IV. HELLENISTIC NATURAL PHILOSOPHY
Hellenistic culture: the culture of the Greek empire established by Alexander -- mainly
Greek, but with elements borrowed from the other, conquered territories.
Schools & Education
The Greeks lacked the formal school system we have -- no compulsory education, no state-run schools; education was for the few.
Early education efforts: focused on athletics (gymnastike) and the arts (mousike)
The sophists: introduced intellectual, esp. political education. Trained people to be good citizens & statesmen. They taught in public places, for a fee. (Socrates did not approve of the sophists.)
The Academy: Founded by Plato just outside Athens. People could listen to lectures & discussions at no charge. It became a permanent school. Aristotle studied at the Academy, with Plato.
The Lyceum: School founded by Aristotle after Plato's death [possibly because Aristotle was denied leadership of the Academy]. Started the practice of cooperative research, as in his work on natural history. Followers of Aristotle came to be called "peripatetics" [either after the colonnaded walk they met in, or after Aristotle's habit of walking about while lecturing.]
The Stoa: Another school founded by Zeno of Citium (not to be confused with Zeno of Elea). They met in a covered walkway (a stoa). This led to their being called stoics (leading to the present-day adjective "stoic" or "stoical"). [The stoics favored learning to accept whatever happens in life and freeing oneself of strong passions.]
The Epicurean Garden: Place where Epicurus taught. [He advocated a mild-mannered hedonism & egoism. People should seek the greatest pleasure or satisfaction in life, which will be achieved by learning to be content with the simple pleasures. Led to the present-day adjective "epicurean."]
After Alexander's death the empire is split. [Alexander left his empire, in his own words, "To the strongest."] Ptolemy takes control of Alexandria (in Egypt), which becomes another center of learning, surpassing Athens and including the Museum (a temple to the Muses). This is the first instance of state support of education.
Alexandria was originally founded by Alexander during one of his military campaigns.
It became the site of a famous library, housing almost 500,000 books. The
Library of Alexandria, however, was destroyed over several centuries.
The Lyceum after Aristotle
Theophrastus: Friend of Aristotle. Succeeded him as head of the Lyceum after Aristotle's death. Continued Aristotle's investigations of natural history. Also questioned some aspects of Aristotle's theories, including: observed that not everything in nature seems to have a purpose. Composed the definitive work on botany for his time through the middle ages. Left his land to the school upon his death.
Strato: Successor of Theophrastus. Further carried on the Aristotelian program. Important corrections to Aristotle:
Argued that bodies had a range of weights, not just 'heavy' and 'light'.
Air and fire rise, not because of their 'levity', but because they are displaced by heavier bodies. [This is the correct account -- i.e., there is no force internal to light objects pushing them upward; they are merely less pulled downward than the surrounding heavier objects.]
Bodies accelerate as they fall. Evidence:
Falling water makes a continuous stream near the top; discontinuous near the bottom.
The impact of a body is related to the height from which it falls, not just its weight.
[All correct, and astute.]
Strato allowed void spaces, within bodies. (But was not a full-fledged atomist.) This could explain how a body could expand or contract.
Aristotle remains influential until the 500's A.D. Later philosophers comment on
and systematize his works.
Epicureans & Stoics
Epicurean doctrines:
Happiness as the end of life. Ethics as the central branch of philosophy.
Atomism & materialism: Everything consists of atoms in the void.
[ Atomism first invented by Democritus.]
No final causes; only mechanistic, efficient causes.
Atoms lack secondary qualities; they have only primary qualities (size, shape, weight)
The atomic swerve: accounts for
a) Why atoms can collide
b) how we can have free will. Note: Epicurus was apparently the first to perceive the conflict between free will and mechanism.
No gods.
Stoic doctrines:
Happiness as the end of life. Ethics as the central branch of philosophy.
Also accepted materialism: Only physical stuff exists.
But matter is not wholly passive. It has an active element, pneuma (breath):
Pneuma is a subtle substance that permeates everything. 3 kinds of pneumas:
1) Hexis: present in inorganic matter. Explains cohesion, by varying amounts of tension. (How could the epicureans explain why objects stick together?)
2) Physis: Present in plants & animals. Explains vital properties.
3) Psyche (soul): Present in humans, explains rationality.
Pneumas occupy the same space as the ordinary, passive matter.
Cosmology: The universe is in an infinite cycle of expansion and contraction.
The universe is purposeful (due to the pneuma existing throughout it), but
deterministic (everything has a cause). Cicero's remark: "...This
makes it intelligible that fate should be, not the 'fate' of superstition,
but that of physics."
The Application of Mathematics to Nature
How important is mathematics to understanding nature?
Plato & Pythagoras -- mathematical objects are the fundamental realities. Pythagoras is said to have thought that everything consists of numbers; Plato thought matter composed of geometric figures.
Aristotle -- Physics and mathematics are distinct, but both useful sciences. They deal with different aspects of natural objects. Mathematicians abstract away from the sensible qualities of bodies, leaving only "quantity and continuity."
[How is this issue resolved in modern thought? No one thinks nature is
actually composed of mathematical objects. At the same time, physicists
deal mainly with equations, vectors, and other mathematical objects.
Learning physics is largely learning to manipulate these mathematical
systems.]
Greek Mathematics
Incommensurable quantities:
Greeks discovered the existence of incommensurable lines, which at the time was felt to be strange and paradoxical. They are called 'incommensurable' meaning "incapable of being compared" because, roughly, they have no determinate ratio to each other. Ex.: The diagonal and the side of a square are incommensurable.
Correspond to: Irrational numbers. Called "irrational" because they cannot be stated as a ratio (of whole numbers). 2 is irrational, and so is .
Geometry:
Euclid's Elements from ca. 300 b.c. systematizes geometry. This becomes the definitive work on geometry until the 19th century.
Important: uses deductive proof starting from definitions and self-evident axioms. This becomes an ideal for scientists, mathematicians and philosophers to strive for, for the rest of history.
The Elements is divided into:
Definitions, including:
A point is that which has no part.
A line is breadthless length.
A straight line is a line which lies evenly with the points on itself.
A surface is that which has length and breadth only.
A plane surface is a surface which lies evenly with the straight lines on itself.
A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Etc.
Postulates [really, axioms pertaining specifically to geometry]:
1. To draw a straight line from any point to any point.
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any center and radius.
4. That all right angles equal one another.
5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. [The famous 'axiom of parallels,' rejected in non-Euclidean geometries]
Axioms, or common notions: [general mathematical axioms not specific to geometry]
1. Things which equal the same thing also equal one another.
2. If equals are added to equals, then the wholes are equal.
3. If equals are subtracted from equals, then the remainders are equal.
4. Things which coincide with one another equal one another.
5. The whole is greater than the part.
Propositions:
A series of theorems proved from the above, and constructions allowed according to the above, which you should have learned about in high school geometry class. Ex.:
The interior angles of any triangle sum to two right angles.
To draw a straight line perpendicular to a given plane from a given elevated point.
The 'propositions' cover plane geometry, solid geometry, and even some of number theory.
Archimedes:
Follows Euclid. More work on plane & solid geometry, arithmetic, & mechanics. Among other things, he was proud of discovering that the volume of a sphere is 2/3 the volume of the cylinder that circumscribes it. It is said that this formula was put on his tombstone. Made a more accurate estimate of : 3 10/70 < < 3 10/71. More on his mechanics later.
Apollonius: work on conic sections.
Early Greek Astronomy
Early astronomy used to set the calender. Problem:
They attempted to account for the lunar cycle and the solar cycle in the calendar (hence months & years). But the lunar cycle does not divide evenly into the solar cycle.
One solution: the Metonic calendar, based on the fact that 19 solar cycles = 235 lunar cycles. Thus, you can have a 19-yr. cycle, with 12 yrs of 12 months + 7 yrs of 13 months. (12×12 + 7×13 = 235.)
[Modern solution: Forget the lunar cycle.]
The 2-sphere model (Plato & Eudoxus): Involves uniform circular motions superimposed on the daily rotation of the 'celestial sphere'.
Every heavenly body circles the celestial sphere once per day. [Modern explanation: the earth's daily rotation.]
But each heavenly body also makes a circuit around the ecliptic, in its own peculiar time period. [Modern explanation: the earth's yearly circuit around the sun]
Important astronomical terms:
Ecliptic: circular path that bodies follow (roughly) around the earth. It is tilted at 23 to the equator of the celestial sphere.
Equinox: time when the ecliptic intersects the equator of the celestial sphere. (Days & nights equally long.) Spring equinox: this happens at the beginning of spring. Fall equinox: at the beginning of fall.
Solstice: Time when the sun is farthest from the equator of the celestial sphere. Summer solstice: This happens in mid-summer (days are longest). Winter solstice: This happens in mid-winter (nights are longest).
An anomaly: Retrograde motions. Periodically, on its path around the ecliptic, a planet reverses direction for a bit. Each planet is on its own cycle for retrograde motions. This only applies to Mercury, Venus, Mars, Jupiter, Saturn; not the sun or moon. [They couldn't see Neptune, Pluto, or Uranus.] [Modern explanation: planets' circuit around the sun.]
Eudoxus' solution: A series of nested, concentric spheres, each tilted with respect to the others, and each rotating uniformly (but not all in the same direction).
This provides a rough, qualitative account for the observable motions of planets.
Eudoxus did not conceive the spheres as physically real; they're just a mathematical device for describing planetary motions, i.e. breaking complex motions into components consisting of uniform circular motions.
Interestingly, Mercury & Venus never stray very far from the sun.
Aristotle took the spheres more seriously, as physically real. He inserted 'counter-acting' spheres so that the spheres of one planet would not transmit their
motion to those of another planet farther in. (E.g., you need 3 counter-acting
spheres between Jupiter & Saturn, so that Saturn's innermost sphere will not
transmit its complex motion to Jupiter's outer-most sphere.)
Cosmological Developments
Heraclides proposes that the earth rotates once daily, which explains why all celestial objects appear to circle the earth once daily.
Aristarchus proposed a heliocentric model: the earth orbiting the sun. However, there was no good reason for accepting it at the time.
One problem with the heliocentric model: No stellar parallax is observable.
Others attempted to calculate cosmological constants, including: The earth-sun distance, the earth-moon distance, the ratio between the two, the size of the earth. Notable:
Aristarchus' method for calculating (earth/sun distance : earth/moon distance). See diagram in book. You can determine C/B by trigonometry (it is Cos ). Aristarchus measured = 87, leading to B/C = 19. Modern value: 89.85, leading to B/C = 390.
[Note: The concept of error analysis had not been developed. A's method was 'theoretically' ok, but highly sensitive to error, as the above figures show.]
Eratosthenes estimates circumference of the earth: 252,000 stades (=28,600 mi.). [modern value: 25,000 mi.] [Method: Assumed sun rays are parallel, measured distance between 2 cities, and the angles a sun ray makes to the ground at each city at a fixed time. See picture below: Angle A is a right angle. The measure of angle B, and the ground distance between the vertices of A and B, can be used to determine the radius of the circle, according to the formula: r = 2d / ( - 2B). Amusing side note: The distance between A and B was measured by the time it took camels to travel the distance.]
Hellenistic Planetary Astronomy
Hipparchus: great Hellenistic astronomer. Most important contribution was introducing the idea of numerical precision -- i.e. quantitative, and not just qualitative predictions for an astronomical model.
Claudius Ptolemy (no relation to Alexander's general Ptolemy, who assumed control of Alexandria 500 years earlier): lived around 150 A.D. Inherited astronomical knowledge & methods from earlier astronomers, including Hipparchus. Aimed to account for apparent motions of planets using combinations of uniform circular motion. Aimed at quantitative predictions.
Ptolemaic model, dominant from 2nd - 16th century A.D.
1) The Eccentric Model: Planet moves uniformly in a circle with center C. Earth is located off-center (hence the term "eccentric" which in this context means 'off-center').
2) The Epicycle-on-Deferent Model (famous): Planet moves uniformly in a small circle, the 'epicycle.' In addition, superimposed on this motion, the center of the epicycle itself moves in a large circle around the Earth. This large circle is the "deferent."
Note: this explains retrograde motion.
3) The Equant Model: Planet moves in a circle. Earth is off-center. An equal distance from the center, but in the opposite direction, is the 'equant point'. The planet moves at varying speeds such that it sweeps out equal angles in equal times, as measured from the equant point. (So the angular velocity is uniform, relative to the equant point, but not relative to the center.)
These 3 models can be combined, particularly for Venus, Mars, Jupiter, and Saturn.
Why uniform circular motions?
The aim was to bring simplicity to the apparent chaos. Uniform circular motion is the simplest kind of motion [other than straight-line motion which won't work].
Aesthetic/religious reason: the perfection of the heavens demanded the most 'perfect' of motions.
Reliance on tradition & past authority.
Ancient mathematical methods could make predictions using circles, but they didn't know how to deal with other curves.
Ptolemy's system was the first system to offer accurate, quantitative
predictions. Before the 16th century, it was the only known theory to
do so.
The Science of Optics
Optics: roughly, the study of how vision works.
Euclid: The eye sends forth some kind of rays; we see objects when the rays strike them.
Gave a geometrical treatment of optics, esp. laws of perspective. Ex.: Why farther away objects appear "higher" (think about drawing).
Ptolemy: Further developed Euclid's theory.
Unlike Euclid, Ptolemy was interested in the physical properties of the visual radiation.
More geometrical treatment of perspective.
Theory of reflection derived from Euclid: angle of incidence = angle of reflection.
Developed his own theories of refraction:
When light enters a denser medium, it is refracted away from the surface.
Ptolemy collected a lot of empirical data on refraction (using different media & different angles).
He tried to find a mathematical law relating angle of incidence &
angle of refraction. He found some mathematical regularities,
but did not discover the correct law. [Modern relation: Sine of
the angle of incidence is proportional to the sine of the angle
of refraction.]
The Science of Weights
Empirical law: weights on opposite sides of a balance beam balance when d1w1 = d2w2 (d1 and d2 being the distances of the weights from the fulcrum, w1 and w2 being their respective weights).
Problem: to explain this law.
The 'dynamic' solution:
Suppose weight A has weight of 10 and B has weight 20 and A is twice as far from the fulcrum as B.
Now, suppose they weren't in equilibrium, so one of them is moving up. Then A would move a distance of 2d in the time that B moved a distance of d (this is provable by purely geometric considerations). Vague idea: the greater velocity of A exactly compensates for the greater weight of B.
A rational reconstruction: On Aristotelian assumptions, the force required to move A at speed 2v would equal the force required to move B at v. That is why they are in balance. If the weight of A is changed (without changing anything else), it will put them out of balance, since then the weight required to move A up will be made either less or more than that required to move B up.
Archimedes proves the law geometrically, from two assumptions:
1) That equal weights at equal distances from the fulcrum are in equilibrium.
2) That if you have two equal weights anywhere on the beam, you can substitute a weight twice as heavy, located at their center of gravity (halfway between them).
Note: this is interesting because of the integration of mathematics & natural science.
Archimedes says that with a lever long enough, he could move the Earth.
Early Greek Medicine
Prior to about 400's B.C.:
Greek medical practice influenced by Egyptian & probably Mesopotamian practice.
Divine intervention is often supposed to cause disease.
The cult of Asclepius:
Asclepius: originally a (human) physician who probably lived around 1200 BC, later considered as the god of healing. [Note the difficulty of separating Greek myth from actual history. Asclepius probably existed, but not as a god of course.]
Temples to Asclepius offered healing, including both physical and 'spiritual' remedies.
Most famous was the healing dream, where you slept in the temple, and the god would either heal you in your sleep, or offer advice during your dream.
The symbol of Asclepius, a snake wrapped around a staff (the caduceus)
remains as the symbol of the medical profession today.
Hippocratic Medicine
Hippocrates:
Lived around 400 B.C. Often called "the father of medicine."
His followers wrote over 60 medical books, the "Hippocratic writings."
Important contributions: The Hippocratic doctors represented 'learned medicine':
They opposed religious explanations of disease (i.e., divine intervention). Instead, they proposed natural causes for diseases & ailments.
They stressed observation, diagnosis, and prognosis. Thus,
They made detailed case studies.
On the basis of these, they could predict the course of a disease (prognosis).
Treatment:
Usually involved sensible things like good diet, exercise, sleep, bathing.
Occasional prescriptions for internal and external medicine.
The theory of the humors: This theory was held by many (not all) of the Hippocratic doctors.
There are four fluids (humors) in the body: Phlegm, blood, black bile, and yellow bile.
Disease is caused by an imbalance in the humors.
Humors are linked to the hot/cold and moist/dry dualities, leading to the conclusion that cold tends to cause certain diseases, etc. (For instance, a 'cold' is caused by coldness and wetness, which leads to too much phlegm in the body.)
There are 4 basic temperaments, arising from dominance of one of the 4 humors: phlegmatic (for phlegm), sanguine (blood), choleric (yellow bile), and melanholic (black bile). This is supposed to explain personality differences. The ideal personality has an even balance of humors.
The Hippocratic oath: According to tradition, Hippocrates established this oath to set a standard of ethical & professional conduct for physicians (though he probably didn't really write it). His followers all took the oath. Many physicians today still take modified versions of the Hippocratic Oath, which, in case you're curious, is as follows:
(Original version):
"I swear by Apollo Physician, by Aesculapius, by Health, by Heal-all, and by all the gods and goddesses, making them witnesses, that I will carry out, according to my ability and judgment, this oath and this indenture: To regard my teacher in this art as equal to my parents; to make him partner in my livelihood, and when he is in need of money to share mine with him; to consider his offspring equal to my brothers; to teach them this art, if they require to learn it, without fee or indenture; and to impart precept, oral instruction, and all the other learning, to my sons, to the sons of my teacher, and to pupils who have signed the indenture and sworn obedience to the physicians' Law, but to none other. I will use treatment to help the sick according to my ability and judgment, but I will never use it to injure or wrong them. I will not give poison to anyone though asked to do so, nor will I suggest such a plan. Similarly I will not give a pessary to a woman to cause abortion. But in purity and in holiness I will guard my life and my art. I will not use the knife on sufferers from stone, but I will give place to such as are craftsmen therein. Into whatsoever houses I enter, I will do so to help the sick, keeping myself free from all intentional wrongdoing and harm, especially from fornication with woman or man, bond or free. Whatsoever in the course of practice I see or hear (or even outside my practice in social intercourse) that ought never to be published abroad, I will not divulge, but consider such things to be holy secrets. Now if I keep this oath, and break it not, may I enjoy honor, in my life and art, among all men for all time; but if I transgress and forswear myself, may the opposite befall me."
(One contemporary version, approved by the AMA)
"You do solemnly swear, each by whatever he or she holds most
sacred: That you will be loyal to the Profession of Medicine and just
and generous to its members, That you will lead your lives and
practice your art in uprightness and honor, That into whatsoever
house you shall enter, it shall be for the good of the sick to the utmost
of your power, your holding yourselves far aloof from wrong, from
corruption, from the tempting of others to vice, That you will exercise
your art solely for the cure of your patients, and will give no drug,
perform no operation, for a criminal purpose, even if solicited, far less
suggest it, That whatsoever you shall see or hear of the lives of men
or women which is not fitting to be spoken, you will keep inviolably
secret, These things do you swear. Let each bow the head in sign of
acquiescence. And now, if you will be true to this, your oath, may
prosperity and good repute be ever yours; the opposite, if you shall
prove yourselves forsworn."
Hellenistic Anatomy and Physiology
3rd century B.C.: Human dissection begins in Alexandria. This leads to advances in anatomy & physiology. They may also have used vivisection (dissection of live people).
Herophilus: Mainly interested in anatomy (study of the structure of the body & organs). He described the various internal organs. Interesting discoveries include:
Distinguished veins & arteries by the thickness of their walls. (This is fairly subtle.)
Studied the valves in the heart.
Erasistratus: Did more physiology (study of the functions of organs). Interesting contributions include:
Distinguished sensory & motor nerves.
Discovered that the pulse is a passive, mechanical response to the contractions of the heart.
His theory of digestion, respiration, & circulation:
Food is turned into blood in the stomach.
The veins carry this blood to all the parts of the body.
The arteries carry only 'pneuma', which we inhale through the lungs.
This pneuma is turned into a finer form of pneuma, 'psychic' pneuma, in the brain.
Psychic pneuma is carried to the rest of the body by the nerves. It causes sensation & movement.
Stuff moves through the body mechanically, according to the principle that nature abhors a vacuum.
Disease is caused by an excess of blood. Remedy: eat less. Alternately: Blood letting. [This last would seem to be a rather primitive theory, in comparison with his other achievements.]
Objection: how come blood comes out of arteries? When an artery
is cut, the negative pressure causes channels between the
veins & arteries to open, so that blood flows from veins into the
arteries.
Hellenistic Medical Sects
After Erasistratus & Herophilus, numerous medical sects emerged with great debates among them:
'Rationalists': broad grouping of approaches to medicine, characterized by an inquiry into the hidden causes of disease. Some defended human dissection as a tool for discovering such hidden causes.
'Empiricists': Generally rejected human dissection & the search for hidden causes of disease. Instead, they thought one should just observe symptoms externally and prescribe treatments based on past experience.
'Methodists': Thought that disease was caused by tenseness or laxness of the body.
'Pneumatists': Built a medical philosophy based on Stoicism. [whatever
that means.]
Galen and the Culmination of Hellenistic Medicine
Along with Hippocrates, one of the most famous physicians in history. Lived around 200 AD. Became the accepted authority on medical matters up to the Renaissance. Important contributions:
Produced a large number of books, summing up the state of medical knowledge at the time.
One of his innovations: To locate certain diseases in specific organs in the body.
Pursued his own anatomical & physiological investigations. His reliance on animals led to some mistakes. Famous mistake:
The rete mirabile: a mesh of blood vessels found in some ungulates (hoofed animals). He thought that it refined arterial blood to produce psychic pneuma. Actually, this structure does not exist in humans.
Correctly argued that the arteries carry blood.
His theories:
Accepted the theory of the 4 humors
Believed knowledge of anatomy & physiology was essential to medicine.
There are 3 basic physiological functions:
(i) A system for venous blood: Stomach & liver produce venous blood, which nourishes the bodily organs. Veins carry it to the rest of the body.
(ii) A system for arterial blood: Heart produces vital heat (which, of course, comes from 'fire'). The lungs help keep the right amount of heat in the heart (cooling it and providing 'air' to it). After the heart heats up the blood, the arteries carry it to the rest of the body, thus supplying life (vital heat) to them.
(iii) A system for psychic pneuma: This is produced by the rete mirabile. The nerves carry it to the rest of the body, endowing other parts of the body with the capacities for sensation and movement.
Galen's teleology:
He thought the human body, in all of its parts and aspects, was just perfectly designed for its functions. This showed the wisdom & goodness of the Demiurge (remember him from Plato's cosmology).
This made him popular during the very religious middle ages -- and not so popular in modern times.
[ Was this a reasonable idea on Galen's part, given what he was able to
observe?]