Sophie's World: A Novel About the History of Philosophy (27 page)

"I guess they didn't have any of the technical apparatus we have today."

"Of course they had neither calculators nor electronic scales. But they had mathematics and they had scales. And it was now above all imperative to express scientific observations in precise mathematical terms. 'Measure what can be measured, and make measurable what can-not be measured,' said the Italian Galileo Galilei, who was one of the most important scientists of the seventeenth century. He also said that the book of nature is written in the language of mathematics."

"And all these experiments and measurements made new inventions possible."

"The first phase was a new scientific method. This made the technical revolution itself possible, and the technical breakthrough opened the way for every invention since. You could say that man had begun to break away from his natural condition. Nature was no longer something man was simply a part of. 'Knowledge is power,' said the English philosopher Francis Bacon, thereby underlining the practical value of knowledge-- and this was indeed new. Man was seriously starting to intervene in nature and beginning to control it."

"But not only in a good way?"

"No, this is what I was referring to before when I spoke of the good and the evil threads that are constantly intertwined in everything we do. The technical revolution that began in the Renaissance led to the spinning jenny and to unemployment, to medicines and new diseases, to the improved efficiency of agriculture and the impoverishment of the environment, to practical appliances such as the washing machine and the refrigerator and pollution and industrial waste. The serious threat to the environment we are facing today has made many people see the technical revolution itself as a perilous maladjustment to natural conditions. It has been pointed out that we have started something we can no longer control. More optimistic spirits think we are still living in the cradle of technology, and that although the scientific age has certainly had its teething troubles, we will gradually learn to control nature without at the same time threatening its very existence and thus our own."

"Which do you think?"

"I think perhaps there may be some truth in both views. In some areas we must stop interfering with nature, but in others we can succeed. One thing is certain: There is no way back to the Middle Ages. Ever since the Renaissance, mankind has been more than just part of creation. Man has begun to intervene in nature and form it after his own image. In truth, 'what a piece of work is man!' "

"We have already been to the moon. What medieval person would have believed such a thing possible?"

"No, that's for sure. Which brings us to the new world view. All through the Middle Ages people had stood beneath the sky and gazed up at the sun, the moon, the stars, and the planets. But nobody had doubted that the earth was the center of the universe. No observations had sown any doubt that the earth remained still while the 'heavenly bodies' traveled in their orbits around it. We call this the geocentric world picture, or in other words, the belief that everything revolves around the earth. The Christian belief that God ruled from on high, up above all the heavenly bodies, also contributed to maintaining this world picture."

"I wish it were that simple!"

"But in 1543 a little book was published entitled On the Revolutions of the Celestial Spheres. It was written by the Polish astronomer Nicolaus Copernicus, who died on the day the book was published. Copernicus claimed that it was not the sun that moved round the earth, it was vice versa. He thought this was completely possible from the observations of the heavenly bodies that existed. The reason people had always believed that the sun went round the earth was that the earth turns on its own axis, he said. He pointed out that all observations of heavenly bodies were far easier to understand if one assumed that both the earth and the other planets circle around the sun. We call this the heliocentric world picture, which means that everything centers around the sun."

"And that world picture was the right one?"

"Not entirely. His main point--that the earth moves round the sun--is of course correct. But he claimed that the sun was the center of the universe. Today we know that the sun is only one of an infinite number of stars, and that all the stars around us make up only one of many billions of galaxies. Copernicus also believed that the earth and the other planets moved in circular orbits around the sun."

"Don't they?"

"No. He had nothing on which to base his belief in the circular orbits other than the ancient idea that heavenly bodies were round and moved in circles simply because they were 'heavenly.' Since the time of Plato the sphere and the circle had been considered the most per-fect geometrical figures. But in the early 1600s, the German astronomer Johannes Kepler presented the results of comprehensive observations which showed that the planets move in elliptical--or oval--orbits with the sun at one focus. He also pointed out that the speed of a planet is greatest when it is closest to the sun, and that the farther a planet's orbit is from the sun the slower it moves. Not until Kepler's time was it actually stated that the earth was a planet just like other planets. Kepler also emphasized that the same physical laws apply everywhere throughout the universe."

"How could he know that?"

"Because he had investigated the movements of the planets with his own senses instead of blindly trusting ancient superstitions. Galileo Galilei, who was roughly contemporary with Kepler, also used a telescope to observe the heavenly bodies. He studied the moon's craters and said that the moon had mountains and valleys similar to those on earth. Moreover, he discovered that the planet Jupiter had four moons. So the earth was not alone in having a moon. But the greatest significance of Galileo was that he first formulated the so-called Law of Inertia."

"And that is?" "Galileo formulated it thus: A body remains in the state which it is in, at rest or in motion, as long as no external force compels it to change its state."

"If you say so."

"But this was a significant observation. Since antiquity, one of the central arguments against the earth moving round its own axis was that the earth would then move so quickly that a stone hurled straight into the air would fall yards away from the spot it was hurled from."

"So why doesn't it?"

"If you're sitting in a train and you drop an apple, it doesn't fall backward because the train is moving. It falls straight down. That is because of the law of inertia. The apple retains exactly the same speed it had before you dropped it."

"I think I understand."

"Now in Galileo's time there were no trains. But if you roll a ball along the ground--and suddenly let go..."

"... it goes on rolling ..."

"... because it retains its speed after you let go."

"But it will stop eventually, if the room is long enough."

"That's because other forces slow it down. First, the floor, especially if it is a rough wooden floor. Then the force of gravity will sooner or later bring it to a halt. But wait, I'll show you something."

Alberto Knox got up and went over to the old desk. He took something out of one of the drawers. When he returned to his place he put it on the coffee table. It was just a wooden board, a few millimeters thick at one end and thin at the other. Beside the board, which almost covered the whole table, he laid a green marble.

"This is called an inclined plane," he said. "What do you think will happen if I let go the marble up here, where the plane is thickest?"

Sophie sighed resignedly.

"I bet you ten crowns it rolls down onto the table and ends on the floor."

"Let's see."

Alberto let go of the marble and it behaved exactly as Sophie had said. It rolled onto the table, over the tabletop, hit the floor with a little thud and finally bumped into the wall.

"Impressive," said Sophie.

"Yes, wasn't it! This was the kind of experiment Galileo did, you see."

"Was he really that stupid?"

"Patience! He wanted to investigate things with all his senses, so we have only just begun. Tell me first why the marble rolled down the inclined plane."

"It began to roll because it was heavy."

"All right. And what is weight actually, child?"

"That's a silly question."

"It's not a silly question if you can't answer it. Why did the marble roll onto the floor?"

"Because of gravity."

"Exactly--or gravitation, as we also say. Weight has something to do with gravity. That was the force that set the marble in motion."

Alberto had already picked the marble up from the floor. He stood bowed over the inclined plane with the marble again. "Now I shall try to roll the marble across the plane," he said. "Watch carefully how it moves."

Sophie watched as the marble gradually curved away and was drawn down the incline.

"What happened?" asked Alberto.

"It rolled sloping because the board is sloping."

"Now I'm going to brush the marble with ink ... then perhaps we can study exactly what you mean by sloping."

He dug out an ink brush and painted the whole marble black. Then he rolled it again. Now Sophie could see exactly where on the plane the marble had rolled because it had left a black line on the board.

"How would you describe the marble's path?"

"It's curved ... it looks like part of a circle."

"Precisely."

Alberto looked up at her and raised his eyebrows.

"However, it is not quite a circle. This figure is called a parabola."

"That's fine with me."

"Ah, but why did the marble travel in precisely that way?"

Sophie thought deeply. Then she said, "Because the board was sloping, the marble was drawn toward the floor by the force of gravity."-"Yes, yes! This is nothing less than a sensation! Here I go, dragging a girl who's not yet fifteen up to my attic, and she realizes exactly the same thing Galileo did after one single experiment!"

He clapped his hands. For a moment Sophie was afraid he had gone mad. He continued: "You saw what happened when two forces worked simultaneously on the same object. Galileo discovered that the same thing applied, for instance, to a cannonball. It is propelled into the air, it continues its path over the earth, but will eventually be drawn toward the earth. So it will have described a trajectory corresponding to the marble's path across the inclined plane. And this was actually a new discovery at the time of Galileo. Aristotle thought that a projectile hurled obliquely into the air would first describe a gentle curve and then fall vertically to the earth. This was not so, but nobody could know Aristotle was wrong before it had been demonstrated."

"Does all this really matter?"

"Does it matter? You bet it matters! This has cosmic significance, my child. Of all the scientific discoveries in the history of mankind, this is positively the most important."

"I'm sure you are going to tell me why."

"Then along came the English physicist Isaac Newton, who lived from 1642 to 1727. He was the one who provided the final description of the solar system and the planetary orbits. Not only could he describe how the planets moved round the sun, he could also explain why they did so. He was able to do so partly by referring to what we call Galileo's dynamics."

"Are the planets marbles on an inclined plane then?"

"Something like that, yes. But wait a bit, Sophie."

"Do I have a choice?"

"Kepler had already pointed out that there had to be a force that caused the heavenly bodies to attract each other. There had to be, for example, a solar force which held the planets fast in their orbits. Such a force would moreover explain why the planets moved more slowly in their orbit the further away from the sun they traveled. Kepler also believed that the ebb and flow of the tides-- the rise and fall in sea level--must be the result of a lunar force."

"And that's true."

"Yes, it's true. But it was a theory Galileo rejected. He mocked Kepler, who he said had given his approval to the idea that the moon rules the water. That was because Galileo rejected the idea that the forces of gravitation could work over great distances, and also between the heavenly bodies."

"He was wrong there."

"Yes. On that particular point he was wrong. And that was funny, really, because he was very preoccupied with the earth's gravity and falling bodies. He had even indicated how increased force can control the movement of a body."

"But you were talking about Newton."

"Yes, along came Newton. He formulated what we call the Law of Universal Gravitation. This law states that every object attracts every other object with a force that increases in proportion to the size of the objects and decreases in proportion to the distance between the objects."

"I think I understand. For example, there is greater attraction between two elephants than there is between two mice. And there is greater attraction between two elephants in the same zoo than there is between an Indian elephant in India and an African elephant in Africa."

"Then you have understood it. And now comes the central point. Newton proved that this attraction--or gravitation--is universal, which means it is operative everywhere, also in space between heavenly bodies. He is said to have gotten this idea while he was sitting under an apple tree. When he saw an apple fall from the tree he had to ask himself if the moon was drawn to earth with the same force, and if this was the reason why the moon continued to orbit the earth to all eternity."

"Smart. But not so smart really."

"Why not, Sophie?"

"Well, if the moon was drawn to the earth with the same force that causes the apple to fall, one day the moon would come crashing to earth instead of going round and round it for ever."

"Which brings us to Newton's law on planetary orbits. In the case of how the earth attracts the moon, you are fifty percent right but fifty percent wrong. Why doesn't the moon fall to earth? Because it really is true that the earth's gravitational force attracting the moon is tremendous. Just think of the force required to lift sea level a meter or two at high tide."