by Ian Miller
"Then let's have some contrary evidence! If the surface of the Earth is moving, there should be a contrary wind," Timothy said firmly, "and if the Earth goes around the sun, there should be a steady wind for that too, different between night and day as the surface is either going in the same direction, or the opposite direction, to its path around the sun."
"Not if the contraries come from the medium the motion is in," Gaius intervened in a triumphant tone.
"Oh?" Timothy was puzzled.
"The motion around the sun is eternal," Gaius smiled, "therefore there is no contrary. If the motion receives its contraries from the medium, and the motion is eternal, then there is no medium. The motion is in a void."
"The spinning Earth is in air," Timothy frowned.
"I have here a bucket of water and I'll put it on this potter's wheel and spin it," Gaius offered. He had been ready for this argument, and had brought the potter's wheel and put it in the corner of the room. "Watch! The water quickly catches up with the bucket."
"So?"
"Aristotle made the excellent point that everything, no matter how light, falls to the centre. So does air, but because of Archimedes' principle, it's on top. Outside that, there is void, and the bodies and air move with eternal motion. There's no contrary wind because there is nothing on the outside and the air has caught up with the Earth, just as the water does in that bowl. Furthermore," he added, and wagged a finger at Timothy, "we can prove there's nothing out there."
"We can?" Timothy gave an even more perplexed look.
"Yes! Watch stars come up from the horizon. They really shimmer, and that must be because of the air. Now, as the ancients noted, stars go behind the Moon quite sharply. The reason there're no clouds on the Moon is simply because there's no air there. The Moon is not in air, so its motion is eternal!"
Timothy gave Gaius a look that seemed as if it was true respect, then he nodded and said, "That was good logic. I concede that if there is a void, the argument of the winds is not valid, and there's no way to prove there is air around the Moon." He paused, then added, "How about this?
"Let's suppose for a moment the Earth travels around the sun. It must therefore move with two motions. Think of going around a table in a circle. You go left to right and front to back"
"So?"
"Think of people scattered around a field, and you walk a circle. Sometimes, someone will seem to be to the left of someone else, then as you keep walking they may appear to pass in front and end up on the right. That does not happen with the stars. No matter what, they are always in the same position relative to each other."
"If you're far enough away, and the stars are far enough apart, you wouldn't notice," Gaius said. He had seen this argument, and was prepared. "If Democritus is correct, and the stars are other suns, to get that dim they have to be very far away." He paused, then continued, "Added to which, something like that does happen to the paths of the planets."
"First, the planets," Timothy nodded. "They are on separate spheres, which travel around the Earth at different speeds and at times meet epicycles, so yes, your argument about the planets is correct, but in different forms it is the same for both explanations."
"Except for one point," Gaius frowned.
"Which is?"
"If the planets are on different spheres, one inside the other, how come you can see through them to the outer spheres? Why is nothing shaded?"
"The spheres are made of material you can see through," Timothy shrugged.
"There's nothing like that on Earth," Gaius shrugged, "which is clear enough and strong enough."
"Firstly, there's glass, and secondly there's no reason why the material of the heavens can't be different from on Earth."
"Firstly, as you put it," Gaius smiled, "there's good reason to believe the material of the heavens are the same as those of Earth. Bits of meteors have been found, and they comprise stone and iron. In your model, these fall to the centre, and would break anything like glass, or would never reach the Earth."
"They could fall through holes in the lowest sphere," Timothy pointed out.
"That's little better than resorting to magic," Gaius countered, "and there's no reason to resort to that when there's the perfectly simple explanation of everything falling to the centre, in this case the sun."
"But the Moon falls around the Earth?"
"While both of them are falling around the Sun," Gaius replied. "Smaller falls around bigger. And there's more. Let's suppose the Sun moves around the Earth on your spheres, and the Moon does also. There is now the issue of eclipses."
"I thought we'd dealt with them," Timothy frowned. "We agreed that eclipses happen when the Moon, being closer, crosses the Earth – Sun line, with a solar eclipse when the Moon is on the sun side and . . ."
"We agree the cause of eclipses," Gaius interposed. "It's just that this can't happen with your spheres."
"And why not?" Timothy said in a puzzled tone. "This is usually thought to be the stronger point of the argument about the spheres."
"Because if the Moon falls around the Earth, and does so to also pull on the tides, it must move with two motions."
"So?" Timothy opened is hands as if he could not understand.
"Once the bodies get back into the same positions, the same thing should happen, but it doesn't. Eclipses are rather rare," Gaius pointed out. "No frequent repeating cycle means your moon has to move with three motions, one of which has to be like a pendulum. There's no physical cause for that, but on the other hand, if the Moon goes around the Earth on a plane different from that on which the Earth goes around the Sun, then eclipses occur when the three bodies are fortuitously in line."
"Interesting," Timothy shrugged, then said, "Let's deal with this spinning Earth. For the Earth to spin, it needs a continual applied force and . . ."
"That assumes there is a contrary to overcome," Gaius replied. "If it is spinning in a void, nothing will slow it down. It would be like a top, going on forever."
"Then if it were spinning," Timothy continued, "there would be a natural tendency for light things like leaves not to be able to keep up . . ."
"If the air keeps up by friction, so do they," Gaius countered.
"Hmmm. In that case, what about this," Timothy said. "Suppose I throw a stone straight up in the air. Force from the hand causes energy to come to be and the stone rises in the air. The energy slowly passes away until the stone reaches a point where it has no energy, then it begins to fall towards the centre. More energy comes to be, the stone speeds up, then it hits the ground and the energy passes away again. Do you agree so far?"
Gaius thought for a moment, then remembering Timothy' tactics, he said, "Perhaps, perhaps not, but for the moment let's assume that is so."
Timothy gave him a smile, then continued, "Think of the geometry. If the Earth is spinning, then the stone is travelling horizontally at a speed of, say, v, such that v times twenty-four hours equals 2πr, where r is the radius of the Earth. Now, let me throw the stone high in the air, say to a height h. At that point, it has to travel 2π(r+h) in twenty-four hours. Since no force has been added other than in the up and down direction, it cannot speed up in terms of rotation, so it should slip back on its path. But no matter how high you throw such a stone, it always falls back to where you threw it up."
"That depends on no lateral forces coming to be or passing away."
"What's the objection to that?" Timothy asked.
"Nothing. I'm just thinking," Gaius admitted. "I also note that, except at the equator, your line of length r and your line h have an angle between them. I also note your h is very small compared with r."
"Agreed, but so what? The distance you can measure on the ground is of a similar distance compared with the circumference of the planet."
"Perhaps," Gaius said. He paused, then added confidently, "You define the perpendicular as the point from where you drop something so that it lands in the desired spot. Obviously if you stand on that spot and throw
something in such a way as it just reaches that point and effectively stops, it will fall back to your spot, and the motion will have been perpendicular by definition."
"Let me get this straight," Timothy frowned. "Are you saying Aristotle's argument is wrong or not?"
"The argument may be correct," Gaius wagged his finger, "but as Lucretius would say, and indeed said on different matters, the argument is not valid because you can't carry out the test properly. Not only that, but obviously Aristotle missed a chance to shine here."
"What do you mean by that?"
"Suppose you dropped the stone off a very high tower, and you could accurately locate the point vertically underneath it. With your assumption that no lateral forces came to be or passed away, which means they're conserved, then the motion at the top of the tower is faster than the bottom, so the stone will fall east, slightly. But there's more. The stone falls to the centre, but the bottom of the tower doesn't move towards the equator, so by simple geometry, the stone will also fall slightly south."
"Nobody's seen anything like that," Timothy protested.
"Because nobody's tried. According to you, logic is sufficient, and that is logical."
"It seems you have learned something from all this," Timothy nodded.
"So you have more objections?" Gaius challenged.
"Then let's get to the real heart of the problem," Timothy nodded. "You recall we discussed circular motion?"
"I do."
"As Aristotle noted, circular motion is really two motions. There is the steady falling towards the centre, and the steady moving sideways. Do you agree?"
"I've already agreed," Gaius said, "when we were discussing eclipses."
"So describe the motion of something going around the centre with no string."
"The stone, say, is falling towards the centre. It also moves aside. When it has moved aside, it has also fallen sufficiently that it is the same distance from the centre. Because it is falling towards the centre, the direction of falling has changed, but so has the direction of moving aside. Accordingly it stays at the same distance."
"Well put," Timothy nodded with approval. "Now you must see why the Earth cannot go around the sun?"
"No I do not!" Gaius responded irritably. "The Earth can fall around the Sun just as easily as the Moon fall around the Earth. The Sun is, after all, bigger than the Earth, so why shouldn't the smaller object fall around the bigger?"
"The objection is not to one object falling around the Sun," Timothy said. "Rather, the objection is to many objects falling around the Sun."
"Why not? If I take a bucket of sand, there're many objects, and they all fall when I empty the bucket."
"Exactly! And what happens when you empty a bucket of sand and stones?"
"They all fall."
"Yes, they do" Timothy said. "Now, how about a bucket of stones, and some lighter sand?"
"They still all fall," Gaius said. He was now somewhat apprehensive. This seemed to be Timothy's big point, and for the life of him, he could not see what it was.
"Of course they all fall," Timothy nodded, "as Aristotle said they would. But think about it. As Aristotle noted, objects with superior weight fall with superior speed."
"Well?" a puzzled Gaius said.
"Now you should see it," Timothy said triumphantly. "They do not all fall at the same rate. The heavy stones fall first, the lightest sand reaches the ground last."
"I'm not sure I follow." However, for the first time, he looked concerned.
"Heavier things fall fastest because by the definition of heavier, they sustain more force," Timothy emphasized. "If circular motion requires constant falling, the heaviest things with more force will receive more acceleration and hence fall the fastest, the light things the slowest, and the Earth would simply fall to pieces, or at the very least, the air would all fall slower and get left behind. Light things like air and leaves can't fall as fast, so from the night side they should stream off away from the sun, like the tail of a comet. This simply doesn't happen."
"No, it doesn't," a stunned Gaius replied.
"Except possibly for comets," Timothy added helpfully. "If you wish to say they go around the sun, I might have to agree."
"But they're not really relevant, are they," Gaius muttered.
"Oh, but they are," Timothy pointed out. "They are evidence that the streaming effect actually occurs. Clearly comets are made of heavy and light stuff. In fact the tails of comets are reasonably clear evidence that the physics outlined by the great Aristotle are correct."
Gaius remained silent, somewhat stunned by this turn of events.
"Now, think about being on a chariot," Timothy continued. "When the chariot turns a corner, you tend to be thrown to one side because there's nothing joining you to the floor of the chariot. If Aristarchus is right, and everything is that big, the Earth is travelling far faster than any chariot, but have you ever noticed being flung to one side? Or even being slightly nudged?
"And there's more," Timothy added. "Your arguments negate mine, but to properly argue for the Earth to go around the sun, you have to formulate a proposition where you say, only if the Earth goes around the sun will I see this, and then you must show it. You have not suggested anything like that."
"Give me a moment," Gaius frowned. This was impossible! He was so sure he was correct, but . . . There seemed to be no answer!
"So?" Timothy eventually challenged again. "You can't win by sitting there and hoping I'll eventually die."
"I know," Gaius muttered. He was no further ahead, and he suspected he would be no further ahead tomorrow, but that did not mean he was wrong. But where? He looked up at Timothy and nodded as he said, "I'm sure you're wrong, but I can't win on this field today. Since I've lost, I'll add in twenty aureii. With that, and the fuss you made earlier, I expect you'll go."
"Expect?"
"If you wish to stay with me, you may," Gaius said. "You'll still be free, and I'll pay you more, but if you wish to leave, I fully respect that, but I think you're wrong! I don't care what you say, all that talk about the sun being stuck on a sphere, moving tens or maybe hundreds of millions of kilometers a day! Not only that, but it is so hot it should melt the disk. That's just plain wrong, but . . ." Aristarchus had to be correct. After all, Athene had asked him to prove it, and what was the point of that if it were wrong?
"But?"
"I've got to admit the Earth doesn't fall to bits, and I've got to admit circular motion requires falling. Something's wrong somewhere, and one of these days I'm going to find out. It'd be nice to see your face on that day!"
"I see," Timothy stared at him. "So when do I have to decide whether to stay?"
"You don't," Gaius shrugged. "Your only decision is if, and if so, when you leave."
"And I can leave any time?"
"You're a free man," Gaius shrugged. "You can do what you wish. I want you to stay as a friend or not at all."
It was then that he remembered the expression Timothy had on his face when he first entered the room: Athene! Her expression had been, 'This has got to work.' But why? Whatever else that had been, it was not a dream. Dreams were always forgotten after a couple of days, but this had been so vivid, effectively imprinted on his mind so he would not forget. Why? Who was she? If his interpretation of her expression was correct, then whatever he did had to be important for her future as well as, or even instead of his, but how could he possibly affect someone whom he had never met, and had no conceivable mechanism for ever meeting?
Why did it matter whether planets go around the star? How could that affect his future? Or hers? Then again, perhaps it didn't. What Athene had said was that the method by which he came to understand was important, which meant . . . What did it mean? Assuming it meant something, he had a few years to achieve three things. As Timothy had often remarked about slaves, he must keep going.
Chapter 20
Gaius was surprised that Timothy wished to remain with him, particularly when he told
him about the note he had received from Tiberius, which ordered him to Alexandria where he would be contacted over his military appointment. Timothy could have stayed where he was, except perhaps the villa belonged to Tiberius. When he politely asked Timothy why, the explanation surprised him.
"Simple curiosity."
"Oh? About what?"
"About your so-called retreat," Timothy said, not entirely truthfully. Timothy also saw Gaius as a further source of gold coins. "You really think you're right!"
"I'm quite convinced that that sequence of spheres is just plain wrong," Gaius said quietly. "Almost everything's a special case. That's ridiculous."
"But the only alternative is Aristarchus," Timothy said, "and as we've established, he's plain wrong on clear physical grounds."
"I'm still convinced there's something wrong there, but I can't see what," Gaius admitted.
"Which gets me to why I'm staying," Timothy nodded. "I can't see why a Roman would care."
"Because I don't like to be wrong."
"Then perhaps I'm staying in case I can put this obstinacy to better purpose."
"Like freeing slaves?" Gaius smiled.
"Hah!" Timothy laughed. "You couldn't do that."
"I freed you," Gaius pointed out.
"And I'm grateful," Timothy replied quickly. "I meant you couldn't remove the need for slavery."
"Not even by building machines to do the work of slaves?" Gaius remarked querulously.
"You couldn't do that. Ever!"
"Not even based on that machine that opens doors you kept on about?"
"It opens a door well balanced with a counterweight," Timothy admitted. "It's a stunt."