"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 b.u.mped 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 n.o.body 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 s.p.a.ce 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."
"I don"t think I understand."
"Remember Galileo"s inclined plane. What happened when I rolled the marble across it?"
"Are there two different forces working on the moon?"
"Exactly. Once upon a time when the solar system began, the moon was hurled outward-outward from the earth, that is-with tremendous force. This force will remain in effect forever because it moves in a vacuum without resistance..."
"But it is also attracted to the earth because of earth"s gravitational force, isn"t it?"
"Exactly. Both forces are constant, and both work simultaneously. Therefore the moon will continue to orbit the earth."
"Is it really as simple as that?"
"As simple as that, and this very same simplicity was Newton"s whole point. He demonstrated that a few natural laws apply to the whole universe. In calculating the planetary orbits he had merely applied two natural laws which Galileo had already proposed. One was the law of inertia, which Newton expressed thus: "A body remains in its state of rest or rectilinear motion until it is compelled to change that state by a force impressed on it." The other law had been demonstrated by Galileo on an inclined plane: When two forces work on a body simultaneously, the body will move on an elliptical path."
"And that"s how Newton could explain why all the planets go round the sun."
"Yes. All the planets travel in elliptical orbits round the sun as the result of two unequal movements: first, the rectilinear movement they had when the solar system was formed, and second, the movement toward the sun due to gravitation."
"Very clever."
"Very. Newton demonstrated that the same laws of moving bodies apply everywhere in the entire universe. He thus did away with the medieval belief that there is one set of laws for heaven and another here on earth. The heliocentric world view had found its final confirmation and its final explanation."
Alberto got up and put the inclined plane away again. He picked up the marble and placed it on the table between them.
Sophie thought it was amazing how much they had gotten out of a bit of slanting wood and a marble. As she looked at the green marble, which was still smudged with ink, she couldn"t help thinking of the earth"s globe. She said, "And people just had to accept that they were living on a random planet somewhere in s.p.a.ce?"
"Yes-the new world view was in many ways a great burden. The situation was comparable to what happened later on when Darwin proved that mankind had developed from animals. In both cases mankind lost some of its special status in creation. And in both cases the Church put up a ma.s.sive resistance."
"I can well understand that. Because where was G.o.d in all this new stuff? It was simpler when the earth was the center and G.o.d and the planets were upstairs."
"But that was not the greatest challenge. When Newton had proved that the same natural laws applied everywhere in the universe, one might think that he thereby undermined people"s faith in G.o.d"s omnipotence. But Newton"s own faith was never shaken. He regarded the natural laws as proof of the existence of the great and almighty G.o.d. It"s possible that man"s picture of himself fared worse."
"How do you mean?"
"Since the Renaissance, people have had to get used to living their life on a random planet in the vast galaxy. I am not sure we have wholly accepted it even now. But there were those even in the Renaissance who said that every single one of us now had a more central position than before."
"I don"t quite understand."
"Formerly, the earth was the center of the world. But since astronomers now said that there was no absolute center to the universe, it came to be thought that there were just as many centers as there were people. Each person could be the center of a universe."
"Ah, I think I see."
"The Renaissance resulted in a new religiosity. As philosophy and science gradually broke away from theology, a new Christian piety developed. Then the Renaissance arrived with its new view of man. This had its effect on religious life. The individual"s personal relationship to G.o.d was now more important than his relationship to the church as an organization."
"Like saying one"s prayers at night, for instance?"
"Yes, that too. In the medieval Catholic Church, the church"s liturgy in Latin and the church"s ritual prayers had been the backbone of the religious service. Only priests and monks read the Bible because it only existed in Latin. But during the Renaissance, the Bible was translated from Hebrew and Greek into national languages. It was central to what we call the Reformation."
"Martin Luther..."
"Yes, Martin Luther was important, but he was not the only reformer. There were also ecclesiastical reformers who chose to remain within the Roman Catholic church. One of them was Erasmus of Rotterdam."
"Luther broke with the Catholic Church because he wouldn"t buy indulgences, didn"t he?"
"Yes, that was one of the reasons. But there was a more important reason. According to Luther, people did not need the intercession of the church or its priests in order to receive G.o.d"s forgiveness. Neither was G.o.d"s forgiveness dependent on the buying of "indulgences" from the church. Trading in these so-called letters of indulgence was forbidden by the Catholic Church from the middle of the sixteenth century."
"G.o.d was probably glad of that."
"In general, Luther distanced himself from many of the religious customs and dogmas that had become rooted in ecclesiastical history during the Middle Ages. He wanted to return to early Christianity as it was in the New Testament. The Scripture alone," he said. With this slogan Luther wished to return to the "source" of Christianity, just as the Renaissance humanists had wanted to turn to the ancient sources of art and culture. Luther translated the Bible into German, thereby founding the German written language. He believed every man should be able to read the Bible and thus in a sense become his own priest."
"His own priest? Wasn"t that taking it a bit far?"
"What he meant was that priests had no preferential position in relation to G.o.d. The Lutheran congregations employed priests for practical reasons, such as conducting services and attending to the daily clerical tasks, but Luther did not believe that anyone received G.o.d"s forgiveness and redemption from sin through church rituals. Man received "free" redemption through faith alone, he said. This was a belief he arrived at by reading the Bible."
"So Luther was also a typical Renaissance man?"
"Yes and no. A characteristic Renaissance feature was his emphasis on the individual and the individual"s personal relationship to G.o.d. So he taught himself Greek at the age of thirty-five and began the laborious job of translating the Bible from the ancient Greek version into German. Allowing the language of the people to take precedence over Latin was also a characteristic Renaissance feature. But Luther was not a humanist like Ficino or Leonardo da Vinci. He was also opposed by humanists such as Erasmus of Rotterdam because they thought his view of man was far too negative; Luther had proclaimed that mankind was totally depraved after the Fall from Grace. Only through the grace of G.o.d could mankind be "justified," he believed. For the wages of sin is death."
"That sounds very gloomy."
Alberto Knox rose. He picked up the little green and black marble and put it in his top pocket.
"It"s after four!" Sophie exclaimed in horror.
"And the next great epoch in the history of mankind is the Baroque. But we shall have to keep that for another day, my dear Hilde."
"What did you say?" Sophie shot up from the chair she had been sitting in. "You called me Hilde!"