by David Orrell
Aristotle viewed material substance as bestowed with a kind of life force with its own wants and desires. He believed that all substances were composed of the four elements—earth, water, air, and fire. The tendency of earth is to sink strongly down. Water trickles down less strongly, while air rises and fire positively springs to the sky. An air bubble in water will rise upwards because air “wants” to be higher than water. Motion, therefore, occurs either because an object wants to find its own level or because it is pushed. A full explanation of any object had to take into account its final cause, the purpose for which the thing existed. The stars in heaven were made of the fifth element, called ether, the lightest of all, and moved in a circle, which was the figure of eternal motion. Earth had to be in the middle of the universe, because it was the heaviest thing around.
In this teleological view of the world, the earth itself was a kind of organism. Natural phenomena such as earthquakes, winds, or even meteors were the result of the planet’s “windy exhalations.” The son of a doctor, Aristotle constantly drew comparisons between the earth and human bodies. He believed that tremors or spasms were caused by a kind of wind within the body, and that earthquakes were caused by a similar wind, but on a larger scale.
Perhaps Aristotle’s most significant contribution to science was his axiomatic development of logic. In his work Prior Analytics, he proposed his syllogistic form of argument—the ultimate in linear, left-brain thinking—which consisted of two premises and a conclusion. His gloomy but hard-to-counter example was:
(i) Every Greek is a person.
(ii) Every person is mortal.
(iii) Every Greek is mortal.
(One imagines that the first spinoff from the Lyceum was a life-insurance company.) This systematic, logic-based approach to science laid the foundation for Euclid’s development of geometry and helped establish what became known as the scientific method. While Aristotle’s work in biology has been much admired, his theories in physics were less reliable. He postulated two laws of motion. The first was that the heavier an object is, the faster it will fall. The second was that the speed of fall decreases with the density of the medium—so, for example, a stone will fall more slowly in water than it will in air. Curiously, while Aristotle made detailed observations of many biological specimens and natural phenomena, he didn’t verify his theories of physics. It was left to Galileo, nineteen centuries later, to actually drop stones off buildings and disprove Aristotle’s first law.
GREEK CIRCLE MODEL,VERSION II
At the Lyceum and elsewhere, astronomers continued to improve the Greek Circle Model. The original version of Eudoxus captured
both the daily and yearly cycles of the sun and the general motion of the planets, but it didn’t match some of the details. In particular, it was known that the seasonal motion of the sun, as measured by the time between solstices, was not uniform. This was repaired by adding more spheres of motion. The final model, which was presented by Aristotle and accounted for the motions of all the visible planets and the moon, included no fewer than fifty-five concentric spheres. It matched the observed movement of the planets around the sky and consisted solely of circular motion, which was the only type that could occur in the ether.
After Aristotle’s death, a mathematician called Aristarchus of Samos proposed the novel theory that the earth revolved around the sun, rather than the other way round. The stars do not rotate around the earth, he suggested, but stay in their positions an enormously far distance away. (The large distance was required so that the stars appear not to move relative to one another as the earth rotates.) Perhaps because it was incompatible with the views of Aristotle, the idea did not catch on.
The serious mathematicians continued to tinker with the Greek Circle Model. Around 150 A.D., Ptolemy of Alexandria put the finishing touches on a new version. It included some tweaks of Aristotle’s model, and some major changes. It was known that the size of the moon and the brightness of the planets tended to vary, which suggested that their distance from the earth changed with time. The most straightforward way to address this would have been to adopt non-circular motion, but again this would have contravened dogma. Ptolemy wrote: “Our problem is to demonstrate, in the case of the five planets as in the case of the sun and moon, all their apparent irregularities are produced by means of regular and circular motions (for these are strangers to disparities and disorders).”34 He achieved this by incorporating a new type of circular motion, first proposed by Hipparchus, known as epicycles—that is, circles within circles. In Ptolemy’s model, the planet rotates around a small circle, which in turn rotates around the earth (as shown in figure1.4). Its distance from the earth therefore varies, as does the rate at which the planet moves. Working all this out required the invention of trigonometry, which some attribute to Hipparchus.
FIGURE 1.4 In the Greek Circle Model, Version II,planets move in epicycles-circles within circles.
With its cycles, epicycles, and even eccentric epicycles (whose centres were slightly offset from the main cycles), the entire model was even more complicated than Aristotle’s. By insisting at a basic level on the Pythagorean simplicity of circular motion, the model effectively exported the system’s complexity to a higher level. The extreme flexibility in the model meant that it could be made to closely match the observational data. Ptolemy wrote up his results, which included scores of tables detailing the motions of the heavens,in the Almagest (from the Arab al-majisti, meaning “the greatest”). Its publication marked the transformation of astronomy from a theoretical pursuit into a predictive science. Just as Apollo’s arrow had allowed the druid Abaris to fly across obstacles, the mathematically based Greek Circle Model allowed the Greeks to forecast the future by looking it up in a book.
STARGAZERS
It may seem to the modern reader that predicting the motion of the stars and planets, while useful for chronology and navigation, has little to do with practical forecasting in weather, medicine, or economics. Indeed, for most people living in urban areas, the heavens are rendered all but invisible by light pollution. However, prior to the invention of the electric light bulb (or for that matter, competition from the stars on TV), the night sky played a rather more important role in people’s lives. The Greeks, like others before and after them, believed that life here on earth was in harmony with the heavens. The arrival of a comet could herald drought, famine, or political upheaval. The positions of the moon and the planets could be interpreted to make predictions about the weather and the harvests (as described in Ptolemy’s astrological work, Tetrabiblos). Astrology was also used to determine the optimal timing for medical interventions, and to cast horoscopes of newborn children.
Astrology is rooted in the belief that the soul comes from and is united with the heavens. In Plato’s dialogue Phadros, Socrates (whose violent death was predicted to him by a Syrian astrologer) says that “soul, considered collectively, has the care of all that is soulless, and it traverses the whole heaven, appearing sometimes in one form and sometimes in another. . . . The whole, compounded of body and soul, is called a living being, and is further designated as mortal.”35
The first astrological text, from the second millennium B.C. (the Old Babylonian period), offers the following advice, inferred from the state of the moon and the sky at the start of the New Year:36
If the sky is dark, the year will be bad.
If the face of the sky is bright when the New Moon appears and [it is greeted] with joy, the year will be good.
If the North Wind blows across the face of the sky before the New Moon, the corn will grow abundantly.
If on the day of the crescent the Moon-God does not disappear quickly enough from the sky, quaking [presumably some disease] will come upon the Land.
More detailed and sophisticated astrological forecasts based on the zodiac rely on knowledge of the positions of the sun, the moon, and the planets at particular times of day, like the exact time of a child’s birth. Since direct observations are
impossible during the day or when it is overcast, astrologists needed to first predict the state of the heavens. As a result, astronomy and astrology were viewed throughout much of history almost as separate branches of the same science.
Astrological forecasters still play a role, of course—even in the highest circles of business and politics. Nancy Reagan consulted with an astrologist to help avoid assassination attempts against her husband after the one on March 30, 1981.37 In a dangerous, chaotic world, any predictions can sometimes seem better than none at all. And unlike many other methods of prognostication—say, the reading of animal entrails (hard to imagine that in the White House)— astrology is based on a defined, apparently rational method, which to many gives it an aura of credibility.
METHODS OF DIVINATION
Traditional techniques of foretelling the future include:
Stars and planets (astrology)
Rolling dice/drawing lots (cleromancy)
Tarot cards (cartomancy)
Palm reading (chiromancy)
Crystal balls (crystallomancy)
Shape of head (phrenology)
Atmospheric conditions (aeromancy)
Dreams (oneiromancy)
Animal entrails (haruspicy)
Moles on the body (moleosophy)
Lightning and thunder (ceraunoscopy)
Smoke and fire (pyromancy)
Flight of birds (ornithomancy)
Neighing of horses (hippomancy)
Tea leaves or coffee grounds (tasseomancy)
Passages of sacred texts (bibliomancy)
Numbers (numerology)
I Ching
Guessing
To which we can add:
Mathematical models (meteorology/biology/economics)
Whether distant planets control the hand of an assassin is certainly debatable, but subtle astronomical rhythms have been implicated in the timing of the ice ages (as will be discussed later). Perhaps the biggest reason for wanting to predict the movements of the stars and planets, though, is to prove that unlike most other things here on the ground, they do move in a predictable fashion. As Karl Marx said, “Mankind always sets itself only such problems as it can solve.”38 The Greek Circle Model was a first step in the tradition of using mathematics to make predictions about the physical universe.
During his own time, Aristotle was not regarded as highly as Plato. His work, much of it compiled from lecture notes, was probably not even published until hundreds of years after his death, and it gained prominence in Christian Europe only when translated into Latin in the twelfth and thirteenth centuries. From that point on, however, he became the almost unquestioned authority, his word the gospel truth.
Aristotle, therefore, both greatly advanced and inadvertently retarded the progress of science. On the one hand, he helped develop the system of rational, logical thinking—the legacy of Pythagoras— that culminated in modern scientific models. On the other hand, his enormous, if belated, prestige seems to have stilted the application of those methods to the natural world. In the Middle Ages, his texts had become as solid as a star in the firmament, and the Greek Circle Model had taken on the status of a perfect form. It was as if he opened his own eyes, only to close those of other people for hundreds of years.
In many ways this is ironic, since Aristotle was no blind follower of authority himself. He criticized earlier philosophers for defending their fixed ideas, their mental models of the universe, against all the facts.39 It took Tycho Brahe and other scientists of the sixteenth century to show that even the stars in heaven aren’t as immutable as they appear.
2 LET THERE BE LIGHT
TYCHO BRAHE AND THE MODEL MAKERS
Do not the Delphic prophets walk among their crowded flock,
With attentive ear perceiving mysterious sounds,
When in heaven the flock of secret movers
Were delivered by Tycho Brahe’s written work?
The prophets are silent now; oracles stay away from Earth,
Go! Delphic flock, look for gods in another place!
—Johannes Kepler, eulogy for Tycho Brahe
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
—William Shakespeare, Hamlet
LIGHT VS DARKNESS
One often thinks of science as a linear enterprise, with knowledge accreted piece by piece to bring us to the current massive edifice. However, as James Watson wrote in his book The Double Helix, “Science seldom proceeds in the straightforward logical manner imagined. . . . Instead its steps forward (and backward) are often very human events in which personalities and cultural traditions play major roles.”1 The science of numerical prediction, which was born in Pythagoras’s cult and developed by the ancient Greeks, entered in the Dark Ages into what might be called a static phase, where little progress was made for hundreds of years. Many advances were made in mathematics—one of the biggest being the introduction of Arabic numerals, which considerably simplified computation—but in the fifteenth century, the state-of-the-art model of the cosmos was still the Greek Circle Model. Part of the problem was the “lock-in” phenomenon, which gives ideas or technologies that first gain a foothold a kind of historical inevitability, as if they were God-given truths (rather like the Windows operating system on my computer). When new ideas do eventually emerge, they tend to spring out of a number of places at around the same time, as if they can be repressed no longer.
The Greek Circle Model had originally been based on the belief that earth is the heaviest and basest of the four elements, and therefore has a tendency to sink down. Since the planet and the cosmos itself were spherical, down meant towards the middle. The stars and planets, which are made up of ether, the lightest and most pure element, would naturally tend to spin around this dense, immobile core. Our earth was not so much at the centre of the universe as it was at the bottom. Perfection was up there in the heavens, not down here on the ground.
When the Greek Circle Model was adopted by men like St. Thomas Aquinas to build a Christian cosmology, it came to represent not just a physical model of the cosmos but a theological one. According to the Christian view, humans were made in the image of God. It followed that our place in the universe was at the centre, with everything revolving around us. The Greeks’ original ordering of the universe was therefore inverted: the perfect stars of God’s creation were here on earth. The Greek Circle Model became the bible for the heavens—questioning it was like questioning the whole foundation of the Christian model of reality.
FIGURE 2.1. Leonardo da Vinci, The Proportions of the Human Figure (after Vitruvius), c. 1490.
The momentum for change—which would lead from the Dark Ages to a huge blossoming of science in the Enlightenment of the seventeenth and eighteenth centuries—came not from astronomers but from Renaissance figures such as Leonardo da Vinci. Leonardo—who was lauded by the poet Baldassare Taccone as a “geometer” as well as an artist, and spent as much time working on military inventions and engineering projects as he did on canvas— described his desire for knowledge as follows: “Unable to resist my eager desire and wanting to see the great [wealth] of the various and strange shapes made by formative nature, and having wandered some distance among gloomy rocks, I came to the entrance of a great cavern, in front of which I stood some time, astonished and unaware of such a thing. . . . [T]wo contrary emotions arose in me, fear and desire—fear of the threatening dark cavern, desire to see whether there were any marvellous things within it.”2
Renaissance artists like Leonardo created their works using both careful observations and mathematical theory (such as perspective techniques), and therefore elevated art to the same exalted level occupied by the classical, physical sciences. His 1490 work on human proportion (shown in figure 2.1 on page 53) is based on the only ancient work on the subject to have survived. The original, by Vitruvius, an architect and engineer during the time of the Roman Empire, positioned a man’s hands and feet at the c
orners of a square inscribed inside a circle, with the navel at the centre. The result was a man whose appendages were unnaturally distended, as though striving to comply with the demands of classical geometry. Leonardo’s version, which was informed by careful measurements that he carried out on actual people, adjusts the position of the square, as if to say that theory is great, but it has to agree with reality.
NEW WORLD ORDER
The New World independently developed agriculture, civilization, astronomy, and methods of prediction. The Mayan predictive system was based on the ancient Long Count calendar. It prophesied, among other things, that December 21, 2012, would mark the beginning of a new cycle of time; some associate this with a great purification, when the earth will cleanse itself and many living things will die. So that’s a good day to stay in.
The Aztec rulers of Yucatán, in pre-Columbian Mexico, predicted that 1519 would mark the birth of a blond, bearded deity known as Quetzalcóatl, or Feathered Serpent. That year, the Spaniard Hernán Cortés arrived with his army at what is now Veracruz. Cortés had blond hair and a beard. Believing their forecast had come true, the Aztecs greeted him as a god. It could have been the start of a great relationship, but unknown to Cortés, one of his men carried a different kind of serpent—smallpox. The Aztecs had no immunity; a quarter of their population is estimated to have died in the ensuing epidemic.
The impact of smallpox on the Incas was even stronger. The disease swept through their entire society within months, killing the emperor and much of the rest of the population. In 1636 it reached Lake Ontario, and by the end of that century millions of Native Americans had perished. The true conquistadors, the conquerors of America, were not men but microbes. (If smallpox had been a disease of the New World, instead of the Old, those age descriptions might have been different.) As discussed in Chapter 7, disease epidemics still sometimes come from where they are least expected.