by Ian Miller
* * *
"I have it!" Gaius exclaimed the following day. "Besides providing the less accelerating force through the stone being lighter, the water also provides the greater contrary, which makes the stone accelerate even more slowly."
"And how did you deduce that?"
"I didn't! Unlike you Greeks who like to sit around and contemplate, I devised a means of measuring this. I built a little bow that fires a little copper arrow. If I fire the arrow horizontally in the air it goes very much further than if the bow is immersed in water. The water must provide a greater contrary!"
"Of course," Timothy remarked with a smile, "a Greek could have worked that out without going to all that trouble."
"But he wouldn't have known absolutely that he was correct!" Gaius smiled. "Like most Greeks, he would only have argued that he was correct."
"Hmmph!" Timothy stared at him, then laughed a little and added, "We Greeks argue to show that we are correct. In fact, we even help our Roman friends when we suspect they will need it."
"This sounds rich!" Gaius jibed.
"I must give you some help for your coming discussion," Timothy said. One of the advantages of being right was that you could afford to look generous, and give what were sometimes known as Greek gifts. "Remember the great Aristotle showed why the Earth was a sphere? We can prove that the Earth is a sphere, and you always fall towards the centre. If you travel far enough . . ."
"You get back to where you started, although I am unaware anyone has tried."
"The Earth is simply too big," Timothy nodded. The young man was assertive, confident. Good! Now to be 'helpful'. "If you look at the Moon it has an image, right?"
"Yes."
"Carthaginians travelled south along the coast of Africa, where the desert changes to very hot jungle, to desert again, and then it starts to get cooler. What do you deduce?"
"The sun is over the middle part of the sphere," Gaius said, "and so the travellers went past the middle, and then to the corresponding part . . . well . . . down, or south."
"And the moon?"
"I presume it was about the same size, the same colour, the same image. What else?"
"The image is upside down," Timothy explained. "Of course the moon is the same. The traveller is the other way up."
Gaius stared at him, then said, "Of course!"
"Of course we don't know much more than that," Timothy added. "The noble Romans ploughed the Carthaginians into the soil, and destroyed any records they might have had."
"They were barbarians," Gaius shrugged. "They didn't leave records."
"On the contrary, the reason there are no records is because the noble Romans burned their great library to the ground. And why do you think they were barbarians?"
"They sacrificed little children to their Gods, just to get rain. And even then, it didn't rain!"
"So the noble Romans put an end to baby killing by killing everyone! They didn't do it out of greed? Your leading families didn't get hugely rich?"
"Yes, they did," Gaius admitted.
"And it wasn't as if they shared it out? Your senators got all the farmers to join the army and defeat the Carthaginians, and what did they do? They stole the peasants' land, so now they have a great landless class in Rome who have to be fed and entertained with barbaric games, all paid for by the taxes you impose."
"I agree the games are barbaric, however, they get rid of vicious criminals and make a bit of money doing it. Anyway, I'm not sure what that has to do with Aristarchus."
"You have to select your facts," Timothy nodded. "Some are irrelevant. Now, besides going south, you can go north, which is what the Greek Pytheas did. He sailed out of the sea you know, past the Pillars of Hercules, out to the great ocean and then sailed north, past Gaul, past Britain, and eventually reached the island of Thule, where in winter it is always dark."
"And cold," Gaius offered.
"And cold. Now, on the coasts of the great ocean, the water rises up and down in what are called tides, and Pytheas noted that these tides are related to where the moon is. The water is pulled up by the moon, which is providing a small contrary to the force of the Earth. Of course the Moon's force is much weaker than Earth's. Why?"
"Because the moon is smaller and further away?"
"Exactly. The tides are higher when the sun and moon pull together. The sun is huge, but it is much further away, so its effect is much smaller."
"He must have been observant to see this," Gaius muttered. "I've never noticed much."
"In our sea, tides are very small. But in the great ocean, with more water, they're much bigger, with the water level changing more than the height of a man in places. Now, that's enough for today." And with any luck, Timothy thought, he will waste a lot of time thinking about that.
* * *
Once again, it was pleasant to sit in the sun. By now Gaius was quite at home on Rhodes, and there was little about Rome that he missed, other than his family. His only concern was that these lessons, while quite pleasant, were not leading anywhere. Athene had implied they were important, but if they were, he could not see how. Wretched dream! It was so obviously a dream, but he could not put it out of his mind. Athene was so beautiful . . . But that was the trouble. She looked different from any Greek girl he had ever seen, she had blonde hair and grey eyes, and that was more like what he had heard of those wretched Germans. And therein lay his problem. She looked like nothing he had seen before, particularly her clothes, but at the same time she did not look like a Goddess. She looked like a woman. Surely Gods would look different in some ways?
"Since you are basically anti-Greek, there are two other Greek theories," Timothy brought him back to reality, "which I presume you will also refute?"
"That depends on what they say. I should know what it is before I say it's wrong."
"Good!" Timothy seemed genuinely pleased. "And feel free to refute them, because both have been refuted by the great Aristotle. The one that actually came second was due to the Stoics. They said nature is continuous, and infused with a spirit called pneuma. If you take a cylinder and piston, such as we use for water pumps, with nothing but air in it, seal an end, and press the piston down as hard as you can, then let go, the piston bounces back. The air is springy. Now, if you fill the cylinder with water, you simply cannot compress it. The element water therefore cannot be compressed, but it will transmit pressure, for you can use a pump to force water uphill. Do you understand that?"
"I understand what you can do with a pump," Gaius said, "but I do not understand this pneuma. It could be just the air."
"Aristotle didn't agree with that either," Timothy continued, "and if you are right and air provides the contrary to motion, it is providing the contrary to this piston."
"Your Greek, Democritus, might have the answer here," Gaius offered. "If he is correct about heat being atoms moving about, and air pressure being the atoms striking the wall, then if you reduce the volume and keep the heat the same, then atoms will strike the wall of the pump more frequently, which presumably means more force on it."
"You might be right," Timothy replied, "Whatever causes it, you can make pumps to lift water, or blow air, and in Egypt Hero has built a device by which the sun's heat makes air blow to move water that opens the door of a temple. Now, I'm trying to spark creative thought, so go away and think of something useful that comes to you from this pneuma. You can use Democritus' theory if you like."
* * *
Once again Gaius walked, and eventually arrived at the temple. He had been there several times, but never again had he received the vision of the young woman. Still, this was as good a place as any to think. He ate his bread and cheese, took some water, and sat with his back to a stone column.
At first, nothing came. Then later, it seemed that only nonsense had come. Accordingly, he was apprehensive when he met Timothy again.
"Well?"
"Suppose you have a fire, and to make it go faster, you have bellows. The fire heats som
e air, and when you take it to Hero's device, it lifts the bellows up and down. So, and you'll be pleased to hear this," Gaius added sarcastically, "you don't need a slave to keep the fire going. Of course, if you never lit the fire in the first place, you also wouldn't need the slave."
"Ah, but you've improved the life of one slave," Timothy said.
"Not necessarily," Gaius shrugged. "The fire is going faster, so you need two more slaves to keep up the wood supply. Unless," he added with a grin, "we could get Hero's device to chop wood, but that's hardly likely, is it?"
"One of these days, if you wish, I can take you to Egypt to see this device open doors, but in answer to your question, no, this won't. I have heard there are some Egyptians who have found that if you heat water and get steam, the steam can be made to push against something. Go away again and think what could happen if you can give steam enough pneuma. Imagine you could do something more than blow your own bellows!"
* * *
"Well?" Timothy smiled when they met again.
"If we believe Democritus, then in water all the atoms are much closer together than in steam, so if we boil water in an enclosed space, we get much more pressure, and if you did that, you could make it push a lever and lift something."
"Anything else?"
"You'll think this stupid, but if you put your fire and steam on a chariot, you could do away with the horse!"
"Why would I think that stupid? What's wrong with what you're saying?"
"The chariot would burn, and the weight of everything would be so great it probably wouldn't move anyway."
"They're good thoughts," Timothy said. "Now, let us return to Democritus and his theory that everything is made up of atoms that are continually moving around in a void. The hotter the stuff, the faster the atoms must be going. What do you say to that?"
"It would confirm the theory that coldness is the absence of hotness, however I haven't ever seen an atom and I can't see a void, almost by definition, but that doesn't mean they don't exist."
"The issue is difficult" Timothy agreed. "Democritus believed atoms were eternal, and never came to be nor passed away, but are combined to form things, and these combinations can come to be and pass away. Aristotle did not believe in atoms, but he did believe there was a substratum from which all things came to be and perhaps return to, and in some ways Aristotle's substratum is difficult to separate from Democritus' atoms. Also Aristotle was clear that it is very easy to refute arguments that prove the existence of the void, but he is equally clear that people who try to prove the void does not exist merely demonstrate their erroneous logic."
"Presumably there are arguments for such a void?"
"One argument is motion itself. If something moves, and there is no void, it must move to where something else is, in which case there would be two things in the same place, which is impossible, therefore there is a void. Comment."
"There is a town square," Gaius replied, after some time. "It is full of people. But I can get through because people will move aside."
"An excellent point. In fact that is similar to one made by the great Aristotle himself!" Timothy beamed. "Another reason for the void lies in fresh white ashes."
"They are full of void?"
"That is the argument," Timothy said. "If I take such ashes and add water, the volume of the ashes stays the same, but the weight is that of ashes plus water. The water has gone into the ashes, presumably into the void. Comment."
"Perhaps air has come out," Gaius offered. "It weighs almost nothing, and we know it requires space and if it can open doors, it should be able to keep bits of ash apart. Also . . ."
"Also?" Timothy was again puzzled. He was now beginning to recognize the look on Gaius' face as he headed into new territory.
"If we think ice, water and steam are made from the same atoms, then I guess in ice the atoms are hanging onto each other firmly; in water they are hanging on, but they can swap links, and in steam, they are moving too fast and don't really grasp each other at all."
"Very good!" Timothy nodded. "So, is there or is there not a void?"
"Yes, there is," Gaius said slowly. "If steam has the same number of atoms as water, and it occupies a lot more space, there must be void between the atoms. Also, if there is not, according to what I did with water there cannot be eternal motion. I refer to the void not as a thing, but rather as the absence of a thing."
"That is a good argument," Timothy nodded. "Now, atoms? An argument against atoms is that basically, everything that is in motion eventually falls. Heavier things fall faster, but sooner or later, everything falls, no matter how light."
"Until they hit the ground," Gaius offered, "then they stop and . . ."
"And?" Timothy smiled.
"According to you, Aristotle said that everything, no matter how light, fell to the centre?"
"Correct." Timothy was puzzled. Why was that objectionable?
"In which case," Gaius said very slowly, "air will fall too. But you said it rises?"
"You can see it rises," Timothy smiled. "Tip a jar over into water, tilt it, and watch the air come out."
"With a force lifting them equal to the weight of the water displaced," Gaius said triumphantly. When Timothy looked puzzled, he smiled, and added, "According to the great Archimedes, anyway."
"That is quite logical," Timothy agreed. He stared at Gaius in surprise. Once again he had not expected a fresh conclusion.
"So the Moon could move in a void!" Gaius insisted. "The layer of air may merely be at the top of the heap on Earth."
"From which you would consider this evidence supporting Aristarchus?"
"Well, yes."
"Persistent, if nothing else," Timothy nodded, "but since it is logic I am trying to get into your head, persistence has its merits. Anyway, let us consider two consequences of atoms. The first was due to Epicurus. He reasoned that if atoms were continually moving in the void, and if the properties of everything depended on how the atoms were joined together, and on the sun's light, and a number of other things, much of which we do not know, there is no need for Gods. Accordingly, there are no Gods. Comment?"
"Many of us Romans find the Gods to be more of a convenience than a necessity," Gaius replied, then suddenly felt apprehensive. He had effectively denied Athene. He paused, and continued, ". . . but that's not an answer, is it?"
"No. It isn't."
"There's no answer, then!" Gaius said in an irritated way.
"Apparently, not from you."
"And what's that supposed to mean? How's that argument supposed to help know whether there's a God?" Gaius said, waving an arm in desperation.
"And I don't suppose you would stop to think that that might be an answer?" Timothy said, evenly. "Suppose the argument does not follow? Suppose the logic is not there?"
"That's what I said! But it doesn't help decide whether there's a God."
"That's not the issue. What I am trying to do is to get you to use logic, to find fault in arguments, so that wherever you go, if a problem is given to you, your mind can cut through the irrelevancies and see things for what they are, or, as our example with the map, to see what is not there."
"Then my answer," Gaius said, "is that atoms and Gods are not connected logically, therefore the first part of the argument is silly. As I said, even if the first part happened to be true, and Gods are not required, it does not follow that they are not there. Equally, this argument does not mean that they are."
* * *
"Now, there is a really strange aberration in physics, namely Lucretius. The aberration is that he is Roman and who had something constructive to say. Comment?"
"I have no idea what he said," Gaius replied, "but the fact he's Roman doesn't make him wrong," Gaius looked almost challenging, then a thought struck him, "or right, for that matter."
"A nice addition," Timothy said caustically. "Lucretius said that atoms form some groupings that are immutable. One such grouping is in living things, for example, sparrows h
ave a sparrow grouping, which means all sparrow eggs give sparrows with the same brown markings in the same place, and this immutable grouping is a fixed joining of a lot of atoms. Comment?"
"I presume the comment about a lot of atoms comes from the fact that if a grouping makes sparrows, and another makes gulls, and another makes fish, there must be a huge variation of groupings, so it makes sense that there are a lot of atoms in the grouping," Gaius said, "and if sparrows are the same as they used to be, I suppose it means the groupings are immutable."
"Anything else?"
Gaius thought for a moment, then added, "Two things. The first is that this doesn't prove atoms, but it looks to me to be more likely than those five elements you were talking about, because if the differences came through mixing different amounts, why wouldn't the mix change? The second is, that if you could change the groupings, you could breed sparrows into something else."
"That's logical," Timothy smiled.
"Can you change an animal into something else?" Gaius asked curiously.
"That is your exercise for tomorrow," Timothy smiled.
Chapter 13
"So, today we think about changing animals," Timothy smiled. "Your thoughts?"
"Animals have been changed. The dogs we have were at one time supposed to have come from wolves," Gaius said, "and I believe some other animals and plants have changed too. Farmers can manage flocks by breeding the best with the best, but . . ."
"But?"
"The usual explanation I've heard is that the animals have a mixture of features, and by careful breeding you keep the features you want. That's not really changing, although I suppose if you say there are groups of atoms, if the odd one moved a bit, maybe that would do what you wish."
"So, does this support or not support Lucretius."
"I would say support," Gaius said. "As far as I know, you can't decide the changes. You might get bigger horses by continually breeding the biggest you have and not letting the small ones breed, but you just can't take a horse and make it into something as big as an elephant."