Science is No Better than its Practitioners

Perhaps I am getting grumpy as I age, but I feel that much in science is not right. One place lies in the fallacy ad verecundiam. This is the fallacy of resorting to authority. As the motto of the Royal Society puts it, nullius in verba. Now, nobody expects you to personally check everything, and if someone has measured something and either clearly shows how he/she did it, or it is something that is done reasonably often, then you take their word for it. Thus if I want to know the melting point of benzoic acid I look it up, and know that if the reported value is wrong, someone would have noticed. However, a different problem arises with theory because you cannot measure it. Further, science has got so complicated that any expert is usually an expert in a very narrow field. The net result is that  because things have got so complicated, most scientists find theories too difficult to examine in detail and do defer to experts. In physics, this tends to be because there is a tendency for the theory to descend into obscure mathematics and worse, the proponents seem to believe that mathematics IS the basis of nature. That means there is no need to think of causes. There is another problem, that also drifts over to chemistry, and that is the results of a computer-driven calculation must be right. True, there will be no arithmetical mistake but as was driven into our heads in my early computer lectures: garbage in, garbage out.

This post was sparked by an answer I gave to a chemistry question on Quora. Chemical bonds are usually formed by taking two atoms with a single electron in an orbital. Think of that as a wave that can only have one or two electrons. The reason it can have only two electrons is the Pauli Exclusion Principle, which is a very fundamental principle in physics. If each atom has only one in  such an orbital, they can combine and form a wave with two electrons, and that binds the two atoms. Yes, oversimplified. So the question was, how does phosphorus pentafluoride form. The fluorine atoms have one such unpaired electron each, and the phosphorus has three, and additionally a pair in one wave. Accordingly, you expect phosphorus to form a trifluoride, which it does, but how come the pentafluoride? Without going into too many details, my answer was that the paired electrons are unpaired, one is put into another wave and to make this legitimate, an extra node is placed in the second wave, a process called hybridization. This has been a fairly standard answer in text books.

So, what happened next? I posted that, and also shared it to something called “The Chemistry Space”. A moderator there rejected it, and said he did so because he did not believe it. Computer calculations showed there was no extra node. Eh?? So I replied and asked how this computation got around the Exclusion Principle, then to be additionally annoying I asked how the computation set the constants of integration. If you look at John Pople’s Nobel lecture, you will see he set these constants for hydrocarbons by optimizing the results for 250 different hydrocarbons, but leaving aside the case that simply degenerates into a glorified empirical procedure, for phosphorus pentafluoride there is only one relevant compound. Needless to say, I received no answer, but I find this annoying. Sure, this issue is somewhat trivial, but it highlights the greater problem that some scientists are perfectly happy to hide behind obscure mathematics, or even more obscure computer programming.

It is interesting to consider what a theory should do. First, it should be consistent with what we see. Second, it should encompass as many different types of observation as possible. To show what I mean, in phosphorus pentafluoride example, the method I described can be transferred to other structures of different molecules. That does not make it right, but at least it is not obviously wrong. The problem with a computation is, unless you know the details of how it was carried out, it cannot be applied elsewhere, and interestingly I saw a recent comment in a publication by the Royal Society of Chemistry that computations from a couple of decades ago cannot be checked or used because the details of the code are lost. Oops. A third requirement, in my opinion, is it should assist in understanding what we see, and even lead to a prediction of something new.

Fundamental theories cannot be deduced; the principles have to come from nature. Thus mathematics describes what we see in quantum mechanics, but you could find an alternative mathematical description for anything else nature decided to do, for example, classical mechanics is also fully self-consistent. For relativity, velocities are either additive or they are not, and you can find mathematics either way. The problem then is that if someone draws a wrong premise early, mathematics can be made to fit a lot of other material to it. A major discovery and change of paradigm only occurs if there is a major fault discovered that cannot be papered over.

So, to finish this post in a slightly different way to usual: a challenge. I once wrote a novel, Athene’s Prophecy, in which the main character in the first century was asked by the “Goddess” Athene to prove that the Earth went around the sun. Can you do it, with what could reasonably be seen at the time? The details had already been worked out by Aristarchus of Samos, who also worked out the size and distance of the Moon and Sun, and the huge distances are a possible clue. (Thanks to the limits of his equipment, Aristarchus’ measurements are erroneous, but good enough to show the huge distances.) So there was already a theory that showed it might work. The problem was that the alternative also worked, as shown by Claudius Ptolemy. So you have to show why one is the true one. 

Problems you might encounter are as follows. Aristotle had shown that the Earth cannot rotate. The argument was that if you threw a ball into the air so that when it reached the top of its flight it would be directly above you, when the ball fell to the ground it would be to the east of you. He did it, and it wasn’t, so the Earth does not rotate. (Can you see what is wrong? Hint – the argument implies the conservation of angular momentum, and that is correct.) Further, if the Earth went around the sun, to do so orbital motion involves falling and since heavier things fall faster than light things, the Earth would fall to pieces. Comets may well fall around the Sun. Another point was that since air rises, the cosmos must be full of air, and if the Earth went around the Sun, there would be a continual easterly wind. 

So part of the problem in overturning any theory is first to find out what is wrong with the existing one. Then to assert you are correct, your theory has to do something the other theory cannot do, or show the other theory has something that falsifies it. The point of this challenge is to show by example just how difficult forming a scientific theory actually is, until you hear the answer and then it is easy.

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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.