In 334 B.C., Alexander, the twenty-two-year-old king of the Greek state of Macedon, led an army of seasoned citizen warriors across the Hellespont at the beginning of a long campaign to conquer the vast Persian Empire. By chance, as I write this, I myself have a twenty-two-year-old son whose name—Alexei—has the same Greek root. They say that kids grow up faster today than ever, but one thing I cannot imagine my Alexei doing is leading an army of seasoned Greek citizen warriors into Mesopotamia to confront the Persian Empire. There are several ancient accounts of how the young Macedonian king achieved his victory, most of which involve drinking large quantities of wine. However he did it, his long course of conquest took him all the way to the Khyber Pass and beyond. By the time he died at age thirty-three, he had accomplished enough in his brief existence that he has ever since been referred to as Alexander the Great.
At the time of Alexander’s invasion, the Near East was peppered with cities like Uruk that had existed for thousands of years. To put this in perspective: if the United States had been in existence as long as Uruk, we would now be on roughly our six hundredth president.
To walk the streets of those ancient cities Alexander conquered must have inspired awe, for one would have found oneself roaming among immense palaces, vast gardens irrigated by special channels, and grand stone buildings graced by columns topped with carvings of griffins and bulls. These were vibrant and complex societies, not at all in decline. Yet their cultures had been surpassed intellectually by the Greek-speaking world that conquered them, epitomized by its young leader—a man who had been schooled by Aristotle himself.
With the conquest of Mesopotamia by Alexander, the feeling that all things Greek were superior quickly spread throughout the Near East. Children, always at the vanguard of a cultural shift, learned the Greek language, memorized Greek poetry, and took up the sport of wrestling. Greek art grew popular in Persia. Berosus, a priest of Babylon, Sanchuniathon, a Phoenician, and Flavius Josephus, a Jew, all wrote histories of their people aimed at showing their compatibility with Greek ideas. Even taxes were Hellenized—they began to be recorded in the relatively new Greek alphabet, and on papyrus rather than in cuneiform on tablets. But the greatest aspect of the Greek culture that Alexander brought with him had nothing to do with arts or administration. It was what he had learned firsthand from Aristotle: a new, rational approach to the struggle to know our world, a magnificent turning point in the history of human ideas. And Aristotle himself was building on the ideas of several generations’ worth of scientists and philosophers who had begun to challenge the old verities about the universe.
In the early years of ancient Greece, the Greek understanding of nature was not very different from that of the Mesopotamians. Inclement weather might have been explained by saying that Zeus had indigestion, and if farmers had a bad crop, people would have thought it was because the gods were angry. There might not have been a creation myth stating that the earth is a droplet in the sneeze of the hay fever god, but there might as well have been, for, in the millennia after writing was invented, the body of recorded human words reveals a wild profusion of stories about how the world came into being and what forces governed it. What all had in common was the description of a turbulent universe created by an inscrutable god out of some type of formless void. The word “chaos” itself comes from the Greek term for the nothingness that was said to have preceded the creation of the universe.
If before creation all was chaos, after creating the world, the gods of Greek mythology didn’t seem to put a lot of energy into their effort to bring order to it. Lightning, windstorms, droughts, floods, earthquakes, volcanoes, infestations, accidents, disease—all these and many other irregular plagues of nature took their toll on human health and life. Egoistic, treacherous, and capricious, the gods were thought to be constantly causing calamities through their anger or just through carelessness, as if they were bulls in a china shop and we were the china. This is the primitive theory of the cosmos that passed orally from generation to generation in Greece, until finally being written down by Homer and Hesiod around 700 B.C., a century or so after writing finally spread to Greek culture. From then on, it was a staple of Greek education, forming the accepted wisdom of generations of thinkers.
For those of us living in modern society, the beneficiaries of a long history of scientific thought, it is difficult to understand how nature could have appeared this way to those ancient peoples. The idea of structure and order in nature seems as obvious to us as the idea that the gods controlled everything seemed to them. Today, our daily activities are quantitatively mapped, assigned certain hours and minutes. Our lands are delineated by latitude and longitude, our addresses marked by street names and numbers. Today, if the stock market goes down three points, a pundit will give us an explanation, such as that the decline was due to new worries over inflation. True, another expert might say it was due to developments in China, and a third may pin it on unusual sunspot activity, but, right or wrong, our explanations are expected to be based on cause and effect.
We demand from our world causality and order because these concepts are ingrained in our culture, in our very consciousness. Unlike us, however, the ancients lacked a mathematical and scientific tradition, and so the conceptual framework of modern science—the idea of precise numerical predictions, the notion that repeated experiments should give identical results, the use of time as a parameter to follow the unfolding of events—would have been difficult to grasp or accept. To the ancients nature appeared to be ruled by tumult, and to believe in orderly physical laws would have seemed as outlandish to them as the tales of their wild and capricious gods seem to us (or, perhaps, as our own dear theories will seem to historians who study them a thousand years from now).
Why should nature be predictable, explainable in terms of concepts that can be discovered by the human intellect? Albert Einstein, a man who wouldn’t have been surprised to find that the space-time continuum could be warped into the shape of a salted pretzel, was astonished by the much simpler fact that nature has order. He wrote that “one should expect a chaotic world, which cannot be grasped by the mind in any way.” But he went on to write that, contrary to his expectation, “the most incomprehensible thing about the universe is that it is comprehensible.”
Cattle don’t understand the forces that hold them to the earth, nor do crows know anything about the aerodynamics that give them flight. With his statement, Einstein was expressing a momentous and uniquely human observation: that order rules the world, and that the rules governing nature’s order don’t have to be explained by myths. They are knowable, and humans have the ability, unique among all the creatures on earth, to decipher nature’s blueprint. That lesson has profound implications, for if we can decipher the design of the universe, we can use that knowledge to understand our place in it, and we can seek to manipulate nature to create products and technologies that make our lives better.
The new rational approach to nature originated during the sixth century B.C., with a group of revolutionary thinkers who lived in greater Greece, on the shores of the Aegean, that large Mediterranean bay that separates present-day Greece and Turkey. Several hundred years before Aristotle, at the same time that Buddha was bringing a new philosophical tradition to India, and Confucius to China, these earliest of the Greek philosophers made the paradigmatic shift to viewing the universe as ordered, not random—as Cosmos, not Chaos. It is hard to overstate what a profound shift that was, or the degree to which it has shaped human consciousness ever since.
The area that gave rise to these radical thinkers was a magical land of grapevines, fig orchards, and olive trees and of prosperous, cosmopolitan cities. Those cities lay at the mouths of rivers and gulfs that emptied into the sea, and at the ends of roads that ran inland. According to Herodotus, it was a paradise where “the air and climate are the most beautiful in the whole world.” It was called Ionia.
The Greeks had founded many city-states on what is now the Greek mainland and in southern Italy, but they were merely provinces—the center of Greek civilization was in Turkish Ionia, just hundreds of miles west of Göbekli Tepe and Çatalhöyük. And the vanguard of the Greek enlightenment was to be found in the city of Miletus, located on the shores of a gulf, the Gulf of Latmus, which gave it access to the Aegean and hence the Mediterranean.
According to Herodotus, at the turn of the first millennium B.C. Miletus had been a modest settlement populated by Carians, a people of Minoan descent. Then, around 1000 B.C., soldiers from Athens and its vicinity overran the area. By 600 B.C. the new Miletus had become a kind of ancient New York City, attracting, from all over Greece, poor, hardworking refugees seeking a better life.
Over the centuries, the population of Miletus ballooned to 100,000, and the city developed into a center of great wealth and luxury, becoming the richest of the Ionian cities, indeed the richest city in the entire Greek world. From the Aegean, the fishermen of Miletus harvested bass, red mullet, and mussels. From the rich soil, farmers harvested corn and figs—the only fruit known to the Greeks that they could keep for any length of time—while orchards provided olives, for food as well as for pressing into oil, the ancient Greeks’ version of butter, soap, and fuel. What’s more, access to the sea made Miletus an important center of trade. Commodities like flax, timber, iron, and silver were brought in from the dozens of colonies the citizens of Miletus had established as far away as Egypt, while its skilled artisans created pottery, furniture, and fine woolens to ship abroad.
But Miletus was not just a crossroads for the exchange of goods; it was also a place for the sharing of ideas. Within the city, people from dozens of scattered cultures met and spoke, and Milesians also traveled widely, exposing them to many disparate languages and cultures. And so, as its inhabitants argued over the price of salted fish, tradition met tradition and superstition confronted superstition, creating an openness to new ways of thinking and fostering a culture of innovation—in particular, the all-important willingness to question conventional wisdom. What’s more, the wealth of Miletus created leisure, and with leisure came the freedom to devote time to pondering the issues of our existence. Thus, through the confluence of so many favorable circumstances, Miletus became a sophisticated, cosmopolitan paradise and a center of scholarship, creating a perfect storm of all the factors necessary for a revolution in thought.
It was in this environment, in Miletus and eventually in wider Ionia, that there emerged a group of thinkers who began to question the religious and mythological explanations of nature that had been passed down for thousands of years. They were the Copernicuses and Galileos of their day, the formative pioneers of both philosophy and science.
The first of these scholars, according to Aristotle, was a man named Thales, born around 624 B.C. Many Greek philosophers were said to live in poverty. Indeed, if ancient times were anything like today, even a famous philosopher could have achieved a more prosperous existence by finding a better job, like selling olives at the side of the road. Tradition has it, though, that Thales was an exception, a cunning and wealthy merchant who had no trouble financing his time to think and ponder. It is said that, in one instance, he made a fortune by cornering the market on olive presses and then charging exorbitant prices for the oil, like a one-man OPEC. He is also said to have been very involved in his city’s politics and to have known its dictator, Thrasybulus, intimately.
Thales used his wealth to travel. In Egypt, he found that although the Egyptians had the expertise to build the pyramids, they lacked the insight to measure their height. As we’ve seen, however, they had developed a novel set of mathematical rules that they used to determine the area of plots of land for purposes of taxation. Thales adapted those Egyptian techniques of geometry to calculate the heights of the pyramids—and also showed how, using them, one could determine the distance of ships at sea. This made him quite a celebrity in ancient Egypt.
When Thales returned to Greece, he brought Egyptian mathematics with him, translating its name to his native tongue. But in Thales’s hands, geometry was not just a tool for measuring and calculating; it was a body of theorems connected by logical deduction. He was the first to prove geometric truths, rather than simply stating as facts conclusions that seemed to work, and the great geometer Euclid would later include some of Thales’s theorems in his Elements. Still, as impressive as Thales’s mathematical insight was, his real claim to fame was his approach to explaining the phenomena of the physical world.
Nature, in Thales’s view, wasn’t the stuff of mythology; it operated according to principles of science that could be used to explain and predict all the phenomena hitherto attributable to the intervention of the gods. He was said to be the first person to understand the cause of eclipses, and he was the first Greek to propose that the moon shone by reflected sunlight.
Even when he was off base, Thales was remarkable in the originality of his thinking and his ideas. Consider his explanation of earthquakes. In Thales’s day, these were thought to occur when the god Poseidon became irritated and struck the earth with his trident. But Thales held what must have seemed like an oddball view: that earthquakes had nothing to do with the gods. His explanation wasn’t one I’d hear from any of my Caltech seismologist friends—he believed that the world was a hemisphere floating on an endless expanse of water, and that earthquakes occurred when the water sloshed around. Thales’s analysis is nonetheless groundbreaking in its implications, because he attempted to account for earthquakes as a consequence of a natural process, and he employed empirical and logical arguments to back up his idea. Perhaps most important of all is his having focused on the question of why earthquakes occur in the first place.
In 1903, the poet Rainer Maria Rilke gave advice to a student that holds as true for science as it does for poetry: “Be patient toward all that is unsolved in your heart and try to love the questions,” he wrote, and “live the questions.” The greatest skill in science (and often in business as well) is the ability to ask the right questions—and Thales practically invented the idea of asking scientific questions. Everywhere he looked, including in the heavens, he saw phenomena that begged to be explained, and his intuition led him to ponder phenomena that would eventually shed light on the fundamental workings of nature. He asked questions not just about earthquakes but about the size and shape of the earth, the dates of the solstices, and the relation of the earth to the sun and moon—the very same questions that two thousand years later led Isaac Newton to his great discovery of gravity and the laws of motion.
In acknowledgment of what a radical break with the past Thales had made, Aristotle referred to Thales and later Ionian thinkers as the first of the physikoi, or physicists—the group to which I am proud to belong, and to which Aristotle felt he himself belonged. The term comes from the Greek physis, meaning “nature,” a term Aristotle chose to describe those who sought natural explanations for phenomena, in contrast to the theologoi, or theologians, who sought supernatural explanations.
Aristotle had less admiration, however, for members of another radical group: those who used mathematics to model nature. Credit for that innovation goes to a thinker of the generation following Thales, who lived not far away from him on the Aegean island of Samos.
Some of us spend our work hours trying to understand how the universe functions. Others haven’t mastered algebra. In Thales’s day, members of the former group were also members of the latter, for, as we’ve seen, algebra as we know it—and most of the rest of mathematics—hadn’t yet been invented.
To today’s scientist, understanding nature without equations would be like trying to understand your partner’s feelings when all he ever says is “I’m fine.” For mathematics is the vocabulary of science—it is how a theoretical idea communicates. We scientists may not always be good at using language to reveal intimate personal thoughts, but we’ve gotten very adept at communicating our theories through mathematics. The language of mathematics enables science to delve deeper into theories, and with more insight and precision than ordinary language, for it is a language with built-in rules of reasoning and logic that keep extending the meaning, allowing it to unfold and reverberate in sometimes quite unexpected ways.
Poets describe their observations through language; physicists describe theirs with math. When a poet completes a poem, the poet’s job is done. But when the physicist sets down a mathematical “poem,” that is just the beginning of the job. By applying the rules and theorems of mathematics, the physicist must then coax that poem into revealing new lessons of nature that its own author might never have imagined. For equations not only embody ideas; they offer the consequences of those ideas to anyone with sufficient skill and persistence to extract them. That is what the language of mathematics achieves: it facilitates the expression of physical principles, it illuminates the relationships between them, and it guides human reasoning about them.
At the beginning of the sixth century B.C., however, no one knew this. The human species hadn’t yet come up with the idea that mathematics could help us understand how nature operates. It was Pythagoras (c. 570–c. 490 B.C.)—founder of Greek mathematics, inventor of the term “philosophy,” and curse of middle school students the world round who must stop texting long enough to learn the meaning of a2 + b2 = c2—who is said to have first helped us use mathematics as the language of scientific ideas.
The name Pythagoras, in ancient times, not only was associated with genius but also carried a magical and religious aura. He was looked upon as Einstein might have been had he been not just a physicist but also the pope. We have, from many later writers, a lot of information on the life of Pythagoras, and several biographies. But by the first centuries after Christ, the tales had become unreliable, tainted by ulterior religious and political motives that caused writers to distort his ideas and magnify his place in history.
One thing that does seem to be true is that Pythagoras grew up on Samos, across the bay from Miletus. Also, all his ancient biographers agree that sometime between the ages of eighteen and twenty Pythagoras visited Thales, who was by then very old and near death. Aware that his earlier brilliance had faded considerably, Thales is said to have apologized for his diminished mental state. Whatever lessons Thales imparted, Pythagoras went away impressed. Many years later, he could sometimes be spotted sitting at home, singing songs of praise to his late teacher.
Like Thales, Pythagoras traveled a great deal, probably to Egypt, Babylon, and Phoenicia. He left Samos at age forty, finding life under the island’s tyrant, Polycrates, unbearable, and landed in Croton, in what is now southern Italy. There, he attracted a large number of followers. It was also there that he was said to have had his epiphany about the mathematical ordering of the physical world.
Nobody knows how language was first developed, though I have always imagined some caveman stubbing his toe and spontaneously blurting, Ow!, at which time someone thought, What a novel way to express one’s feelings, and soon everyone was talking. The origin of mathematics as the language of science is also shrouded in mystery; but in that case we do at least have a legend that describes it.
According to the legend, while walking past a blacksmith’s shop one day, Pythagoras heard the sound of the blacksmith’s hammers ringing out, and he noticed a pattern in the tones produced by different hammers pounding on the iron. Pythagoras ran into the forge and experimented with the hammers, noting that the differences in tone did not depend on the force employed by the man delivering the blow, nor on the precise shape of the hammer, but rather on the hammer’s size or, equivalently, its weight.
Pythagoras returned home and continued his experimentation, not on hammers but on strings of different lengths and tensions. He had, like other Greek youths, been schooled in music, especially the flute and the lyre. Greek musical instruments at the time were the product of guesswork, experience, and intuition. But in his experiments Pythagoras is said to have discovered a mathematical law governing stringed instruments that could be used to define a precise relationship between the length of musical strings and the tones they produce.
Today we would describe the Pythagorean relation by saying that the frequency of the tone is inversely proportional to the length of the string. Suppose, for example, that a string produces a certain note when plucked. Hold the string down at the halfway point and it produces a note one octave higher—that is, of twice the frequency. Hold it down at one-fourth the length and the tone goes up another octave, to four times the original frequency.
Did Pythagoras actually discover this relationship? No one knows to what extent the legends about Pythagoras are true. For example, he probably did not prove the “Pythagorean theorem” that plagues middle school students—it is believed that it was one of his followers who first proved it, but the formula had already been known for centuries. Regardless, the real contribution of Pythagoras was not in deriving any specific laws but in promoting the idea of a cosmos that was structured according to numerical relationships, and his influence came not from discovering the mathematical connections in nature but from celebrating them. As classicist Carl Huffman put it, Pythagoras was important “for the honor he gives to number and for removing it from the practical realm of trade and instead pointing to correspondences between the behavior of number and the behavior of things.”
Where Thales said that nature follows orderly rules, Pythagoras went even further, asserting that nature follows mathematical rules. He preached that it is mathematical law that is the fundamental truth about the universe. Number, the Pythagoreans believed, is the essence of reality.
Pythagoras’s ideas had a great influence on later Greek thinkers—most notably on Plato—and on scientists and philosophers throughout Europe. But of all the Greek champions of reason, of all the great Greek scholars who believed that the universe could be understood through rational analysis, by far the most influential as far as the future development of science is concerned was not Thales, who invented the approach, nor Pythagoras, who brought mathematics to it, nor even Plato, but rather that student of Plato’s who later became the tutor of Alexander the Great: Aristotle.
Born in Stagira, a town in northeastern Greece, Aristotle (384–322 B.C.) was the son of a man who had been the personal physician to Alexander’s grandfather, King Amyntas. He was orphaned young and sent to Athens to study at Plato’s Academy when he was seventeen. After Plato, the word “academy” came to mean a place of learning, but in his day it was simply the name of a public garden on the outskirts of Athens that harbored the grove of trees where Plato and his students liked to assemble. Aristotle remained there for twenty years.
At Plato’s death, in 347 B.C., Aristotle left the Academy, and a few years later he became Alexander’s tutor. It’s unclear why King Philip II chose him to tutor his son, since Aristotle had not yet made his reputation. To Aristotle, though, becoming the tutor of the heir apparent to the king of Macedon must have seemed like a good idea. He was paid handsomely, and reaped other benefits when Alexander went on to conquer Persia and much of the rest of the world. But after Alexander succeeded to the throne, Aristotle, then nearly fifty, returned to Athens, where, over the course of thirteen years, he produced most of the works for which he is known. He never again saw Alexander.
The kind of science that Aristotle taught probably wouldn’t have been identical to what he himself had learned from Plato. Aristotle was a prize pupil at the Academy, but he was never comfortable with Plato’s emphasis on mathematics. His own bent was toward detailed, natural observation, not abstract laws—very different both from Plato’s kind of science and from science as it is practiced today.
When I was in high school, I loved my courses in chemistry and physics. Seeing how passionate I was about them, my father sometimes asked me to explain those sciences to him. Coming from a poor Jewish family that could afford to send him only to the local religious school, he had gotten an education focused more on theories of the Sabbath than on theories of science, and since he had never progressed beyond the seventh grade, I had my work cut out for me.
I began our exploration by saying that physics is largely the study of one thing: change. My father pondered for a moment and then grunted. “You know nothing of change,” he told me. “You’re too young, and you’ve never experienced it.” I protested that of course I’d experienced change, but he answered with one of those old Yiddish expressions that sounds either deep or idiotic, depending on your tolerance level for old Yiddish expressions. “There is change,” he said, “and there is change.”
I dismissed his aphorism in the way only a teenager can. In physics, I said, there is not change and change—there is only CHANGE. In fact, one might say that Isaac Newton’s central contribution in creating physics as we know it today was his invention of a unified mathematical approach that could be used to describe all change, whatever its nature. Aristotle’s physics—which originated in Athens two thousand years before Newton—has its roots in a far more intuitive and less mathematical approach to understanding the world, which I thought might be more accessible to my father. And so, hoping I would find something there that would make it easier to explain things to him, I began to read about Aristotle’s concept of change. After much effort, I learned that although Aristotle spoke Greek and had never uttered a word of Yiddish, what he essentially believed was this: “There is change, and there is change.”
In my father’s version, the second invocation of the word “change” sounded ominous, and he meant it to convey the kind of violent change he had experienced when the Nazis invaded. That distinction between ordinary or natural change, on the one hand, and violent change, on the other, is the same distinction that Aristotle made: he believed that all transformations one observes in nature could be categorized as either natural or violent.
In Aristotle’s theory of the world, natural change was that which originated within the object itself. In other words, the cause of natural change is intrinsic to the nature or composition of the object. For example, consider the type of change we call motion—the change of position. Aristotle believed that everything is made of various combinations of four fundamental elements—earth, air, fire, and water—each of which has a built-in tendency to move. Rocks fall toward the earth and rain falls toward the oceans, according to Aristotle, because the earth and sea are the natural resting places of those substances. To cause a rock to fly upward requires external intervention, but when a rock falls, it is following its built-in tendency and executing “natural” motion.
In modern physics, no cause is required to explain why an object remains at rest or in uniform motion with a constant speed and direction. Similarly, in Aristotle’s physics, it was not necessary to explain why objects execute natural motion—why things made of earth and water fall, or why air and fire rise. This analysis reflects what we see in the world around us—in which bubbles rise out of water, flames seem to rise into the air, massive objects fall from the sky, oceans and seas rest upon the land, and the atmosphere lies above all.
To Aristotle, motion was but one of many natural processes, like growth, decay, and fermentation, all of which are governed by the same principles. He viewed natural change, in all its various forms—the burning of a log, the aging of a person, the flight of a bird, the falling of an acorn—as the fulfillment of inherent potential. Natural change, in Aristotle’s system of beliefs, is what propels us through our daily lives. It is the kind of change that wouldn’t raise eyebrows, that we tend to take for granted.
But sometimes the natural course of events is disrupted, and motion, or change, is imposed by something external. This is what happens when a rock is tossed into the air, when grapevines are ripped out of the earth or chickens slaughtered for food, or when you lose your job, or fascists take over a continent. These are the kinds of change that Aristotle termed “violent.”
In violent change, according to Aristotle, an object changes or moves in a direction that violates its nature. Aristotle sought to understand the cause of that kind of change, and he chose a term for it: he called it “force.”
Like his concept of natural change, Aristotle’s doctrine of violent change corresponds well with what we observe in nature—solid matter, for example, plummets downward on its own, but to get it going in any other direction, such as upward or sideways, requires force, or effort.
Aristotle’s analysis of change was remarkable because although he saw the same environmental phenomena as the other great thinkers of his time, unlike the others, he rolled up his sleeves and made observations about change in unprecedented and encyclopedic detail—the changes both in people’s lives and in nature. Trying to discover what all the different kinds of change have in common, he studied the causes of accidents, the dynamics of politics, the motion of oxen hauling heavy burdens, the growth of chicken embryos, the eruption of volcanoes, the alterations in the Nile River delta, the nature of sunlight, the rising of heat, the motion of the planets, the evaporation of water, the digestion of food in animals with multiple stomachs, the way things melt and burn. He dissected animals of all sorts, sometimes far past their sell-by dates, but if others objected to the foul smell, he simply scoffed.
Aristotle called his attempt to create a systematic account of change Physics—thus associating himself with the heritage of Thales. His physics was vast in scope, encompassing both the living and the inanimate, and the phenomena of both the heavens and the earth. Today the different categories of change he studied are the subjects of entire branches of science: physics, astronomy, climatology, biology, embryology, sociology, and so on. In fact, Aristotle was a prolific writer—a veritable one-man Wikipedia. His contributions include some of the most comprehensive studies ever undertaken by a person never diagnosed with OCD. All told, he produced—according to records from antiquity—170 scholarly works, about one-third of which have been preserved until today. There was Meteorology; Metaphysics; Ethics; Politics; Rhetoric; Poetics; On the Heavens; On Generation and Corruption; On the Soul; On Memory; On Sleep and Sleeplessness; On Dreams; On Prophesying, Longevity, Youth and Age; On the History and Parts of Animals; and on and on.
While his former pupil Alexander went on to conquer Asia, Aristotle returned to Athens and established a school called the Lyceum. There, while strolling along a public walk or pacing in a garden, he would teach his students what he had learned over the years.* But though he was a great teacher and a brilliant and prolific observer of nature, Aristotle’s approach to knowledge was far different from the approach of what we call science today.
According to philosopher Bertrand Russell, Aristotle was “the first to write like a professor … a professional teacher, not an inspired prophet.” Russell said that Aristotle is Plato “diluted by common sense.” Indeed, Aristotle placed a great value on that trait. Most of us do. It’s what keeps us from responding to those kind fellows in Nigeria whose emails promise that if we wire them one thousand dollars today, they will wire us one hundred billion dollars tomorrow. However, looking back on Aristotle’s ideas, and knowing what we know now, one might argue that it is precisely in Aristotle’s devotion to conventional ideas that we find one of the greatest differences between today’s approach to science and Aristotle’s—and one of the greatest shortcomings of Aristotelian physics. For though common sense is not to be ignored, sometimes what is needed is uncommon sense.
In science, in order to make progress, you often have to defy what historian Daniel Boorstin referred to as “the tyranny of common sense.” It is common sense, for example, that if you push an object it will slide, then slow down and stop. But to perceive the underlying laws of motion, you must look beyond the obvious, as Newton did, and envision how an object in a theoretically frictionless world would move. Similarly, to understand the ultimate mechanism of friction, you must be able to look past the facade of the material world, to “see” how objects might be made of invisible atoms, a concept that had been proposed by Leucippus and Democritus about a century earlier, but which Aristotle did not accept.
Aristotle also showed great deference to common opinion, to the institutions and ideas of his time. He wrote, “What everyone believes is true.” And to the doubters, he said, “Whoever destroys this faith will hardly find a more credible one.” A vivid example of Aristotle’s reliance on conventional wisdom—and the way it distorted his vision—is his somewhat tortured argument that slavery, which he and most of his fellow citizens accepted, is inherent in the nature of the physical world. Employing the kind of argument that is strangely reminiscent of his writings in physics, Aristotle asserted that “in all things which form a composite whole and which are made up of parts … a distinction between the ruling and the subject element comes to light. Such a duality exists in living creatures, but not in them only; it originates in the constitution of the universe.” Because of that duality, Aristotle argued, there are men who are, by their nature, free, and men who are by nature slaves.
Today scientists and other innovators are often portrayed as odd and unconventional. I suppose there is some truth to that stereotype. One physics professor I knew selected his lunch each day from the free offerings at the cafeteria’s condiments table. Mayonnaise provided fat, ketchup was his vegetable, and saltines his carbs. Another friend loved cold cuts but hated bread, and at a restaurant had no qualms ordering for lunch a lonely pile of salami, which he would eat with a knife and fork as if it were a steak.
Conventional thinking is not a good attitude for a scientist—or anyone who wants to innovate—and sometimes that has its costs in the way people view you. But as we will see repeatedly, science is the natural enemy of preconceived notions, and of authority, even the authority of the scientific establishment itself. For revolutionary breakthroughs necessarily require a willingness to fly in the face of what everyone else believes to be true, to replace old ideas with credible new ones. In fact, if there is one barrier to progress that stands out in the history of science, and of human thought in general, it is an undue allegiance to the ideas of the past—and present. And so if I were hiring for a creative position, I’d beware of too much common sense, but I’d count oddball traits in the plus column, and keep that condiments table well supplied.
Another important clash between Aristotle’s approach and that of later science is that it was qualitative, not quantitative. Today physics is, even in its simple high school form, a science of quantity. Students taking even the most elementary versions of physics learn that a car moving sixty miles per hour is going eighty-eight feet each second. They learn that if you drop an apple, its speed will increase by twenty-two miles per hour each second that it falls. They do mathematical calculations such as computing that when you plop down into a chair, the force exerted on your spine as the chair stops you can be—for a split second—more than a thousand pounds. Aristotle’s physics was nothing like that. On the contrary, he complained loudly about philosophers who sought to turn philosophy “into mathematics.”
Any attempt to turn natural philosophy into a quantitative pursuit in Aristotle’s day was, of course, impeded by the state of knowledge in ancient Greece. Aristotle had no stopwatch, no clock with a second hand, nor was he ever exposed to thinking of events in terms of their precise durations. Also, the fields of algebra and arithmetic that would be needed to manipulate such data were no more advanced than they had been in Thales’s time. As we’ve seen, the plus, minus, and equal signs had not yet been invented, nor had our number system or concepts like “miles per hour.” But scholars in the thirteenth century and later made progress in quantitative physics with instruments and mathematics that were not terribly more advanced, so these were not the only barriers to a science of equations, measurement, and numerical prediction. More important was the fact that Aristotle was, like everyone else, simply not interested in quantitative description.
Even when studying motion, Aristotle’s analysis was only qualitative. For example, he had just a vague understanding of speed—as in “some things go farther than others in a similar amount of time.” That sounds to us like a message we might find inside a fortune cookie, but in Aristotle’s time, people considered it precise enough. And with only a qualitative notion of speed, there could be only the foggiest notion of acceleration, which is change in speed or direction—and which we teach as early as middle school. Given these profound differences, if someone with a time machine had gone back and given Aristotle a text on Newton’s physics, it would have meant no more to him than a book of microwave pasta recipes. Not only would he have been unable to understand what Newton meant by “force” or “acceleration”—he would not have cared.
What did interest Aristotle, as he conducted his thorough observations, was that motion and other kinds of change seemed to happen toward some end. He understood movement, for example, not as something to be measured but as a phenomenon whose purpose could be discerned. A horse pulls on a cart to move it down the road; a goat walks in order to find food; a mouse runs to avoid being eaten; boy rabbits defile girl rabbits to make more rabbits.
Aristotle believed that the universe was one large ecosystem designed to function harmoniously. He saw purpose everywhere he looked. Rain falls because plants need water to grow. Plants grow so that animals can eat them. Grape seeds grow into grapevines, and eggs turn into chickens, to actualize the potential that exists within those seeds and eggs. From time immemorial, people had always arrived at their understanding of the world through projections of their own experience. And so it was that in ancient Greece it was far more natural to analyze the purpose of events in the physical world than it would have been to try to explain them through the mathematical laws being developed by Pythagoras and his followers.
Here again we see the importance in science of the particular questions you choose to ask. For even if Aristotle had embraced Pythagoras’s notion that nature obeys quantitative laws, he would have missed the point, because he was simply less interested in the quantitative specifics of the laws than in the question of why objects follow them. What compels the string in a musical instrument, or a falling rock, to behave with numerical regularity? These were the issues that would have excited Aristotle, and it is here that we see the greatest disconnect between his philosophy and the way science is conducted now—for while Aristotle perceived what he interpreted as purpose in nature, today’s science does not.
That characteristic of Aristotle’s analysis—his search for purpose—had a huge influence on later human thought. It would endear him to many Christian philosophers through the ages, but it impeded scientific progress for nearly two thousand years, for it was completely incompatible with the powerful principles of science that guide our research today. When two billiard balls collide, the laws that were first set forth by Newton—not a grand underlying purpose—determine what happens next.
Science first arose from the fundamental human desire to know our world and to find meaning in it, so it’s not surprising that the yearning for purpose that motivated Aristotle still resonates with many people today. The idea that “everything happens for a reason” may give comfort to those seeking to understand a natural disaster or other tragedy. And for such people the scientist’s insistence that the universe is not guided by any sense of purpose can make the discipline of science seem cold and soulless.
Yet there is another way of looking at this, and it’s one that I am familiar with from my father. When the issue of purpose would arise, my father often referred not to anything that had befallen him but to a particular incident my mother had experienced before they met, when she was just seventeen. The Nazis had occupied her city, and one of them, for a reason my mother never knew, ordered a few dozen Jews, my mother among them, to kneel in a neat row in the snow. He then walked from one end to the other, stopping every few steps to shoot one of his captives through the head. If this was part of God’s or nature’s grand plan, my father wanted nothing to do with such a God. For people like my father, there can be relief in the thought that our lives, however tragic or triumphant they may be, are all the result of the same indifferent laws that create exploding stars and that, good or bad, they are ultimately a gift, a miracle that somehow springs from those sterile equations that rule our world.
Though Aristotle’s ideas dominated thinking about the natural world until Newton’s day, over the years there were plenty of observers who cast doubt on his theories. For example, consider the idea that objects not executing their natural motion will move only when a force is acting upon them. Aristotle himself realized that this raised the question of what propels an arrow, a javelin, or any other projectile after the initial impetus. His explanation was that, due to the fact that nature “abhors” a vacuum, particles of air rush in behind the projectile after the initial impetus and push it along. The Japanese seem to have successfully adapted that idea to pack passengers into Tokyo subway cars, but even Aristotle himself was only lukewarm about his theory. Its weakness became more obvious than ever during the fourteenth century, when the proliferation of cannons made the idea of air particles rushing behind heavy cannonballs to push them along seem absurd.
Just as important, the soldiers firing those cannons cared little about whether it was particles of air or tiny, invisible nymphs that pushed their cannonballs along. What they did desire to know was the trajectory their projectiles would follow, and in particular whether that trajectory would end on the heads of their enemies. This disconnect illustrates the real chasm that stood between Aristotle and those who would later call themselves scientists: issues like the trajectory of a projectile—its speed and position at various instants—were, for Aristotle, beside the point. But if one wants to apply the laws of physics to make predictions, then those issues are critical. And so the sciences that would eventually replace Aristotle’s physics, the ones that would make it possible, among other things, to calculate the trajectory of a cannonball, were concerned with the quantitative details of the processes at work in the world—measurable forces, speeds, and rates of acceleration—not with the purpose or philosophical reasons for those processes.
Aristotle knew that his physics was not perfect. He wrote, “Mine is the first step and therefore a small one, though worked out with much thought and hard labor. It must be looked at as a first step, and judged with indulgence. You, my readers or hearers of my lectures, if you think I have done as much as can fairly be expected of an initial start … will acknowledge what I have achieved and will pardon what I have left for others to accomplish.” Here Aristotle is voicing a feeling he shared with most of the later geniuses of physics. We think of them, the Newtons and Einsteins, as all-knowing, and confident, even arrogant, about their knowledge. But as we’ll see, like Aristotle, they were confused about a lot of things, and, also like Aristotle, they knew it.
Aristotle died in 322 B.C., at age sixty-two, apparently of a stomach ailment. A year earlier, he had fled Athens when its pro-Macedonian government was overthrown after the death of his former student Alexander. Though Aristotle spent twenty years in Plato’s Academy, he had always felt like an outsider in Athens. Of that city, he wrote, “the same things are not proper for a stranger as for a citizen; it is difficult to stay.” With Alexander gone, however, the issue of whether to stay became a critical one, for there was a dangerous backlash directed at anyone associated with Macedon, and Aristotle was aware that the politically motivated execution of Socrates had established the precedent that a cup of hemlock is a potent rebuttal to any philosophical argument. Always the deep thinker, Aristotle had the idea to run rather than risk becoming a martyr. He supplied a lofty reason for his decision—to keep the Athenians from once again sinning “against philosophy”—but the decision, like Aristotle’s approach to life in general, was a very practical one.
After Aristotle’s death, his ideas were passed along by generations of students at the Lyceum and by others who wrote commentaries on his works. His theories faded, along with all learning, during the early Middle Ages but became prominent again during the High Middle Ages among Arab philosophers, from whom later Western scholars learned of it. With some modifications, his thinking eventually became the official philosophy of the Roman Catholic Church. And so, for the next nineteen centuries, to study nature meant to study Aristotle.
We’ve seen how our species developed both a brain for asking questions and a propensity to ask them, as well as the tools—writing, mathematics, and the idea of laws—with which to begin to answer them. With the Greeks, by learning to use reason to analyze the cosmos, we reached the shores of a glorious new world of science. But that was only the beginning of a greater adventure of exploration that lay ahead.
*Afterward, the students would be rubbed with oil. I’ve always thought that offering an option like that would be an easy way to increase my popularity with my own students, but unfortunately it would probably have the opposite effect on the university administration.
