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Atoms Old and New, 2: From Newton to Einstein

Part 1 of this series, “Atoms Old and New: Atoms in Antiquity” can be read here.

The transition to modern thinking

“It seems probable to me, that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles… even so very hard, as never to wear or break in pieces; no ordinary power being able to divide what God Himself made one in the first creation.” So wrote Sir Isaac Newton in his 1704 work, Opticks. Apart from the reference to God, there is nothing here that Democritus would have disagreed with. There is, however, very little that the present-day scientist would fully accept. In this and later posts, I discuss how atoms reemerged as fundamental particles, only to be exposed, in their turn, as less than fundamental.

The scientific revolution and the revival of corpuscular theory – 1543–1687

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Eight basic laws of physics, and one that isn’t

Reposted from 3 Quarks Daily:

GodfreyKneller-IsaacNewton-1689

Isaac Newton, 1689

Michael Gove (remember him?), when England’s Secretary of State for Education, told teachers

“What [students] need is a rooting in the basic scientific principles, Newton’s Laws of thermodynamics and Boyle’s law.”

Never have I seen so many major errors expressed in so few words. But the wise learn from everyone, [1] so let us see what we can learn here from Gove.

From the top: Newton’s laws. Gove most probably meant Newton’s Laws of Motion, but he may also have been thinking of Newton’s Law (note singular) of Gravity. It was by combining all four of these that Newton explained the hitherto mysterious phenomena of lunar and planetary motion, and related these to the motion of falling bodies on Earth; an intellectual achievement not equalled until Einstein’s General Theory of Relativity. Read the rest of this entry

Science and the Supernatural (II); Why We Get It Wrong and Why It Matters

Paul1

“I have no need of that hypothesis.” So, according to legend, said the great astronomer and mathematician Piere-Simon, marquis de Laplace, when asked by Napoleon why he had not mentioned God in his book. If so, Laplace was not referring to the hypothesis that God exists, but to the much more interesting hypothesis that He intervenes in the material world. And Laplace’s point was not, fundamentally, philosophical or theological, but scientific.

The planets do not move round the Sun in circular orbits, but in elliptical pathways, moving fastest when closest. All this and more Newton had explained using his laws of motion, combined with his inverse square law for gravitational attraction. There is one small problem, however. The planets are attracted, not only to the Sun, but to each other, perturbing each other’s pathways away from a perfect ellipse. These perturbations are not trivial, and in fact it was the perturbation of the orbit of Uranus that would lead to the discovery of Neptune. Newton himself surmised that they could, eventually, render the entire system unstable so that God would need, from time to time, to intervene and correct it. Laplace devoted much of his career to developing the mathematical tools for estimating the size of the perturbations, and concluded that the Solar System was in fact stable. So Newton’s hypothesis of divine intervention was redundant, and it was this hypothesis that Laplace was supposedly referring to.

There is an irony here. Laplace’s calculation that the solar system is stable is true only in the short term, (say a few tens or hundreds of millions of years). In the long enough term, the situation is much more uncertain. As Henri Poincaré was to show a century later, a system of three or more gravitationally interacting bodies is potentially chaotic. Under certain circumstances, an initially minute difference in starting conditions can lead to an ever increasing divergence of outcomes, so that eventually planets can adopt highly elongated orbits, or even be thrown out of their solar systems altogether. Modern computer simulations show (see here and here) that the solar system is indeed chaotic, that Mercury is vulnerable to extreme change or even ejection from the Solar System, and that it is possible that in some 3.5 billion years Mercury’s instability could be transferred to the other inner planets, including Earth, leading to the possibility of collision.

Science, some say, rejects supernatural explanations on principle; this is called intrinsic methodological naturalism (IMN). In Part I I argued, following the work of Boudry et al. (herehere , and here), that this strategy is misguided. Here I go into more detail, using this example, and other past and present controversies, to illustrate the point.

Stephen Hawking has commented on Laplace’s remark, in much the same spirit as I am suggesting regarding the God question, but assumes for him a much more absolute position:

I don’t think that Laplace was claiming that God didn’t exist. It is just that He doesn’t intervene, to break the laws of Science. That must be the position of every scientist. A scientific law is not a scientific law if it only holds when some supernatural being decides to let things run, and not intervene.

Paul2A similar point of view had been put forward by Richard Lewontin, in his uncomfortably perceptive review, available here, of Sagan’s Demon Haunted World); I consider this review required reading for those defending science because of its all too rare recognition of creationism as a complex social problem:

Perhaps we ought to add to the menu of Saganic demonology, just after spoon-bending, ten-second seat-of-the-pants explanations of social realities.

I cannot do justice to Lewontin’s reasoning by brief truncated quotations from his complex argument. It is clear, however, that he uses two very different arguments in rapid succession:

Nearly every present-day scientist would agree with Carl Sagan that our explanations of material phenomena exclude any role for supernatural demons, witches, and spirits of every kind, including any of the various gods from Adonai to Zeus…. We also exclude from our explanations little green men from Mars riding in spaceships, although they are supposed to be quite as corporeal as you and I, because the evidence is overwhelming that Mars hasn’t got any…

We take the side of science … because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door. … To appeal to an omnipotent deity is to allow that at any moment the regularities of nature may be ruptured, that miracles may happen.

The first paragraph is one that I can accept and advocate in its entirety. We reject supernatural causes in the same way that we reject implausible material explanations, because the evidence tells us that they don’t exist. The second, intertwined with observations that I have had to omit for brevity regarding the tenuousness of the pretensions of science and what he calls the patent absurdity of some of its constructs, is of a very different kind. Science, he says, is committed in principle to material causes, and the reason for doing so is, again, to exclude divine intervention.

Leave aside for now the problem of defining “materialism”; at a time when our concept of the material includes dark energy, particle entanglement, and quantum fluctuations in nothingness of which our entire Universe may be but one example, this is much the same as the problem of defining “naturalism” that I mentioned in Part I. Leave aside also the deliberately provocative antireligious language, inconvenient though that be for coalition builders. After all, Lewontin has, and is entitled to, his own agenda here. Leave aside even the possibility that miracles need not disrupt the normal business of science, as long as they are sufficiently rare. Hawking has followed Lewontin into the trap that awaits all those who would legislate the metaphysical out of existence. They lay themselves open to the charge that they are, themselves, arbitrarily introducing yet another metaphysical rule.

Paul3So, alas, does the National Science Teachers Association, whose commitment to IMN is quoted with approval by the National Academy of Sciences (Teaching About Evolution and the Nature of Science, 1998 but still current, and freely available here, p. 124):

 Science is a method of explaining the natural world. It assumes the universe operates according to regularities and that through systematic investigation we can understand these regularities. The methodology of science emphasizes the logical testing of alternate explanations of natural phenomena against empirical data. Because science is limited to explaining the natural world by means of natural processes, it cannot use supernatural causation in its explanations. Similarly, science is precluded from making statements about supernatural forces because these are outside its provenance. Science has increased our knowledge because of this insistence on the search for natural causes. [Emphasis added]

This is very bad. We slide from an innocent-seeming description of the domain of science as the “natural” world, through the uncontroversial idea of testing explanations against each other, to the non sequitur of the sentence I have highlighted. There is an illusion of logic, based on an assumed dichotomy between the natural and the supernatural, but this is mere wordplay. We are given no other reason for this leap, even though it could have been justified, as Hawking and Lewontin justify their own exclusion of the supernatural, by reference to the assumption of regularity. As we saw in Part I, the claim that “science is precluded from making statements about supernatural forces” is simply untrue. Time and again, science has refuted the appeal to the supernatural by providing alternatives – if this is not “making statements about supernatural forces”, what is?

Present-day science does indeed make statements highly relevant to the existence or otherwise of supernatural forces. To raise the stakes to their utmost, some consider the Universe to be fine tuned for life, and regard this as scientific evidence for a purposeful Creator.[1] Others regard this as yet another argument from ignorance, since it may well be that the Universe is not really all that special, or that there are as yet unknown constraints of some kind on the relevant physical constants, or that quantum fluctuations will generate such a superabundance of Universes that some, statistically, are bound to have the required properties. While it may be premature to test these suggestions, they are part of a clearly scientific agenda. The suggested causes would be “natural.” by any standards, but if established would have the effect of making the appeal to a supernatural Creator unnecessary. Science would then have made a clear statement about the purported supernatural force responsible for fine tuning, exactly as it did about the purported supernatural force responsible for the stability of the Solar System, namely that there was, in Lavoisier’s words, no need for that hypothesis.

Two other examples spring to mind. First, the argument from Intelligent Design as applied to the mammalian eye. This fails, because the mammalian eye is in one crucial detail very poorly designed. The nerve endings, and the blood supply, run in front of, rather than behind, the photosensors, partly occluding them and giving rise to each eye’s blind spot. It does not have to be that way, since the octopus eye is built the right way round. At this point, the defender of design has two options. He can admit defeat, or at least accept that the Designer’s options are restricted by our evolutionary history. So in this case the argument from design is refuted or, at any rate, enfeebled. Or he can argue, as Behe does in Darwin’s Black Box, that the refutation fails because we do not know the Designer’s full intent. At this point, we lose interest because the argument from design has become so well immunized against observation, to borrow a term from Maarten Boudry’s PhD thesis Here be Dragons, that it has ceased to be science. In neither case have we referred to the supernatural nature of the argument as the reason for dismissing it.

Secondly, there is a version of theistic evolution in which the Creator intervenes at the level of quantum mechanical indeterminacy to set in course one mutation rather than another, and used this to ensure the evolution of intelligent humans. I first heard this suggestion from Alvin Plantinga,[2] and if I understand Ken Miller’s Finding Darwin’s God correctly I think that on this topic, for once, he and Plantinga would agree. Certainly there is nothing here that violates the laws of physics and chemistry, since the chance breakdown of one single radioactive atom at one moment rather than the next may well disrupt a growing chain of DNA, and a single mutation may well have far-reaching consequences.[3] Were such a mutation to have happened under the Creator’s guidance, that would be supernatural causation par excellence.

I would argue against this on the grounds that there is little or no evidence of a bias towards beneficial mutations, and that since intelligence has emerged independently in cephalopods, cetaceans, parrots, velociraptors (if cerebral capacity is anything to go by), and simians, the emergence of such little intelligence as we have requires no special explanation. Now you may regard my argument as mistaken, banal, or ill-informed, but I do not see how you can describe it as outside the domain of science.

Thus we do, as I just did, use scientific reasoning to discuss the claims of supernaturalists, so IMN is untrue. It was untrue in the 18th century when science explored solar system stability; it was untrue in the 19th when natural selection rendered Paley’s watchmaker redundant; it was untrue in the 20th when claims of extrasensory perception were scientifically examined and found wanting; and it is untrue in the present century as we prepare to grapple with such problems as the origin of our Universe and its appearance of being fine-tuned for the emergence of life. To propagating IMN is to propagate a falsehood.

Paul4Does this matter? Yes, very much indeed. There is a war on, between the supporters of science as we know it, and the creationists and endarkeners who wish to replace it with what the Discovery Institute’s Institute for Science and Culture calls in its notorious “wedge” document “the theistic understanding that nature and human beings are created by God.”

The unwarranted and inaccurate grafting onto the methods of science the arbitrary rule that it must not traffic in the supernatural exposes a flank to its enemies, which they have been quick to exploit. The central argument of Phillip Johnson’s Defeating Darwinism by Opening Minds, which predates the Wedge Document, is that mainstream science (including, crucially, the study of human origins) is illegitimate because it arbitrarily excludes explanations that lie outside the limits of naturalism. His disciple Alastair Noble, director of the Glasgow-based, Centre for Intelligent Design, says in the Centre’s introductory video

One of the key questions posed by the world around us is whether we are here by chance or by design.  There is a strident strain of science which insists that all the design in the world is apparent, not real, and that natural selection acting on random mutations is sufficient to explain it all.  That kind of science is derived from a view that the only explanations which are acceptable are those which depend purely on physical or materialist processes.  That is not a scientific finding that is derived from the evidence.  It is, in fact a philosophical position, and a biased one at that, which is brought to the actual evidence.  It excludes other types of explanation which the evidence may merit.

Here the claim that mainstream science excludes design-based explanations a priori is used to bolster the common creationist tactic of misrepresenting the outcomes of its investigations, including evolution, as inputs. Going further downmarket, we come to the creationist claims that evolution science is a religion like any other, or that evolution and creationism differ only in their starting assumptions, and as long as the scientific community itself presents the rejection of the supernatural as an input rather than an output, we have scant grounds for complaint against such vulgarizations.

Why do we persist in exposing ourselves in this way? Boudry and colleagues (2010) suggest several reasons. One of these we have already demolished; the claim that IMN is built in to the definition of science. There is a large literature (see e.g. here) on how and indeed if science should be defined, and I have nothing to add to this, beyond reminding readers that “supernatural” is itself difficult to define, and repeating my earlier point that insisting on IMN would exclude much activity that we generally consider scientific. A second, mentioned by both Hawking and Lewontin in the essays I quoted, is that it would undermine the assumption of regularity that underpins science. Miracles such as those claimed for Jesus would indeed undermine that assumption, but only in rare and very special cases; so rare and special that they can hardly constitute a serious threat to our business.[4]

Our faith in the regularity of nature derives from our having lived and evolved in a world where it holds good, not from some special rule about the nature of science. It is confirmed, over huge reaches of space and time, by observation. We can interpret the spectra of galaxies whose light has taken 12 billion years to reach us, and the suggestion (since subjected to highly critical scrutiny) that the constants of physics might have changed even in the fourth decimal place was enough to arouse the interest of The Economist.

From constancy to change. On current thinking, the early Universe underwent a period of rapid inflation, in which space expanded at such a rate that the distance between points initially close together grew at a rate faster than the speed of light. Thus during this expansionary stage the laws of nature were very different from what they are today. And the state of the Universe before this stage may be to us in principle unknowable.

All the conclusions of the last two paragraphs may be subject to revision. But this very fact reinforces my claim, that our faith in the constancy of nature is testable by science, and that science can (and currently does) tell us that the domain of this faith is wide, but not unlimited. Thus it is as much an outcome of our experience as a methodological input.

A third argument for IMN is that in its absence the possibility of invoking supernatural explanations may discourage the search for natural ones. This is a purely pragmatic argument, and I cannot imagine it having any real effect. Those who prefer supernatural explanations invoke them anyway. Millions of Americans believe humans to have arisen through a special supernatural act, but this is not for lack of a naturalistic explanation. Intelligent Design creationists argue that undirected evolution cannot possibly generate new information, or that protein sequences are too improbable to have arisen naturally. Young Earth creationists, a separate group (although in the UK the two groups strongly overlap) point to anomalies in radiometric dating, or to polonium halos in rocks that did not contain polonium’s ultimate parent, uranium, and claim that these somehow cause the naturalistic account of earth’s geological history to unravel. This they do because of their prior commitment to mystification. Debunking their nonsense is a proper matter for science, and the talkorigins website has a very useful page listing numerous such claims and their rebuttals[5] although experience shows that mere refutation will not stop their proponents from repeating them. And there are important unsolved problems, such as the origin of life, which some claim as evidence for supernatural intervention, but I do not think that any scientist interested in the topic would be so easily fobbed off. In any case, defining their activities as unscientific would not make the supernaturalists disappear. On the contrary; they would (and do; see above) triumphantly hail such definitions as proof that we impose arbitrary limitations on our science.

There are more technical arguments, which boil down to the untestability of supernatural explanations. But we already have the rule that science deals with the (in principle) testable, so that there is no need to invoke IMN. And finally there is the argument from legal expediency, which I maintain is both unnecessary and two-edged.

Unnecessary. Judge Jones famously ruled in Kitzmiller vs Dover School District that Intelligent Design (ID) is not science, but a form of religiously motivated creationism, thus barring it from publicly funded schools in the US. What is primary here is the ruling that is religion; the finding that it is not science is secondary. The ID argument from the design of the eye is not science, because it is immunized against scientific examination. But the ID argument from the irreducible complexity of the bacterial flagellum is science. Just hopelessly wrong science,[6] as shown by the piles of scientific documents produced in court, and the persistence in this wrongheadedness was also accepted as evidence that ID’s agenda is religious. The distinction, if there is one, between bad science and not science was immaterial.

Double edged. There is a real cost to the ruling that ID is religion, and schools in the UK are paying that cost right now. While ID is officially shut out of the science lab, at least in state funded schools in England (the situation in Scotland is less clear), it is in the process of infiltrating itself into the Religious Education classroom, by way of such materials as The God Question, and RE teachers will be less able (and in some cases less willing) than their Science colleagues to dispose of its pretensions.

In short, IMN is untrue and carries a heavy rhetorical cost to science. But everything that can be accomplished by including IMN in our definition of science and then appealing to that definition as criterion, can be accomplished on its own merits by less circuitous means. So let’s cut out the middleman.

Instead, I would appeal once more to Laplace, who took as examples such purported phenomena as animal magnetism, dowsing, and solar and lunar influences on mood, and concluded:

Paul5

We are so far from knowing all the agents of nature and their diverse modes of action that it would not be philosophical to deny phenomena solely because they are inexplicable in the actual state of our knowledge. But we ought to examine them with an attention all the more scrupulous as it appears more difficult to admit them, and it is here that the calculation of probabilities becomes indispensable, to decide to what point one must multiply observations or experiments, in order to obtain for the agents that they indicate a probability that outweighs the reasons we would otherwise have against admitting them.


Or, in the abbreviated form that has come down to us to us through Carl Sagan,

Extraordinary claims require extraordinary evidence.

That’s all we need.

I thank Maarten Boudry and Stephen Law for helpful discussions. Posthumous portrait of Laplace by Guérin through here. An earlier version of this piece originally appeared in 3 Quarks Daily

1] Capital letters for Creator and Designer because I do not wish to collude in the polite fiction that the Intelligent Design programme is anything other than an argument for the existence of God. Separate technical questions have been raised about the validity of the statistical argument from fine-tuning, but these do not affect my argument.

2] Personal communication, ca. 2006

3] Consider the mutation that made Queen Victoria, grandmother of the last Tsarevich, a carrier of haemophilia, and what difference this might have made to Russian history.

4] For some believers, the Mass might be a counter-example. But since the claimed miraculous trans-substantiation changes no accidental (i.e. observable) properties, it is irrelevant to science.

5] Alternating mutation and selection can and demonstrably does generate new information, protein sequences have considerable flexibility and do not arise in a single step, polonium halos in uranium-free rocks can be traced to the diffusion of radon, dating anomalies are exceptional and indeed informative, since they can be traced to heating episodes and other post-depositional events, and so on.

6] Since there is an excellent scientific, indeed Darwinian, explanation in terms of exaptation. Although if this is excluded by moving the goalposts, a typical ID ploy, perhaps we have again moved into the domain of non-science.

Boyle’s Law is not a principle; so does the UK Education Secretary know what a principle is?

What [students] need is a rooting in the basic scientific principles, Newton’s laws of thermodynamics and Boyle’s law. [Education Secretary Michael Gove, reported here].

He has been justly mocked for confusing Newton’s laws with the laws of thermodynamics (e.g. here and here and, by me, here). But the kind of ignorance involved in describing Boyle’s Law as a “basic scientific principle” is far more damaging.

Disclosure: I taught Boyle’s Law for over 40 years, and it gets three index entries in my book, From Stars to Stalagmites.

Bottom line: Boyle’s Law is not basic. It is a secondary consequence of the kinetic theory of gases, which is basic. The difference is enormous, and matters. Anyone who thinks that Boyle’s Law is a principle doesn’t know what a principle is. (So Gove doesn’t know what a principle is? That figures.)

Reasoning: Boyle’s Law states that if you double the pressure on a sample of gas, you will halve the volume. Boyle thought this was because the molecules of gas repel each other, so it takes more pressure to push them closer together, and Newton put this idea on a mathematical footing, by suggesting an inverse square law for repulsion, rather like his inverse square law for gravitational attraction. They were wrong.

Mathematically, the Law is simply stated, which may be why Mr Gove thinks it is basic: volume is inversely proportional to pressure, which gives you a nice simple equation (P x V = a constant) that even a Cabinet Minister can understand. But on its own, it is of no educational value whatsoever. It only acquires value if you put it in its context, but this involves a concept of education that seems to be beyond his understanding.

Now to what is basic. Boyle’s Law is now explained using the kinetic theory of gases. This describes a gas as a whole lot of molecules, of such small volume compared to their container that we can think of them as points, each wandering around doing their own thing, and, from time to time, bouncing off the walls. It is the impact of these bounces that gives rise to pressure. If you push the same number of molecules (at the same temperature) into half the volume, each area of wall will get twice as many bounces per second, and so will experience twice the pressure. Pressure x volume remains constant.

Actually, Boyle’s Law isn’t even true. Simple kinetic theory neglects the fact that gas molecules attract each other a little, making the pressure less than what the theory tells you it ought to be. And if we compress the gas into a very small volume, we can no longer ignore the volume taken up by the actual molecules themselves.

So what does teaching Boyle’s Law achieve? Firstly, a bit of elementary algebra that gives clear answers, and that can be used to bully students if, as so often happens, they meet it in science before they have been adequately prepared in their maths classes. This, I suspect, is the aspect that Gove finds particularly appealing. Secondly, some rather nice experiments involving balancing weights on top of sealed-off syringes. Thirdly, insight into how to use a mathematical model and, at a more advanced level, how to allow for the fact that real gases do not exactly meet its assumptions. Fourthly, a good example of how the practice of science depends on the technology of the society that produces it. In this case, seventeenth century improvements in glassmaking made it possible to construct tubes of uniform cross-section, which were needed to measure volumes of gas accurately. Fifthly … but that’s enough to be going on with. Further elaboration would, ironically, lead us on to introductory thermodynamics. Ironically, given the interview that started this discussion.

Educationally, context is everything, the key to understanding and to making that understanding worthwhile. A person who decries the study of context is unfit for involvement with education.

Even at Cabinet level.

UK Education Secretary says students need to know how Newton invented thermodynamics [!]

I would like to say that Michael Gove shows a knowledge of what counts as basic science that is some 300+ years out of date, but that would be too kind.

Gove said there had been previous attempts to make science relevant, by linking it to contemporary concerns such as climate change or food scares. But he said: “What [students] need is a rooting in the basic scientific principles, Newton’s laws of thermodynamics and Boyle’s law.” [Times interview, reported here]

As many readers will know, but the Education Secretary clearly doesn’t, Newton’s laws describe the motion of individual particles. Thermodynamics is intrinsically statistical, and was developed over a century after Newton’s death. Boyle’s Law is not a basic scientific principle, although it is a corollary of the basic principles followed by (ideal) gases. And here we have someone ignorant of these elementary facts, in a position of enormous power, telling the schools how to teach, and the examination boards how to examine.

And in this same interview, he says he wants schools to form chains and brands, like businesses. Satire falls silent.

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