In praise of fallibility; why science needs philosophy, with examples from astronomy and chemistry

[Adapted from 3 Quarks Daily] More recent strata lie on top of older strata, except when they lie beneath them. Radiometric dates obtained by different methods always agree, except when they differ.  And the planets in their courses obey Newton’s laws of gravity and motion, except when they depart from them.

As Isaac Asimov reportedly said, “The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ [I have found it], but ‘That’s funny …’ ” And there is nothing that distinguishes so clearly between the scientific and the dogmatic mindset as the response to anomalies. For the dogmatist, the anomaly is a “gotcha”, proof that the theory under consideration is, quite simply, wrong. For the scientist, it is an opportunity. If an idea is generally useful, but occasionally breaks down, something unusual is going on and it’s worth finding out what. The dogmatist wants to see questions closed, where the scientist wants to keep them open. This is perhaps why the creationist denial of science can often be found among those professions that seek decision and closure, such as law and theology.

The rights and wrongs of falsification

Karl Popper (LSE Library photo, 1980s)

Dogmatists regularly invoke the name of Karl Popper, and the work he did in the 1930s. Popper placed heavy emphasis on falsifiability, denouncing as unscientific any doctrine that could not be falsified. Freud’s theories, for example, were unscientific, because a patient’s disagreement with its findings could be explained away as the result of repression. Marxism, likewise, he regarded as unscientific because when events failed to unfold as Marx had predicted, his followers could always say that the right historical conditions had not yet arisen. The theory that biological diversity is a product of Intelligent Design is also unscientific by this criterion, since its advocates can and do say¹ that any apparent failure of design may merely reflect our lack of insight into the motivations of the designer.

But what about theories that almost all of us would agree to regard as scientific, such as the theory of planetary motion, or atomic theory, or the theories of geology, or of the origin of species by evolution? Here, current thinking can be and at various times has been falsified by observation. But what, precisely, was falsified?

No theory exists on its own, as the philosopher-scientist Duhem pointed out over a century ago,² and when a theory fails an observational test there are two kinds of possible explanation. The fault may lie with the theory itself, or with the assumptions we make while testing it. More specifically, as Lakatos pointed out in 1970,³ every application of a theory involves ancillary hypotheses, which can range from the grandiose (the laws of nature are unchanging) to the trivial (the telescope was functioning correctly). When a theoretical prediction fails, we do not know if the fault is in one of these, rather than the core theory itself. Much of the time, we are not even aware of our ancillary hypotheses, which is one reason why we need philosophers of science.

Imre Lakatos (LSE Library photo, 1960s)

Lakatos goes further. To simplify one of the most subtle and influential papers in the philosophy of science, every scientific theory gives rise to anomalies, as revealed by observation. But there is no such thing as a pure observation, because observation is nothing without interpretation, and every interpretation is theory-laden. That last statement is not, as it might seem, a weakness of observational science, but a hidden strength. It implies that, when we use observations to test a theory, we are also as a bonus testing the implicit assumptions that we use to interpret our results. No scientific theory is rejected simply on the basis of its anomalies. It is rejected only when a superior theory is put forward, and the new theory is superior if it explains as much as the old theory, and more besides. Thus we should not even see theories as existing in isolation, but as part of a sequence or research programme. You are bound to be wrong, but don’t let that worry you unduly, because error is opportunity, and the way science progresses is by being less wrong about more things. I find this viewpoint liberating.

Example 1: the dynamics of the Solar System

Take as our first example the motion of planets in the Solar System. According to Kepler’s Laws, which follow from Newton’s laws of gravity and motion, these should follow elliptical orbits, as a result of the gravitational attraction between each planet and the Sun, slightly perturbed by the attraction of the planets for each other. In the mid-19^th-century, accurate observations showed that the orbits of two planets, Mercury and Uranus, were anomalous. The anomaly in the orbit of Uranus could be explained by the gravitational influence of an additional planet, whose position could be calculated, leading to the discovery of Neptune. The anomaly in the orbit of Mercury, however, could not be resolved in this way, and remained unexplained until the formulation of Einstein’s General Theory of Relativity. In the case of Uranus, the anomaly was associated with the ancillary hypothesis that we had a complete list of planets, and it was this ancillary hypothesis that was overthrown. In the case of Mercury, however, the shortcoming was in the theory itself.

Mercury’s orbit precesses round the Sun

It is worth remembering that the anomaly of Mercury was known for some fifty years before Einstein explained it. During that period, physicists did not reject Newton’s theory of planetary motion, despite this evident failure. It did, after all, make correct predictions to within the limits of experimental testing in every other case, and so it was assumed that there was some good reason why the anomaly affected just the one planet. And so there is. The deviation from Newton’s laws is associated with the curvature of space-time by the Sun’s gravitational field, and the orbit of Mercury is the only case where this field is strong enough for the resulting deviation to be observable by early 20^th century techniques. (But higher precision makes greater demands on theory. If you want to steer a tractor by GPS, you will need the relativistic correction to keep it out of the ditch.)

Example 2: Prout’s theory of atomic weights

Consider now another example, also discussed by Lakatos. In 1816, the Scottish physician William Prout conjectured that all chemical substances were condensates of hydrogen, thereby explaining the fact that in the case of gases, their densities (and we would now say⁴ molecular weights), relative to hydrogen, were whole numbers. In rebuttal, Stas pointed out that the relative density of chlorine was 35.5. So Prout was wrong. This is the story that I learnt at school, as an edifying tale of how an over-ambitious theoretician was given his comeuppance by a scrupulous experimentalist.

Mass specrum of chlorine,showing isotopes 35 and 37

Not so. In this particular case, Stas had used all means at his disposal to purify the chlorine, and therefore assumed (a key theoretical assumption) that he was dealing with a pure substance. In terms of the present discussion, we would say that Stas’s experiment did not disprove Proust’s conjecture, but, rather, the conjunction of that conjecture with the ancillary hypothesis that his chlorine was a pure single substance. It was not until much later that it became clear that the atomic weight of 35.5 arises because chlorine is in fact a 3:1 mixture of two different kinds of atom, chlorine-35 and chlorine-37. Isotopes, separate substances differing in weight, but with virtually indistinguishable chemical properties, and therefore occupying the same place (Greek, isos, same, topos, place) in the Periodic Table. So the mismatch between Prout’s prediction and Stas’s observation results from the failure of the ancillary hypothesis, while the relative densities of the two separate isotopes, 35 and 37, are indeed whole numbers, to within the limits of measurement at that time, just as Prout’s conjecture requires.

Example 3: the anomalous density of atmospheric nitrogen

Even when Prout’s conjecture appeared to have been disproved, it remained a focus of interest. After all, many elements, including carbon, nitrogen, oxygen, fluorine, sodium, aluminium, an even platinum and gold, have atomic weights very close to a whole number.⁵ This is, to say the least, suggestive, so much so that in 1888 Lord Rayleigh, one of the UK’s most distinguished scientists, decided to redetermine the density of nitrogen as accurately as he could.

He used two separate methods to obtain nitrogen. One method was decomposition of ammonia, which is a compound of nitrogen and hydrogen. The other was from air, by removal of water vapour, oxygen, and carbon dioxide. To his surprise, the densities did not agree; “atmospheric” nitrogen was slightly but measurably denser than “chemical” nitrogen. The difference was only one part in a thousand, but there was no reason to expect any difference at all.

Unable to resolve this anomaly, Rayleigh appealed publicly for assistance, and got it from William Ramsay, Chemistry Professor at University College London, who happened to know of an earlier anomalous finding involving air. In 1785, Henry Cavendish had sparked together air and oxygen, and found that they reacted together to give products that were soluble in water,⁶ but a small fraction of the air, around 1%, failed to react. This led Ramsay to suggest that air contained an extra, hitherto unidentified, constituent. Removal of oxygen and nitrogen⁷ did indeed leave behind a relatively dense, highly unreactive, gas which Ramsay and Rayleigh christened argon, “the lazy one”. From the perspective of this essay, Rayleigh’s initial thinking included the ancillary hypothesis that all the components of air had been identified. This was not true, and (as readers with a knowledge of chemistry will be aware) the additional component was to play a vital role in explaining chemical bonding.

L: Vanity Fair caricature of Ramsay lecturing on the Periodic Table. He is pointing to Group VIII, the noble gas elements, that he and Rayleigh discovered and of which argon (here labelled A rather than Ar) was the first member to be identified as such. Click for larger image

No one, as far as I know, objects to the Periodic Table on theological grounds, and (ignoring Nancy Reagan for the moment) it is some time since anyone in a position of power in the West claimed that we were linked to the planets by supernatural forces, so that astronomy and atomic theory are not politically contentious. The same, alas, is not true regarding geology, and what it tells us about the age of the Earth and our links to its former inhabitants. Here the creationist movement, with supporters up to and including the Vice President of what is still the most powerful country in the world, seize on real or imagined anomalies in attempts to discredit three hundred years worth of earth science. I will be discussing such geological anomalies, together with examples of how creationists use them to distort reality, in my next post.

1] M.J. Behe, Darwin’s Black Box  : “The argument from imperfection overlooks the possibility that the designer might have multiple motives, with engineering excellence oftentimes relegated to a secondary role … [T]he reasons that the designer award old not do anything are virtually impossible to know unless the designer tells you specifically what those reasons are.”

2] See https://plato.stanford.edu/entries/scientific-underdetermination/, Sec. 2.1.

3] Available at http://www.csun.edu/~vcsoc00i/classes/s497f09/s690s08/Lakatos.pdf ; see also the Stanford Encyclopaedia of Philosophy articles on Lakatos https://plato.stanford.edu/entries/lakatos/ and Popper https://plato.stanford.edu/entries/popper/.

4] Invoking the ideas of Dalton and Avogadro.

5] These are some of the elements that occur entirely, or almost entirely, as a single isotope.

6] Nitrogen and oxygen, when heated or sparked together, give nitric oxide, NO, which reacts further with oxygen and water to give, eventually, nitric acid.

7] This was accomplished initially by reaction with magnesium, and subsequently by fractional distillation.

Mercury precession image from Georgia State University site. Chlorine isotopes from Chemguide. Ramsay image Vanity Fair via Wikipedia.

I thank  Massimo Pigliucci for helpful correspondence. The responsibility, however, for the errors that I have no doubt committed in this piece is entirely my own. An earlier version of this material appeared in 3 Quarks Daily