An ancient theory: how does the sun work?

One of the peculiarities of forming theories is that there is tendency to try to explain everything. For Aristotle, one of the most peculiar aspects of nature was the power of the sun. Where did the heat and light come from? An important observation was that the Sun’s output was known to have been constant for several thousand years, and a quick calculation showed that had it been powered by combustion, such as burning coal, it should have faded. It had not. Now there was a questionable issue here: how far away was the sun? Some time after Aristotle, Aristarchus measured this distance, and was the first to realize how big the solar system really was, and since his measurement was somewhat error-prone, he seriously underestimated the size of the star. Nevertheless, the argument was correct in another sense: if the star was further away, the power had to be correspondingly greater, so qualitatively the argument stood. So, what powered the sun?

There was only one possible explanation that Aristotle could see: the Sun had to be moving, and by moving, it generated a lot of friction, because such friction would be the only physical means of powering the star. The earth did not generate heat, therefore it was not moving. Note that it was not Rumford who established that friction generated heat, in fact the first would be the one who discovered how to start a fire by rubbing one stick in the cavity of another. Aristotle knew that, but somehow in the middle ages the knowledge got overturned by the concept that heat was some subtle fluid called caloric. So, what Aristotle did was to take the only explanation he had that was possible, and also one that helped his theory. It would be too much to expect the ancient Greeks to guess nuclear fusion, but it shows that when developing a theory, every now and again something turns up that should not be explained. There is no fault in admitting you do not know everything.

So, what was the weakness in that theory? The first one might be the phases of the moon. The moon was moving as well, but the phases of the moon were to be explained in terms of reflected sunlight, which is correct, but it meant that the moon was moving approximately as fast, but generating trivial amounts of heat and light. Why was this? Yes, you could find an explanation, but the problem then became, a new explanation was required for one additional fact.

Another interesting fact is that Aristotle and other ancient Greeks considered stars to be other suns, but a long way away. Again, true, but their light was considered to come from the same source: friction. The problem with that is that for those on the equatorial regions their angular velocity was very close to the same as that of the sun, which meant that if they were x times further away, they were going x times faster across whatever was providing the friction, and hence they would emit x times the energy. They should be a lot brighter than they are. A second problem was that those near the poles are travelling much slower, and in principle, the pole star does insignificant travelling. If so, there should be a general dimming from equator to pole, but there was not. Finally, since they have different degrees of brightness, it was argued (correctly) that they were different distances away, but if that were the case, they all had to be travelling on separate disks, all with the same periodic time, but all with different velocities. At the very best, an incredibly complicated scenario. Now the interesting fact is that these difficulties were recognized, but were swept under the carpet. That habit may not have died out just yet. 

 

What is involved in developing a scientific theory? (2)

In my previous post, I showed how the protagonist in Athene’s Prophecy could falsify Aristotle’s proof that the earth did not rotate, but he could not prove it did. He identified a method, but very wisely he decided that there was no point in trying it because there was too much scope for error. At this stage, all he could do was suggest that whether the earth rotated was an open question. If it did not, then the planets could not go around the sun, otherwise the day and the year would be the same length, and they did not. At this point it is necessary, while developing a theory, to assume that as long as it has no further part to play in the theory it does, if for no other reason than it is necessary. By doing so, it creates a test by which the new theory can be falsified.

The logic now is, either the earth moves or it does not. If it does move, it must move in a circle, because the sun’s size was constant. (Actually, it moves in an ellipse, but it is so close to a circle that this test would not distinguish it. If you knew the dynamics of elliptical motion, you could just about prove it did follow an ellipse. The reason is, it moves faster when closer to the sun, and the solstices and the equinoxes were known. A proper calendar shows the northern hemisphere summer side of the equinoxes is longer than the southern hemisphere’s one by about 2 – 3 days, and is the reason why February is the shortest month. We, in the southern hemisphere, get cheated by two days of summer. Sob! However, if you have not worked out Newton’s laws of motion, this is no help.) So, before we can prove the earth moves, we must first overturn Aristotle’s proofs that it did not, and that raises the question, where can a theory go wrong?

The most likely thing to go wrong in forming a scientific theory can be summarized simply: if you start with a wrong premise, you may draw a wrong conclusion. Your conclusion may agree with observation, because as Aristotle emphasized, a wrong premise can still agree with observation. One of Aristotle’s examples of false logic is as follows:

Man is a stone

A stone is an animal

Therefore, man is an animal.

The conclusion is absolutely correct, but the means of getting there is ridiculous. A major problem when developing a theory is that a wrong premise that brings considerable agreement with observation is extremely difficult to get rid of, and invariably it has pervasive effects for a long time thereafter.

One reason why, in classical times, it was felt that the Earth must be stationary was because of Aristotle’s premise that air rises. If so, the fact that we have air at all must be because the Universe is full of it. If so, then if the earth moves, it must move through air. If so, there would be a contrary wind, the speed difference of which on either side would depend on the rate of rotation. There was no such wind, therefore no such orbit. We can forgive Aristotle here, but we forgive those who followed Archimedes less well. Had Aristotle known of Archimedes Principle, this argument would probably never have been made. According to Archimedes, air rises to the top because it is the least dense, but it still falls towards the earth. Space is empty. There were clues in classical times that space was empty. One such clue was that when a star went behind the moon, it did so sharply, which indicated there was no air to refract it. It was also known there were no clouds on the moon.

This shows another characteristic that unfortunately still pervades science. Once someone establishes a concept, evidence that falsifies that concept tends to be swept under the carpet as long as by doing so, it does not affect anything else. No clouds on the moon might mean anything. So, perhaps, you will now begin to see how difficult it was to get the heliocentric theory accepted, and how difficult it is to find the truth in science when you do not know the answer. That applies just as much today as then. The intellectual ability of the ancients was as great as now, and Aristotle would have been one of the greatest intellects of all times. He just made some mistakes.

What is involved in developing a scientific theory? (2)

In my previous post, I suggested that forming the theory that the Earth was a planet that went around the sun was an interesting example of how a scientist forms a theory. When starting, the first task is to review the literature, which at the time, was largely determined by Aristotle. Since Aristotle asserted that the earth was fixed, it therefore follows that you must first overturn his assertions. One place to start is to decide why we have day and night. Let us use Aristotle’s own methodology, which is to break the issue down into discrete issues. Thus we say, either the Earth is fixed and everything rotates around it, or everything is more or less fixed, and the Earth rotates. Aristotle had reached that step, and had “proven” that the Earth did not rotate. Therefore the day/night must occur through the sun orbiting the Earth. The heliocentric theory, despite its advantages, is falsified unless we can falsify Aristotle’s proofs.

At this point, we should recognize that Aristotle was very clear on one point, and he has been badly misrepresented on this ever since. Aristotle clearly asserted that logic must be applied to experimental observations, and that observation alone was critical. So, what was his experiment? Aristotle argued that if you threw a stone vertically into the air, it always came back to the same place. Had the earth been rotating, the path length of a rotation increased with height, in which case the stone should drag back westwards. It did not, so the earth did not rotate. Note that at this point, Aristotle was effectively arguing for the conservation of angular momentum, similarly to the ice skater slowing her spin by extending her arms. Before reading any further, what do you think about Aristotle’s experiment? What is wrong, and how would you correct it, bearing in mind you have only ancient technology?

In my ebook, Athene’s Prophecy, my protagonist dismisses the experiment by arguing that vertical is defined as the point where the stone falls back to the same place. By defining the point thus, if the stone does not come back to the same place, it was not thrown vertically. He then criticizes Aristotle by arguing that the correct way to do the experiment is to simply drop the stone from a high tower. The reason is that while Aristotle would be correct in that there should be a drag to the west going up, exactly the opposite should occur on the way back down. What should happen if dropped from a tower is that the stone would strike the ground slightly to the east of the vertical position, and in Rhodes, where this was being discussed, also slightly to the south. Can you see why?

That the stone should go east follows from the fact that the angular velocity is constant, but the path length is longer the higher you are, so it is going east faster higher up. The reason it goes south is because the stone falls towards the centre of the earth, and thus very slightly decreases its latitude, but the point at the base of the tower does not. In my ebook, however, my protagonist wisely refused to carry out the experiment, because it is not that easy to carry out, even with modern equipment, and in those days the errors in measurement would most likely exceed the effect. Notwithstanding that, the logic is correct in that any effect like that going up will be exactly countered coming down, and consequently Aristotle’s “proof” is not valid. Thus one can falsify an experiment through logic alone. Of course, disproving Aristotle does not prove the earth is rotating, but it leaves it open as a possibility. Carrying out the dropped stone experiment would, provided you could guarantee that what you saw was real and not experimental error. That is not easy to do, even now.

What is involved in developing a scientific theory?

Everyone knows about people like Galileo, Newton, etc, but how are such theories discovered? Now obviously I have no idea exactly how they did it, but I think there are some principles involved, and I also think some readers might find these of interest. I hope so, because therein lies the third task for my protagonist in my novel Athene’s Prophecy.

The reason that is in the novel is because the overall plot requires a young Roman to get help from superior aliens to avoid a disaster in the 24th century. The reason for the time difference is, of course, relativity. Getting to the aliens involves being abducted by other aliens, but once taken to another world, the protagonist has to be something more than a specimen that can talk. To get the aliens to respond, he has to be someone of interest to talk to. Suppose you had the chance to talk to someone from the 16th century, or to Galileo, who would you choose? My proposition is, Galileo, so the task for my young protagonist is to prove the heliocentric theory, i.e. that the earth moves around the sun. That is similar to what was in the film Agora. The big problem was, everybody was so sure the earth was fixed and everything else went around it. Not only were they sure, but they could also use their theory to calculate everything that mattered, such as when the solstices and equinoxes would be, when Easter would be, and when various planets would be where in the sky. What else did they need?

The alternative theory was due to Aristarchus of Samos. What Aristarchus maintained was that the earth was a planet, and all planets went around the sun, the moon went around the earth, and the solar system was huge. This latter point was of interest, because Aristarchus measured the system. His first measurement was to obtain the size and distance of the Moon, and what he did was to get two people to measure the angle at the exact moment an eclipse of the moon started. These two people were separated by as much distance as he could manage, and with one distance and two angles he had a triangle that would permit the measurement of the distance to the moon. The size then followed from its solid angle. The method is completely logical, although the amount of experimental error was somewhat large, and his answer was out by a factor of approximately two. He then measured the distance to the sun by measuring the angle between the sun and moon lines when the moon was half shaded, and used his moon distance and Pythagoras’ theorem. His error here was about a factor of five, and would have been about a factor of ten had not the error in the moon distance favoured him. The error range here was too great (to see why, check how tangents get very large as they approach 90 degrees) but he was the first to realize that the solar system is really very large. He also showed that the sun is huge compared to the earth.

Aristarchus, following Aristotle, also postulated that the stars were other suns, but so far away, and they would have to be going at even greater speeds. This did not make sense, so he needed an alternative theory. In my opinion, this is invariably the first step in forming a new theory: there is some observation that simply does not make sense within the old theory. Newton’s theory was born through something that did not make sense. If you believed Copernicus, or Aristarchus, if you had heard of him, or of Galileo, then the earth and the other planets went around the sun, but there was a problem: Mars could only be explained through elliptical orbits, and nobody could explain how a body could orbit in an elliptical path with only a central force. Newton showed that elliptical orbits followed from his inverse square law of gravity. Relativity was also born the same way. What did not make sense was the observation that no matter what direction you looked, the speed of light was constant. What Einstein did was to accept that as a fact, and put that into the classical Galilean relativity, and came up with what we call relativity.

So we now get to the second step in building a new theory. That involves reading about what is known, or thought to be known, about the subject. If we think about the heliocentric theory in classical times, we now know that much of what was thought to be correct was not. So, here is a challenge. If you had to, could you prove that the earth goes around the sun, while being restricted to what was known or knowable in the first century? Answers in the next few posts, but feel free to offer your thoughts.

Could a Roman have built a steam engine?

In last week’s post, I raised the question outlined by the title of this post, and I mentioned the main problem being that a Roman would never consider doing it. Hero’s device in the Great Library of Alexandria is a dinky toy, but nobody would seriously consider that it could do useful work. In my ebook, Athene’s Prophecy, that problem was overcome by Athene telling the protagonist to do it. Easy, yes. Cheating, yes, but in fiction, why not? One problem for Romans is that primitive steam engines have to be very big to do a useful amount of work, or operate at high pressures. Newcomen designed the first one because too many miners were required to bucket water out of mines.

 The first question is, how much steam pressure? Actually, the required pressure need not be exceptionally high, because Newcomen’s engine (the first steam engine that did something useful) actually worked by atmospheric pressure. The way it worked was that there was a finely balanced beam, and the steam provided just enough pressure above atmospheric pressure to lift the piston and push the beam. A squirt of water then condensed the steam, and air pressure pushed the piston down, and it was this down stroke that did the work. However, I did not want to simply reproduce the Newcomen engine, so I made the concept use higher pressure so the steam did much of the work, although there was (or will be, in Book 3 of the trilogy) also a steam condensation cylinder.

 A major problem then arises: how to join large pieces of metal together? The Romans knew the principle of the bolt, and they made very small ones by soldering wire onto a metal shaft to make jewellery but they did not know how to make them reproducibly. They knew about soldering, and some of their mixtures were of sufficiently high temperature when melting that they were more akin to welding or brazing, they knew about the rivet, and finally, they had a process known as sweating, essentially heating one piece of metal (preferably a pipe) so that it expanded and could slip over a cold piece, then when it contracted as it cooled down, there was a firm joint. My answer was to use a variety, but emphasise the bolt to get the strength, the idea being to join cast pieces through a flange while employing a leather gasket. To make the bolt, I had my protagonist find workmen in Damascus to develop cutting tools similar to that used by plumbers to thread metal. Is that reasonable? I leave that to the reader to decide. The tools have to be harder than what they are cutting, so the bolts were to be made in bronze, and the tools in Damascus steel, which was actually harder than standard steel, the reason being that the local ores had a small vanadium content.

 The next issue was, could they make the necessary metal objects. They had developed quite intricate ability at casting bronze, so I assumed they could, given practice. The engine I thought up for my protagonist was in part based on a design for a fluid hand pump that you can see in the British Museum (or at least I saw it there). The concept was that instead of the piston going up and down and pulling and pushing fluid, the steam would push the piston, the cycle being completed by the inertia of a flywheel. They could make a small piston and cylinder, so I hoped they could scale up.  

 Perhaps the biggest single problem lay in pipes. I have no idea how long a pipe the ancients could have made, so the design had to assume they would be short. The next problem lay in valves. The valves in the hand pump were simple flap valves, which work well enough when the force comes from the piston, which can exert force either way, but steam will hold a flap valve open from the boiler, and force the exit valve the same way. All that will happen is that you have the most complicated kettle exit! So, I suggested valves that operate by slightly rotating a metal cylinder with a hole in it embedded into a pipe, and operated by a rocker arm. Two valves were needed, or a double valve. I opted for the latter, on the basis that now only one rocker arm was required.

 Could something designed like that work? I think so, given enough effort, but maybe not in practice. But the point of the story is not to design a steam engine, but rather to illustrate the process of invention, which is essentially a lot of trial and error, and the making of incremental improvements on a principle. Also, of course, this is only a side-issue for the story underpinning the trilogy.

What stalled Roman industrialization?

About the first century, Roman society reached some sort of a peak in terms of advance. Their science and literature reached a high point, with Gaius Plinius Secundus’ Naturalis Historia, an encyclopaedia that contained accounts of Roman technology to that point (as well as just about everything else, such as science, medicine, cookery, biology, etc). To the best of my knowledge, there were no significant Roman technology advances following that point. The question is, why not? Furthermore, in response to the question, it should be noted that the concept of the factory was embedded. Roman cloth making, such as dyeing, was carried out in what could be described as chemical processing plants. Such Roman manufacturing was obviously much more primitive than ours, and mainly relied on heat or man-power. However, the concept of the factory was there, but it was never taken further.

One possibility is that imperial control stalled effort. Perhaps there was no observable need. If you do not see the need to find an easier way of doing something, you might be unlikely to do so. In this context, the hard work in Rome was done first by slaves, and then by the poor who were basically uneducated. They might see the need, but they had no ability to do anything about it.  Another possibility is that nobody could see what could be done.

In my trilogy, starting with, Athene’s Prophecy, my protagonist had three quests. The first was to become a military commander and I have covered some of the learning aspects in my previous posts. The second was to develop a steam engine. The concept of the steam engine was developed by Hero of Alexandria, and this aeolipile involved heating a small cauldron over a fire, the steam then being sent to two pipes that entered a ball on a bearing, the ball having two small exit pipes that were bent so that the exit was tangential to the ball, and the plane of the pipes was normal to the axis of the ball. The steam exited and conservation of momentum led to the ball spinning. This, of course, was merely a toy, but it did introduce the concept that you could get steam to do work. So, why was it not taken further?

I think it was a mixture of the above reasons. The main way to advance in Rome from this period was the army. Armies throughout history were not inherently inventive, although the Roman army was adaptive. The educated class tended to be the rich who exploited the poor, so they were not going to get their hands dirty developing new machinery. But perhaps the biggest challenge was that nobody could see why a steam engine would be such an advantage. I also doubt they could see how to do it. If you look at the history of the steam engine, there were a number of attempts that finally came to fruition with Newcomen’s engine, which happened mainly to be a larger and slightly improved version of previous ones. Newcomen’s engine was extremely inefficient, and used huge amounts of coal for the work it did, but since the useful work was to lift water out of coal mines, the coal was available.

So, here is a reader’s question: with your engineering limited to first century technology, how would you design a steam engine? You have the advantages of now knowing the principles, so feel free to comment. My thoughts next week.

History in a novel: The Battle of Actium

Actium is the second battle that my young protagonist had as a final examination in my ebook, Athene’s Prophecy . He had to imagine he was fighting in Antony’s place. Antony and Octavian had faced off before, and as a peace offering, Antony had to marry Octavian’s sister. He did, but then abandoned her for Cleopatra, so this time there was war. For some reason that I do not understand, Antony and Cleopatra took their forces to the south side of the Gulf of Ambracia, although there was a small force on the north side. Then, for another reason I do not understand, when Octavian’s forces arrived, almost a year passed during which Antony did very little. During this time, his forces degenerated, either through a lack of adequate supply, or possibly disease struck. At the same time, Antony seemed to have spent too much time being drunk. The Egyptian fleet was bottled up inside the Gulf, which was in effect a large harbour, and outside, Octavian was blockading him with a much larger fleet. There was much discussion as to what were the appropriate tactics, and rather than engage in a land battle, Antony elected to fight at sea. Part of this decision may have arisen from an argument with Cleopatra. In my opinion, the optimal strategy would have been to take the most strategic positions when it became apparent that Octavian was on his way, and to engage Octavian in a land battle as soon as possible after Octavian’s forces landed. Antony had Caesar’s legions, the most battle-hardened in the Roman army. Further, Antony may have learned that Marcus Agrippa was with the fleet. Agrippa was by far the greatest commander on Octavian’s side. However, for the purposes of the story, my protagonist had to fight at sea.

Accordingly, on September 2, 31 BC, the Egyptian fleet put to sea to engage Octavian. Octavian seriously outnumbered Antony, and had small and very agile ships, while the Egyptian fleet were far more massive, and had plated hulls. Sinking a ship in those days was achieved mainly by ramming, while boarding was a lesser means, but the only means of capturing a ship. Neither side could manage either method. Octavian’s ships could not do much to the plated hulls of the Egyptian fleet, and boarding was not practical because the bigger ships had far more soldiers on them. The Egyptians could not ram Octavian’s ships, except by accident because they could not catch them. Accordingly, both sides sailed around, yelling insults, throwing spears, and not doing much damage. Cleopatra fled, and the besotted Antony set out after her, apparently desirous of trying to make up for an argument of the previous night. His abandoned troops then more or less gave up. Why fight for a commander who flees?

So, how should my young protagonist answer? This is a question of strategy, and the first rule of strategy is, you have to say, “We are here,” and if you know, “and they are there.” In other words the young strategist has to accept what has happened, although for the purposes of the exercise, while he had to fight on September 2, he was allowed to prepare for a naval battle.

My protagonist dealt with this problem this way. The first problem was that the characteristics of both fleets were known, and each side would know that following standard procedures, neither side could do much to the other. Therefore, the answer must involve finding a way to do more damage to the other ships. Because the Egyptian ships were much bigger, and much higher, I had my protagonist resort to “Greek Fire”. Actually, I could be accused of error here, because the official “Greek fire” was not developed until several centuries later, nevertheless incendiary devices involving petroleum and sulphur had been used by Greeks over 400 years before Actium, and I had my protagonist describe what he was going to do as mixing pitch and sulphur, and having it able to be set alight, after which it would be propelled onto the enemy ship. Not exactly what later became called “Greek Fire”, but I think it should still have worked.

You might ask, why bother imagining a different result in an ancient battle? The purpose of all this was to build up my protagonist as someone with ability to use logic, and to take advice. Claudius (the stutterer) had advised my protagonist that it would please Tiberius to use something Timothy had taught him, and had also advised him to try to think up new ways of fighting. Pleasing Tiberius was imperative for my protagonist. Finally, my protagonist had to show that he appreciated military situations and could do something unusual. I suppose also it was fun to imagine what could have happened, although it is most likely that all Antony really had to do to win was to drink a lot less, concentrate on his immediate problems, and keep Cleopatra in perspective.