"And you think I'm like that," Gaius interrupted. Yes, he had to admit that he had been a little arrogant towards Timothy at times, but usually in jest.
"No, I don't," Timothy said quickly. "If I did, I wouldn't be saying all this."
"Then I'm not quite sure I understand," a rather puzzled Gaius said slowly.
"You won't change the way the world works," Timothy said softly, "and there's no point in refusing to participate. However, there're ways of going about things. Put yourself in their shoes from time to time and ask what would you feel if you were them? Then, once the battle's over, there's no need to gloat, no need to needlessly kill, and no harm in making the conquered's lives a little easier. And if you minimize the hurt, you also minimize the hatred, and it might be just a little easier to reach those noble goals you keep saying Rome stands for. Think about this over night."
Chapter 10
"Now, today I want you to tell me, what use do you see geometry as having?" Timothy asked.
"Building, surveying, and. . I mentioned Aristarchus before," Gaius added, with a touch of satisfaction in is voice. He was getting good value out of that scroll Claudius had left for him to read. "His reasoning required geometry."
"It did," Timothy nodded. He paused, then added, "You seem to have been taken by Aristarchus' reasoning?"
"It never occurred to me before reading about Aristarchus that the moon was so huge, or that the sun was so far away, and therefore so immense. But even more, it would never have occurred to me that you could get a reasonable measure."
"It's a pity you've picked on the only Greek whose conclusions were basically wrong," Timothy shrugged, "but it gives me an idea. I shall teach you what I can about physics, and at the end of this course we shall have a debate. You shall present Aristarchus' ideas, I shall counter them."
"And you expect to demonstrate your superiority by beating me in this debate?" Gaius laughed.
"No, I don't," and to Gaius' surprise, Timothy laughed back. "You can't expect to win, because Aristarchus was basically wrong. No, I want you to argue logically, and when the logic is insurmountable against your position, you have to recognize that. Why?"
Gaius stared at him, then he remembered something old Libo had said. "In the army," Gaius said, "probably the biggest disaster is a pig-headed commander, one who won't accept that what he thought out isn't going to work."
"Exactly," Timothy nodded. "You will have to make the best you can of what you have, but there comes a time when you must recognize that you have to change your mind. It's just as wrong to back down too quickly, otherwise you would always be retreating. Instead, you must recognize when the logic is totally against you, then you have to change position. In any case, even a losing position has grounds to use logic. So, read what you can about these issues. In a few months we shall have this debate. Meanwhile, for next week think of a military use for geometry."
* * *
"Well?" Timothy challenged.
This challenge had proved to be easy, because Geminus had already taken him through the mathematics of levers as demonstrated by Archimedes, where the product of the force and the distance over which it applied could be equated to the energy used, or available. From the use of this, it was a simple matter to design siege engines, catapults, and a number of other devices.
"See, geometry is useful after all," Timothy smiled, after Gaius had finished explaining.
"So was Archimedes," Gaius continued. "He also found this rule that if you put a weight of material into a full pail of water, and weigh how much water overflows, you can tell what the material was made of. Like a given weight of iron will displace more water than the same weight of gold. You can tell whether some Greek has filled your gold with lead," he added helpfully.
"It would have to be a Greek wouldn't it," Timothy said in the tired tone of someone who had been waiting some time for this particular comment.
"It was a Greek who caused the problem Archimedes had to solve," Gaius pointed out.
"Was it now? Then in terms of physics, exactly what does this principle of Archimedes say?"
"That when you immerse an object in water, the force towards the centre is reduced by the weight of the water displaced by the object."
"That's quite correct," Timothy nodded. He was somewhat surprised that Gaius had bothered to actually learn what Archimedes had done.
"Archimedes also devised a means of burning boats with many mirrors. If the sunlight from each mirror lands on a single spot, then the heat from each mirror is concentrated, and the heat may be enough to start a fire, at least that's what geometry says."
"You've got the idea," Timothy nodded. "Now, what is matter? What is heat? What is light? Think about what connections you can make."
"It seems to me," Gaius said slowly, "that light causes heat, or maybe heat travels in light. When the light is stopped by something, it gets warm, if the light is strong enough. If enough light can be directed at the same place, as Archimedes showed, wood gets hot enough to burn. When the wood burns, it gives off heat and light, but. ."
"But?" Timothy said in a puzzled tone. Again he had not quite expected this.
"There's more heat than light, so maybe the two aren't quite the same, but can be turned into each other. A piece of steel embedded in a fire gets very hot, and glows red. I guess that's the excess heat trying to get out."
"And matter?"
"All I can say is that matter absorbs heat and gets hot. I suppose the heat is flowing around inside the matter."
"That's one view," Timothy said slowly. "There is another. The philosopher Democritus had a different view. He claimed that if you divided matter into smaller pieces, eventually you got to a stage where you could divide them no longer. He called these fundamental pieces atoms, and said all matter is made of atoms, which are indestructible and only differ in terms of shape and size. These atoms were moving around, and as matter gets hotter, the atoms move faster. Comment?"
"I suppose fire would be wood giving off atoms?" Gaius suggested after some delay.
"And you think that is what fire is?"
"I doubt it," Gaius replied, "because so much extra heat is given off by fire. The wood is cold, but you can get huge flames! That heat has to come from somewhere."
"Suppose it was from all the sunlight falling on the tree during its life?" Timothy suggested softly. More interestingly, why was this young man so sure it had to come from somewhere? He was anticipating, perhaps, some of what was coming next.
"Yes, but that heat was not turned into atoms running around quickly. If the heat of the fire really did come from the sunlight originally, it had to be stored some other way."
"That's very good," Timothy nodded. "We shall return to Democritus at a later date. For the present, we turn to Empedocles. He deduced there were four elements, earth, water, air and fire, and these are acted on by love and strife. ."
"You're not trying to tell me bits of wood fall in love with each other?" Gaius scowled.
"Of course not," Timothy replied tartly. "Sometimes in physics we meet a concept for which there is no simple explanation. Now we have to try to find words. What Empedocles meant was that there are forces that either bring things together or push them apart. It is the same with the elements. Earth means solidity, not literally soil; water is the flowing property of water. Thus oil has the property of water, although, as we shall see, these elements can be acted on in parts. Now Empedocles believed that while the elements can be combined or changed, their sum remains constant, which, and you will like this, seemed to contradict Aristotle. What you said before seemed to be that the sum of the light and the heat, and maybe some way of storing it, was constant.