"It was really embarrassing. I told them you went home because we got mad at each other."

"What did you tell her?"

"You've been gone for five hours!" Joanna said sharply.

"Where on earth have you been? You're crazy. Your mom called half an hour ago."

It was just twelve when Sophie reached Joanna's front gate, out of breath with running. Joanna was standing in the front yard outside her family's yellow house.

Joanna shrugged. Just then her father came around the corner with a wheelbarrow. He had a pair of coveralls on and was busy clearing up last year's leaves and twigs.

Sophie shook her head.

"No, I've been gone for more than a thousand years."

"I said you were at the drugstore. She said would you call her when you got back. But you should have seen my mom and dad when they came in with hot chocolate and rolls at ten this morning… and your bed was empty."

"What did you say to them?"

"So we'd better hurry up and be friends again. And we have to make sure your parents don't talk to my mom for a few days. Do you think we can do that?"

… O divine lineage in mortal guise…

"Fine," said Sophie. "So perhaps we can have our hot chocolate there instead of in bed."

"Sure, if you walk home with me. Because it's not for the ears of financial advisers or overgrown Barbie dolls."

"Maybe. Maybe not."

Joanna was clearly not enthusiastic about all this secrecy.

They began to walk toward Clover Close.

"Probably not. But I hardly slept last night. And another thing, I've begun to wonder whether Hilde can see everything we do."

"You mean she might have second sight?"

"Aha -- so you're friends again, I see. Well, there's not so much as a single leaf left on the basement steps now."

"Are you going to tell me about it?"

"That's a rotten thing to say! I suppose you think a rocky marriage that drives one of the partners away to sea is better?"

"I'm sorry, Joanna, but I felt I ought to take part in this cover-up operation as well."

Joanna's dad gave a forced laugh, but Joanna gasped. Verbal exchanges had always been more robust in Sophie's family than at the more well-to-do home of Mr. Ingebrigtsen, the financial adviser, and his wife.

Lunch was on the table when Sophie walked into the kitchen. Nothing was said about her not having called from Joanna's.

"Do you want to tell me where you have been?"

She stopped at Sophie's gate and turned to go home again.

"Yes, but we don't even learn to ask them!"

"I admit that is a weak spot."

"Nobody can answer questions like that anyway."

After lunch Sophie announced that she was going to take a nap. She admitted she had hardly slept at Joanna's house, which was not at all unusual at a sleepover.

"Nobody asked you to like it. But philosophy is not a harmless party game. It's about who we are and where we come from. Do you think we learn enough about that at school?"

"But that doesn't explain why her father sent a lot of crazy postcards to an empty cabin in the woods."

They walked for a long time without speaking. As they approached Clover Close, Joanna said, "I don't like it."

So she did. Sophie told her everything, about the mysterious philosophy course as well. She made Joanna swear to keep everything secret.

Wasn't it odd, how she always experienced mysterious things like this when she was dead tired. It meant that afterward she always had to ask herself whether it really had happened.

She studied the sharp contours of her own pale face framed by that impossible hair which defied any style but nature's own. But beyond that face was the apparition of another girl. Suddenly the other girl began to wink frantically with both eyes, as if to signal that she was really in there on the other side. The apparition lasted only a few seconds. Then she was gone.

Before getting into bed she stood in front of the big brass mirror which now hung on her wall. At first she only saw her own white and exhausted face. But then -- behind her own face, the faintest suggestion of another face seemed to appear. Sophie took one or two deep breaths. It was no good starting to imagine things.

Sophie sat down on the edge of the bed. She had absolutely no doubt that it was Hilde she had seen in the mirror. She had caught a glimpse of her picture on a school I. D. in the major's cabin. It must have been the same girl she had seen in the mirror.

She dreamed she was standing in a large garden that sloped down to a red boathouse. On the dock behind it sat a young fair-haired girl gazing out over the water. Sophie walked down and sat beside her. But the girl seemed not to notice her. Sophie introduced herself. "I'm Sophie," she said. But the other girl could apparently neither see nor hear her. Suddenly Sophie heard a voice calling, "Hilde!" At once the girl jumped up from where she was sitting and ran as fast as she could up to the house. She couldn't have been deaf or blind after all. A middle-aged man came striding from the house toward her. He was wearing a khaki uniform and a blue beret. The girl threw her arms around his neck and he swung her around a few times. Sophie noticed a little gold crucifix on a chain lying on the dock where the girl had been sitting. She picked it up and held it in her hand. Then she woke up.

Sophie laid her clothes on the chair and crawled into bed. She fell asleep at once and had a strangely vivid dream.

Sophie looked at the clock. She had been asleep for two hours. She sat up in bed, thinking about the strange dream. It was so real that she felt as if she had actually lived the experience. She was equally sure that the house and the dock really existed somewhere. Surely it resembled the picture she had seen hanging in the major's cabin? Anyway, there was no doubt at all that the girl in her dream was Hilde Moller Knag and that the man was her father, home from Lebanon. In her dream he had looked a lot like Alberto Knox…

As Sophie stood up and began to tidy her bed, she found a gold crucifix on a chain under her pillow. On the back of the crucifix there were three letters engraved: HMK.

She was so mad that she opened the closet door and hurled the delicate crucifix up onto the top shelf with the silk scarf, the white stocking, and the postcards from Lebanon.

This was not the first time Sophie had dreamed she found a treasure. But this was definitely the first time she had brought it back from the dream.

"Damn!" she said aloud.

The next morning Sophie woke up to a big breakfast of hot rolls, orange juice, eggs, and vegetable salad. It was not often that her mother was up before Sophie on a Sunday morning. When she was, she liked to fix a solid meal for Sophie.

"Yes!" Sophie burst out, and at once regretted it.

While they were eating, Mom said, "There's a strange dog in the garden. It's been sniffing round the old hedge all morning. I can't imagine what it's doing here, can you?"

"Has it been here before?"

Sophie had already left the table and gone into the living room to look out of the window facing the large garden. It was just as she thought.

"Good boy, Hermes!" said Sophie.

She knew her mother was watching from the window. She prayed he would not go through the hedge. But the dog dashed toward the gravel path in front of the house, streaked across the front yard, and jumped up to the gate.

Hermes was lying in front of the secret entrance to her den.

"Did you say it had been here before?" she asked.

Sophie thought feverishly.

"I expect it buried a bone there and now it's come to fetch its treasure. Dogs have memories too…"

"I'll take it home," she said.

Sophie shrugged her shoulders.

"You know where it lives, then?"

"It's probably got an address on its collar."

A couple of minutes later Sophie was on her way down the garden. When Hermes caught sight of her he came lolloping toward her, wagging his tail and jumping up to her.

What should she say? She had no time to think of anything before her mother came and stood beside her.

"Maybe you're right, Sophie. You're the animal psychologist in the family."

When they had shut the gate behind them, Hermes continued to run a few yards in front of Sophie. It was a long way. Sophie and Hermes were not the only ones out for a Sunday walk. Whole families were setting off for the day. Sophie felt a pang of envy.

Hermes walked toward No. 14, where he stood still and waited for Sophie to open the door. Her heart began to beat faster.

From time to time Hermes would run off and sniff at another dog or at something interesting by a garden hedge, but as soon as Sophie called "Here, boy!" he would come back to her at once.

They crossed an old pasture, a large playing field, and a playground, and emerged into an area with more traffic. They continued toward the town center along a broad street with cobbled stones and streetcars. Hermes led the way across the town square and up Church Street. They came out into the Old Town, with its massive staid town houses from the turn of the century. It was almost half past one.

Now they were on the other side of town. Sophie had not been there very often. Once when she was little, she remembered, she had been taken to visit an old aunt in one of these streets.

Eventually they reached a little square between several old houses. It was called New Square, although it all looked very old. But then the whole town was old; it had been founded way back in the Middle Ages.

The addressee was Hilde Moller Knag, 14 New Square. It was postmarked June 15. That was not for two weeks, but the mailman had obviously not noticed that.

Dear Hilde, Now Sophie is coming to the philosopher's house. She will soon be fifteen, but you were fifteen yesterday. Or is it today, Hilde? If it is today, it must be late, then. But our watches do not always agree. One generation ages while another generation is brought forth. In the meantime history takes its course. Have you ever thought that the history of Europe is like a human life? Antiquity is like the childhood of Europe. Then come the interminable Middle Ages -- Europe's schoolday. But at last comes the Renaissance; the long school-day is over. Europe comes of age in a burst of exuberance and a thirst for life. We could say that the Renaissance is Europe's fifteenth birthday! It is mid-June, my child, and it is wonderful to be alive!

Sophie took the card down and read it:

Inside the front door there were a number of green mailboxes attached to a panel. Sophie noticed a postcard hanging from one of the mailboxes in the top row. It had a stamped message from the mailman across it to the effect that the addressee was unknown.

Once again she had taken out her fear and shyness on the unfortunate philosophy teacher. Sophie's thoughts were in a turmoil because of the postcard she had found down in the hallway.

Hermes was already on his way up the stairs. Sophie took the postcard with her and followed. She had to run to keep up with him; he was wagging his tail delightedly. They passed the second, third, and fourth stories. From then on there was only an attic staircase. Were they going up to the roof? Hermes clambered on up the stairs and stopped outside a narrow door, which he scratched at with his paw.

"What a clown!" Sophie exclaimed, giving him a little push so that she could go inside the apartment.

Sophie heard footsteps approaching from inside. The door opened, and there stood Alberto Knox. He had changed his clothes and was now wearing another costume. It consisted of white hose, red knee-breeches, and a yellow jacket with padded shoulders. He reminded Sophie of a joker in a deck of cards. If she was not much mistaken, this was a typical Renaissance costume.

P. S. Sorry to hear you lost your gold crucifix. You must learn to take better care of your things. Love, Dad -- who is just around the corner.

"So I read."

"It said that Hilde has lost her crucifix," said Sophie.

They went into the living room. It was one of the most extraordinary rooms Sophie had ever seen.

"He gets more and more audacious. I wouldn't be surprised if he isn't using us as a kind of birthday diversion for his daughter."

With that he tore the postcard into small pieces and threw them into the wastepaper basket.

"Be calm, my child," said Alberto, closing the door behind her.

"And I found it, the same one, under my pillow at home. Can you understand how it got there?"

"And here's the mail," she said, handing him the postcard as if she held him responsible for it.

Alberto read it and shook his head.

Alberto looked gravely into her eyes. "It may seem alluring. But it's just a cheap trick that costs him no effort whatsoever. Let us rather concentrate on the big white rabbit that is pulled out of the universe's top hat."

Alberto lived in a spacious attic apartment with sloping walls. A sharp light directly from the sky flooded the room from a skylight set into one of the walls. There was also another window facing the town. Through this window Sophie could look over all the roofs in the Old Town.

Sophie stood for several minutes without speaking and took everything in. "What a lot of old junk you've collected," she said.

But what amazed Sophie most was all the stuff the room was filled with -- furniture and objects from various historical periods. There was a sofa from the thirties, an old desk from the beginning of the century, and a chair that had to be hundreds of years old. But it wasn't just the furniture. Old objects, either useful or decorative, were jumbled together on shelves and cupboards. There were old clocks and vases, mortars and retorts, knives and dolls, quill pens and bookends, octants and sextants, compasses and barometers. One entire wall was covered with books, but not the sort of books found in most bookstores. The book collection itself was a cross section of the production of many hundreds of years. On the other walls hung drawings and paintings, some from recent decades, but most of them also very old. There were a lot of old charts and maps on the walls too, and as far as Norway was concerned, they were not very accurate.

"Do you manage an antique shop or something?"

"Yes, but none the less true, child. We do not live in our own time alone; we carry our history within us. Don't forget that everything you see in this room was once brand new. That old sixteenth-century wooden doll might have been made for a five-year-old girl's birthday. By her old grandfather, maybe… then she became a teenager, then an adult, and then she married. Maybe she had a daughter of her own and gave the doll to her. She grew old, and one day she died. Although she had lived for a very long time, one day she was dead and gone. And she will never return. Actually she was only here for a short visit. But her doll -- well, there it is on the shelf."

Alberto looked almost pained.

"Now then! Just think of how many centuries of history I have preserved in this room. I wouldn't exactly call it junk."

"We can't all let ourselves be washed away by the tide of history, Sophie. Some of us must tarry in order to gather up what has been left along the river banks."

"What an odd thing to say."

Alberto smiled archly.

"Then maybe you can also explain how Hilde's father knew you were there."

"Even things like that are a pure bagatelle for Hilde's father. Cheap hocus-pocus, simple sleight of hand. We are living under what is possibly the world's closest surveillance."

"So that we would not be so far from each other, when we were only talking by letter. I knew the old cabin would be empty."

"So you just moved in?"

"Why did you move into the major's cabin?"

"That's right. I moved in."

"If I am right, he knows practically everything."

"May I ask you something?"

"But I still can't understand at all how you get a mailman to deliver mail in the middle of the woods!"

"We're not playing hide-and-seek any more."

"Everything sounds so sad and solemn when you talk like that."

"Life is both sad and solemn. We are let into a wonderful world, we meet one another here, greet each other -- and wander together for a brief moment. Then we lose each other and disappear as suddenly and unreasonably as we arrived."

"Shoot."

"Only philosophy can bring us closer to Hilde's father," Alberto said at last. "Today I shall tell you about the Renaissance."

Alberto walked over and sat down on the sofa. Sophie followed and sank into a deep armchair.

"If I ever meet him, I'll scratch his eyes out!"

"Not very long after St. Thomas Aquinas, cracks began to appear in the unifying culture of Christianity. Philosophy and science broke away more and more from the theology of the Church, thus enabling religious life to attain a freer relationship to reasoning. More people now emphasized that we cannot reach God through rationalism because God is in all ways unknowable. The important thing for a man was not to understand the divine mystery but to submit to God's will.

Sophie could feel herself getting angry.

"As religion and science could now relate more freely to each other, the way was open both to new scientific methods and a new religious fervor. Thus the basis was created for two powerful upheavals in the fifteenth and sixteenth centuries, namely, the Renaissance and the Reformation."

"Didn't you tell me that the word 'renaissance' meant rebirth?"

"I did indeed, and that which was to be reborn was the art and culture of antiquity. We also speak of Renaissance humanism, since now, after the long Dark Ages in which every aspect of life was seen through divine light, everything once again revolved around man. 'Go to the source' was the motto, and that meant the humanism of antiquity first and foremost.

"By the Renaissance we mean the rich cultural development that began in the late fourteenth century. It started in Northern Italy and spread rapidly northward during the fifteenth and sixteenth centuries."

"Can we take them one at a time?"

"It almost became a popular pastime to dig up ancient sculptures and scrolls, just as it became fashionable to learn Greek. The study of Greek humanism also had a pedagogical aim. Reading humanistic subjects provided a 'classical education' and developed what may be called human qualities. 'Horses are born,' it was said, 'but human beings are not born -- they are formed.'"

"Do we have to be educated to be human beings?"

"It's an old book."

"Actually, it means 'cradle.' The word is used about books printed in the cradle days of printing. That is, before 1500."

"It looks like an old compass."

"What is that?" he asked.

He then pointed to an ancient firearm hanging on the wall above the sofa.

"And that?"

"An old-fashioned rifle."

"Exactly -- and this?"

"Yes, that was the thought. But before we take a closer look at the ideas of Renaissance humanism, we must say a little about the political and cultural background of the Renaissance."

"To be absolutely precise, it is an incunabulum."

"That old, yes. And these three discoveries -- the compass, firearms, and the printing press -- were essential preconditions for this new period we call the Renaissance."

Alberto pulled a large book off one of the bookshelves.

Alberto rose from the sofa and began to wander about the room. After a while he paused and pointed to an antique instrument on one of the shelves.

"An incunabulum?"

"Quite right."

"Is it really that old?"

"You'll have to explain that a bit more clearly."

"The compass made it easier to navigate. In other words, it was the basis for the great voyages of discovery. So were firearms in a way. The new weapons gave the Europeans military superiority over American and Asiatic cultures, although firearms were also an important factor in Europe. Printing played an important part in spreading the Renaissance humanists' new ideas. And the art of printing was, not least, one of the factors that forced the Church to relinquish its former position as sole disseminator of knowledge. New inventions and instruments began to follow thick and fast. One important instrument, for example, was the telescope, which resulted in a completely new basis for astronomy."

"And finally came rockets and space probes."

"Now you're going too fast. But you could say that a process started in the Renaissance finally brought people to the moon. Or for that matter to Hiroshima and Chernobyl. However, it all began with changes on the cultural and economic front. An important condition was the transition from a subsistence economy to a monetary economy.

"It's a bit like the way Greek cities developed two thousand years earlier."

"The three diverging streams from antiquity joined into one great river."

Toward the end of the Middle Ages, cities had developed, with effective trades and a lively commerce of new goods, a monetary economy and banking. A middle class arose which developed a certain freedom with regard to the basic conditions of life. Necessities became something that could be bought for money. This state of affairs rewarded people's diligence, imagination, and ingenuity. New demands were made on the individual."

"Not altogether untrue. I told you how Greek philosophy broke away from the mythological world picture that was linked to peasant culture. In the same way, the Renaissance middle class began to break away from the feudal lords and the power of the church. As this was happening, Greek culture was being rediscovered through a closer contact with the Arabs in Spain and the Byzantine culture in the east."

"You are an attentive pupil. That gives you some background on the Renaissance. I shall now tell you about the new ideas."

"That is precisely why we speak of a 'rebirth' of antiquity's humanism. But Renaissance humanism was to an even greater extent characterized by individualism. We are not only human beings, we are unique individuals. This idea could then lead to an almost unrestrained worship of genius. The ideal became what we call the Renaissance man, a man of universal genius embracing all aspects of life, art, and science. The new view of man also manifested itself in an interest in the human anatomy. As in ancient times, people once again began to dissect the dead to discover how the body was constructed. It was imperative both for medical science and for art. Once again it became usual for works of art to depict the nude. High time, after a thousand years of prudery. Man was bold enough to be himself again. There was no longer anything to be ashamed of."

"Above all else, the Renaissance resulted in a new view of mankind. The humanism of the Renaissance brought a new belief in man and his worth, in striking contrast to the biased medieval emphasis on the sinful nature of man. Man was now considered infinitely great and valuable. One of the central figures of the Renaissance was Marsilio Ficino, who exclaimed: 'Know thyself, O divine lineage in mortal guise!' Another central figure, Picadella Mirandola, wrote the Oration on the Dignity of Man, something that would have been unthinkable in the Middle Ages.

Alberto sat down on the sofa again. He looked at Sophie.

"Okay, but I'll have to go home and eat."

"Throughout the whole medieval period, the point of departure had always been God. The humanists of the Renaissance took as their point of departure man himself."

"But so did the Greek philosophers."

"They were certainly not especially moderate. They behaved as if the whole world had been reawakened. They became intensely conscious of their epoch, which is what led them to introduce the term 'Middle Ages' to cover the centuries between antiquity and their own time. There was an unrivaled development in all spheres of life. Art and architecture, literature, music, philosophy, and science flourished as never before. I will mention one concrete example. We have spoken of Ancient Rome, which gloried in titles such as the 'city of cities' and the 'hub of the universe.' During the Middle Ages the city declined, and by 1417 the old metropolis had only 17,000 inhabitants."

"Undeniably. The new view of mankind led to a whole new outlook. Man did not exist purely for God's sake. Man could therefore delight in life here and now. And with this new freedom to develop, the possibilities were limitless. The aim was now to exceed all boundaries. This was also a new idea, seen from the Greek humanistic point of view; the humanists of antiquity had emphasized the importance of tranquility, moderation, and restraint."

"It sounds intoxicating," said Sophie, leaning her arms on the little table that stood between her and the philosopher.

"And the Renaissance humanists lost their restraint?"

"It must be a gigantic church!"

"Not much more than Lillesand, where Hilde lives."

"It is over 200 meters long and 130 meters high, and it covers an area of more than 16,000 square meters. But enough about the boldness of Renaissance man. It was also significant that the Renaissance brought with it a new view of nature. The fact that man felt at home in the world and did not consider life solely as a preparation for the hereafter, created a whole new approach to the physical world. Nature was now regarded as a positive thing. Many held the view that God was also present in his creation. If he is indeed infinite, he must be present in everything. This idea is called pantheism. The medieval philosophers had insisted that there is an insurmountable barrier between God and the Creation. It could now be said that nature is divine -- and even that it is 'God's blossoming.' Ideas of this kind were not always looked kindly on by the church. The fate of Gior-dano Bruno was a dramatic example of this. Not only did he claim that God was present in nature, he also believed that the universe was infinite in scope. He was punished very severely for his ideas."

"The Renaissance humanists saw it as their cultural duty to restore Rome: first and foremost, to begin the construction of the great St. Peter's Church over the grave of Peter the Apostle. And St. Peter's Church can boast neither of moderation nor restraint. Many great artists of the Renaissance took part in this building project, the greatest in the world. It began in 1506 and lasted for a hundred and twenty years, and it took another fifty before the huge St. Peter's Square was completed."

"He was burned at the stake in Rome's Flower Market in the year 1600."

"No, not at all. Bruno was the humanist, not his executioners. During the Renaissance, what we call anti-humanism flourished as well. By this I mean the authoritarian power of State and Church. During the Renaissance there was a tremendous thirst for trying witches, burning heretics, magic and superstition, bloody religious wars -- and not least, the brutal conquest of America. But humanism has always had a shadow side. No epoch is either purely good or purely evil. Good and evil are twin threads that run through the history of mankind. And often they intertwine. This is not least true of our next key phrase, a new scientific method, another Renaissance innovation which I will tell you about."

"How?"

"Was that when they built the first factories?"

"No, not yet. But a precondition for all the technical development that took place after the Renaissance was the new scientific method. By that I mean the completely new approach to what science was. The technical fruits of this method only became apparent later on."

"How horrible… and stupid. And you call that humanism?"

"Mainly it was a process of investigating nature with our own senses. Since the fourteenth century there had been an increasing number of thinkers who warned against blind faith in old authority, be it religious doctrine or the natural philosophy of Aristotle. There were also warnings against the belief that problems can be solved purely by thinking. An exaggerated belief in the importance of reason had been valid all through the Middle Ages. Now it was said that every investigation of natural phenomena must be based on observation, experience, and experiment. We call this the empirical method."

"Which means?"

"It only means that one bases one's knowledge of things on one's own experience -- and not on dusty parchments or figments of the imagination. Empirical science was known in antiquity, but systematic experiments were something quite new."

"What was this new method?"

"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."

"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!'"

"Which do you think?"

"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."

"And that world picture was the right one?"

"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."

"I wish it were that simple!"

"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."

"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."

"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 perfect 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?"

"Don't they?"

"So why doesn't it?"

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

"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."

"And that is?"

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

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

"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."

"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."

"… it goes on rolling…"

"If you say so."

"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."

Sophie sighed resignedly.

"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?"

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.

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.

"Let's see."

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

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

"Impressive," said Sophie.

"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."

"Was he really that stupid?"

"What happened?" asked Alberto.

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

Alberto had already picked the marble up from the floor. He stood bowed over the inclined plane with the marble again.

"It rolled sloping because the board is sloping."

"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."

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.

"It began to roll because it was heavy."

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

"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.

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

"That's a silly question."

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

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

Alberto looked up at her and raised his eyebrows.

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

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

"That's fine with me."

"Precisely."

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."

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!"

"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."

"Does all this really matter?"

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

"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."

"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."

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

"Do I have a choice?"

"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."

"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."

"And that's true."

"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."

"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."

"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."

"Are there two different forces working on the moon?"

"I don't think I understand."

"Remember Galileo's inclined plane. What happened when I rolled the marble across it?"

"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…"

"Exactly. Both forces are constant, and both work simultaneously. Therefore the moon will continue to orbit the earth."

"But it is also attracted to the earth because of earth's gravitational force, isn't it?"

"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."

"Is it really as simple as that?"

"And that's how Newton could explain why all the planets go round the sun?"

"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."

"Very clever."

Alberto got up and put the inclined plane away again. He picked up the marble and placed it on the table between them.

"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."

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 space?"

"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 God'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 God. It's possible that man's picture of himself fared worse."

"How do you mean?"

"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 massive resistance."

"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 can well understand that. Because where was God in all this new stuff? It was simpler when the earth was the center and God and the planets were upstairs."

"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."

"I don't quite understand."

"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 God was now more important than his relationship to the church as an organization."

"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."

"Like saying one's prayers at night, for instance?"

"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 God's forgiveness. Neither was God'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."

"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."

"God was probably glad of that."

"Yes and no. A characteristic Renaissance feature was his emphasis on the individual and the individual's personal relationship to God. 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 God could mankind be 'justified,' he believed. For the wages of sin is death."

"His own priest? Wasn't that taking it a bit far?"

"What he meant was that priests had no preferential position in relation to God. 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 God's for-giveness 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?"

Alberto nodded.

"You said once that you are not Hilde's father. Is that really true?"

"You may be right. You'll notice that Hilde's father has begun to put words in our mouths. I think he is exploiting the fact that we are getting weary and are not defending ourselves very well."

Sophie felt almost as if he was trying to throw her out. As she went into the little hall, she thought intensely about why he had made that slip. Alberto came out after her.

"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."

Alberto Knox rose. He picked up the little green and black marble and put it in his top pocket.

"But a slip of the tongue is never wholly accidental."

"That was a serious slip of the tongue."

"I'm tired now, Sophie. You have to understand that. We have been sitting here for over two hours, and I have been doing most of the talking. Don't you have to go home to eat?"

"What did you say?" Sophie shot up from the chair she had been sitting in. "You called me Hilde!"

"It's after four!" Sophie exclaimed in horror.

"But am I Hilde?"

"That sounds very gloomy."

"Thank you for my lesson," said Sophie.

Hermes was lying asleep under a small row of pegs on which hung several strange-looking garments that could have been theatrical costumes. Alberto nodded toward the dog and said, "He will come and fetch you."

With that she opened the door to the staircase. As the door closed, Alberto said, "It won't be long before we meet again, Hilde."

Sophie was left with those words.

She gave Alberto an impulsive hug. "You're the best and kindest philosophy teacher I've ever had," she said.

Another slip of the tongue, the villain! Sophie had a strong desire to turn around and hammer on the door but something held her back.

She had not gone more than a few yards when she suddenly noticed a coin on the sidewalk. It was ten crowns, exactly the price of a bus ticket.

On reaching the street she remembered that she had no money on her. She would have to walk all the long way home. How annoying! Her mother would be both angry and worried if she didn't get back by six, that was for sure.

How could he, if he was in Lebanon?

Not until she was standing at the Main Square waiting for the second bus did she begin to wonder why she had been lucky enough to find the coin just when she needed it.

Sophie found her way to the bus stop and waited for a bus to the Main Square. From there she could take a bus on the same ticket and ride almost to her door.

Could Hilde's father have left it there? He was a master at leaving things in the most convenient places.

Sophie shivered. She felt a chill run down her spine.

And why had Alberto made that slip? Not once but twice!