To Explain the World: The Discovery of Modern Science
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Thales had a pupil or associate, Anaximander, who came to a different conclusion. He too thought that there is a single fundamental substance, but he did not associate it with any common material. Rather, he identified it as a mysterious substance he called the unlimited, or infinite. On this, we have a description of his views by Simplicius, a Neoplatonist who lived about a thousand years later. Simplicius includes what seems to be a direct quotation from Anaximander, indicated here in italics:
Of those who say that [the principle] is one and in motion and unlimited, Anaximander, son of Praxiades, a Milesian who became successor and pupil to Thales, said that the unlimited is both principle and element of the things that exist. He says that it is neither water nor any other of the so-called elements, but some other unlimited nature, from which the heavens and the worlds in them come about; and the things from which is the coming into being for the things that exist are also those into which their destruction comes about, in accordance with what must be. For they give justice and reparation to one another for their offence in accordance with the ordinance of time—speaking of them thus in rather poetical terms. And it is clear that, having observed the change of the four elements into one another, he did not think fit to make any one of these an underlying stuff, but something else apart from these.3
A little later another Milesian, Anaximenes, returned to the idea that everything is made of some one common substance, but for Anaximenes it was not water but air. He wrote one book, of which just one whole sentence has survived: “The soul, being our air, controls us, and breath and air encompass the whole world.”4
With Anaximenes the contributions of the Milesians came to an end. Miletus and the other Ionian cities of Asia Minor became subject to the growing Persian Empire in about 550 BC. Miletus started a revolt in 499 BC and was devastated by the Persians. It revived later as an important Greek city, but it never again became a center of Greek science.
Concern with the nature of matter continued outside Miletus among the Ionian Greeks. There is a hint that earth was nominated as the fundamental substance by Xenophanes, who was born around 570 BC at Colophon in Ionia and migrated to southern Italy. In one of his poems, there is the line “For all things come from earth, and in earth all things end.”5 But perhaps this was just his version of the familiar funerary sentiment, “Ashes to ashes, dust to dust.” We will meet Xenophanes again in another connection, when we come to religion in Chapter 5.
At Ephesus, not far from Miletus, around 500 BC Heraclitus taught that the fundamental substance is fire. He wrote a book, of which only fragments survive. One of these fragments tells us, “This ordered kosmos,* which is the same for all, was not created by any one of the gods or of mankind, but it was ever and is and shall be ever-living Fire, kindled in measure and quenched in measure.”6 Heraclitus elsewhere emphasized the endless changes in nature, so for him it was more natural to take flickering fire, an agent of change, as the fundamental element than the more stable earth, air, or water.
The classic view that all matter is composed not of one but of four elements—water, air, earth, and fire—is probably due to Empedocles. He lived in Acragas, in Sicily (the modern Agrigento), in the mid-400s BC, and he is the first and nearly the only Greek in this early part of the story to have been of Dorian rather than of Ionian stock. He wrote two hexameter poems, of which many fragments have survived. In On Nature, we find “how from the mixture of Water, Earth, Aether, and Sun [fire] there came into being the forms and colours of mortal things”7 and also “fire and water and earth and the endless height of air, and cursed Strife apart from them, balanced in every way, and Love among them, equal in height and breadth.”8
It is possible that Empedocles and Anaximander used terms like “love” and “strife” or “justice” and “injustice” only as metaphors for order and disorder, in something like the way Einstein occasionally used “God” as a metaphor for the unknown fundamental laws of nature. But we should not force a modern interpretation onto the pre-Socratics’ words. As I see it, the intrusion of human emotions like Empedocles’ love and strife, or of values like Anaximander’s justice and reparation, into speculations about the nature of matter is more likely to be a sign of the great distance of the thought of the pre-Socratics from the spirit of modern physics.
These pre-Socratics, from Thales to Empedocles, seem to have thought of the elements as smooth undifferentiated substances. A different view that is closer to modern understanding was introduced a little later at Abdera, a town on the seacoast of Thrace founded by refugees from the revolt of the Ionian cities against Persia started in 499 BC. The first known Abderite philosopher is Leucippus, from whom just one sentence survives, suggesting a deterministic worldview: “No thing happens in vain, but everything for a reason and by necessity.”9 Much more is known of Leucippus’ successor Democritus. He was born at Miletus, and had traveled in Babylon, Egypt, and Athens before settling in Abdera in the late 400s BC. Democritus wrote books on ethics, natural science, mathematics, and music, of which many fragments survive. One of these fragments expresses the view that all matter consists of tiny indivisible particles called atoms (from the Greek for “uncuttable”), moving in empty space: “Sweet exists by convention, bitter by convention; atoms and Void [alone] exist in reality.”10
Like modern scientists, these early Greeks were willing to look beneath the surface appearance of the world, pursuing knowledge about a deeper level of reality. The matter of the world does not appear at first glance as if it is all made of water, or air, or earth, or fire, or all four together, or even of atoms.
Acceptance of the esoteric was taken to an extreme by Parmenides of Elea (the modern Velia) in southern Italy, who was greatly admired by Plato. In the early 400s BC Parmenides taught, contra Heraclitus, that the apparent change and variety in nature are an illusion. His ideas were defended by his pupil Zeno of Elea (not to be confused with other Zenos, such as Zeno the Stoic). In his book Attacks, Zeno offered a number of paradoxes to show the impossibility of motion. For instance, to traverse the whole course of a racetrack, it is necessary first to cover half the distance, and then half the remaining distance, and so on indefinitely, so that it is impossible ever to traverse the whole track. By the same reasoning, as far as we can tell from surviving fragments, it appeared to Zeno to be impossible ever to travel any given distance, so that all motion is impossible.
Of course, Zeno’s reasoning was wrong. As pointed out later by Aristotle,11 there is no reason why we cannot accomplish an infinite number of steps in a finite time, as long as the time needed for each successive step decreases sufficiently rapidly. It is true that an infinite series like ½ + ⅓ + ¼ + . . . has an infinite sum, but the infinite series ½ + ¼ + ⅛ + . . . has a finite sum, in this case equal to 1.
What is most striking is not so much that Parmenides and Zeno were wrong as that they did not bother to explain why, if motion is impossible, things appear to move. Indeed, none of the early Greeks from Thales to Plato, in either Miletus or Abdera or Elea or Athens, ever took it on themselves to explain in detail how their theories about ultimate reality accounted for the appearances of things.
This was not just intellectual laziness. There was a strain of intellectual snobbery among the early Greeks that led them to regard an understanding of appearances as not worth having. This is just one example of an attitude that has blighted much of the history of science. At various times it has been thought that circular orbits are more perfect than elliptical orbits, that gold is more noble than lead, and that man is a higher being than his fellow simians.
Are we now making similar mistakes, passing up opportunities for scientific progress because we ignore phenomena that seem unworthy of our attention? One can’t be sure, but I doubt it. Of course, we cannot explore everything, but we choose problems that we think, rightly or wrongly, offer the best prospect for scientific understanding. Biologists who are interested in chromosomes or nerve cells study animals like fruit flies and squid, no
t noble eagles and lions. Elementary particle physicists are sometimes accused of a snobbish and expensive preoccupation with phenomena at the highest attainable energies, but it is only at high energies that we can create and study hypothetical particles of high mass, like the dark matter particles that astronomers tell us make up five-sixths of the matter of the universe. In any case, we give plenty of attention to phenomena at low energies, like the intriguing mass of neutrinos, about a millionth the mass of the electron.
In commenting on the prejudices of the pre-Socratics, I don’t mean to say that a priori reasoning has no place in science. Today, for instance, we expect to find that our deepest physical laws satisfy principles of symmetry, which state that physical laws do not change when we change our point of view in certain definite ways. Just like Parmenides’ principle of changelessness, some of these symmetry principles are not immediately apparent in physical phenomena—they are said to be spontaneously broken. That is, the equations of our theories have certain simplicities, for instance treating certain species of particles in the same way, but these simplicities are not shared by the solutions of the equations, which govern actual phenomena. Nevertheless, unlike the commitment of Parmenides to changelessness, the a priori presumption in favor of principles of symmetry arose from many years of experience in searching for physical principles that describe the real world, and broken as well as unbroken symmetries are validated by experiments that confirm their consequences. They do not involve value judgments of the sort we apply to human affairs.
With Socrates, in the late fifth century BC, and Plato, some forty years later, the center of the stage for Greek intellectual life moved to Athens, one of the few cities of Ionian Greeks on the Greek mainland. Almost all of what we know about Socrates comes from his appearance in the dialogues of Plato, and as a comic character in Aristophanes’ play The Clouds. Socrates does not seem to have put any of his ideas into writing, but as far as we can tell he was not very interested in natural science. In Plato’s dialogue Phaedo Socrates recalls how he was disappointed in reading a book by Anaxagoras (about whom more in Chapter 7) because Anaxagoras described the Earth, Sun, Moon, and stars in purely physical terms, without regard to what is best.12
Plato, unlike his hero Socrates, was an Athenian aristocrat. He was the first Greek philosopher from whom many writings have survived pretty much intact. Plato, like Socrates, was more concerned with human affairs than with the nature of matter. He hoped for a political career that would allow him to put his utopian and antidemocratic ideas into practice. In 367 BC Plato accepted an invitation from Dionysius II to come to Syracuse and help reform its government, but, fortunately for Syracuse, nothing came of the reform project.
In one of his dialogues, the Timaeus, Plato brought together the idea of four elements with the Abderite notion of atoms. Plato supposed that the four elements of Empedocles consisted of particles shaped like four of the five solid bodies known in mathematics as regular polyhedrons: bodies with faces that are all identical polygons, with all edges identical, coming together at identical vertices. (See Technical Note 2.) For instance, one of the regular polyhedrons is the cube, whose faces are all identical squares, three squares meeting at each vertex. Plato took atoms of earth to have the shape of cubes. The other regular polyhedrons are the tetrahedron (a pyramid with four triangular faces), the eight-sided octahedron, the twenty-sided icosahedron, and the twelve-sided dodecahedron. Plato supposed that the atoms of fire, air, and water have the shapes respectively of the tetrahedron, octahedron, and icosahedron. This left the dodecahedron unaccounted for. Plato regarded it as representing the kosmos. Later Aristotle introduced a fifth element, the ether or quintessence, which he supposed filled the space above the orbit of the Moon.
It has been common in writing about these early speculations regarding the nature of matter to emphasize how they prefigure features of modern science. Democritus is particularly admired; one of the leading universities in modern Greece is named Democritus University. Indeed, the effort to identify the fundamental constituents of matter continued for millennia, though with changes from time to time in the menu of elements. By early modern times alchemists had identified three supposed elements: mercury, salt, and sulfur. The modern idea of chemical elements dates from the chemical revolution instigated by Priestley, Lavoisier, Dalton, and others at the end of the eighteenth century, and now incorporates 92 naturally occurring elements, from hydrogen to uranium (including mercury and sulfur but not salt) plus a growing list of artificially created elements heavier than uranium. Under normal conditions, a pure chemical element consists of atoms all of the same type, and the elements are distinguished from one another by the type of atom of which they are composed. Today we look beyond the chemical elements to the elementary particles of which atoms are composed, but one way or another we continue the search, begun at Miletus, for the fundamental constituents of nature.
Nevertheless, I think one should not overemphasize the modern aspects of Archaic or Classical Greek science. There is an important feature of modern science that is almost completely missing in all the thinkers I have mentioned, from Thales to Plato: none of them attempted to verify or even (aside perhaps from Zeno) seriously to justify their speculations. In reading their writings, one continually wants to ask, “How do you know?” This is just as true of Democritus as of the others. Nowhere in the fragments of his books that survive do we see any effort to show that matter really is composed of atoms.
Plato’s ideas about the five elements give a good example of his insouciant attitude toward justification. In Timaeus, he starts not with regular polyhedrons but with triangles, which he proposes to join together to form the faces of the polyhedrons. What sort of triangles? Plato proposes that these should be the isosceles right triangle, with angles 45°, 45°, and 90°; and the right triangle with angles 30°, 60°, and 90°. The square faces of the cubic atoms of earth can be formed from two isosceles right triangles, and the triangular faces of the tetrahedral, octahedral, and icosahedral atoms of fire, air, and water (respectively) can each be formed from two of the other right triangles. (The dodecahedron, which mysteriously represents the cosmos, cannot be constructed in this way.) To explain this choice, Plato in Timaeus says, “If anyone can tell us of a better choice of triangle for the construction of the four bodies, his criticism will be welcome; but for our part we propose to pass over all the rest. . . . It would be too long a story to give the reason, but if anyone can produce a proof that it is not so we will welcome his achievement.”13 I can imagine the reaction today if I supported a new conjecture about matter in a physics article by saying that it would take too long to explain my reasoning, and challenging my colleagues to prove the conjecture is not true.
Aristotle called the earlier Greek philosophers physiologi, and this is sometimes translated as “physicists,”14 but that is misleading. The word physiologi simply means students of nature (physis), and the early Greeks had very little in common with today’s physicists. Their theories had no bite. Empedocles could speculate about the elements, and Democritus about atoms, but their speculations led to no new information about nature—and certainly to nothing that would allow their theories to be tested.
It seems to me that to understand these early Greeks, it is better to think of them not as physicists or scientists or even philosophers, but as poets.
I should be clear about what I mean by this. There is a narrow sense of poetry, as language that uses verbal devices like meter, rhyme, or alliteration. Even in this narrow sense, Xenophanes, Parmenides, and Empedocles all wrote in poetry. After the Dorian invasions and the breakup of the Bronze Age Mycenaean civilization in the twelfth century BC, the Greeks had become largely illiterate. Without writing, poetry is almost the only way that people can communicate to later generations, because poetry can be remembered in a way that prose cannot. Literacy revived among the Greeks sometime around 700 BC, but the new alphabet borrowed from the Phoenicians was first used by Homer and Hesiod to
write poetry, some of it the long-remembered poetry of the Greek dark ages. Prose came later.
Even the early Greek philosophers who wrote in prose, like Anaximander, Heraclitus, and Democritus, adopted a poetic style. Cicero said of Democritus that he was more poetic than many poets. Plato when young had wanted to be a poet, and though he wrote prose and was hostile to poetry in the Republic, his literary style has always been widely admired.
I have in mind here poetry in a broader sense: language chosen for aesthetic effect, rather than in an attempt to say clearly what one actually believes to be true. When Dylan Thomas writes, “The force that through the green fuse drives the flower drives my green age,” we do not regard this as a serious statement about the unification of the forces of botany and zoology, and we do not seek verification; we (or at least I) take it rather as an expression of sadness about age and death.
At times it seems clear that Plato did not intend to be taken literally. One example mentioned above is his extraordinarily weak argument for the choice he made of two triangles as the basis of all matter. As an even clearer example, in the Timaeus Plato introduced the story of Atlantis, which supposedly flourished thousands of years before his own time. Plato could not possibly have seriously thought that he really knew anything about what had happened thousands of years earlier.
I don’t at all mean to say that the early Greeks decided to write poetically in order to avoid the need to validate their theories. They felt no such need. Today we test our speculations about nature by using proposed theories to draw more or less precise conclusions that can be tested by observation. This did not occur to the early Greeks, or to many of their successors, for a very simple reason: they had never seen it done.