What is Democritus's place in the history of philosophy? Not very high by conventional standards—certainly not high compared with that of virtual contemporaries such as Socrates, Aristotle, and Plato. Some historians treat his atomic theory as a kind of curious footnote to Greek philosophy. Yet there is at least one potent minority opinion. The British philosopher Bertrand Russell said that philosophy went downhill after Democritus and did not recover until the Renaissance. Democritus and his predecessors were "engaged in a disinterested effort to understand the world," wrote Russell. Their attitude was "imaginative and vigorous and filled with the delight of adventure. They were interested in everything—meteors and eclipses, fishes and whirlwinds, religion and morality; with a penetrating intellect they combined the zest of children." They were not superstitious but genuinely scientific, and they were not greatly influenced by the prejudices of their age.
Of course Russell, like Democritus, was a serious mathematician, and these guys stick together. It's only natural that a mathematician would have a bias toward such rigorous thinkers as Democritus, Leucippus, and Empedocles. Russell pointed out that although Aristotle and others reproached the atomists for not accounting for the original motion of the atoms, Leucippus and Democritus were far more scientific than their critics by not bothering to ascribe purpose to the universe. The atomists knew that causation must start from something, and that no cause can be assigned to this original something. Motion was simply a given. The atomists asked mechanistic questions and gave mechanistic answers. When they asked "Why?" they meant: what was the cause of an event? When their successors—Plato, Aristotle, and so on—asked "Why?" they were searching for the purpose of an event. Unfortunately, this latter course of inquiry, said Russell, "usually arrives, before long, at a Creator, or at least an Artificer." This Creator must then be left unaccounted for, unless one wishes to posit a super-Creator, and so on. This kind of thinking, said Russell, led science up a blind alley, where it remained trapped for centuries.
Where do we stand today compared to Greece circa 400 B.C.? Today's experiment-driven "standard model" is not all that dissimilar to Democritus's speculative atomic theory. We can make anything in the past or present universe, from chicken soup to neutron stars, with just twelve particles of matter. Our a-toms come in two families: six quarks and six leptons. The six quarks are named the up, the down, the charm, the strange, the top (or truth), and the bottom (or beauty). The leptons include the familiar electron, the electron neutrino, the muon, the muon neutrino, the tau, and the tau neutrino.
But note that we said "past or present" universe. If we're talking about our present environment only, from the South Side of Chicago to the edge of the universe, we can get by nicely with even fewer particles. For quarks, all we really need are the up and the down, which can be used in different combinations to assemble the nucleus of the atom (the kind in the periodic table). Among the leptons, we can't live without the good old electron, which "orbits" the nucleus, and the neutrino, which is essential in many kinds of reactions. But why do we need the muon and the tau particles? Or the charm, the strange, and the heavier quarks? Yes, we can make them in our accelerators or observe them in cosmic ray collisions. But why are they here? More about these "extra" a-toms later.
LOOKING THROUGH THE KALEIDOSCOPE
The fortunes of atomism went through a lot of ups and downs, fits and starts, before we arrived at our standard model. It started with Thales saying all is water (atom count: 1). Empedocles came up with air-earth-fire-water (count: 4). Democritus had an uncomfortable number of shapes but only one concept (count: ?). Then there was a long historical pause, although atoms remained a philosophical concept discussed as such by Lucretius, Newton, Roger Joseph Boscovich, and many others. Finally atoms were reduced to experimental necessity by John Dalton in 1803. Then, firmly in the hands of chemists, the number of atoms increased—20, 48, and by the early years of this century, 92. Soon nuclear chemists began making new ones (count: 112 and rising). Lord Rutherford took a giant step back to simplicity when he discovered (circa 1910) that Dalton's atom wasn't indivisible but contained a nucleus plus electrons (count: 2). Oh yes, there was also the photon (count: 3). In 1930, the nucleus was found to house neutrons as well as protons (count: 4). Today, we have 6 quarks, 6 leptons, 12 gauge bosons and, if you want to be mean, you can count the antiparticles and the colors, because quarks come in three shades (count: 60). But who's counting?
History suggests that we may find things, call them "prequarks," thus reducing the total number of basic building blocks. But history isn't always right. The newer concept is that we are looking through a glass, darkly—that the proliferation of "a-toms" in our standard model is a consequence of how we look. A children's toy, the kaleidoscope, shows lovely patterns by using mirrors to add complexity to a simple pattern. A star pattern is seen to be an artifact of a gravitational lens. As now conceived, the Higgs boson—the God Particle—may well provide the mechanism that reveals a simple world of pristine symmetry behind our increasingly complex standard model.
This brings us back to an old philosophical debate. Is this universe real? If so, can we know it? Theorists don't often grapple with this problem. They simply accept objective reality at face value, like Democritus, and go about their calculations. (A smart choice if you're going to get anywhere with a pencil and pad.) But an experimenter, tormented by the frailty of his instruments and his senses, can break out in a cold sweat over the task of measuring this reality, which can be a slippery thing when you lay a ruler down on it. Sometimes the numbers that come out of an experiment are so strange and unexpected that they raise the hairs on a physicist's neck.
Take this problem of mass. The data we have gathered on the masses of the quarks and the W and Z particles are absolutely baffling. The leptons—the electron, muon, and tau—present us with particles that appear identical in every way except for their mass. Is mass real? Or is it an illusion, an artifact of the cosmic environment? One opinion bubbling up in the literature of the 1980s and '90s is that something pervades this empty space and provides atoms with an illusory weight. That "something" will one day manifest itself in our instruments as a particle.
In the meantime, nothing exists except atoms and empty space; everything else is opinion.
I can hear old Democritus giggling.
Interlude A
A Tale of Two Cities
3. LOOKING FOR THE ATOM: THE MECHANICS
To you who are preparing to mark the 350th anniversary of the publication of Galileo Galilei's great work, Dialoghi sui due massimi sistemi del mondo, I would like to say that the Church's experience, during the Galileo affair and after it, has led to a more mature attitude and to a more accurate grasp of the authority proper to her. I repeat before you what I stated before the Pontifical Academy of Sciences on 10 November 1979: "I hope that theologians, scholars and historians, animated by a spirit of sincere collaboration, will study the Galileo case more deeply and, in frank recognition of wrongs, from whichever side they come, will dispel the mistrust that still forms an obstacle, in the minds of many, to a fruitful concord between science and faith."
—His Holiness Pope John Paul II, 1986
VINCENZO GALILEI hated mathematicians. This might seem odd, since he was a highly skilled mathematician himself. First and foremost, however, he was a musician, a lutenist of great repute in sixteenth-century Florence. In the 1580s he turned his skills to musical theory and found it lacking. The blame, said Vincenzo, lay with a mathematician who had been dead for two thousand years, Pythagoras.
Pythagoras, a mystic, was born on the Greek island of Samos about a century before Democritus. He spent most of his life in Italy, where he organized the Pythagoreans, a kind of secret society of men who held a religious regard for numbers and whose lives were governed by a set of obsessive taboos. They refused to eat beans or to pick up objects they had dropped. When they awakened in the morning, they took care to smooth out the sheets to eradicate the impressio
ns of their bodies. They believed in reincarnation, refusing to eat or beat dogs in case they might be long-lost friends.
They were obsessed with numbers. They believed that things were numbers. Not just that objects could be enumerated, but that they were numbers, such as 1, 2, 7, or 32. Pythagoras thought of numbers as shapes and came up with the idea of squares and cubes of numbers, terms that stay with us today. (He also talked about "oblong" and "triangular" numbers, terms we no longer think about.)
Pythagoras was the first to divine a great truth about right triangles. He pointed out that the sum of the squares of the sides is equal to the square of the hypotenuse, a formula that is hammered into every teenage brain that wanders into a geometry classroom from Des Moines to Ulan Bator. This reminds me of the time one of my students was conscripted into the army and, with a group of fellow buck privates, was being lectured about the metric system by his sergeant.
SERGEANT: In the metric system water boils at ninety degrees.
PRIVATE: Begging your pardon, sir, it boils at one hundred degrees.
SERGEANT: Of course. How stupid of me. It's a right angle that boils at ninety degrees.
The Pythagoreans loved to study ratios, proportions. They came up with the "golden rectangle," the perfect shape, whose proportions are evident in the Parthenon and many other Greek structures and found in Renaissance paintings.
Pythagoras was the first cosmic guy. It was he (and not Carl Sagan) who coined the word kosmos to refer to everything in our universe, from human beings to the earth to the whirling stars overhead. Kosmos is an untranslatable Greek word that denotes the qualities of order and beauty. The universe is a kosmos, he said, an ordered whole, and each of us humans is also a kosmos (some more than others).
If Pythagoras were alive today, he would live in the Malibu hills or perhaps Marin County. He'd hang out at health-food restaurants accompanied by an avid following of bean-hating young women with names like Sundance Acacia or Princess Gaia. Or maybe he'd be an adjunct professor of mathematics at the University of California at Santa Cruz.
But I digress. The crucial fact for our story is that the Pythagoreans were lovers of music, to which they brought their obsession with numbers. Pythagoras believed consonance in music depended on "sonorous numbers." He claimed that the perfect consonances were intervals of the musical scale that can be expressed as ratios between the numbers 1, 2, 3, and 4. These numbers add up to 10, the perfect number in the Pythagorean world view. The Pythagoreans brought their musical instruments to their gatherings, which turned into jam sessions. We don't know how good they were, there being no compact disk recorders at the time. But one later critic made an educated guess.
Vincenzo Galilei figured that the Pythagoreans must have had a collective tin ear, given their ideas about consonance. His ear told him that Pythagoras was dead wrong. Other practicing musicians of the sixteenth century also paid no attention to these ancient Greeks. Yet the Pythagoreans' ideas endured even into Vincenzo's day, and the sonorous numbers were still a respected component of musical theory, if not practice. The greatest defender of Pythagoras in sixteenth-century Italy was Gioseffo Zarlino, the foremost music theorist of his day and also Vincenzo's teacher.
Vincenzo and Zarlino entered into a bitter debate over the matter, and Vincenzo came up with a method of proving his point that was revolutionary for the time: he experimented. By setting up experiments with strings of different lengths or strings of equal length but different tensions, he found new, non-Pythagorean mathematical relationships in the musical scale. Some claim that Vincenzo was the first person to dislodge a universally accepted mathematical law through experimentation. At the very least, he was in the forefront of a movement that replaced the old polyphony with modern harmony.
We know there was at least one interested spectator at these musical experiments. Vincenzo's eldest son watched as he measured and calculated. Exasperated by the dogma of musical theory, Vincenzo railed at his son about the stupidity of mathematics. We don't know his exact words, but in my mind I can hear Vincenzo screaming something like, "Forget about these theories with dumb numbers. Listen to what your ear tells you. Don't let me ever hear you talking about becoming a mathematician!" He taught the boy well, turning him into a competent performer on the lute and other instruments. He trained his son's senses, teaching him to detect errors in timing, an essential ability for a musician. But he wanted his eldest son to forsake both music and mathematics. A typical father, Vincenzo wanted him to become a doctor, wanted him to have a decent income.
Watching those experiments had a greater impact on the young man than Vincenzo could have imagined. The boy was especially fascinated by an experiment in which his father applied various tensions to his strings by hanging different weights from their ends. When plucked, these weighted strings acted as pendulums, and this may have started the young Galilei thinking about the distinctive ways objects move in this universe.
The son's name, of course, was Galileo. To modern eyes his achievements are so luminous it is difficult to see anyone else in that period of history. Galileo ignored Vincenzo's diatribes against the spuriousness of pure mathematics and became a math professor. But as much as he loved mathematical reasoning, he made it subservient to observation and measurement. In fact, his adroit blending of the two is frequently cited as the true beginning of the "scientific method."
GALILEO, ZSA ZSA, AND ME
Galileo was a new beginning. In this chapter and the one that follows, we will see the creation of classical physics. We'll meet an awesome set of heroes: Galileo, Newton, Lavoisier, Mendeleev, Faraday, Maxwell, and Hertz, among others. Each attacked the problem of finding the ultimate building block of matter from a new angle. For me this is an intimidating chapter. All of these people have been written about time and again. The physics is well-covered territory. I feel like Zsa Zsa Gabor's seventh husband. I know what to do, but how do you make it interesting?
Thanks to the post-Democritan thinkers, there was little action in science from the time of the atomists until the dawn of the Renaissance. That's one reason the Dark Ages were so dark. The nice thing about particle physics is that we can ignore almost two thousand years of intellectual thought. Aristotelian logic—geocentric, human-centered, religious—dominated Western culture during this period, creating a sterile environment for physics. Of course, Galileo didn't spring full-grown from a complete desert. He gave much credit to Archimedes, Democritus, and the Roman poet-philosopher Lucretius. No doubt he studied and built on other predecessors who are now known well only to scholars. Galileo accepted Copernicus's world view (after careful checking), and that determined his personal and political future.
We'll see a departure from the Greek method in this period. No longer is Pure Reason good enough. We enter an era of experimentation. As Vincenzo told his son, between the real world and pure reason (that is, mathematics) there lie the senses and, most important, measurement. We'll meet several generations of measurers as well as theorists. We'll see how the interplay between these camps helped forge a magnificent intellectual edifice, known now as classical physics. Their work did not benefit just scholars and philosophers. From their discoveries emerged technologies that changed the way humans live on this planet.
Of course, measurers are nothing without their measuring sticks, their instruments. It was a period of wonderful scientists, but also of wonderful instruments.
BALLS AND INCLINATIONS
Galileo gave particular attention to the study of motion. He may or may not have dropped rocks from the Leaning Tower, but his logical analysis of how distance, time, and speed are related probably predated the experiments he did carry out. Galileo studied how things move, not by allowing objects to fall free, but by using a trick, a substitute, the inclined plane. Galileo reasoned that the motion of a ball rolling down a smooth, slanting board would bear a close relationship to that of a ball in free fall, but the plane would have the enormous advantage of slowing the motion enough that it
could be measured.
In principle he could check this reasoning by starting with very gentle inclinations—raising one end of his six-foot-long board by a few inches to create a gentle slide—and by repeating his measurements with increasing inclinations until the speed became too great to measure precisely. This would give him confidence in extending his conclusions to the ultimate inclination, a vertical free fall.
Now, he needed something to time his rolling balls. Galileo's visit to the local shopping mall to buy a stopwatch failed; the invention was still three hundred years away. Here is where his father's training came in. Remember that Vincenzo refined Galileo's ear for musical beats. A march, for example, might have a beat every half second. At that beat a competent musician, as Galileo was, can detect an error of about one sixty-fourth of a second.
Galileo, lost in a land without timepieces, decided to make a sort of musical instrument out of his inclined plane. He strung a series of lute strings at intervals across the plane. Now when he rolled a ball down, it made a click as it passed over each string. Galileo then slid the strings up and down until the beat of each interval was exactly the same to his ear. He sang a march tune, releasing the ball on one beat, and when the strings were finally set just right, the ball struck each lute string precisely on successive beats, each a half second apart. When Galileo measured the spaces between the strings— mirabile dictu! —he found that they increased geometrically down the plane. In other words, the distance from start to the second string was four times the distance from start to the first string. The distance from start to the third string was nine times the first interval; the fourth string was sixteen times farther down the plane than the first; and so on, even though each gap between strings always represented a half second. (The ratios of the intervals, 1 to 4 to 9 to 16, can also be expressed as squares: l2, 22, 32, 42, and so on.)
The God Particle: If the Universe Is the Answer, What Is the Question? Page 9