The Greeks had developed the intellectual characteristics that served to underpin fresh advances in mathematics and science. They were naturally curious and reluctant to believe that events unfolded only according to the will of the gods. So it was well accepted that the workings of the natural world could be understood. The importance of reason, how arguments work or fail to work, and what can be done with logic to advance from premisses to new conclusions, was widely acknowledged. Educated Greeks were willing to gather evidence and speculate on it. Perhaps most crucial of all, authority was not accepted for authority’s sake; any argument could be challenged through the use of reason or the gathering of fresh empirical evidence.
Such intellectual engagement was, of course, the activity only of an elite and any idea that this elite achieved scientific objectivity independently of the wider political, religious, and social contexts of their age is illusory. There was no separate discipline called ‘science’ with professionals working within it to the exclusion of other intellectual concerns. Even so the breadth of the achievement and the ingenuity with which difficulties were confronted was remarkable. These were some of the greatest minds in history tackling scientific problems, some of which remain impenetrable today. A list of subject areas with origins in the Greek language makes the point: optics, acoustics, mechanics, chemistry, geography, geology, astronomy,
Biology, medicine, and psychology. (See the relevant chapters in Jacques Brunschwig and Geoffrey Lloyd (eds.), Greek Thought: A Guide to Classical Knowledge, Cambridge. Mass., and London, 2000; chapters 1 to 6 of David Lindberg, The Beginnings of Western Science, 2nd edition, Chicago and London, 2007; and Stephen Bertman, The Genesis of Science, New York, 2010.)
In the sciences and mathematics the centre of activity was the very urban and cosmopolitan setting of Alexandria. The Ptolemies actively encouraged scientific research. The three great mathematicians of the day, Euclid (active about 300 Bc), Archimedes (287-212 Bc), and Apollonius of Perge (active about 200 Bc), the last two ‘original geniuses of the highest order, in the words of Geoffrey Lloyd, were all based in Alexandria. In his Elements, Euclid produced what has possibly been the most successful textbook in history. His method was to set out a series of axioms, propositions so basic that everyone must accept them, and then through rational argument systematically deduce theorems from them. The simplicity of his work and the method he used has made The Elements the foundation of all subsequent mathematics. Archimedes built further on Euclid’s work. He devised sophisticated ways of measuring the area of a circle and was the first man to calculate accurately the size of pi and devise the formula for measuring the volume of a sphere. He virtually invented the science of hydrostatics. Overall it could be argued that Archimedes made more advances in mathematics than any other mathematician in history. (Galileo, one of his greatest admirers, described him as ‘superhuman’.) Apollonius’ contribution was in geometry, where his work with conic sections taxes even the most advanced mathematician today.
In general these early mathematicians had to contend with limited technology but the unravelling of the Antikythera mechanism, an astonishing calculator found in a shipwreck off the island of Antikythera as long ago as 1900 but whose complexity has only recently been appreciated, shows that sophisticated mechanisms for plotting the stars were available. The mechanism dates from the early first century BC with accompanying textual information in Greek (although it appears to have been programmed from Babylonian records). It is unique as a survival but the intricacy and precision of its many, well over thirty, gears show that there must have been prototypes, now all lost. There are scattered references in the literature to similar devices. A major continuing research project on the mechanism is discovering even more functions.
The Antikythera mechanism confirms that astronomy was the most fruitful area of scientific speculation. Discoveries went far ahead of the conventional wisdom of the time. Aristarchus of Samos (c.275 Bc), for instance, suggested that the earth went round the sun, although he failed to convince the mainstream astronomers, who continued for another 1,700 years to believe in the earth-centred universe. In the third century Eratosthenes calculated the circumference of the earth by comparing the shadow, or lack of it, thrown by the sun at two different points on the Nile at midday. Although his final result is disputed, he may have come within 300 kilometres of the correct figure. (The Greeks had no problems in accepting the world as round.)
The most influential figure in astronomy was the mathematician Apollonius (beginning of the second century bc). He started with the premiss that the earth is at rest in the centre of the universe. To the Greek astronomers this seemed the best explanation of the constancy of the relationship between distant stars, and also accorded with Aristotle’s theory that, as the evidence of gravity suggested, everything was attracted to the earth as the natural centre of the universe. From this premiss Apollonius evolved a system with which to explain the movements of the planets. He assumed that they always moved in circles but that the centre of each circle itself moved along the circumference of a second circle. Sometimes the centre of this second circle was the earth but other points were possible. The system allowed a wide range of astronomical phenomena, including the varying length of the seasons, to be explained more easily. It was Apollonius’ system, as elaborated by Hipparchus of Nicaea, that was to be used in the second century ad by the greatest astronomer of all, Ptolemy (active in Alexandria ad 127-45, see below, p. 550). Hipparchus (end of second century bc) achieved the remarkable feat of spotting and defining the precession of the equinoxes. As the earth is not an exact sphere its axes oscillate slightly and this means that its position as a viewing platform for the stars shifts slightly but consistently, achieving a full revolution in 26,000 years. Hipparchus spotted this and made the first calculation of the speed of change.
Greek medicine, in contrast, claimed to give first place to observation. The earliest surviving body of texts on Greek medicine, some sixty in all, dating from between 430 and 330 bc, were traditionally attributed to Hippocrates, a physician who lived on the island of Kos in the fifth century. Even though there is no evidence that he actually wrote any of the texts, and many show the terminology of a later period, that of the superb Hellenistic Aesclepium whose ruins survive in Kos to this day, Hippocrates continues to be associated with many of the maxims outlined in them: that the patient needs to be viewed as a whole, that much healing takes place naturally, that a simple diet is conducive to good health, and that the first duty of a doctor is to his patients rather than to himself or to the accumulation of wealth. (For a full survey see Vivian Nutton, Ancient Medicine, London and New York, 2004.)
One of the most influential texts attributed to Hippocrates is entitled On the Sacred Disease. It deals with epilepsy, the disorder that was traditionally most easily associated with a direct intervention by the gods. The text points out that epilepsy occurs naturally, is rooted in the brain, has defined causes, possibly inherited, and might be cured by drugs if treated early. The text challenges those who peddle ‘magic’ cures for such illnesses; only the trained doctor can help. Here is the birth of modern scientific medicine.
Any serious advance in the field depended on the gathering of empirical information about the working of the human body. The Greeks were used to cutting up animals after sacrificing and to some extent they applied what they learnt of anatomy by analogy to the human body. There is a report that Herophilus of Chalcedon and Erasistratus of Ceos, both active in the 260s, went one step further in taking living criminals as the subjects of their observations and gained the first significant insights into the working of the human body. Their methods included dissection of
Their subjects, possibly even when they were still alive. Between them Herophilus and Erasistratus were the first to investigate the nervous system and understand the difference between sensory and motor nerves, and they came close to discovering the circulation of the blood. It was Herophilus who described and named the duodenum for the first time. Inevitably they were limited, as were all Greek scientists, by their lack of instruments. They worked only with the naked eye and had no chance of seeing bacteria or viruses. Their conception of the causes of illness was circumscribed by the theory of the four humours. Nevertheless, their work provided the foundations on which Galen, the greatest of the Greek doctors, built his pioneering studies of physiology in the second century ad (see below, p. 551).
Underlying the achievements of these ‘scientists’ was an obsessive curiosity, and it can be seen in the Hellenistic period in a passion for exploration. Alexander had created a surge of interest in geography after so many apparently exotic lands and cultures had been revealed in the east and the ‘scientists’ he took with him reported back their experiences. In the next three centuries Greek travellers explored the furthest reaches of the accessible world. One of the most remarkable voyages was that of Pytheas, a sea captain from Massilia (modern Marseilles), who sailed through the Straits of Gibraltar and then northwards to make a circumnavigation of Britain in about 320. He reached a point where the nights were only two to three hours long, a latitude of about 65 degrees. Pytheas was a genuine adventurer, a mathematician and astronomer who seems to have had no commercial interests and simply an urge to understand how the world worked. Other travellers reached the river Ganges in India and, in Africa, as far south as Somaliland, where elephants were found and brought back for the armies of the Ptolemies. One fruit of these travels was the first world map, produced by Dicaearchus of Messenia about 300. It incorporated a line of latitude. At the end of the century Eratosthenes introduced a map that showed longitude as well.
World History
