In the spring of 1998 I found myself standing on the stones of the Lyceum of Aristotle in Athens. It was strange to think that for two millennia no-one had stood on this spot and known the significance of the place. The location of the Lyceum – the world’s first university – had been roughly known to archaeologists, but the serendipitous discovery of it by Ephi Ligouri in 1997 was without doubt one of the most momentous classical discoveries of modern times.
By persistence and immense good fortune, I found myself being shown round the site – which was at the time still closed to the public – by Ligouri herself. The site is large – some 50 metres across – and consists of the exposed foundations of a large building sitting on bedrock. When Ligouri realized that she had stumbled on a “gymnasio” – a building given over to physical exercise and training – she knew at once that it must have been the Lyceum. It was not exactly in the location traditionally assigned to the Lyceum, but the site satisfied all known requirements: to the east of the city walls and on the banks of the river Iliso.
Archaeologists were still working on the site when I visited. However, the future of the site, which is intended to be the venue for a museum of modern art, remains uncertain. The dig was an emergency one before concrete foundations were to be poured onto the site. I hope that these foundations will never be laid. Given its significance in the history of western culture, this is a building that must be preserved for posterity.
Aristotle’s Lyceum provided the world’s first comprehensive set of courses on all aspects of knowledge. Although the little room where Aristotle probably taught had space for perhaps just 10 students, the scope of the courses that he gave there, which miraculously survive today in some 30 books of his lecture notes, was phenomenal. It is hard to believe they were written by a single person.
Aristotle had an extraordinary range of interests and learning. His courses included philosophy, logic, astronomy, physics, biology, meteorology, poetry, drama, ethics, politics, psychology and economics – in fact, many of the subjects of a modern university. Some of his biological insights were not rediscovered until the 19th century and his logic was not superseded until the work of Gottlob Frege in the early part of the 20th century.
Born in northern Greece in 384 BC (see box), Aristotle’s ideas dominated western science and philosophy for nearly 2000 years, from his death in 322 BC until Galileo’s destruction of his mechanics in 1609. Unfortunately, with the rise of modern physics over the past three centuries, Aristotle’s achievements have been eclipsed. We honour the thinkers of antiquity who guessed right – the atomic theory of Democritus, the heliocentric view of Aristarchus – but not the man who we can truly say invented science. For his physics and astronomy, Aristotle has become identified as the barrier to scientific progress in the renaissance.
After he died, Aristotle’s books, which represent perhaps just one-third of his total output, are said to have been buried in a cave in Asia Minor for 200 years. Although the Peripatetic philosopher Andronicus did prepare an edition of Aristotle’s works in Rome shortly after their rediscovery, they were entirely lost to Europe following the fall of the Roman empire. It was not until the 11th and 12th centuries – thanks to Arabic translations from the Islamic kingdoms of Sicily and Spain – that his writings were rediscovered in Europe.
The modern view of Aristotle
The image of Aristotle we have today is profoundly affected by Galileo’s attack on his physics and on his world view. We are left with the idea that Aristotle represents all the worst aspects of medieval philosophy. Plato, on the other hand, is still cited with approval by theorists and mathematicians, who love to imagine that their ideas represent some underlying reality about the universe.
A fairly characteristic view of Aristotle is given by the physicist J D Bernal in his book Science in History (1969 Penguin). “Bruno had to be burnt and Galileo condemned before doctrines which were derived from Aristotle…could be overthrown,” he wrote. “The subsequent history of science is largely, in fact, the story of how Aristotle was overthrown in one field after another. Indeed Ramus was not far from the mark when he maintained in his famous thesis of 1536 ‘that everything Aristotle taught is false’.”
Of course, Aristotle’s incorrect picture of the Earth as the centre of the solar system had to be overthrown, as did several aspects of his dynamics, in order for the new physics of Galileo and Newton to emerge. But we are left with a diminished and usually inaccurate view of Aristotle’s views and work. After all, many of Aristotle’s insights and hypotheses were not superseded until well into the 19th century. His concept of a uniform, ever-flowing time was adopted unaltered by Newton and still has its place in relativistic physics in an inertial frame. We can surely not fail to take seriously someone whose scientific ideas are still alive after more than 2000 years.
Aristotle’s dynamics
Some insight into Aristotle’s scientific views can be obtained from his two great works on physics – Physics and On the Heavens. Aristotle had no mathematical machinery for dealing with the concept of acceleration, so he analysed only states of uniform velocity. He did not analyse frictionless uniform motion because such motion is not seen in the world. It was not until Newton that this Platonic concept of uniform motion in a straight line under no force was seen to be fundamental to dynamics.
The first state that Aristotle did analyse was motion under a constant force resisted by friction – such as a body of mass m being pulled or pushed along the ground. The corresponding Newtonian equation of motion is mdv/dt = F – µmg, where dv/dt is the acceleration, µ is the coefficient of friction, and g is the acceleration due to gravity. For uniform motion we then require, as stated by Aristotle, that a constant force (equal to µmg) must be exerted to overcome friction.
The second state analysed by Aristotle is uniform motion through a resistive medium like air or water – such as a body in free fall through a viscous medium. This was first correctly analysed by Stokes in the 19th century, who recognized that the resistive force is proportional to the velocity. For a slowly falling sphere of radius r then (neglecting buoyancy) mdv/dt = mg – 6 pi rnv, where n is the coefficient of viscosity. Thus the terminal velocity achieved by the falling body is v = mg/6 pi nr.
Aristotle, however, stated that the terminal velocity is inversely proportional to the cross-sectional area, rather than the radius. In place of the coefficient of viscosity, he talked of the “thickness” of the medium. “The medium causes a difference [in the motion],” he wrote, “because it impedes the moving body, most markedly if it is moving in the opposite direction, but to a lesser degree even if it is at rest; and this is particularly true of a medium that is not easily cut through, i.e. a medium that is on the thick side. A body will move through a given medium in a given time, and through the same distance in a thinner medium in a shorter time, in proportion to the thicknesses of the hindering media.”
In other words, Aristotle came close to a correct statement of Stoke’s formula for the terminal velocity in a resistive medium. His analysis of the real, frictional and viscous world is therefore superior in some respects to that of Newton. Newton’s great advance was to deal with accelerated motions. Aristotle was aware that accelerations took place, but he was not able to incorporate them quantitatively.
In retrospect, the Achilles’ heel of Aristotle’s theory was his treatment of bodies moving against slight resistance. The problem is that the Stokes-Aristotle terminal velocity becomes very large as the viscosity tends to zero (as in air) and becomes infinite in the limit of a vacuum. Aristotle responded by saying a vacuum was impossible, but this still did not obviate the need to consider accelerations properly for motion of a projectile in air.
Another fundamental insight of Aristotle’s that was not correctly formulated in the Newtonian programme was the concept of power. Aristotle correctly defined the power of a machine lifting a body as being the weight multiplied by the distance moved, divided by time – in other words the rate of doing mechanical work. He also, very practically, pointed out that there is a threshold to get something moving when there is resistance by friction – “One man cannot move a ship,” as he put it.
Cosmological insights
Aristotle had a reasonably clear notion of buoyancy – that a denser body sinks through a medium while a lighter one rises. He elevated this to a universal process of bodies either seeking the centre of the Earth or moving away from it, depending on whether they are lighter (hot air or fire) or heavier (earth) than air or water. When he considered if the Earth itself could be moving round the Sun, he found that this idea conflicted with the seemingly more powerful notion of a natural motion towards or away from the centre of the Earth.
This led him to postulate that the circular motions of heavenly bodies about the Earth once a day must also be one of the possible natural states of motion. He also had to argue that the universe is finite to avoid infinite circular velocities at the periphery. This picture is another reason why he rejected the idea of uniform motion in a straight line, because it would have implied the concept of an infinite straight line, which is not permitted in a finite universe. Aristotle reduced all forces to pushes or pulls and could not conceive of gravity holding the planets in circular orbits. He did, however, see that forces act at a point and have a definite direction, i.e. that force is a vector.
Aristotle also showed some surprising insights into astronomy. He thought that the stars were at a range of distances from the Earth, and believed that the stars were spheres. Thus the crude medieval picture of the stars as “holes” in the surface of a sphere that let through light from behind had absolutely nothing to do with Aristotle.
Perhaps Aristotle’s most enduring contribution to cosmology was his concept of a uniform ever-flowing time. This was taken over without modification by Newton and was not questioned until the rise of relativity theory at the start of the 20th century. In the special theory of relativity, the rate at which time flows depends on the relative motion of the observer and the clock, although an inertial, uniformly moving observer would still see a uniform time pervading the universe within his or her own frame of reference. In general relativity, the patch over which a freely falling, inertial observer can measure such a uniform time becomes localized to the zone in which the gravitational field is uniform.
Amazingly, though, when we apply general relativity to a homogeneous and isotropic universe – and there exist strong observational reasons for supporting such a model – Aristotle’s uniform cosmic time pervading the universe reappears. Moreover, it is the same time for every observer co-moving with the universe. I find this one of the most paradoxical features of the universe we appear to find ourselves in.
The goal of Aristotle’s physics was to be able to comprehend all phenomena. Newton’s programme was different: he wanted to analyse and predict a subset of the phenomena that are amenable to equations. Goethe made one last-ditch attempt to reinstate this Aristotelean goal of comprehending and experiencing the unity of nature. Although Goethe’s impact on literature was immense, his assault on Newtonian physics failed completely.
Aristotle in perspective
Aristotle’s set of courses at the Lyceum must have been a wonderful experience. In some senses, however, his physics and astronomy were the least successful of his works. His biology was much more potent and permanent in its influence. His ethics, as popularized by Montaigne, permeate the plays of Shakespeare, and remain close to being a unifying core of decency in human history – the middle way to which we escape from the excesses of the Platonic idealism of the world’s religions and cults.
Aristotle’s views on drama still influence the theatre of today – we still speak of the cathartic effect of tragedy – and his precepts were still taken extremely literally by 17th-century playwrights like Ben Johnson and Jean Racine. This was a teacher who loved science and loved poetry, whereas Plato rejected both.
Standing on the stones of the Lyceum, I could hear again the words of the greatest teacher in western culture: “One swallow does not make a summer, and a single day does not make a happy life.”
| Aristotle in a nutshell |
| Born in 384 BC in Stagira, part of ancient Macedonia in northern Greece, Aristotle went at the age of 18 to Athens to study at Plato’s Academy. He stayed there for 19 years, becoming a teacher and independent researcher. But on Plato’s death in 347 BC, Aristotle was forced to leave. It is tempting to speculate that while Plato was a great enough spirit to tolerate – and even encourage – Aristotle’s completely anti-Platonic line of thought, Plato’s disciples could not tolerate the man who should have been Plato’s successor as head of the academy.
For the next 12 years, Aristotle was forced to live in various places around the northern Aegean Sea. It was during this period that Philip of Macedon summoned him to be tutor to his son Alexander for three years. In 335 BC the hegemony of Philip over Athens allowed Aristotle to return the city, where he founded the Lyceum as a rival to the Academy.
He taught there for 12 years and the 2000 pages of his surviving collected works represent the notes he used for his lectures. He also prepared books for publication, which were reputed to be beautifully written, although none has survived. In 323 BC, with the death of Alexander the Great and the loss of Macedonian control of Athens, Aristotle was forced to leave Athens. He died a year later in Asia Minor, aged 62.
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