by Ian Miller
"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.
"Empedocles also said that you saw colours because different types of light entered your eye. He thought light was very important, and that the velocity of light was one of the most fundamental things of all. He thought that sound was a pulsation in matter, and showed that air is such matter, by showing that if a cup is inverted over water, the water that goes in is equal in volume to the air permitted to escape.
"He also showed something you can see for yourself later. If you put a lodestone under a parchment, and put on iron dust, which I have got here from the sword sharpeners, you will see lines. Empedocles argued that one end was attracted to the other and a flow of something was going around to the other end. It is repulsed, however, by itself. You can see this for yourself with this small collection of lodestones. Hold them close together, then rotate one. Now, take these lodestones, and take the iron dust, and see for yourself. See if you can come up with a conclusion."
Lodestones! Yes, Athene had mentioned them, and he was supposed to find something significant about them. But how? He recalled that Athene had said he must note what he found, not that as yet he had found anything. He moved the lodestones, felt an attraction, so he let the two join together, at which point he noted the lines of iron filings were a larger version of what one lodestone would give. He turned one lodestone around and noticed that they now repulsed each other, but the force was not strong so he could leave them in place, at which point he saw the lines of filings behave as if the lines were pushing against each other.
So, something was going out one end and going in the other. If that were the cause of the repulsion, then the repulsion should be stronger between one pair of ends than the other pair. Yes, he could find that. The only problem was, when he tried it, both pairs of repelling ends behaved more or less that same. Something to note: a wrong idea!
Why did the iron filings line up? Other dust did not, but the filings lined up similar to how tiny pieces of lodestone did. Perhaps the iron was taking up that property? He got a small nail, and began rubbing one of the lodestones along it, and after some time, it too would align iron filings, albeit weakly. Yes, the reason why the lodestones pointed north! They were lining up like the iron filings. The middle of the Earth must be either a massive lodestone, or maybe a massive lump of iron. Not that he could ever prove that.
It was then that he thought some more, moved the lodestones again, and found that the lines never crossed. Something to note that worked! What about numbers of lines? They seemed to be the same for a given lodestone, but ones that seemed to be stronger seemed to give more lines. He thought about this a little more, then he started to count the lines emanating from a lodestone, and he wrote down the numbers. He then fixed one of the stronger lodestones into a piece of wood, then he tied another onto a piece of string and lowered it down towards the other so that the ends attracted. By moving the support, he could make the force of attraction swing the stringed lodestone like a pendulum and measure how high he could get it to lift for a given distance between lodestones. As he suspected the angle he could make it move was much higher the shorter the distance. He made some measurements then changed lodestones, and repeated the experiment, intending to correlate his distances with the number of lines he had counted. There would be a constant weight towards the centre of the Earth for each lodestone, so what he was measuring was the force between them countering that weight. Later he would do some calculations. But then what? Show what he worked out to no person?
It was then he had another idea. He remembered his amber that attracted hair and very light pieces of dust. He got his pieces out again and rubbed vigorously, and yes, the fur seemed attracted to the amber in lines. He got two charged up and suspended them, and yes, they repelled each other, but when he tried to turn them around, the repulsion stayed, except that with his fiddling, the repulsion lowered, no matter what he did. The rubbed amber was like the lodestone in some ways, but not in others. What did that mean? He did some more experiments, writing down what he did, but at the end he seemed more confused.
* * *
Gaius expected Timothy to ask him about lodestones, but to his surprise, he did not. Obviously, Timothy had forgotten. Actually, Timothy had not. He had seen Gaius with his lodestone suspended from a string, while moving a piece of wood towards it, then making measurements. He had later seen Gaius doing some rather awkward calculations, and he had no intention of being drawn into those. As far as Timothy was concerned, there was to be no further discussion of lodestones. Still, if Gaius was so intent on mathematics, he could easily divert his attention.
"Today we recall Pythagoras argued that everything is underpinned by numbers. Plato applied this to Empedocles' elements, and noted that there are five regular shapes with faces, or six if you consider a sphere to have one face. There is the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. Now, Plato thought about this. Do you notice a connection with the number five?"
"It follows four and precedes six?"
"That's not exactly what I mean. Some Greeks," and he emphasized the word some, "have noticed that there are five elements, seven metals, and five planets."
Yes, Gaius thought to himself, if there were a record for the most tendentious nonsense in the world, this would be it.
"It all follows from the fundamental importance of symmetry. The primitive matter is represented by a circle, the most symmetric of shapes. Such matter is worked on by two properties: hotness and its contrary coldness, and dryness and its contrary, wetness, such that opposites have nothing in common. Thus on opposite sides are fire and water, air and earth, while the properties can be shared by adjacent elements, thus fire and air can share hotness, air and water wetness, and so on."
"According to this," Gaius frowned, "you can't heat water. That must be wrong."
"Not at all," Timothy said in a firm tone. "Fire can heat earth, and hot earth makes water hot. You have to place your water in a pot, or it puts out fire. That's a fine example of the symmetry at work."
"Perhaps, but you can explain anything like that," Gaius shrugged disparagingly.
"Because it's a fundamental truth!" Timothy snorted. "Of course substances may be mixtures of the ideal elements. Suppose I put a pot of seawater on a fire. If the real fire contains some earth, the bottom of the pot becomes black. The seawater is a mixture of water and earth, so when water is driven off you get wet air and leave behind dry earth. The underlying material has had its properties changed, which changes the elements."
"Changes the elements? You mean, things aren't made of unchanging elements."
"Not according to Aristotle," Timothy smiled. "The elements are states, and the change of elements changes the state of being. When burning wood, wood does not combine with fire or anything else. Instead, fire is an agent of change and is coming into being while the wood is passing away. Water has the property of wetness, but so does oil; fire cannot come into being from water, though, but it can from oil, so oil is not a fundamental element of change, but is changed itself by the element fire, which liberates air and perhaps a little earth from the oil."
"Why does oil have air rather than water? Because of fire?" Here was a theory that explained everything and nothing both at the same time!
"Oil has air and water," Timothy stated. "It has wetness, but yes, the fire shows it has air. Also, elements tend to separate and go to their natural place, determined by the contraries up and down. Fire, being like the heavens, goes up strongly, while earth, being the heaviest, and most earth-like, falls fastest. Water falls slowly, air rises slowly. Oil sits on the top of water, so obviously it has more of the nature of air."
"Which presumably means," Gaius countered, "that the air should rise to the heavens and disappear. Eventually we won't be able to breathe!"
Timothy stared at him, and then laughed. "According to the great Aristotle, you have a correct premise, but you've failed to draw the correct conclusion. Look at the logic! Air rises yet we still breathe. Therefore?"
"I don't know!" Gaius said irritably.
"The obvious conclusion is that we shall not run out of air because the heavens are filled with air already! As the great Aristotle noted, nature abhors a void. There can be no permanent void, otherwise air would rush in and fill it!"
"Oh!" Gaius said. "I hadn't thought of that."
"Whether or not there's a void is unimportant. What matters is whether you consider every possibility, then by sheer logic, arrive at the correct conclusion. That's what I'm trying to teach you. I can help you expand your thinking, to give you exercises in logic, but you have to do your part. If you are just going to sit there, then you might as well do what you will with me now, because this will just be a complete waste of time!"
"Two responses," Gaius said firmly, as he stood to take a position of authority. "Whatever the outcome of this, you need not fear. Any failings on my part are not your problem, that I promise."
"Thank you," Timothy said, in a voice of slight surprise.
"Secondly," Gaius continued, "it is not my intention to fail. But that doesn't mean I intend to agree with your theories about . . ."
"Gaius!" Timothy interrupted, "that's good. I don't want your agreement! I want you to think! Rome will stand, even if no Roman has the first clue about the elements!" He paused, then added, "If you wish me not to say such things about Rome . . ."
"You may say what you wish about Rome, short of inciting a revolt," Gaius said. "Many Romans have been highly critical, so say what you wish! O
n the other hand, be prepared for some fairly caustic Greek comments!"
"I've noted some already," Timothy said. "Now, as I was saying, if you are to be successful, you have to be able to filter out that which is important from that which is not, and physics is as good as anything to practise on. So, to make things more difficult, soon we shall discuss further the elements, but tomorrow we discuss the Battle of Issus."
Chapter 11
"Battles can be won before they're fought," Timothy started, "through supply, morale, belief in the cause, reason to fight, but assume for this discussion there was only one major difference: Alexander's army was professional, Darius' was far bigger.
"Before the battle, Darius had lost the western seaboard to Alexander, at least down to the Gulf of Iskanderun. Darius had sent a small force forward to hold Tarsus, but Alexander had already taken it. Alexander then fell ill with fever, and Darius, who was now camped on the plain of Sochi, thought that Alexander's apparent immobility signified that he was afraid of his large army. Comment."
Gaius paused. The answer was obvious, so why ask? Eventually he said, "Darius jumped to the conclusion he wanted to, but he still should have sent out spies."
"Suppose he learns that Alexander is ill? To win, you must take the initiative. Your men mustn't see you as indecisive. Even if you're defensive, building fortifications helps them to feel that the commander has a plan and knows what he's doing. However, Darius remained at Sochi for some time, seemingly doing nothing. Comment?"
"There's no need for Darius to build fortifications, but he should have used all the available time and been busy carrying out exercises, drilling his troops."
"You would be quite happy for Darius to remain at Sochi?"
"If you significantly outnumber the enemy, why not force the battle on flat terrain? And with soldiers of poorer quality, why not use the time to drill them and make them better?"
