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  Several of the ancient Greeks emphasised the need for mathematics in their understanding of the cosmos. However, it was by no means evident how mathematics related to the natural world, and the Greeks, except in a few isolated instances, never really employed the idea of mathematically formulated laws of nature. They were also too optimistic about how well-arranged life forms and the cosmos were, and too liberal with their use of teleology. There were reasons for these specific weaknesses, not least of which is that the Greeks were the pioneers of science, and science is not easy. Ideas such as universal gravitation do not come easily, as is evidenced by the fact that it took a further millennium after the end of Greek science for this idea to be formulated. Non-teleological accounts of the cosmos and of life processes require a great deal of sophistication to become plausible, and this has been achieved only in the last few hundred years. The weaknesses need to be placed in context against the great achievements and advances of Greek science, and the remarkable fact that the Greeks managed to get science off the ground at all. That cannot have been easy in a culture which still relied heavily on mythology and a theology of mischievous, interfering gods.

  There are, of course, other important differences between modern and ancient science, particularly in terms of organisation and funding. Whereas science nowadays is funded by industry and the state, ancient research was carried out on a purely amateur basis by those with the interest, resources and leisure time to pursue it. Instead of the laboratory, university or research institute, the ancients had at best a crude observatory. The philosophical schools, such as the Academy or the Lyceum, important as they were, gave no support comparable to that which we can find in the modern world. The relationship between science and technology is now much tighter and much better understood, but was considered virtually irrelevant by the ancients. The number of people doing science in the ancient world was proportionally far smaller than nowadays, and it is always wise to remember that the history of Greek science is the history of a small but influential group of thinkers. Finally, we might compare the instruments available to the ancients with those nowadays. They had a few crude instruments for observing the heavens, but little else with which to investigate their world – no microscopes or telescopes, no thermometers, and only relatively primitive means of measuring distance and weight. Modern science depends on precision instruments to investigate accurately. The ancients were virtually devoid of these.

  When summing up the work of the ancient Greeks, it is important to remember that prior to the scientific revolution of the seventeenth century, there was little reason to suppose that the mechanical and atomistic world view that came to prominence at that time was correct. There were many other possibilities, and because of the problems that mechanical and atomist accounts had in explaining how the order of the cosmos came about, and how life originated, the teleological accounts of Plato and Aristotle would have seemed at least as plausible to the ancients. In general, atomist and mechanical accounts were weak in antiquity, lacking as they did many modern resources. One result of this was some ancient attitudes to explanation. The ancients tended to have a more organic conception of the cosmos, use more organic metaphors and explain more holistically than we would, since, for them, this seemed a more convincing approach than attempting mechanical and atomistic explanations. It is also important to recognise the length of time involved with Greek science. We are talking of nearly a millennium, from around 600 BC to 200–300 AD. We would be very cautious in considering the science of the period from 1200 to the present day as one entity, and drawing general conclusions from it. We should be duly cautious of doing so with the Greeks as well. This is especially so given the diversity of thinkers and ideas that proliferated in ancient Greece.

  Having said that, Greek science stands as one of the great achievements of the ancient world, and indeed one of the great achievements of humankind. To have begun science is remarkable enough in itself, but especially so in the ancient world. The vision and clarity of purpose of the ancient Greeks was exceptional, as was their tenacity in pursuing the view that the world is comprehensible and can be explained in a rational manner. The way in which Greek theories increase so rapidly in sophistication once they get the elements of science in place is astounding, and is comparable to any of the great periods of human intellectual endeavour, such as the Renaissance, the scientific revolution and the Enlightenment. They bequeathed a wealth of fascinating ideas and arguments about the nature of the physical world, many of which have been important in the development of science, and some of which are still relevant today. Above all, though, they gave us the basic structures and vision of science. That is something that stays with us as we find out more and more about the cosmos that we live in.

  Appendices

  Map of Ancient Greece

  Glossary of Terms

  Academy: The school of philosophers founded by Plato.

  Actual: In Aristotle’s theory of explanation, things had a potential which they would actualise.

  Aether: In Aristotle’s cosmology, the fifth element which makes up the celestial realm.

  Alchemy (ancient): The art of transforming less valuable or useful things into more valuable or useful things; a wider art than the transmutation of base metals into gold.

  Apparent motion: (Apparent) motions of the heavenly bodies which are in fact due to the motion of the earth.

  Astrology (ancient): The study of the effect of the heavens on the earth; broader than the modern conception of astrology.

  Atoms: Pieces of matter which could not be divided any further (from the Greek atomos, uncuttable).

  Babylonians: Important culture prior to the Greeks, also known as the Mesopotamians, living between the Tigris and the Euphrates rivers (modern Iraq).

  bibbu: Babylonian for sheep; used for planets as well, since it appeared that the planets wandered across the night sky.

  Black bile: One of the four humours of the humoural system.

  Celestial realm: In Aristotle’s cosmology, the realm from the moon outwards, composed entirely of aether.

  Centrifocal cosmology: A cosmology in which there is a central point to the cosmos and the natural motion of objects is relative to that point. Contrast parallel cosmology.

  Concentric sphere astronomy: A view in which the motions of the heavenly bodies are conceived of as combinations of regular circular motion around a common point.

  cosmos (pl. cosmoi): From the Greek cosmeo, to order, with a sense of good order.

  demiourgos: Plato’s god, who was a craftsman working to geometrical principles when he ordered the cosmos out of chaos.

  Ecliptic: Path followed by the sun against the background of the fixed stars, plotted by watching which stars appear at the point on the horizon where the sun sets.

  Efficient cause: In Aristotle’s theory of explanation, similar to the modern idea of cause.

  Enforced motion: In Aristotle’s theory of motion, any motion that is not a natural motion and requires force.

  Epicycle: The basic unit of the astronomy of Ptolemy, in which a planet is imagined to be rotating on a sphere which is itself rotating around a central point.

  Epicyclic astronomy: The astronomy of Ptolemy, which used the epicycle as its basic unit.

  Epigenesis: Epigenesis is the view that the embryo develops its different parts from an amorphous beginning, rather than having all of its parts pre-formed. Contrast preformation.

  Equinox: A day of equal night and day.

  Final cause: In Aristotle’s theory of explanation, teleological explanation.

  Formal cause: In Aristotle’s theory of explanation, an explanation which cites the form that an object has.

  Four causes: The material, final, efficient and formal causes which make up Aristotle’s theory of explanation.

  Four humours: Blood, black bile, yellow bile and phlegm. When these were in balance the body was healthy; disease was an imbalance of these humours.

  Geocentrism: The v
iew that the earth is at the centre of the cosmos.

  Geometrical atomism: Plato’s atomism, in which the atoms are conceived as being perfect geometrical shapes.

  Geometry: Literally land measuring (ge, earth, metreo, to measure), but developed by the Greeks into a rigorous theoretical system.

  Harmony of the heavens: The Pythagorean idea that the heavens moved in such a way as to create a harmonious sound.

  Heliocentrism: The view that the sun is at the centre of the cosmos.

  Hellenistic period: The period after the deaths of Aristotle (322 BC) and Alexander the Great (323 BC).

  hippopede: The shape, like an 8 laid on its side, made by two of the spheres in Eudoxus’ theory of planetary motion. From the Greek meaning a horse fetter. When combined with the motion of the two other spheres, retrograde motion could be reproduced.

  Holism: Explanation in terms of wholes, rather than constituent parts.

  Homocentric sphere astronomy: See concentric sphere astronomy.

  Humoural system: A view of the human body whereby certain humours (usually blood, black bile, yellow bile and phlegm) were given importance and were critical in health.

  Humoural theory of disease: The view that there were certain humours of the body (usually blood, black bile, yellow bile and phlegm) which when they were balanced led to good health.

  idiotes: Early Greek term for a medical layman, from which we derive ‘idiot’.

  Inequality of the seasons: The number of days between solstice and equinox (which defines a season) are not in fact equal, as discovered by Euctemon and Meton.

  Irrational number: A number which cannot be expressed as the ratio of two integers, such as .

  logos (pl. logoi): Greek for word, account, or ratio.

  Love: In Empedocles’ cosmology, the principle by which the cosmos is brought together.

  Lyceum: The school of philosophers founded by Aristotle.

  Material cause: In Aristotle’s theory of explanation, an explanation which cites the material that an object is made of.

  Mesopotamians: See Babylonians.

  Natural motion: In Aristotle’s theory of motion, the motion that an object will execute when it is unimpeded. The natural motion of earth and water was down, air and fire up, and aether in a circle.

  Natural place: In Aristotle’s theory of motion, objects had a natural place. The natural place of earth and water was at the centre of the cosmos, air and fire at the edge of the terrestrial realm, aether in the celestial realm.

  Nutritive blood: In Galen’s physiology, nutritive blood flowed in the veins and distributed nutrition to the body.

  Pangenesis: Pangenesis is the idea that characteristics acquired during life are passed on to the offspring, e.g., if giraffes stretch their necks to feed, then baby giraffes are born with longer necks.

  Parallax: In astronomy, the angle between apparent positions in the sky at six month intervals, the difference being generated by the fact that the earth is in motion around the sun.

  Parallel cosmology: A cosmology in which objects are believed to fall from the top of the cosmos to the bottom, hence the problem of why the earth does not fall. Contrast centrifocal cosmology.

  Phlegm: One of the four humours.

  planetes: The Greek for planet, also meaning a wanderer or a vagabond.

  Plenum: A view of the world in which there is no empty space at all. Objects move like a fish swimming in water. Contrast atomism, in which there are small pieces of matter moving in empty space.

  pneuma: In Stoic cosmology, the active principle, also associated with fire and god.

  Potential: In Aristotle’s theory of explanation, things had a potential which they would actualise.

  Precession of the equinoxes: Because the axis of the earth’s rotation itself has a slow motion (taking 26,000 years to complete a cycle), the position of the night sky looks very slightly different with successive equinoxes.

  Pre-formation: The view that embryos are small pre-formed human beings, and merely grow rather than develop parts which they did not initially have. Contrast epigenesis.

  Pre-Socratic: A philosopher or scientist who worked prior to Socrates (469–399 BC).

  Prime mover: In Aristotle’s cosmology, god, who is unmoved but causes the motions of the heavenly bodies.

  Prognosis: The art of telling what course a disease will take.

  Ptolemaic astronomy: The system of astronomy devised by Ptolemy (building on work by Hipparchus and Apollonius) which uses the epicycle as its basic device.

  Pythagoras’ theorem: In right-angled triangles, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.

  Qualitative cosmology: A view of the world which holds that qualities (hotness, wetness, etc.) are the basic items, and are irreducible. The world is best described in terms of these qualities. Contrast quantitative.

  Quantitative cosmology: A view of the world in which quantities can best be used to describe it, qualities reducing to matter and motion which can be treated quantitatively. Contrast qualitative.

  Reductionism: A type of explanation whereby certain entities are said to be no more than matter and motion – so heat is no more than particles in rapid motion.

  Retrograde motion: An apparent reversal of the motion of a planet against the background of the fixed stars.

  Sacred disease: Epilepsy, thought by many in the ancient world to be due to some sort of possession by the gods.

  Solstice: The shortest night/longest day, or vice versa, and also the day on which the setting point of the sun stops moving on the horizon and then returns in the opposite direction.

  Strife: In Empedocles’ cosmology, the principle responsible for the dissolution of order in the cosmos.

  Taxonomy: The science of classifying living organisms.

  Teleology: Literally an end-directed explanation, typically the end being some good.

  Teleology (Aristotle): Teleology for Aristotle is inherent in nature.

  Teleology (Plato): Teleology for Plato is imposed upon nature by the demiourgos when he orders the cosmos from chaos.

  Terrestrial realm: In Aristotle’s cosmology, the earth and the region up to, but not including, the moon; composed of earth, water, air and fire.

  TOE: In modern cosmology, a theory of everything.

  Unmoved mover: In Aristotle’s cosmology, god, who is unmoved but causes the motions of the heavenly bodies.

  Vivified blood: In Galen’s physiology, blood which carries the ‘vivifying’ spirit from the lungs, through the arteries to the rest of the body.

  Yellow bile: One of the four humours in the humoural system.

  Zeno’s paradoxes: A set of paradoxes in which motion and change are shown to be impossible.

  Zodiac: A band across the sky, either side of the ecliptic, through which the planets move.

  Timeline of Ancient Greek Philosopher-scientists

  Thales of Miletus (fl. 585 BC)

  Anaximander of Miletus (fl. 555 BC)

  Anaximenes of Miletus (fl. 525 BC)

  First philosopher-scientists.

  Pythagoras of Samos (fl. 525 BC)

  Geometry, relationship between maths and physics.

  Xenophanes of Colophon (fl. 520)

  Critical theologian-philosopher.

  Heraclitus of Ephesus (fl. 500 BC)

  Philosopher-scientist.

  Parmenides of Elea (fl. 480 BC)

  Zeno of Elea (fl. 445 BC)

  Eleatic philosophers, interested in the question of change.

  Anaxagoras of Clazomenae (c. 500–428 BC)

  Empedocles of Acragas (492–432 BC)

  Philosopher-scientists; worked on theory of matter and cosmology.

  Leucippus of Miletus (fl. 435 BC)

  Democritus of Abdera (fl. 410 BC)

  The first atomists.

  Archytas of Tarentum (fl. 385)

  Follower of Pythagoras.

  Hippocrates of Cos (c. 460–370
BC)

  Founder of rational medicine.

  Euctemon and Meton (Athens, fl. 430 BC)

  Astronomers, discovered inequality of seasons.

  Socrates (469–399 BC)

  Plato (427–348 BC)

  Aristotle (384–322 BC)

  Great Athenian philosophers.

  Theophrastus (371–386 BC)

  Follower of Aristotle, worked on life sciences.

  Eudoxus of Cnidus (fl. 365)

  Callippus of Cyzicus (fl. 330)

  Astronomers, improved models of the heavens.

  Euclid (fl. 300 BC)

  Founder of Euclidean geometry.

  Epicurus of Athens (c. 342–271 BC)

  Atomist philosopher.

  Zeno of Citium (335–263 BC)

  Cleanthes of Assus (331–232 BC)

  Chrysippus of Soli (c. 280–207 BC)

  Founders of Stoicism.

  Erasistratus of Chios (fl. 260 BC)

  Herophilus of Chalcedon (fl. 270 BC)

  Important work in anatomy and physiology.

  Archimedes of Syracuse (287–212 BC)

  Mathematics, physics and ‘Eureka’!

  Eratosthenes of Cyrene (c. 276–195 BC)

  Estimation of size of the earth.

  Apollonius of Perga (262–190 BC)

  Hipparchus of Nichaea (fl. 135 BC)

  Improvements in astronomy.

  Hero (or Heron) of Alexandria (fl. 60 AD)

  Technology, first crude steam engine.

  Ptolemy of Alexandria (c. 100–170 AD)

  Greatest astronomer of antiquity.

  Galen of Pergamum (c. 129–200 AD)

  Greatest anatomist and doctor of antiquity.