré 1968:6,24n1). He also put forth the view that each species has an essence and that divergence
from this type was not possible beyond a certain limit. These remained
the dominant views until the acceptance of those of Johannes Kepler,
in the first case, and Charles Robert Darwin and Alfred Russell
Wallace, in the second. If the properties of a thing are its
'form,' then, according to Aristotle, perception is the process whereby
the form, and not just the representation of it, enters the soul.
This account of perception "was taken as the exact, literal truthby almost
every educated person down to the sixteenth century" (Park 1990:44).
Also. Aristotle "considered the changes undergone by inanimate things to
be analogous to those seen in the biological world. Thus grape juice
is the infantile form of wine, fermentation is the process of maturation;
the further change to vinegar is the death of the wine" (Fruton 1972:24).
Since all matter is formed from the mixture of the four elements, he
taught the elements are not permanent and could be transmuted one into
another, inspiring all who practice alchemy. After
weighing the evidence, Aristotle decided that the organ of thought
and sensation was the heart. But he was also the first
to perceive the antithesis between epigenesis, "fresh development," and
preformation, the "simple unfolding of pre-existing structures."
The subsequent history of this controversy is "almost synonomous with the
history of embryology" (Needham 1934:40). [revised 02/01/03]
About 330 bce, Heraclides of Pontus said that the earth turns
daily on its axis "while the heavenly things were at rest..., considered
the cosmos to be infinite..., [and] with the Pythagoreans, considered each
planet to be a world with an earth-like body and with an atmosphere" (Dreyer
1906:123-125). He also suggested that Mercury and Venus have the
sun at the center of their spheres.
In 323 bce, Theophrastus, suceeded Aristotle as head of the Peripatetic school of philosophy
of which he was the co-founder. In Historia Plantarum and
De Causis Plantarum, he classified and described the "external parts
of plants from root to fruit..., set forth the 'homology' of the perianth
members [or floral envelope] of flowers..., to some extent distinguished
between monocotyledons and dicotyledons, [and] described the fertilization
of the date palm" (Crombie 1952:367).
About 310 bce, Autolycus
of Pitane defined uniform motion as being
when "a point is said to be moved with equal movement when it traverses
equal and similar quantities in equal times" (Clagett 1959:164).
About 300 bce, Eukleides, better known as Euclid, published his Elements,
a reorganized compilation of geometrical proofs including new proofs and
a much earlier essay on the foundations of arithmetic. Elements concludes with the construction of Plato's five
regular solids. Euclidean space has no natural edge, and is thus infinite. In his Optica, he noted that light travels in straight lines
and described the law of reflection.
About 300 bce, Epicurus attempted to deal with the contradiction
between atoms falling through the void in parallel paths at the same speed
and the appearance of novel combinations, or matter, by supposing very
slight, chance deviations, or 'clinamen,' in an atom's path. He saw
this as analogous to the question of human freedom in a determined nature; i.e., there is no room for ethical considerations
Indeed, "Epicureans
saw the development of the world as a random, one-way
process" (Toulmin and Goodfield 1965:50).
About 280 bce, Herophilus of Alexandria studied anatomy and
compared humans and animals, distinguished between sensory and motor nerves,and between the cerebellum and the brain, noted that the cortex was folded into convolutions,
and named the 'duodenum.' [revised 02/01/03]
About 260 bce, Aristarchus
of Samos, in On the Sizes and Distances of the Sun and Moon, used trigonometry
to estimate the size of the Moon and its distance by the Earth's shadow
during a lunar eclipse.
Archimedes and others said that he maintained
that the Moon revolved around the Earth and the Earth around the Sun which
remained stationary like the stars.
About 260 bce, Archimedes of Syracuse contributed numerous advances to
science including the principle that a
body immersed in fluid is buoyed up by a force equal to the weight of the
displaced fluid and the calculation of the value of p. "His method was to select definite and limited problems. He then
formulated hypotheses which he either regarded, in the Euclidean manner,
as self-evident axioms or could verify by simple experiments. The
consequences of these he then deduced and experimentally verified" (Crombie
1952:278).
About 250 bce, Erasistratus of Alexandria dissected the brain
and distinguished between the cerebrum and the cerebellum.
About 250 bce, 'zero' appeared in the Babylonian place-value system.
About 240 bce, Eratosthenes
of Cyrene calculated the diameter of the earth by measuring noontime shadows
at sites 800 km. apart. Assuming the earth is a sphere, the measured
angle between the sites is seven degrees and the circumference is about
50 times 800 km., or about 40,000 km.
Before the end of the third century bce, astrolabes were in use for
taking the angular distance between any two objects, usually the elevation
in the sky of planets.
In the early second century bce, Diocles, in On Burning Mirrors, proved the focal property of a parabola and showed how the Sun's rays can be made to reflect a point by rotating a parabolic mirror (Toomer 1978).
About 210 bce, Apollonius
of Perga, in Conics, introduced
the terms 'parabola' and 'hyperbola,' curves formed when a plane intersects
a conic section, and 'ellipse,' a closed curve formed when a plane intersects
a cone.
About 170 bce, parchment, superior to papyrus because it can be printed
on both sides and folded, was invented in Pergamon.
About 134 bce, Hipparchus
of Rhodes measured the year with great
accuracy and built the first comprehensive star chart with 850 stars and
a luminosity, or brightness, scale. He is credited with the discovery of the precision
of the equinoxes, and seems to have been very impressed that either of
two geometrically constructed hypotheses could 'save the appearance' of
the path that a planet follows: One shows the planets moving in eccentric
circles and the other moving in epicycles carried by concentric circles
(Duhem 1908:8).
In the first half of the first century bce, Titus Lucretius
Carus, writing in Latin, set forth the teachings of the Epicurean school
in De rerum natura. There
he held that "the soul is itself
material and so closely associated with the body that whatever affects
one affects the other. Consciousness ends with death. There
is no immortality of the soul. The universe came into being through
the working of natural laws in the combining of atoms" (Columbia Desk
Encyclopedia 1975:1626). This view is supported by the force of the wind which is the result
of the impact of innumerable atoms.
In 45 bce, Sosigenes of Alexandria designed a calendar of 365.25
days which was introduced by Julius Caesar.
Late in the first century bce, Strabo published his Geographia,
based on his observations and those of his Greek predecessors.
Late in the first century bce, Marcus Vitruvius Pollio, in
De architectura, wrote of the properties of building materials in
terms of atoms. This book remained the standard architectural treatise
into the Renaissance.
About the 25th year of the common era, Pomponius
Mela, in De situ orbis, published
a map of the known world and formalized the notion of climatic latitudes.
In the first century, Pedanius Dioscorides published
recommendations as to the medicinal use of specific plant extracts.
About 100, Hero
of Alexandria explained that the four elements consist of atoms. He also observed
that heated air expanded. In Catoptrica, he demonstrated geometrically that the
"path taken by a ray of light reflected from a plane mirror is shorter
than any other reflected path that might be drawn between the source and
the point of observation" (History of Optics 2001:1).
About 100[?], Plutarch, in On the Face That Can Be Seen
in the Lunar Disk, compared the Moon to the Earth, upheld the idea
of the plurality of worlds, and tried to overturn Aristotle's theory
of 'natural places' (Duhem 1985:479).
Between 127 and 141,
Claudius Ptolemaeus, better known as Ptolemy, put together a thirteen volume compendeum of opinion and data concerning
the stars, including the Mesopotamian eclipse record. In this book,
the Almagest, Ptolemy rejected the Peripatetic physics of the heavens,
using circles rather than spheres. He did so in order to simplify
his calculations, judging the circles to be only models devised for the
purpose of calculation and recognizing that the actual movements were unknowable.
The Almagest
also contains errors which were not corrected until
the sixteenth and seventeenth centuries: e.g., saying that the earth is
the center of the universe, the planets have circular, if eccentric, orbits, and the earth does
not move--because the centrifugal force would cause anything even temporarily
disconnected to lag behind. On the other hand, the tables of the planet's positions
were of such accuracy that Nicholas
Copernicus computed most of
his numbers from them.
About 170, Claudius Galen used pulse taking as a diagnostic, performed numerous animal dissections, and wrote treatises on anatomy
aid. The Galenic doctrine assumed that health depends on a balance
of affinities or antagonisms associated with various bodily fluids or 'humors:'
blood and fire (hot and dry), yellow bile and air (hot and wet), black
bile and earth (cold and dry), and phlegm and water (cold and wet).
"The object of good medical practice...was to restore the balance of the
humors by such treatment as bleeding or purgation with plant extracts"
(Fruton 1972:27). Galen eskewed 'action at a distance' through the agency of gods or spirits,
in his formulas he employed many odd ingredients, such as crocodile bllod
and mouse dung. But, if he can, he relates the efficacy to some mechanism:
for example, for a root worn around the neck, inhalation of the particles
of the root. He
distinguished three ventricles and proposed that nerves are ducts conveying
fluid pneuma secreted by the brain and spinal cord to the periphery of the body,
which was the basis of the idea, widespread until the eighteenth century,
that nervous tissue had a glandular function He broke pneuma, which means spirit or soul in Greek, down into various faculties, motor, sensory including the five senses, and rational. He divided the rational pneuma into several functions, imagination, reason, and memory. He also wrote of 'seeds of disease,' presumably what are now called
germs. [revised 02/01/03]
About 250, Diophantus pioneered in solving
certain indeterminate algebraic equations, i.e., an equation in which the
variables can take on integer values and has an infinite but denumerable
set of solutions: e.g., x+2y=3.
In perhaps the middle of the third century, Calcidius translated
the first 53 chapters of Plato's Timaeus into Latin.
He translated 'analysis' and 'synthesis' as resolutio and compositio,
and maintained in his commentary that combining these was the proper method
of philosophical research.
In the late third century, Porphyry wrote an introduction
to Aristotle's logic, the Eisagoge, which was much read in
the course of the Middle Ages. It emphasized the distinction between
facts held to be universally true because they existed 'prior to experience,'
the Platonic opinion, or 'posterior to experience,' the Aristotelian opinion.
This difference grew into the distinction between 'realists,' who hold
that universals are the ultimate reality, and 'nominalists,' who hold that
universals are derived from real experience. In our time, this distinction
lives in the controversy concerning the 'humanity' of a fetus (Park 1990:100).
About 385, Aurelius Augustinus, later known as Augustine,
a Christian saint, writing in Latin, found the Platonist notion of eternal
ideas a certain basis for knowledge which he promulgated in his books Confessiones and
Civitas Dei.
[["The fourth and fifth centuries saw the intellectual triumph of
[Roman] Christianity in Europe.... In 389 Christian monks sacked
the great Greek library in Alexandria.... Since Greek was the language
of a literature whose most famous works expressed a pagan culture [and]
by 425 Saint Jerome's [official Latin or] Vulgate Bible was being copied
and distributed..., Western scholars no longer needed Hebrew or Greek"
(Park 1990:78-79).]]
About 450 or later,
Proclus, the final head of Plato's
Academy, said that astronomers "do not arrive at conclusions by starting
from hypotheses, as is done in the the other sciences; rather, taking conclusions
[the appearance of the heavens] as their point of departure, they strive
to construct hypotheses from which effects conformable to the original
conclusions follow with necessity" (Proclus, quoted by Duhem 1908:20).
The astronomer is only interested in saving the appearance of the phenomena,
and whether this conforms to reality is left to the other sciences to decide.
In 458, the Lokavibhaga, a Jain work in Sanscrit on cosmology,
demonstrated a clear understanding of place-values and the concept of zero.
In 517, John Philoponus determined that falling objects
do so with the same acceleration, or 'impetus,' specifically opposing
Aristotle's notion
that the air through which a projectile moved was its motive force.
After about 520, Ancius Manlius Severinus Boethius wrote
De consolatione philosophiae in Latin, probably the most widely
read book in Europe in the Middle Ages, and translated Aristotle's
logical books. "Until the rediscovery of Aristotle in the twelfth
century his translations were the basic texts for all students of logic"
(Park 1990:79). He also wrote a commentary on Porphyry's logic.
Aside from Boethius and Augustine, students in the monasteries read
Pliny's first century Historia Naturalis, Cassiodorus's sixth century
encyclopedia, Isadore of Seville's sixth century Etymolagiarum,
and Discorides' De Materia Medica.
About 530, Simplicius of Cilicia, in a commentary in Greek
on Aristotle's writings on 'gravity', interpreted him to mean that
the intensity of the tendency of bodies toward their natural place varied
with their distance from that place.
In the first half of the seventh century, Brahmagupta regarded
zero, the place holder in the base-10 number system as "an infinitissimal
quantity which ultimately reduces to nought." For Hindus, "arithmetic
and mensuration, rather than geometry and considerations of congruence,
were fundamental" (Boyer 1949:62). By this time, Hindus also conceived
of negative numbers and did not disregard the the irrational roots of quadratics,
as had the Greeks.
In 662, Severus Sebokt referred to calculations with Indian
numerals by fellow Syrians.
In 673, the Muslim fleet, laying seige to Constantinople, probably
used 'Greek fire,' an inflammable mixture of quicklime, naptha, pitch,
and sulphur.
About 700, the venerable
Bede tried to determine an atom
of time, arriving at something like "about 1/6 of our second, and therefore
on the order of the briefest sounds that we can distinguish in speech"
(Park 1990:98). He also made original observations concerning the tides
at ports. His writings are virtually a summary of learning of his time.
His best known scientific treatises are those on chronology.
In the early eighth century, stirrups were introduced in Frankish lands, enabling the development of the armored knight. They were common in China as early as 477, and Muslim cavalry wore them in Persia in 694.
[added 02/01/03]
By 770, iron horseshoes were common.
[added 02/01/03]
In 793, the first paper, a Chinese invention, was made in Baghdad.
About 800, Jabir ibn Hayyan, later known as Geber, was
educated reading translations from Greek and based his chemical system
"on two substances: sulphur, which...is hot and dry, and mercury, which
is cold and wet. Since each contains all four elements, any other
material can be formed by the proper combination of these two, and since
we cannot know substance but only form, our search must aim at the most
desired product, gold" (Park 1990:115). This is the most perfect,
most virtuous product since, as Aristotle said, all things, even
base metals, struggle upward.
About 820, Muhammed ibn Musa al-Kwarizmi wrote essays
on Hindu arithmetic and al jabr, translated as 'the transposition,'
and pronounced 'algebra.' The word 'algorism,' which we have refashioned
'algorithm,' is thought to be derived from his name and denotes the decimal
system of notation, which is thought to have passed from India to the West
in the translation of his algebra into Latin.
About 850, Moors in Spain prepared pure copper by reacting its
salts with iron, a forerunner of electroplating.
About 850, Abu Yusek Yacob ibn Ishak al-Kindi commented
on Aristotle and wrote numerous treatises on optics, perspective,
and medicine.
About 900, Abu Bakr al-Razi, better known as Rhazes, distinguihed smallpox from measles in
the course of writing several medical books in Arabic. Holding against any sort of orthodoxy, particularly Aristotle's
physics, he maintained "the conception of an 'absolute' time, regarded
by him as a never-ending flow" (Pines 1975:125).
About 976, a manuscript from non-Moslem Spain showed the first examples
of the nine Hindu-Arabic numerals in Europe.
About 1000, Ibn Sina, or Avicenna, hypothesized two causes of mountains:
"Either they are the effects of upheavals of the crust of the earth, such
as might occur during a violent earthquake, or they are the effect of water,
which, cutting itself a new route, has denuded the valleys, the strata
being of different kinds, some soft, some hard.... It would require
a long period of time for all such changes to be accomplished, during which
the mountains themselves might be somewhat diminished in size" (Toulmin
and Goodfield 1965:64). In Kitah al-Shifa, he denied the Aristotelian notion that an
object thrown through the air is pushed by that air and held that "every
motion occurs through a power in the moving object by which it is impelled"
(Avicenna, quoted in Pines 1975:141). He also published Al-Quanun, or Canon of Medicine, where he held that medicines were to be known either by experiment
or by reasoning.
About 1000, Ibn al-Haitam, or al-Hazen, in Opticae Thesaurus,
introduced the idea that light rays emanate in straight lines in all directions
from every point on a luminous surface. He also discussed spherical
and parabolic mirrors and was aware of spherical aberration. In Epitome of Astronomy, he took a
position against
Ptolemy, insisting that the hypothetical spheres
corresponded "to the true movements of really existing hard or yielding
bodies [and] so...were accountable to the laws of physics" (Duhem 1908:28).
This led to disageements that persisted through the twelfth century.
Early in the eleventh century, crossbows with sights and mechanical triggers were introduced into warfare.
About 1050, Solomon ben Judah Ibn Gabirol, or Avicebron, held
that every material thing possesed a 'common corporeity' which was continuous
through the universe.
[In 1054, Chinese astronomers at the Sung national observatory at K'ai-feng observed the explosion
of a supernova in the Crab Nebulae, visible in daylight for twenty-three
days. Since then debris has moved out about three light years.]