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Sunday, May 20, 2018

HISTORY OF GREEK SCIENCE IN MATH , ETC

The universe of the Greeks: from the 6th century BC
The Greek interest in scientific speculation is first seen in the city of Miletus, in Ionia. Here the philosopher Thales acquires fame by predicting a solar eclipse in 585 BC. None of his works survive, but his reputation among Greeks in the following centuries is that of a man who takes a reasonable or 'scientific' approach to the mysteries of the natural world.

This reputation seems to be supported by the achievements of his pupil Anaximander. He is credited with being the first man to attempt a map of the world, and he offers a bold explanation of the origin of the universe. 
 








In Anaximander's theory the cosmos results from a struggle between the opposites of heat and cold. In the vast unlimited beginning of time the two begin to separate, resulting in a ball of fire surrounded by mist. The hot ball contracts and hardens, forming a solid sphere at the centre - the earth.

But the separation is not perfect. Some outer rings of fire trap layers of mist within them. The mist is our atmosphere. Through gaps in it we catch glimpses of the surrounding fire, in the form of sun, moon and stars. 
 






If later accounts of Anaximander's ideas are correct (only a single sentence of his work remains), he even imagines a version of gravity. He says that the earth can remain unsupported at the centre of this system, by reason of its equal distance from the surrounding bodies.

Anaximander's concept of the beginning of life is equally astonishing. He argues that humans cannot always have existed (our infants are too defenceless). The first living creatures, he believes, develop in water through the action of heat. They resemble sea urchins. Humans do not evolve from these urchins, but arrive later in a more welcoming environment. 
 





The geographers of Miletus: 6th century BC
Nothing is known of the map of the world supposedly produced in Miletus by Anaximander in the mid-6th century BC. But by the end of the century, also in Miletus, another geographer writes a book of which sufficient details survive for his ideas to be reconstructed. He is Hecataeus.

Like most early mapmakers, Hecataeus puts the most important place at the centre of the world. For medieval Christian cartographers this is Jerusalem. For Hecataeus it is the Aegean Sea, on the east coast of which stands Miletus. 
 








The shape of the world according to Hecataeus has a geometrical simplicity. It is a flat circle, with a continuous ocean forming the rim. The circular land mass is divided into two parts by an almost unbroken stretch of water linked with the ocean on the west at the straits of Gibraltar, then running east the length of the Mediterranean, through the Black Sea and (after a short land bridge) into the Caspian Sea, which joins the ocean on the east.

The semicircle of land above this belt of water is Europe, while the semicircle below is Asia. The part west of the Nile has the subsidiary name of Libya, standing in for Africa. 
 






Hecataeus is at the end of a pioneering century of Greek science in Miletus, which lies to the east of mainland Greece. At the same period a new centre of Greek scientific speculation is being developed far to the west, in the Pythagorean tradition of southern Italy.

Greek philosophy is strongly associated with Athens, because of Socrates, Plato and Aristotle. But scientific history testifies rather more to the colonial spread of Greek culture round the Mediterranean. Ionia and Samos, Italy and Sicily, Alexandria; these are the places where Greeks will establish the rational traditions of western science. 
 





Pythagoras: 6th century BC
Ancient mathematics has reached the modern world largely through the work of Greeks in the classical period, building on the Babylonian tradition. A leading figure among the early Greek mathematicians is Pythagoras.

In about 529 BC Pythagoras moves from Greece to a Greek colony at Crotona, in the heel of Italy. There he establishes a philosophical sect based on the belief that numbers are the underlying and unchangeable truth of the universe. He and his followers soon make precisely the sort of discoveries to reinforce this numerical faith. 
 








The Pythagoreans can show, for example, that musical notes vary in accordance with the length of a vibrating string; whatever length of string a lute player starts with, if it is doubled the note always falls by exactly an octave (still the basis of the scale in music today).

The followers of Pythagoras are also able to prove that whatever the shape of a triangle, its three angles always add up to the sum of two right angles (180 degrees). 
 





The Pythagoreans and astronomy: 5th century BC

Followers of Pythagoras, in the 5th century, are the first to produce an astronomical theory in which a circular earth revolves on its own axis as well as moving in an orbit. The theory derives in part from the need to locate the great fire which they believe fuels the universe.

The Pythagoreans place this fire at the hidden centre of things, with the earth revolving round it more closely than any of the other bodies visible in the sky. The reason why we never see or are scorched by the fire is that we live on only half the sphere of the earth, and the earth revolves so that our half is always turned away from the flames.
 Moving outwards from the earth in the sequence of heavenly bodies, they place the moon next, then the sun, the planets and finally the stars, which are unlike the others in being fixed on an outer sphere.

Heavenly spheres: from the 5th century BC

This theory introduces the concentric circles which become the false orthodoxy of the next 2000 years, as eventually enshrined by Ptolemy. It also starts a wild goose chase which will exercise many brilliant minds: what mechanical model can explain the erratic motion of the planets? Eudoxus of Cnidus, in the 4th century, is the first to propose a series of transparent spheres in the heavens, carrying the heavenly bodies at different speeds in linked groups with slightly varying centres.

To make such machinery conform to what can be observed in the sky, ever more complex arrangements are needed. Later in the 4th century Aristotle believes he has solved it. He requires no fewer than fifty-five transparent spheres.

The Pythagoreans are too far ahead of their time in proposing their one central grain of truth - the revolving globe of the earth. But Copernicus, developing this idea, will acknowledge them as his earliest predecessors.

For most Greek astronomers there seems to be overwhelming evidence that the earth is stationary and the heavens move. This is true even of the greatest among them, Hipparchus. Like his predecessors, he believes that it must be possible to analyze the movement of the spheres. He finds the available data inadequate, so devotes himself not to cosmology but to the prime task of an astronomer - observation of individual stars.

The four elements: c.450 BC

The Greek philosopher Empedocles, a native of Sicily, introduces a theory which will be accepted in Europe until the 17th century. He states that all matter is made up, in differing proportions, of four elemental substances - earth, air, fire and water. Not until the arrival of a 'sceptical chemist' (the title of a book by Robert Boyle in 1661) is there a serious threat to this Greek theory of the elements.

Soon an equivalently simple notion is put forward to account for the make-up of living creatures, in the theory of the four humours.

Electricity and magnetism: 5th century BC

Two natural phenomena, central to the study of physics, are observed and speculated upon by Greek natural scientists - probably in the 5th century BC, though Aristotle gives credit for the first observation of each to the shadowy figure of Thales.

One such phenomenon is the strange property of amber. If rubbed with fur it will attract feathers or bits of straw. Modern science, in its terms for the forces involved, acknowledges this Greek experiment with amber (electron in Greek). The behaviour of the amber is caused by what we call electricity, resulting from the transfer of what are now known as electrons.

The other natural phenomenon, observed in lodestone rather than amber, also derives its scientific name from Greek experiments. Lodestone is a naturally occurring mineral (formed of iron oxide), and it will surprisingly attract small pieces of iron. .

The Greeksfind this mineral in a region of Thessaly called Magnesia. They call it lithos magnetis, the 'stone of Magnesia'. Thus the magnet is identified and named, though like rubbed amber it will only be a source of interest and amusement for the next 1000 years and more - until a practical purpose is found for it in the form of the compass.
Democritus and the atom: c.420 BC

In the late 5th century BC Democritus sets out an interesting theory of elemental physics. Notions of a similar kind have been hinted at by other Greek thinkers, but never so fully elaborated.

He states that all matter is composed of eternal, indivisible, indestructible and infinitely small substances which cling together in different combinations to form the objects perceptible to us. The Greek word for indivisible is atomos. This theory gives birth to the atom.


Democritus describes an extraordinary beginning to the universe. He explains that originally all atoms were whirling about in a chaotic manner, until collisions brought them together to form ever larger units - including eventually the world and all that is in it.

His theory will find few followers over the centuries. But his imagination provides an astonishing first glimpse of the Big Bang.

The birth of biology: 5th - 4th century BC

The Greek philosophers, voracious in their curiosity, look with interest at the range of living creatures, from the humblest plant to man himself. A Greek name is coined by a German naturalist in the early 19th century for this study of all physical aspects of natural life - biology, from bios (life) and logos (word or discourse). It is a subject with clear subdivisions, such as botany, zoology or anatomy. But all are concerned with living organisms.

The first man to make a significant contribution in biology is Alcmaeon, living in Crotona in the 5th century. Crotona is famous at the time for its Pythagorean scholars, but Alcmaeon seems not to have been of their school.
 
Alcmaeon is the first scientist known to have practised dissection in his researches. His aim is not anatomical, for his interest lies in trying to find the whereabouts of human intelligence. But in the course of his researches he makes the first scientific discoveries in the field of anatomy.

The subsequent Greek theory, subscribed to even by Aristotle, is that the heart is the seat of intelligence. Alcmaeon reasons that since a blow to the head can affect the mind, in concussion, this must be where reason lies. In dissecting corpses to pursue this idea, he observes passages linking the brain with the eyes (the optic nerves) and the back of the mouth with the ears (Eustachian tubes).
 
Aristotle may be wrong about the brain being in the heart, but in general he gives a far more complete and well observed account of biology than any other Greek philosopher.

He inaugurates scientific zoology in his reliance on careful observation. He is particularly acute in his study of marine life, having much to say on the habits of fishes, the development of the octopus family, and the nature of whales, dolphins and porpoises. He is also a pioneer in attempting a system of classification. Observing an unbroken chain of gradual developments, as the life of plants shades into that of animals, he acknowledges the complexity of the subject and seems almost to glimpse the pattern of evolution.
 
Aristotle's notes on botany are lost, but many of his observations no doubt survive in the earliest known botanical text - nine books On the History of Plants written by Aristotle's favourite pupil, Theophrastus.

Writing in about 300 BC, Theophrastus attempts to classify plants, as well as describing their structure, habits and uses. His remarks are based on observations carried out in Greece, but he also includes information brought back from the new Hellenisticempire in the Middle East, Persia and India, resulting from the conquests of Alexander the Great.

The Hippocratic Oath and the four humours: 4th c. BC

Hippocrates practises and teaches medicine in about 400 BC on the Greek island of Kos. He will later be regarded as the father of medicine - partly because he is unlike his more theoretical contemporaries in paying close attention to the symptoms of disease, but also because a century or more after his death a group of medical works is gathered together under his name.

This Hippocratic Collection, and in particular the Hippocratic oath which is part of it, has remained the broad basis of medical principle up to our own day.
 
A slightly later Greek text, called On the Nature of Manand attributed to an author by the name of Polybus, introduces a medical theory which will be orthodox in Europe for some 2000 years. It states that human beings are composed of four substances or 'humours', just as inanimate matter is made up of four elements. India has a similar theory based on three.

The humours are blood, phlegm, black bile (melancholia) and yellow bile (chole). Too much of any one will give a person certain recognizable characteristics. He or she will be sanguine, phlegmatic, melancholy or choleric.

Aristotle's variable atoms: 4th century BC

Aristotle, practical as ever in his determination to get things worked out in detail, proposes a new theory to explain how the four elements of Empedoclesand the atoms of Democritusproduce the wide range of substances apprehended by our senses.

He suggests that there are two pairs of alternatives - hot and cold, moist and dry - which provide the exact nature of matter. In broad terms the four possible combinations are the four elements: earth (cold and dry), air (hot and moist), fire (hot and dry), water (cold and moist). But it is the infinitely variable balance between these qualities which creates the different atoms of stone or wood, bone or flesh.


Greek science in Alexandria: from the 3rd century BC

Classical Greece has produced a brilliant tradition of theorists, the dreamers of science. Attracted by the intellectual appeal of good theories, they are disinclined to engage in the manual labour of the laboratory where those theories might be tested.

This limitation is removed when the centre of the Greek world transfers, in the 3rd century BC, to Alexandria. In this bustling commercial centre, linked with long Egyptian traditions of skilled work in precious metals, people are interested in making practical use of Greek scientific theory. If Aristotle says that the difference in material substances is a matter of balance, then that balance might be changed. Copper might become gold.
 
Among the practical scientists of Alexandria are men who can be seen as the first alchemists and the first experimental chemists. Their trade, as workers in precious metals, involves melting gold and silver, mixing alloys, changing the colour of metals by mysterious process.

These are the activities of chemistry. The everyday items of a chemical laboratory - stills, furnaces, flasks - are all in use in Alexandria.

Euclid and Archimedes: 3rd century BC

Euclid teaches in Alexandria during the reign of Ptolemy. No details of his life are known, but his brilliance as a teacher is demonstrated in the Elements, his thirteen books of geometrical theorems. Many of the theorems derive from Euclid's predecessors (in particular Eudoxus), but Euclid presents them with a clarity which ensures the success of his work. It becomes Europe's standard textbook in geometry, retaining that position until the 19th century.

Archimedes is a student at Alexandria, possibly within the lifetime of Euclid. He returns to his native Syracuse, in Sicily, where he far exceeds the teacher in the originality of his geometrical researches.


The fame of Archimedesin history and legend derives largely from his practical inventions and discoveries, but he himself regards these as trivial compared to his work in pure geometry. He is most proud of his calculations of surface area and of volume in spheres and cylinders. He leaves the wish that his tomb be marked by a device of a sphere within a cylinder.

A selection of titles from his surviving treatises suggests well his range of interests: On the Sphere and the Cylinder; On Conoids and Spheroids; On Spirals; The Quadrature of the Parabola; or, closer to one of his practical discoveries, On Floating Bodies.

The earth and the sun: a heresy of the 3rd century BC

A lone voice on the Greek island of Samos. In about 270 BC Aristarchus is busy trying to work out the size of the sun and the moon and their distance from the earth. His only surviving work is on this topic, and his calculations are inevitably wide of the mark.

But references in other authors make it clear that his studies have brought him to a startling conclusion.
 
Aristarchus believes that the earth is in orbit round the sun (quite contrary to what is plain for anyone to see). There is an attempt, which comes to nothing, to have the man prosecuted for impiety. His idea joins the many other dotty notions which enliven the history of human thought, until Copernicusmentions him, in an early draft of his great book, as someone who had the right idea first.

On reflection Copernicus drops the name of Aristarchus from later versions of the text.

The circumference of the earth: calculated c. 220 BC

Eratosthenes, the librarian of the museum at Alexandria, has more on his mind than just looking after the scrolls. He is making a map of the stars (he will eventually catalogue nearly 700), and he is busy with his search for prime numbers; he does this by an infinitely laborious process now known as the Sieve of Eratosthenes.

But his most significant project is working out the circumference of the earth.
 

Eratosthenes hears that in noon at midsummer the sun shines straight down a well at Aswan, in the south of Egypt. He finds that on the same day of the year in Alexandria it casts a shadow 7.2 degrees from the vertical. If he can calculate the distance between Aswan and Alexandria, he will know the circumference of the earth (360 degrees instead of 7.2 degrees, or 50 times greater).

He discovers that camels take 50 days to make the journey from Aswan, and he measures an average day's walk by this fairly predictable beast of burden. It gives him a figure of about 46,000 km for the circumference of the earth. This is, amazingly, only 15% out (40,000 km is closer to the truth).

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