classical greek science

CLASSICAL GREEK SCIENCE [Hist.1] © H. J. Spencer [Revised Dec. 2012;Nov. 2012]

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ABSTRACT Several Greek intellectuals about 2500 years ago started thinking systematically about the nature of the world. These were the first steps in a long development path that has played a central role in western civilization, particularly in creating those human activities today known as science. These early efforts contained some deep assumptions that have been accepted for so long that they are now even forgotten to be assumptions as everyone now presumes that these hypotheses are actually proven features of the world. This essay will expose some of these key assumptions and challenge them with alternatives that make a big difference in how humans can view their world. This essay was inspired by one of the 20th Century’s most original “big thinkers” F. S. C. Northrop, who traced the key ideas underlying the world’s major civilizations in an attempt to increase global understanding in his masterpiece The Meeting of East and West (1946). This particular brief essay is a response to Northrop’s chapter VII, particularly pages 260-290; it complements the essay on Quality – another of the Classical Greek’s foundational ideas that contained another major hidden flaw.

Influence The ideas of these early Greek intellectuals were readily adopted by their conquerors – the Romans, who viewed themselves as more practical men: soldiers, administrators and engineers, rather than abstract thinkers. The success of the Roman Empire ensured that these Greek ideas were spread widely throughout the classical world that was centered on the Mediterranean. Even after the fall of the Roman Empire, Arabic scholars preserved many of these same ideas, which eventually reached medieval Europe following the Muslim conquest of Spain. The rise of European universities ensured that these ancient ideas were transmitted faithfully right through to modern times, particularly as they became central to Catholic theology.

Christianity Alexandrian scholars in in the 3rd Century merged some of the original cosmological ideas of Plato with Egyptian and Jewish theology into a school of mystical theology now known as Neo-Platonism. These ideas strongly influenced St. Augustine (354-430) who incorporated them into early Christian theology. It was not until the 13th Century that European scholars (via Arabic texts) regained access to the writings of Aristotle. It was Thomas Aquinas (1225-1274), who absorbed Aristotle’s more empirical ideas best and subsequently transformed Christian theology into a form that is still found at the core of modern Catholic teaching.

The Early Greek Scientists The earliest Greek interest in scientific speculation (thinking about Nature) first arose in the city of Miletus in Ionia where the philosopher Thales successfully predicted a solar eclipse in 585 BC. His pupil Anaximander attempted to draw a map of the world and proposed a wildly speculative explanation of the origin of the universe.

Pythagoras About 530 BC Pythagoras established a religious cult in the Greek colony at Crotona in southern Italy. This sect was based on his central idea that numbers were the unchanging foundation of the world. This idea (that has continued to seduce many mathematicians ever since) was strongly reinforced by the discovery of the simple harmonies involving the relative lengths of the strings on a lute. (An early example of intellectuals massively over-extrapolating a single discovery about the world.) Indeed, this use of fractions only works for one octave – it needed the ‘well-tempered’ or logarithmic scale to actually span multiple octaves. The followers of Pythagoras were the first to produce an astronomical theory in which a circular earth revolves on its own axis while moving in a circular orbit. This theory was too radical for most Greek astronomers who were convinced by their own eyes that the earth is stationary and it is the heavens that move around. It should be noted that this theory was an early attempt to incorporate the magical shape of the circle into the reality of the world (see later).

Empedocles Empedocles (ca. 495-435 BC), a native of a major Greek city in Sicily, was the first natural philosopher around 450 BC to propose a theory of the fundamental elements of all matter (ontology). He suggested that everything was made up from different mixtures of only four principal substances: earth, air, water and fire. This incredible theory was still universally accepted in Europe until Robert Boyle published his rebuttal entitled The Sceptical Chemist in 1661. Interestingly, today these four ‘elements’ are viewed as the four states of matter: solid, gas, liquid and plasma. This ontological theory, like most Greek thinking, was grounded in the firm belief that all matter was continuous (‘nature hates a vacuum’).

Democritus It was Democritus of Thrace (ca. 460-370 BC), who challenged this orthodoxy with his atomic ontology. This was the radical idea that the world was composed of tiny pieces of matter, far too small to see, that could not be divided any further; he called these atoms (‘uncuttable’). These atoms were also proposed to be eternal and indestructible; they moved around in empty space (‘the void’) combining together in vast numbers to create the world that humans see around them. Most Ancient Greeks viewed this thoroughly materialist and mechanical theory as dangerously atheistic (having no purpose and no Prime Mover) and mathematically wrong (see later). All of these earlier philosophers are today grouped together as Pre-Socratics. This is because they wrote before Socrates who is viewed as the first of the great philosophers.

The Golden Age With the rise of Athens as the dominant Greek city state many philosophers soon began to concentrate there. Unlike most of the Greek philosophers, Socrates (469 – 369 BC) never wrote anything down but was famous for walking around the city marketplace asking awkward questions. We only know this from his most famous admirer Plato, who described several of these Socratic conversations for posterity; unfortunately it is now impossible to distinguish Socrates’ contributions from Plato’s as Plato never spoke for himself. Actually, Plato only knew Socrates for a few years, as Plato was about 25 when Socrates was tried and executed for treason. It is through these dialogues that Socrates has become renowned for his contributions to ethics, logic and the problem of knowledge i.e. how humans learn about the world (epistemology).

Greek Mathematics It is appropriate to begin this survey of the Golden Age of Greek Science with a brief review of the mathematics created at this time since the Greeks themselves viewed this subject not only as a science but their premier science – “the queen of the sciences”. This view was a result of their focus on the central idea of quantity and their conviction that this was the expression in the real world of the idea of number (the Pythagorean theory). Mathematics was separated into countable parts (arithmetic) or continuous forms, like lines (geometry). Apart from the obsession with prime numbers, arithmetic was readily dismissed as just a mundane activity of shop-keepers but geometry appeared to map the universe, as its theorems were valid for all sizes (scale-less); even better, the properties of the circle were seen as very mysterious (they proved that the ratio of the circumference to any diameter, represented by the symbol π, could not be represented by any fraction). In fact, the idea of the circle as the perfect shape has persisted now for thousands of years – the angle generated by any fraction of the circumference could be even infinitely small. This was important as the idea of the infinite was seen as a direct link to the eternal gods. Central to Greek mathematics at this time was a calculational technique known as the Method of Exhaustion, which is seen today as a precursor to the methods of the integral calculus developed in the 17th century. This procedure was invented by the mathematician and astronomer Eudoxus (408 - 347 BC), a student at Plato’s Academy and the creator of the mathematics of 3-dimensional solid geometry. This method was later used by Euclid to prove several of his propositions and by Archimedes to calculate the value of π. This was a repetitive process where, for example, a series of inscribed polygons with N sides could be approximated to the same surrounding circle as N got larger and larger without limit, becoming equal to the circle itself as N reached infinity. This technique was also used to ‘prove’ that any magnitude could be further divided into smaller magnitudes. Since matter in all its forms appeared to the human eye to be continuous (no gaps) it was simply assumed that this was an intrinsic property of all matter and so it could be divided forever into smaller and smaller samples.

Plato Plato (424 – 347 BC) was born into one of the most powerful families in Athens and traveled extensively around the Eastern Mediterranean. He returned to Athens when he was about 40 and established the first formal school, now referred to as the Academy. Plato’s influence has been strongest in the area of metaphysics: he was convinced that the common reality is, in fact, unreal and only eternal, unchanging ideas (‘Forms’) are real – this was expressed most memorably in his allegory of the Cave where most men only live by the fleeting shadows cast by a fire at the back of the cave, far from the light of reality. These Forms are abstractions that can only be perceived by reason – this theory has had wide appeal to intellectuals ever since, as they value their own mental skills very highly. When he was in Italy Plato learned of the work of Pythagoras and came to appreciate the value of mathematics although he made no mathematical discoveries himself. However, he insisted that mathematics play a central role in his Academy as he thought it provided the finest training for the mind. Apparently, a sign at the Academy’s entrance proclaimed “Let no one enter who is ignorant of geometry”. Plato insisted on clear mathematical definitions and emphasized the ‘certainty’ produced from deriving a mathematical proof. This became the model for timeless thinking and how ‘real’ knowledge was obtained. Plato represented the famous four Greek elements mathematically proposing that certain symmetrical 3D shapes such as the cube, tetrahedron, octahedron and icosahedron (now known as the Platonic Solids) corresponded to earth, fire, air and water. Plato went so far as proposing that the 12-sided dodecahedron corresponded to the whole universe. Around 1600, Johannes Kepler devised an ingenious scheme of nested Platonic solids and spheres to approximate the distances of the known planets from the Sun – he later abandoned this model, when his own measurements showed that it was not accurate enough.

Aristotle Aristotle (384 – 322 BC) spent his youth traveling with his father, a famous healer and physician to the king of Macedonia. These travels brought him into continuous contacts with plants and gave Aristotle a life-long interest in biology. The writings of Aristotle covered many subjects including physics, metaphysics, poetry, drama, logic, linguistics, politics, ethics, biology and zoology; these were the first books to create a comprehensive system of western philosophy. Aristotle joined Plato’s Academy when he was about 18 and stayed there for almost 20 years. He became the tutor to Alexander when he was 40. In 335 BC he returned to Athens establishing his own school there known as the Lyceum, Aristotle conducted courses at the school for the next twelve years. As a pupil of Eudoxus, Aristotle accepted the arguments of the Method of Exhaustion and therefore rejected all atomic theories of reality, including those of his master, Plato. This also meant that there was no reason to postulate a hidden world, so he accepted the observed world of the senses as the real world; this then implied that there were no ideas in the intellect that were not first given through the senses. This rejection of the discrete forced Aristotle, based on the analysis of quantity, to the opposite and view matter as a continuous or field theory.

In addition to the four elements introduced earlier by Empedocles, Aristotle proposed a fifth element, the aether, as the divine substance that makes up the heavenly bodies (stars and planets) and the heavenly spheres that holds them all in place around the Earth, seen ‘obviously’ as the center of the universe. Aristotle influenced many generations of later natural philosophers by proposing a new scientific method for investigating nature. This was based on making observations of phenomena and then creating universal generalizations from these particulars (induction). Based on these general principles, theoretical explanations were then suggested by this process using only logical thinking. Although Aristotle saw the importance of numerical and geometrical relationships in the physical sciences, unlike Plato, Aristotle only viewed mathematics as an abstract discipline and not as an explanation of natural phenomena. Aristotle was most proud of his four-fold theory of causes which he used extensively to explain the dynamical changes found in biology that are described in his book Historia Animalium; this work established the tradition of hierarchical classification in biology. Since Aristotle identified the idea of soul with “the form of a natural body having life potentially within it”, he came to the conclusion that all living creatures have souls.

The Alexandrians The influence and attraction of Athens diminished with the triumphs of Alexander. The role of Athens as the intellectual center of Greek civilization was transferred to the new ‘center of the world’ at Alexandria near the mouth of the River Nile around 331 BC.

Euclid Although little is known of his life, Euclid taught mathematics in Alexandria during the reign of Ptolemy. He is famous for his book Elements that is the only book (13 volumes) on geometry from that era to survive – it became the standard textbook throughout all of Europe from medieval times until the 19th century. Although many of the results derived in this book are believed to have originated with earlier mathematicians, Euclid presented them in single, logical framework (based on axioms) that derived all its results using the methods of mathematical proof that remains the basis of mathematics even today.

Archimedes It is thought that Archimedes (287 – 212 BC) was a student in Alexandria at the same time as Euclid. Archimedes’ huge reputation is based mainly on his practical inventions (such as siege engines and his pump) and discoveries (such as measuring densities) but he himself was most proud of his calculations in pure geometry, particularly those involving spheres and cylinders (the ‘magical circle’ once again!). His greatest advances in physics included developing the bases for solid statics and liquid hydrostatics while providing an explanation of the principle of the lever. Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time.

Ptolemy Claudius Ptolemy (90 – 168 AD) was a Greek-Roman citizen of Alexandria who wrote in Greek. He was a mathematician, astronomer, physicist, geographer and astrologer. His book, the Almagest is the only surviving comprehensive, ancient treatise on astronomy; it contained a star catalogue with a list of 48 constellations as well as a set of tables, which could be used to compute the future or past positions of the known planets. Ptolemy is most famous today for his planetary model that used circles rotating on circles (epicycles) to calculate the positions of the Sun, Moon and planets. Ptolemy also wrote an influential work, Harmonics, on the theory of music that extended the Pythagorean tuning beyond the fifth and across several octaves. Ptolemy also wrote about light in his book Optics – this discussed reflection, refraction and color. This also included a theory of visual perception that influenced much later thinking in this area.

Critique of Classical Greek Science The Pre-Socratics The Pythagoreans were the first group of mathematicians to explicitly view mathematics as a form of religion. Their obsession with the circle as the perfect shape influenced many later Greek thinkers. However, their realization that the square root of 2 (i.e. √2) could not be expressed as a rational fraction of two integers shattered their confidence and their cult. Democritus’s atomic theory was based on his studies in acoustics and was re-established by Newton with his particulate theory of matter. This radical viewpoint has now been totally vindicated by 20th century experimental physics confirming that the material world is composed of atoms but they too are formed from electrons that experiments have shown repeatedly to be without size – these are actually the ‘atoms’ of Democritus.

Plato Plato’s beloved mathematical theory of matter (the Platonic Solids) was actually rejected, ironically, by his fellow mathematicians on the grounds that matter should be infinitely divisible (the Method of Exhaustion). This was also why they rejected Democritus’s theory of atoms. This view of continuous magnitudes has been critiqued in the author’s companion paper Quantity as it led to an ongoing obsession with the idea of infinity.

Aristotle Aristotle’s physics was fundamentally flawed in its theory of motion. If Aristotle (or his assistants) had undertaken the kinds of experiments later done by Galileo he would have realized that a body in motion keeps moving without any continuously acting force to compel it. This deep property of matter (now called inertia) was key to Newton’s ideas. This failure to ground his theories in experimental confirmation was almost universal (except for Archimedes) and reflected the Greek preference for thinking over doing. Aristotle’s biological science was the most empirical of all his work. Since it was grounded in extensive observations, descriptions and classifications, it has stood up well.

The Alexandrians The influence of Euclid’s book on geometry cannot be over-stated. It not only placed geometry at the heart of mathematics but it provided a broad model for how rationality was to be defined. Although the Greeks (and many mathematicians today) believe that geometry is simply a reflection of reality, it is actually an intellectual investigation of certain abstract definitions, such as the point, the line and the circle that do not exist. Euclid’s proofs evolve from his five key axioms (actually graphical constructions), viewed as self-evident truths, but how can this be when the objects of the axioms have no physical existence and the constructions relied on manmade devices, like rulers? Archimedes also used the method of axioms to deduce properties of levers. In this he was very successful, for he was able to create wonderful machines through the understanding that he gained. However, again his axioms refer to objects having properties that no real world object will possess: rods with zero weight, levers that are perfectly rigid, etc. As a consequence, theoretical results deduced from these axioms will never fit experimental evidence exactly but Archimedes never discussed such points. One of the great ironies of science is that the followers of Ptolemy came to believe that his planetary model using epicycles actually described the motion of the heavenly bodies through space so that when the Copernican theory of planetary motion arose around 1600 its greatest “selling point” was the simplicity of all the planets’ circular orbits around the fixed Sun compared with the complexity of the Ptolemaic ‘orbits’. This final demise of Ptolemy’s model was a harsh rebuke of what Ptolemy himself had said was not a model of physical reality but only a highly accurate method of computation (much better than the Copernican predictions). In fact, we can now see that Ptolemy’s scheme was just the first few terms in what is known as finite Fourier series – a universal method for mapping any periodic motion into a series of sine functions. Ptolemy also stated clearly that other mathematical models were equivalent to his and would lead to the same observed results. Unfortunately, these ancient words of wisdom are largely forgotten by today’s theorists, who claim that agreement with experiments proves that theirs is the only right theory.

Assumptions Hidden in Greek Science This brief survey of the highlights of Ancient Greek Science is sufficient to cover those areas that have smuggled key assumptions into the mainstream of western thought. These assumptions can be grouped into the areas of mathematics, physics and philosophy.

Mathematics Many intellectuals have been attracted to mathematics because it is a self-contained world that can be explored purely through the imagination. Once its ‘obvious’ initial assumptions (axioms) have been accepted then the conclusions can be reached solely through the use of logic. The Ancient Greeks made great progress in mathematics leading them to assume that they were following the ‘Royal Road’ to understanding Nature. This self-deception was mainly based on the assumption that geometry was a description of reality. As has pointed out above, this cannot be so when it is both without size (scaleless) and is built upon imaginary concepts (not real objects) like the point and the line.

As the Pythagoreans demonstrated, mathematicians are often theologians in disguise – they are fascinated by concepts that are more appropriate to discussions about God than Nature. This is why two of the most powerful concepts introduced by the Ancient Greek mathematicians were the ideas of infinity and the (endless) perfect circle. Real examples of these concepts cannot be found in nature but this has not stopped the mathematicians assuming that they are describing reality – and most people have bought into this ‘con’. This widely accepted self-deception has not been helped by the mathematicians using ‘natural language’ terms like truth, exist, object, real as part of their private vocabulary. One of the most seductive discoveries of these Ancient Greek mathematicians was the method of deductive proof, exemplified by the presentation of geometry by Euclid. This has led to the widely accepted assumption that this is the most valid form of ‘proof’; thus David Hume (1711 – 1776) dismissed human knowledge based on induction (such as the expectation that the Sun will rise again tomorrow) because this method failed to compare with the certainty of Euclidean-style geometric proofs but relied on personal experience. The problem here is that explicit intellectualization is always reduced to linear symbol streams while Nature is overwhelmingly rich in its relationships and complexity. As Henri Poincaré (1854 – 1912), the last 19th Century polymath (mathematician, physicist, engineer and philosopher) argued: “The distinction between mathematical theories and physical situations is that mathematics is a construction of the human mind, whereas nature is independent of the human mind. This requires the human mind to construct a mathematical model of a reality, which is ultimately independent of mind.”

Physics As described above, the Ancient Greek thinkers convinced themselves, by mathematical arguments, that everything in the real world was continuous. It was a massive shock to all intellectuals when experimental physicists demonstrated that matter is actually discrete – first at the level of atoms, then ultimately at the deepest level of electrons. Almost all of today’s theoretical physicists (who are actually mathematicians) still cling to this ancient assumption of continuity in nature: Maxwell’s theory of electromagnetism and Einstein’s theory of gravity use field theories of continuous mathematics; even quantum theory and String theory exclusively use the same type of mathematics. The almost forgotten area of discrete mathematics lies fallow, waiting to be used to represent discrete reality. The social snobbery of Ancient Greece, where the intellectuals were almost all from the small aristocratic ruling class while the skilled trades were performed by anonymous artisans, is reflected today in academic physics; now the theoreticians still see themselves as superior to the experimental physicists, who are forced to work with their hands. Even though Aristotle’s science was adopted in the Middle Ages superseding Plato’s approach, theoretical physicists today have adopted the mathematical, geometrical physics of Plato. Ptolemy’s calculational scheme has been revived in today’s phenomenological approach to simply inventing equations to match the measurements while avoiding any physical (ontological) hypotheses. It is not surprising that this sterile approach has failed to make any significant progress in the last 100 years while biology goes from strength to strength using the observational (and math-less) techniques pioneered by Aristotle.

Philosophy The Ancient Greeks were always fascinated with the religious problems typified by ontology (‘what is the world made of?’). This metaphysical obsession has never been resolved by thinking alone but now seems to being finally determined by experimental physics – the elementary particle called the electron exists both at the human scale and at the deepest levels of matter. The “great chain of being” may be coming to an end. The very small size of atoms proposed by Democritus and Plato led them both to view these tiny examples of matter as being the real form of reality while the observable world was rejected as simply “false appearances”. This view was absorbed into the first one thousand years of Christian theology. Modern scientists still fall into this trap of thinking that only the bricks are real but not the houses constructed from these bricks. All people who are not scientists should reject this ancient assumption that their own world is not real because scientists have discovered smaller components – this is simply a change in scales (length and time): all levels are equally real; especially the human scale: to us. The last philosophical assumption of classical times that still persists today is the idea of causation; the complexity of Aristotle’s four-fold scheme has disappeared but there is still a widespread belief that everything that occurs in the world is caused by earlier events. This is an intuitively attractive idea as it reflects our self-awareness as action-causing agents but this is because the vast complexity of the real world remains hidden from us. The hypothesis of universal determinism lacks any evidence to support this unscientific view of the richness of the inter-relationships that exist in the real world.

Conclusions Classical Greece produced a brilliant tradition of great theorists - the dreamers of science. Attracted by the intellectual appeal of powerful theories, they were disinclined to engage in the manual labor of the laboratory where those theories might be tested. Very few of these famous Greeks were inventors or engineers even though it is this large group of individuals who have contributed most to the material progress of western civilization. Contrary to the scholars, who promote the books written by theorists, it is actually not the theoretical scientists or mathematicians that have had the largest impact on our daily lives – but this statement will be vehemently rejected by the armies of intellectuals, who now benefit from their ‘research’ activities throughout the modern world. It is very likely that no realistic model of nature can ever be constructed using the known techniques of mathematics. Even when theoretical science is viewed as ‘successful’ (in terms of totally artificial situations – like the two-body problem) these solutions cannot be scaled up to describe real biological molecules (often with over 100,000 atoms), never mind attempting to describe the mind-blowing complexity of living cells and systems. As Raphael has illustrated in his famous painting The School of Athens (showing Plato pointing to the heavens and Aristotle pointing at the earth) there is a need for the public to stop financing religious projects, like the ‘Big Bang’, and re-focus scientific research on the real world of human needs.