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.