Athene's Prophecy (Gaius Claudius Scaevola Trilogy) (12 page)

"And what lead you to that conclusion?" Timothy asked.

"Divine inspiration," Gaius shrugged, but the more he thought of this, the more concerned he became. In the dream, or whatever, Athene had stated that this opinion of contraries was important for his future, but it was also important in that it would be an early means of validating the predictions. This analysis of contraries had come to pass, and Gaius was only just beginning to realize that Timothy had never heard any interpretation like that. That meant he had to start his journal with this, which presumably would take him towards his destiny, but how?

"It would be," Timothy shook his head. This was a new problem. Perhaps this boy really did have talent. "Have you any further examples?"

"You asked me to think about locomotion. If I drop something, it has a force driving it towards the centre of the Earth," Gaius said. "Now if it falls further, it falls faster. It's weight presumably stays the same, so force is proportional to acceleration."

"Are you sure?" Timothy asked with a smile. "You have a cart going along the road at a good walking pace. Let the horse go, and what happens?"

"The cart stops," Gaius nodded.

"So the horse is exerting a force," Timothy smiled. "If the horse exerts more force, the cart will go faster, or the same with your stream. Clearly force is proportional to speed, and it is change of force that is proportional to acceleration."

"I see," Gaius frowned. In fact he did not. Something seemed to be wrong, but he could not work out what it was.

"There're plenty of clues, if you stop and think," Timothy smiled. "Which is the heavier, a rock or a feather?"

"Obviously the rock," Gaius replied, in the tone of someone who could see where this was going, and should have an answer for it, but did not.

"So the rock has more force," Timothy smiled, "and, if you don't believe me, drop a rock and a feather on your toe! The more force, the more speed results. Everything has a force; therefore it accelerates you to the centre of the Earth, no matter where you are, which, I might add, is the critical fact the great Aristotle used to show why the Earth must be a sphere. No other shape arises from a universal acceleration towards a point. Now, think about the bow. The arrow from the stronger bow will receive more force and that arrow will go further. Go try out some bows, and see if I'm right."

As Gaius left, Timothy stared pensively at the retreating back. The young man seemed strangely interested in quite a variety of things and he was undoubtedly intelligent. A problem remained, however: what was he doing? Creating a more educated tyrant? The fact remained that Aristotle had helped create a monster, and if Aristotle could not restrain his charge, how could he? But was this young Roman a monster? And if not, was he doing the opposite: teaching and encouraging a Roman in physics, a skill he might find totally unsuited for later life, for who, after all, had heard of a Roman interested in Greek science. Romans found it too abstract, and in truth, too useless.

Meanwhile, Gaius was anything but happy. Something was wrong with Timothy's argument! In the normal course of events, he would not care, but there were those predictions! Athene, or whoever that had been, had stated that his life depended on understanding, and he was in trouble over something so simple!

* * *

Gaius remained in correspondence with Claudius, who kept him informed of the happenings in Rome, and Gaius became increasingly despondent as he heard of the machinations, and the growing number of executions. As time passed, it became apparent that nobody was safe; being a direct descendent of Augustus offered no protection, nor, it appeared from the fate of Sejanus, did being the right hand man of Tiberius. Then there was the method; the senate had bowed to Sejanus so many times that Tiberius must have ordered his fate. Tiberius seemed to be playing brutal games with those he disliked, and, as Gaius was only too painfully aware, Tiberius appeared to be playing a game with him. He must keep a low profile, which, with the continual delivery of messages with the Imperial seal, was easier said than done.

* * *

Then came a message with a different seal: the personal seal of Tiberius,
Princeps
. His hands were shaking slightly as he opened it, and the relief was obvious when he read the cryptic message: "So far, so good. Congratulate Timothy for getting something into your head."

"So," Gaius shrugged to Timothy, "the
Princeps
thinks you are doing a good job."

"That old goat knows squat!" Timothy growled. "What sort of a job I'm doing'll be resolved later rather than sooner. In the meantime, think about why Pythagoras did what he did. He felt his discoveries brought him closer to an understanding of God. Comment."

'The question then was,' Gaius thought to himself, 'If Timothy is not reporting to Tiberius, who is?' Still, he had to answer the rapid change of subject, so he gave a challenging smile and said, "Assume he actually said that, then for him it would be true."

Timothy stared at him, then laughed a little. "Ha! Signs of a philosopher trying to get out! Good! Now Pythagoras also found the rules of harmony, the relations between the lengths of pipes and scales, and he made two further propositions that are quite fundamental. These are that the Universe is essentially constructed from numbers, and governed by symmetry."

"As put," Gaius muttered, "that is sheer nonsense."

"In what way?"

"I have a rock," Gaius said, "and if I threw it at you, it would hurt, so it is more than numbers. And the rock can be any shape."

"True," Timothy nodded, "but what holds the rock together may be governed by numbers. Now, Pythagoras further argued that if something followed from something else, you should be able to prove it by logical argument. I presume through Geminus you have seen some of the proofs Euclid wrote?"

"I can recall them," Gaius said, without any sign of enthusiasm.

"What Euclid did was to show how you could produce conclusions that you could prove to be correct. The ancient Egyptians built huge buildings, and they clearly knew many of the rules of geometry, but they did not prove what they knew. Comment?"

"I don't know anything about that," Gaius admitted.

"And that's a comment?"

"It's an admission that I have no idea what the Egyptians knew or whether they could prove it. For all I know, Euclid could have merely translated a lot of Egyptian scrolls."

"Interesting response," Timothy said. "Continuing the anti-Greek theme, but at least there's some thought there. Anyway, according to Pythagoras, everything has a cause and the effects will be related to the cause by mathematics. Thus if you throw a spear with twice the force it will go twice as far. As Aristotle noted, the motion of the spear is a constrained motion, not a natural motion, so no matter how hard you throw, sooner or later it will stop, and it will fall to the ground because falling towards the centre is a natural motion, and it will not stop until it cannot go further."

"What do you mean, constrained motion?"

"Basically, there're two sorts of motion, natural and constrained. Natural is eternal, like the Sun going around the Earth . . ."

"Or, as the great Aristarchus would have it, the Earth going around the Sun!" Gaius interposed.

Timothy laughed a little. "I shall ignore that particular attempt to rile me up. To continue, constrained motion contains within it its own contrary, so eventually it slows down and stops. Now, a real exercise. Deduce something about constrained motion. Don't argue about labels; that eternal motion is termed natural is simply a convenient definition. Also, don't go to the library. Your job is to think."

Chapter 8

Since once again he needed inspiration, he walked out to his temple but neither thoughts nor goddesses came. He ate some bread and cheese and lay back in the sun. A bird flew overhead, going towards the sea, and since he needed inspiration he walked down to the little cove. In the sandiest spot, a small fishing boat was having its catch unloaded by a small family, while out on the water there were a number of seabirds fishing. They looked so graceful as they swung effortlessly around in the sky, circling, looking for food. It even seemed so effortless when, like a bolt from Jupiter, they would dive into the water, later to emerge, gulping down food.

The speed they entered the water, he thought, must put them in danger of hitting the bottom but they did not. They were too clever for that, which was more than he could say for himself. Another day gone, and no further ahead. With a shake of his head, he turned away, began to eat the last of his bread and cheese, then he threw a piece away.

A stupid question! Think of something new. Maybe there was nothing new. Motion that slows down and stops is constrained, motion that doesn't is natural. He had never seen anything speed up and disappear, other than coins at the tavern, and there were no other options. The one sentence said everything. What else could be said?

Squark!

Gaius turned around to see a gull staring at him. The gull must have got the piece of bread he had thrown away. Perhaps he was saying, "Thank you!"

Squark!

Perhaps he was demanding more. Gaius was about to shoo it away, but then suddenly something struck him. Why the bird did not strike the bottom! The bird would go a lot slower in water. Perhaps that was the answer to his question. The water slowed the bird down! A strangely simple observation, yet when you thought about it, perhaps the secret to constrained motion!

"Thank you," he nodded towards the bird, and threw some more bread, which was gobbled greedily.

Gaius walked down to the beach and picked up a long stick. There was a pool between two large rocks. He walked to the side of the pool and lowered the stick until it reached the bottom, which was waist-deep. He nodded to himself, placed the stick against the rock, then he walked back to the beach. He needed a small piece of driftwood and some pebbles that were as near as he could find to being the same weight. He then heard giggles, and looked up to see two young women staring at him.

He walked back to the pool and carefully placed the piece of wood on the water, and balanced a stone on top. More giggles. Somehow, he felt self-conscious, which made no sense, because these girls were nothing but trouble. He stood up, held the stick in one hand near his piece of driftwood, while he held another pebble at arm's length, the same distance from the water as the water was deep. Then he overturned his little boat and dropped the pebble at the same time. More giggles.

As he expected, the stone splashed well before the pebble reached the floor of the pool. Just to be sure, he did it again, and the same thing happened, then he did it again, but with the stones reversed. Still the same result, and he had his answer. Something to add to his tiny journal, Timothy would not get rid of him that easily, and more to the point, he would not be drawn to Tiberius' attention as a failure.

* * *

"So, you have thought of something?"

"Of course I have," Gaius replied. "I would not have returned had I not."

"I'm beginning to believe that," Timothy muttered to himself.

"Your constrained motion does not carry its own contrary," Gaius said firmly.

"It doesn't?" a surprised Timothy asked, then he added in a more irritated tone, "You can't avoid the obvious just by declaration, you know."

"I didn't say there were no contraries," Gaius wagged a finger of chastisement. "I said the constrained motion does not contain them. Your Aristotle may have been careless here in not using his own procedures."

"What procedures?"

"Logic! Either the contrary comes from within or from without, and all Aristotle did was
assume
the first. But suppose it comes from without? Air gives a small contrary, water a bigger contrary, honey an even bigger one, while rock provides a contrary so big it stops everything in its tracks."

Timothy stared at him. This was something that had never occurred to him, nor, as far as he was aware, to anyone else. But he could not say that to Gaius. The young Roman's head would swell to an intolerable size. He resorted to that great teaching aid: if in trouble, bluff! Eventually he nodded. "Well done. That is quite logical."

"There's more," Gaius added.

"There is?" Timothy frowned in surprise. This was unwelcome, because he, the teacher, was being taken into increasingly unfamiliar territory.

"Yes. Remember when you said that force equalled velocity?"

"So?"

"It doesn't! You should be able to see that."

"Then perhaps you should enlighten me," Timothy replied, in the tone of a teacher who knew, even though he didn't and was trying to get his pupil to save him from having to admit it.

"The horse and cart example," Gaius chided. "The horse doesn't provide a force to provide the velocity, but rather to overcome the contrary force from the ground."

"That is possible," Timothy agreed, "but it doesn't prove it."

"Ha! But do you remember your own example?"

"I'm afraid I don't know what you're talking about," Timothy admitted.

"You said it was change of force that gave acceleration."

"So?" Timothy asked in a puzzled tone.

"The rock falls faster as it drops from a tower, but it doesn't get any heavier, does it?"

"That's quite true," a stunned Timothy replied. Whatever he had expected, this was not it.

"So with constant force you get constant acceleration, not constant velocity."

"Very good," Timothy nodded. "That is good logic." He paused, then added, "You realize, of course, that the end goal has nothing to do with physics?"

"It hasn't?" Gaius asked in a deeply mocking tone.

"No, it is to get you to think logically," Timothy said. "There's no need to study physics for the sake of physics. After all, we know all the physics that are there to know."

"Maybe, maybe not. You realize the corollary of what I said?"

"And what's that?"