Have you got what it takes to form a scientific theory?

Making a scientific theory is actually more difficult than you might think. The first step involves surveying what knowledge is already available. That comes in two subsets: the actual observational data and the interpretation of what everyone thinks that set of data means. I happen to think that set theory is a great start here. A set is a collection of data with something in common, together with the rule that suggests it should be put into one set, as opposed to several. That rule must arise naturally from any theory, so as you form a rule, you are well on your way to forming a theory. The next part is probably the hardest: you have to decide what interpretation that is allegedly established is in fact wrong. It is not that easy to say that the authority is wrong, and your idea is right, but you have to do that, and at the same time know that your version is in accord with all observational data and takes you somewhere else. Why I am going on about this now is I have written two novels that set a problem: how could you prove the Earth goes around the sun if you were an ancient Roman? This is a challenge if you want to test yourself as a theoretician. If you don’t. I like to think there is still an interesting story there.

From September 13 – 20, my novel Athene’s Prophecy will be discounted in the US and UK, and this blog will give some background information to make the reading easier as regards the actual story not regarding this problem. In this, my fictional character, Gaius Claudius Scaevola is on a quest, but he must also survive the imperium of a certain Gaius Julius Caesar, aka Caligulae, who suffered from “fake news”, and a bad subsequent press. First the nickname: no Roman would call him Caligula because even his worst enemies would recognize he had two feet, and his father could easily afford two bootlets. Romans had a number of names, but they tended to be similar. Take Gaius Julius Caesar. There were many of them, including the father, grandfather, great grandfather etc. of the one you recognize. Caligulae was also Gaius Julius Caesar. Gaius is a praenomen, like John. Unfortunately, there were not a lot of such names so there are many called Gaius. Julius is the ancient family name, but it is more like a clan, and eventually there needed to be more, so most of the popular clans had a cognomen. This tended to be anything but grandiose. Thus for Marcus Tullius Cicero, Cicero means chickpea. Scaevola means “lefty”. It is less clear what Caesar means because in Latin the “ar” ending is somewhat unusual. Gaius Plinius Secundus interpreted it as coming from caesaries, which means “hairy”. Ironically, the most famous Julius Caesar was bald. Incidentally, in pronunciation, the latin “C” is the equivalent of the Greek gamma, so it is pronounced as a “G” or “K” – the difference is small and we have now way of knowing. “ae” is pronounced as in “pie”. So Caesar is pronounced something like the German Kaiser.

Caligulae is widely regarded as a tyrant of the worst kind, but during his imperium he was only personally responsible for thirteen executions, and he had three failed coup attempts on his life, the leaders of which contributed to that thirteen. That does not sound excessively tyrannical. However, he did have the bad habit of making outrageous comments (this is prior to a certain President tweeting, but there are strange similarities). He made his horse a senator. That was not mad; it was a clear insult to the senators.

He is accused of making a fatuous invasion of Germany. Actually, the evidence is he got two rebellious legions to build bridges over the Rhine, go over, set up camp, dig lots of earthworks, march around and return. This is actually a text-book account of imposing discipline and carrying out an exercise, following the methods of his brother-in-law Gnaeus Domitius Corbulo, one of the stronger Roman Generals on discipline. He then took these same two legions and ordered them to invade Britain. The men refused to board what are sometimes called decrepit ships. Whatever, Caligulae gave them the choices between “conquering Neptune” and collecting a mass of sea shells, invading Britain, or face decimation. They collected sea shells. The exercise was not madness: it was a total humiliation for the two legions to have to carry these through Rome in the form of a “triumph”. This rather odd behaviour ended legionary rebellion, but it did not stop the coups. The odd behaviour and the fact he despised many senators inevitably led to bad press because it was the senatorial class that wrote histories, but like a certain president, he seemed to go out of his way to encourage the bad press. However, he was not seen as a tyrant by the masses. When he died the masses gave a genuine outpouring of anger at those who killed him. Like the more famous Gaius Julius Caesar, Caligulae had great support from the masses, but not from the senators. I have collected many of his most notorious acts, and one of the most bizarre political incidents I have heard of is quoted in the novel more or less as reported by Philo of Alexandria, with only minor changes for style consistency, and, of course, to report it in English.

As for showing how scientific theory can be developed, in TV shows you find scientists sitting down doing very difficult mathematics, and while that may be needed when theory is applied, all major theories start with relatively simple concepts. If we take quantum mechanics as an example of a reasonably difficult piece of theoretical physics, thus to get to the famous Schrödinger equation, start with the Hamilton-Jacobi equation from classical physics. Now the mathematician Hamilton had already shown you can manipulated that into a wave-like equation, but that went nowhere useful. However, the French physicist de Broglie had argued that there was real wave-like behaviour, and he came up with an equation in which the classical action (momentum times distance in this case) for a wave length was constant, specifically in units of h (Planck’s quantum of action). All that Schrödinger had to do was to manipulate Hamilton’s waves and ensure that the action came in units of h per wavelength. That may seem easy, but everything was present for some time before Schrödinger put that together. Coming up with an original concept is not at all easy.

Anyway, in the novel, Scaevola has to prove the Earth goes around the sun, with what was available then. (No telescopes that helped Galileo.) The novel gives you the material avaiable, including the theory and measurements of Aristarchus. See if you can do it. You, at least, have the advantage you know it does. (And no, you do not have to invent calculus or Newtonian mechanics.)

The above is, of course, merely the background. The main part of the story involves life in Egypt, the aanti-Jewish riots in Egypt, then the religious problems of Judea as Christianty starts.


Why I question many scientific statements.

From a few of the previous posts, where I have ventured into science, it may be obvious that I am not putting forward standard views. That leaves three possibilities: I don’t know what I am talking about; I am wrong; I might even be right. One of those options makes a lot of people who listen to what I say uncomfortable. Comfort comes when everything falls into place with your preconceptions; a challenge to those preconceptions requires you to think, and it is surprising how few scientists want to be the first person to stand up and support a challenge. So, why am I like that?

It started with my PhD. My supervisor gave me a project; it was a good project, but unfortunately it got written up in the latest volume of Journal of the American Chemical Society after I have been three weeks into it. He gave me two new projects to choose from whereupon he went away on summer holidays. One was, as far as I could see, hopeless, and worse than that, it was highly dangerous. The second I could finish straight away! He wanted me to measure the rates of a reaction of certain materials, and according to the scientific journals, it did not go. So, I was told to design my own project, which I did. I entered a controversy that had emerged. For those who know some chemistry, the question was, does a cyclopropane ring engage in electronic conjugative effects with adjacent unsaturated substituents? (Don’t worry if that means nothing to you; it hardly affects the story. A very rough explanation is, do they slosh over to other groups outside the ring, or must they stay within the ring?) There were a number of properties of compounds that included this structure that had unusual properties and there seemed to be two choices: the proposed quantum effects, or the effects of the strain.

This looked fairly straightforward, but I soon found out that my desire to do something that would not be easily done by someone else had its price: the chemical compounds I wanted to use were difficult to make, but I made them. The first series of compounds were not exceptionally helpful because a key one decomposed during measurement of the effect, but I soon got some definitive measurements through a route I had not expected when I started. (Isn’t it always the way that the best way of doing something is not what you started out trying to do?) The results were very clear and very definitive: the answer to the question was, “No.”

The problem then was that the big names had decided that the answer was yes. My problem was, while I had shown conclusively (to my mind, at least) that it did not, nevertheless there were a number of properties that could not be explained by what everyone thought the alternative was, so I re-examined the alternative. I concluded that because the strain was caused by the electrical charge being moved towards the centre of the ring, the movement was responsible for the effects. Essentially, I was applying parts of Maxwell’s electromagnetic theory, which is a very sound part of physics.

What happened next was surprising. In my PhD thesis defence, there were no real questions about my theory. It was almost as if the examiner did not want to go down that path. I continued with my career, waiting for my supervisor to publish my work, but the only paper was one that kept away from controversy. Accordingly, I decided to publish papers on my own. Unfortunately, my first one was not very good. I wanted to get plenty of material in, and I had been told to be brief. Brevity was not a virtue, because I later found out nobody really understood the first part. That was my fault, thanks to the brevity, but the good news was, from my point of view, while that first paper used one piece of observational fact to fix a constant, and thus calculate the key variable, every time subsequently I took the theory into uncharted waters, it always came up with essentially correct agreement with observation. I calculated a sequence of spectral shifts to within almost exact agreement, while the quantum theory everyone else was using could not even get the direction of the shifts right. So I should have been happy, right?

What happened next was that a few years later, a review came out to settle the question, and it landed on the quantum side of things. It did so by ignoring everything that did not agree with it! I was meanwhile employed, and I could not devote time to this matter, but much later, I wrote a different review. The journals I submitted it to did not want it. One rejected it because there were too many mathematics; others said they did not want logic analyses. I posted it on the Chemweb preprint server, but that seems to be history because while it is supposedly still there, I cannot find it. If anyone wants to see it, enquire below. My key point is that the review shows over sixty different types of experiments that falsify the standard position, but nobody is interested. All the work that falsified the prevalent dogma has been buried. Yes, it is still in the literature, but if Google cannot even find my publication when I know the title and the date and the location, how can anyone else find what they do not know about?

So, this is an aberration? I wish. I shall continue in this vein from time to time.

Ancient Physics – What Causes Tides? The Earth Moves!

I am feeling reasonably pleased with myself because I now have book 2 of my Gaius Claudius Scaevola trilogy, Legatus Legionis, out as an ebook on Amazon. This continues the story set during the imperium of Caligulae, and the early imperium of Claudius, and concludes during the invasion of Britain. I shall discuss some of the historical issues in later posts, but the story also has an objective of showing what science is about.

In my last post, I showed how the ancients could “prove” the Earth could not go around thy Sun. Quite simply, orbital motion is falling motion, and if things fell at different rates depending on their mass, the Earth would fall to bits. It doesn’t. So, what went wrong? Quite simply, nobody checked, and even more surprisingly, nobody noticed. Why not? My guess is that, quite simply, they knew, it was obvious, so why bother looking? So the first part is showing the Earth moves around the Sun is to have my protagonist actually see three things fall off a high bridge, and what he sees persuades him to check. I think that part of success in science comes from having an open mind and observing things despite the fact that you were not really intending to look for them. It is the recognizing that which you did not expect that leads to success.

That, however, merely permits the Earth to go around the Sun. The question then is, how could you prove it, at the time? My answer is through the tides. What do you think causes the tides? Quite often you see the statement that the Moon pulls on the water. While true, this is a bit of an oversimplification because it does not lift the water; if it did, there would be a gap below. In fact, the vector addition of forces shows the Moon makes an extremely small change in the Earth’s gravity, and the net force is still very strongly downwards. To illustrate, do you really think you can jump higher when the Moon is above you? There is a second point. In orbital motion (and the Earth goes around a centre of gravity with the Moon) all things fall at the same acceleration, but the falling is cancelled out because the sideways velocity takes the body away at exactly the correct rate to compensate. This allowed my protagonist to see what happens (although the truth is a little more complicated). The key issue is the size of the Earth. The side nearest the Moon is not moving fast enough, so there is a greater tendency to fall towards the Moon; the far side is moving too fast, so there is a greater tendency for water to be thrown outwards. There is, of course, still a strong net force towards the centre of the Earth, but when not directly under the Moon, the two forces are not exactly opposed, and hence the water flows sideways towards the point under the Moon. The same thing happens for the Sun. This is admittedly somewhat approximate, but what I have tried to capture is how someone in the first century who did not know the answer could conceivably reach the important conclusion, namely that the Earth moves. If it moves, because the Sun stays the same size, it must move in a circle. (It actually moves in an ellipse, but the eccentricity is so small you cannot really detect the change in the size of the Sun.)

 What I hope to have shown in these posts, and in the two novels, is the excitement of science, how it works and what is involved using an example that should be reasonably comprehensible to all. The same principles apply in modern science, except of course that once the basic idea is obtained, the following work is a bit more complicated.     


Ancient theory: dynamics proved the Earth was stationary!

Aristotle was one of the greatest minds of all times, but when he came to formulate his theories of dynamics, he got it all wrong. What I find interesting is why he went wrong, and the answer is surprising: he failed to follow his own methodology! Why was that? The reason may be a little mundane, and that is, his book Physica was apparently one of the first he wrote, and he may not have developed his method of logic properly by then. If so, why did he not correct it later? In my view, probably because he was not that interested in physics. Even now, the fraction of the population who find physics interesting is probably rather small. One of the most important features of Aristotle, though, is that he really did believe that experiment and observation were the key, and only theories that complied with observation were valid.

The first problem might be called sloth. He was not one of the most active experimenters, and in fairness to him, much of which he should have done would have been very difficult to do with the very limited equipment that was available. Nevertheless he could have done better in many ways. His first problem was that believed things like energy “came into being and passed away”. For example, suppose you throw a stone up in the air. It starts moving rapidly, then it slows, stops at the top, then turns around and comes back down. What happened to the initial energy when it reached the top? He said, it had passed away. We say the kinetic energy is turned into potential energy, but you cannot see potential energy. We have it because otherwise the law of conservation of energy would be falsified, but who says energy is conserved? (There are very good reasons for why it must be, but these would be beyond Aristotle’s ability to see, bearing in mind what information was available to him.)

The next problem lay in the theory of contraries, which was established before Aristotle. Thus cold was a material that was the contrary of heat. What Aristotle failed to see was that the contrary was the opposite or absence of the other, thus cold is the absence of heat, and this is odd because Aristotle did recognize that dark was the absence of light. When we got to motion, Aristotle failed to see that the contrary of a force was another force in the opposite direction. Instead, he believed that bodies contained their own internal contrary to motion, thus if you had a cart, you needed a horse continually pulling on it to overcome the contrary inherent in the cart. Why was it inherent to the cart? Because different carts would require different forces to keep them going. See the way you can fall into a trap? He just did not carry his thoughts further. The problem was probably the cart, as everybody knew it would stop unless pulled. Nevertheless, had he used his fabled logic, he would have arrived at the correct conclusion. As I put it in my ebook novel, Athene’s Prophecy, what he had to say was, either the contrary was the property of the body, or it was the property of its environment. Back to the cart, it is a lot easier to pull it on a stone road than on boggy earth. He should have been able to identify restraining forces, but he did not.

An even worse problem lay in the assertion that heavy things fall faster than light things. The problem here lay in the contraries. Had he recognized that air provided a restraining force, which he could have determined by watching wind blow leaves, he could drop different weights that were compact. He did not, because to him, the answer was “obvious”. Just because it is obvious does not make it right!

Why was this important? Apart from the fact that it strangled the development of the theory of mechanics, which in turn placed limits on what could be invented, it also provided proof that the Earth did not orbit the Sun. Can you see why? The answer lies in the nature of orbital motion. The ancient Greeks realized that orbital motion required the earth to move sideways, but fall back towards the Sun, and thus stay at the same distance as it went around. If it falls, since heavier things fall faster than light ones, the Earth would fall to pieces, or at the very least, light things would form a stream towards the rear. This was not observed, so the Earth did not move. Simple really, but a wrong premise led to the wrong conclusion.

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.