In Dialogues Concerning the Two New Sciences, Galileo presents his last thoughts on atom structure. In this hypothesis, according to recent historical scholars, atoms are reduced to the mathematical abstraction of points, lacking any dimension, clearly indivisible and uncuttable, but devoid of the shapes that Democritus had envisioned.
Here Galileo moves the idea closer to its most modern version, the pointlike quarks and leptons.
ACCELERATORS AND TELESCOPES
Quarks are even more abstract and difficult to visualize than atoms. No one has ever "seen" one, so how can they exist? Our proof is indirect. Particles collide in an accelerator. Sophisticated electronics receive and process electrical pulses generated by particles in a variety of sensors in the detector. A computer interprets the electronic impulses from the detector, reducing them to a bunch of zeroes and ones. It sends these results to a monitor in our control room. We look at the representation of ones and zeroes and say, "Holy cow, a quark!" It seems so far-fetched to the layman. How can we be so sure? Couldn't the accelerator or the detector or the computer or the wire from the computer to the monitor have "manufactured" the quark? After all, we never see the quark with our own God-given eyes. Oh, for a time when science was simpler! Wouldn't it be great to be back in the sixteenth century? Or would it? Ask Galileo.
Galileo built, according to his records, a huge number of telescopes. He tested his telescope, in his own words, "a hundred thousand times on a hundred thousand stars and other objects." He trusted the thing. Now I have this little mental picture. Here's Galileo with all his graduate students. He's looking out the window with his telescope and describing what he sees, and they're all scribbling it down: "Here's a tree. It's got a branch this way and a leaf that way." After he tells them what he sees through the telescope, they all get on their horses or wagons—maybe a bus—and go across the field to look at the tree close up. They compare it to Galileo's description. That's how you calibrate an instrument. You do that ten thousand times. So a critic of Galileo describes the meticulous nature of the testing and says, "If I follow these experiments on terrestrial objects, the telescope is superb. I trust it, even though it interposes something between the God-given eye and the God-given object. Nevertheless, it does not fool you. On the other hand, if you look up at the sky, there's a star. And if you look through the telescope, there are two stars. It's totally cracked!"
Okay, those weren't his exact words. But one critic did use words to this effect to dispute Galileo's claim that Jupiter has four moons. Since the telescope allowed him to see more than could be seen with the naked eye, it must be lying. A math professor also dismissed Galileo, saying he, too, could find four moons of Jupiter if given enough time "to build them into some glasses."
Anyone who uses an instrument runs into this problem. Is the instrument "manufacturing" the results? Galileo's critics seem foolish today, but were they off the wall or just scientific conservatives? Some of both, no doubt;. In 1600 people believed that the eye had an active role in vision; the eyeball, given to us by God, interpreted the visual world for us. Today we know the eye is no more than a lens with a bunch of receptors in it that passes visual information along to our brain's visual cortex, where we actually "see." The eye is in fact a mediator between the object and the brain, just as the telescope is. Do you wear eyeglasses? You're already modifying. In fact, among devout Christians and philosophers in sixteenth-century Europe, wearing spectacles was considered almost sacrilegious, even though they had been around for three hundred years. One notable exception was Johannes Kepler, who was very religious but who nonetheless wore specs because they helped him see; this was fortunate, given that he became the greatest astronomer of his time.
Let's accept that a well-calibrated instrument can provide a good approximation of reality. As good perhaps as the ultimate instrument, our brain. Even the brain must be calibrated at times, and safeguards and fudge factors applied to compensate for distortion. For example, even if you have 20/20 vision, a few glasses of wine can double the number of friends around you.
THE CARLSAGAN OF 1600
Galileo helped pioneer the acceptance of instruments, an accomplishment whose importance to science and experimentation cannot be overemphasized. What sort of person was he? He comes across as a deep thinker with a subtle mind, capable of intuitive insights that would be the envy of any theoretical physicist today, but with energy and technical skills that included lens polishing and the construction of many instruments, including telescopes, the compound microscope, and the pendulum clock. Politically he alternated from docile conservatism to bold, slashing attacks on his opponents. He must have been a dynamo of activity, constantly engaged, for he left behind an enormous correspondence and monumental volumes of published works. He was a popularizer, giving public lectures to huge audiences after the supernova of 1604, writing in a lucid, vulgarized Latin. No one comes as close as he does to being the Carl Sagan of his day. Not too many faculties would have granted him tenure, so vigorous was his style and so stinging his criticism, at least before his condemnation.
Was Galileo the complete physicist? As complete as one can find in history, in that he combined consummate skills of both the experimenter and the theorist. If he had faults, they fell on the theoretical side. Although this combination was relatively common in the eighteenth and nineteenth centuries, in today's age of specialization it is rare. In the seventeenth century, much of what would be called "theory" was in such close support of experiment as to defy separation. We shall soon see the advantage of having a great experimenter followed by a great theorist. In fact, by Galileo's time there had already been one such pivotal succession.
THE MAN WITH NO NOSE
Let me backtrack for a minute, because no book about instrument and thought, experiment and theory, is complete without two names that go together like Marx and Engels, Emerson and Thoreau, or Siegfried and Roy. I'm speaking of Brahe and Kepler. They were strictly astronomers, not physicists, but they warrant a brief digression.
Tycho Brahe was one of the more bizarre characters in the history of science. This Danish nobleman, born in 1546, was a measurer's measurer. Unlike atomistic physicists, who look downward, he looked up at the heavens, and he did it with unprecedented precision. Brahe constructed all manner of instruments for measuring the positions of the stars, planets, comets, the moon. Brahe missed the telescope's invention by a couple of decades, so he built elaborate sighting devices—azimuthal semicircles, Ptolemaic rulers, brass sextants, azimuthal quadrants, parallactic rulers—that he and his assistants used with the naked eye to nail down coordinates of stars and other heavenly bodies. Most of these variations on today's sextants consisted of crossarms with arcs between them. The astronomers used the quadrants like rifles, lining up stars by looking through metal sights attached to the ends of the arms. The arcs connecting the crossarms functioned like the protractors you used in school, enabling the astronomers to measure the angle of the sightline to the star, planet, or comet being observed.
There was nothing particularly new about the basic concept of Brahe's instruments, but he defined the state of the art. He experimented with different materials. He figured out how to make these cumbersome gadgets easily rotatable in the vertical or horizontal plane, and at the same time fixed them in place so that he could track celestial objects from the same point night after night. Most of all, Brahe's measuring devices were big. As we shall see when we get to the modern era, big is not always, but usually, better. Tycho's most famous instrument was the mural quadrant, which had a radius of six meters, or about eighteen feet! It took forty strong men to wrestle it into place—a veritable Super Collider of its day. The degrees marked off on its arc were so far apart that Brahe was able to divide each of the sixty minutes of arc in each degree into six subdivisions of ten seconds each. In simpler terms, Brahe's margin of error was the width of a needle held at arm's length. All this done with the naked eye! To give you some idea of the man's ego, inside the quadrant
's arc was a life-size portrait of Brahe himself.
You'd think such fastidiousness would indicate a nerdy kind of man. Tycho Brahe was anything but. His most unusual feature was his nose—or lack of one. When Brahe was a twenty-year-old student, he got into a furious argument with a student named Manderup Parsbjerg over a mathematical point. The quarrel, which took place at a celebration at a professor's house, got so heated that friends had to separate the two. (Okay, maybe he was a little nerdy, fighting over formulas rather than girls.) A week later Brahe and his rival met again at a Christmas party, had a few drinks, and began the math argument anew. This time they couldn't be cooled down. They adjourned to a dark spot beside a graveyard and went at each other with swords. Parsbjerg ended the duel quickly by slicing off a good chunk of Brahe's nose.
This nose episode would haunt Brahe all his life. There are two stories concerning what he did in the way of cosmetic surgery. The first, most likely apocryphal, is that he commissioned a whole set of artificial noses made of different materials for different occasions. But the story accepted by most historians is almost as good. This version has Brahe ordering a permanent nose made of gold and silver, skillfully painted and shaped to look like a real nose. Reportedly he carried a little box of glue with him, which he applied whenever the nose became wobbly. The nose was the butt of jokes. One scientific rival claimed that Brahe made his astronomical observations through his nose, using it as a sight vane.
Despite these difficulties, Brahe did have an advantage over many scientists today—his noble birth. He was friends with King Frederick II, and after he became famous because of his observations of a supernova in the constellation Cassiopeia, the king gave him the island of Hven in The Sound to use as an observatory. Brahe was also given rule over all the tenants of the island, the rents derived therefrom, and extra funds from the king. In this fashion, Tycho Brahe became the world's first laboratory director. And what a director he was! With his rents, a grant from the king, and his own fortune, he led a regal existence. He missed only the benefits of dealing with funding agencies in twentieth-century America.
The two-thousand-acre island became an astronomer's paradise, replete with workshops for the artisans who made the instruments, a windmill, a paper mill, and nearly sixty fish ponds. For himself, Brahe built a magnificent home and observatory on the island's highest point. He called it Uraniborg, or "heavenly castle," and enclosed it within a walled square that contained a printing office, servants' quarters, and kennels for Brahe's watchdogs, plus flower gardens, herbaries, and some three hundred trees.
Brahe eventually left the island under less than pleasant circumstances after his benefactor, King Frederick, died of an excess of Carlsberg or whatever mead was popular in Denmark in 1600. The fief of Hven reverted to the crown, and the new king subsequently gave the island to one Karen Andersdatter, a mistress he had picked up at a wedding party. Let this be a lesson to all lab directors, as to their status in the world and their replaceability in the eyes of the powers that be. Fortunately, Brahe landed on his feet, moving his data and instruments to a castle near Prague where he was welcomed to continue his work.
It was the regularity of the universe that prompted Brahe's interest in nature. As a fourteen-year-old he had been fascinated by the total eclipse of the sun predicted for August 21, 1560. How could men understand the motions of the stars and planets so finely that they could foretell their positions years in advance? Brahe left an enormous legacy: a catalogue of the positions of exactly one thousand fixed stars. It surpassed Ptolemy's classic catalogue and destroyed many of the old theories.
A great virtue of Brahe's experimental technique was his attention to possible errors in his measurements. He insisted, and this was unprecedented in 1580, that measurements be repeated many times and that each measurement be accompanied by an estimate of its accuracy. He was far ahead of his time in his dedication to presenting data together with the limits of their trustworthiness.
As a measurer and observer, Brahe had no peer. As a theorist, he left much to be desired. Born just three years after the death of Copernicus, he never fully accepted the Copernican system, which held that the earth orbited the sun rather than vice versa, as Ptolemy had stated many centuries earlier. Brahe's observations proved to him that the Ptolemaic system didn't work but, educated as an Aristotelian, he could never bring himself to believe that the earth rotated, nor could he give up the belief that the earth was at the center of the universe. After all, he reasoned, if the earth really moved and you fired a cannonball in the direction of the earth's rotation, it should go farther than if you fired it in the opposite direction, but that is not the case. So Brahe came up with a compromise: the earth stayed immobile at the center of the universe, but contrary to the Ptolemaic system, the planets revolved about the sun, which in turn circled the earth.
THE MYSTIC DELIVERS
Through his career; Brahe had many superb assistants. The most brilliant of all was a strange, mystical mathematician-astronomer named Johannes Kepler. A devout German-born Lutheran, Kepler would have preferred to be a clergyman, had not mathematics offered him a way of making a living. In truth, he failed the ministerial qualifying exams and stumbled into astronomy with a strong minor in astrology. Even so, he was destined to become the theorist who would discern simple and profound truths in Brahe's mountain of observational data.
Kepler, a Protestant at an unfortunate time (the Counter Reformation was sweeping Europe), was a frail, neurotic, nearsighted man, with none of the self-assurance of a Brahe or a Galileo. The entire Kepler family was a trifle offbeat. Kepler's father was a mercenary, his mother was tried as a witch, and Johannes himself was occupied much of the time with astrology. Fortunately, he was good at it, and it paid some bills. In 1595 he constructed a calendar for the city of Graz that predicted bitter cold weather, peasant uprisings, and invasions by the Turks—all events that came to pass. In fairness to Kepler, he was not alone in moonlighting as an astrologer. Galileo cast horoscopes for the Medicis, and Brahe also dabbled in the art, although he wasn't so good at it: from the lunar eclipse of October 28, 1566, Brahe predicted the death of Sultan Suleiman the Magnificent. Unfortunately the sultan was already dead at the time.
Brahe treated his assistant rather shabbily—more like a postdoc, which Kepler was, than as a peer, which he certainly deserved to be. The sensitive Kepler bristled under the insult, and the two had many fallings-out and an equal number of reconciliations, for Brahe did come to appreciate Kepler's brilliance.
In October 1601, Brahe attended a dinner party and, as was his wont, drank far too much. According to the strict etiquette of the day, it was improper to leave the table during a meal, and when he finally made a mad dash for the bathroom, it was too late. "Something of importance" had burst inside him. Eleven days later he was dead. Having already appointed Kepler as his chief assistant, on his deathbed Brahe bequeathed to him all of the data he had acquired over his illustrious, well-funded career, and beseeched Kepler to use his analytical mind to create a grand synthesis that would further an understanding of the heavens. Of course, Brahe added that he expected Kepler to follow the Tychonian hypothesis of a geocentric universe.
Kepler agreed to the dying man's wish, no doubt with fingers crossed, because he thought Brahe's system was nuts. But the data! The data were nonpareil. Kepler pored over the information, looking for patterns in the motions of the planets. Kepler rejected the Tychonian and Ptolemaic systems out of hand for their clumsiness. But he had to start somewhere. So he began with the Copernican system as a model because, with its system of spherical orbits, it was the most elegant thing around.
The mystic in Kepler also embraced the idea of a centrally positioned sun, which not only illuminated all the planets but provided a force, or motive as it was then called, for the movements of the planets. He didn't quite know how the sun did this—he guessed it was something like magnetism—but he paved the way for Newton. He was among the first to promote the idea that a fo
rce is needed to make sense of the solar system.
Just as important, he found that the Copernican system didn't quite jibe with Brahe's data. The surly old Dane had taught Kepler well, instilling in him the inductive method: lay down a foundation of observations, and only then ascend to the causes of things. Despite his mysticism and his awe of, and obsession with, geometric forms, Kepler stuck faithfully to the data. He emerged from his study of Brahe's observations—especially the data on Mars—with three laws of planetary motion, which, almost four hundred years later, still serve as the basis of modern planetary astronomy. I won't go into the details of these laws here, except to say that his first law destroyed the lovely Copernican notion of circular orbits, a concept that had remained unquestioned since the days of Plato. Kepler established that the planets trace out ellipses in their orbital paths with the sun at one focus. The eccentric Lutheran had saved Copernicanism and freed it from the cumbersome epicycles of the Greeks; he did so by making sure his theories followed Brahe's observations to the precise minute of arc.
Ellipses! Pure mathematics! Or is it pure nature? If, as Kepler discovered, planets move in perfect ellipses with the sun at one focus, then nature must love mathematics. Something—maybe God—looks down on the earth and says, "I like mathematical form." It is easy to demonstrate nature's love of mathematical forms. Pick up a rock and throw it. It traces out a very good parabola. If there were no air it would be a perfect parabola. In addition to being a mathematician, God is kind. She hides complexity when the mind isn't ready for it. We now know that the orbits are not perfect ellipses (because of the pull of the planets on one another) but the deviations were far too small to see with Brahe's apparatus.
The God Particle Page 11
