The Science of Discworld IV Judgement Da

TWELVE



* * *



LONG ARM OF THE LORE





Discworld has a Guild of Lawyers, even though it has no systematic legal system. This is only to be expected: lawyers never let little things like that get in their way. It does have a traditional method for settling legal disputes, however: a tribunal, over which Lord Vetinari, Patrician of Ankh-Morpork, is entitled to preside, should he so wish. On Discworld, as in many parts of Roundworld, disagreements about the law, or alleged infringements of it, are subjected to formal procedures, often involving a written body of legislation, precedents from other (often totally unrelated) cases, arguments, counter-arguments, expert witnesses and … oh, yes, evidence.

What, though, counts as evidence?

On Roundworld, even in countries that consider themselves to be democratic, a surprisingly large part of the legal process involves one or other party trying to arrange for key evidence to be excluded or included, doing its best to rig the jury in its client’s favour, plea-bargaining, and generally subverting the process of obtaining a fair trial. Law trumps justice.

This tendency is universal among lawyers on both worlds.

Roundworld, however, also has laws of another kind. Its inhabitants optimistically call them ‘laws of nature’, by which they mean the rules according to which their world operates. Human laws can be broken; nature’s laws cannot. They are not regulations made by people, but statements about how the universe behaves. The law-court of science also judges evidence, but for a different purpose. Instead of deciding the guilt or innocence of the accused, scientific evidence decides the truth or falsity of the law.

If only it were that simple.

That’s what we used to think, back in the heady days when gravity really did seem to fall off inversely as the square of distance, light was a wave, and time was independent of space. God was a mathematician and the universe was clockwork. But now, alongside the T-shirt bearing the equations of relativity, we find others that read ‘I used to be uncertain, but now I’m not so sure’.

That pretty much sums up the current status of physical law among scientists. Today, we expect longstanding ‘laws’ of nature to be occasionally overturned when better observations become available, or when new contexts for the laws arise. The laws of chemistry do not allow base metal to be transmuted into gold, but the laws of nuclear reactions do. What we call ‘laws’ seem to be recurrent patterns in the physical world, which we can approximate very closely using mathematical equations, in limited contexts. We often call them ‘models’ or ‘rules’ instead, but on the whole we still use ‘laws’ for the deepest and best supported among them.

This rejection of certainty makes science stronger, because it gives scientists the opportunity to revise their views when the evidence proves them wrong. But people like certainty, and many seem unable to understand why informed doubt is a strength. This opens up a huge opportunity for the storytelling ape, who insists on courtroom drama and the struggle between prosecution and defence. The case may pit one scientist against another, because individuals have their own ideas about what nature’s laws are. Or it may pit science against anti-science in the court of public opinion – lung cancer v the tobacco industry, evolution v intelligent design, climate change v scepticism and denial.

Now nature’s laws, and humans’, start to look much more similar, because once again what determines the outcome is not the evidence as such, but whether it is allowed to be taken into account, and how it is interpreted. In place of humans united in a quest to find out how nature works, we find some who want that, but others who think they already know how nature works, and will use any trick in the book to ram their answer down everybody else’s throats. Scientific doubt provides the latter with a useful weapon: it opens science up to the criticism that it doesn’t actually know anything.

Scientists do not make laws, or enforce them, or try to wriggle out of them. They do not, as social relativists and postmodernists seem to imagine, get together, decide what laws will suit their purposes and then declare them to be correct. Instead, the scientists of Roundworld, and their predecessors – the natural philosophers – have always spent much of their time investigating the potential consequences of hypothetical versions of natural law, hoping either to support theories or to demolish them. Being human, they tend to prefer support for their own theories and demolition of the opposition’s, but most of them make a genuine effort to avoid that kind of bias if the evidence that they are wrong becomes sufficiently strong.

A topical example is Richard Muller, leader of the 2009 Berkeley Earth Project and (until July 2012) a prominent climate change sceptic. In an analysis aimed at refuting claimed evidence of man-made global warming, the Project (funded by groups that support lobbying to resist action on climate change) made a fresh analysis of historical data on the Earth’s temperature over the last two hundred and fifty years. In the event, the study was entirely in line with, and strengthened, the existing evidence in favour of man-made global warming. The analysis showed that during that period, the Earth’s average land temperature increased by 1.5°C. Nearly two thirds of that rise occurred in the last fifty years.

Muller promptlyfn1 announced that his previous concerns about possible errors of data collection and analysis had proved unfounded. ‘Last year,’ he said, ‘I concluded that global warming was real and that the prior estimates of the rate of warming were correct. I’m now going a step further: humans are almost entirely the cause.’

That’s the difference between scepticism and denial.

There are two big philosophical problems about laws of nature. What are they? Where do they come from?

To complicate matters, the phrase itself can mean several different things. The philosopher Thomas Hobbes, who published Leviathan in 1651, proposed essentially God-given laws: ‘The first law of nature is that every man ought to endeavour peace, as far as he has hope of obtaining it’ – which determined what humankind should do. Another usage was that of John Locke, an early Fellow of the Royal Society, who cheerfully assumed that God had ruled against slavery: ‘The state of nature has a law of nature to govern it, which obliges every one: and reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions.’ Fine: consult reason and produce a system with liberty for all. That’s all right to start with, perhaps. But then you must make exceptions: for witches, of course; or for children caught stealing bread; or for malefactors in general. For a given value of ‘mal’.

Laws of nature in these senses were much nearer to human laws than is our common usage today, physical law. Examples are the law of gravity and Ohm’s law about the relation between voltage, current and resistance in electrical circuits. This meaning seems much closer to ‘how things work’, and it will be our starting point.

In The Nature of Physical Law, Richard Feynman wrote that in order to discover a law of nature, we start with a hypothesis, like Newton’s theory of gravitational attraction. Then we do some calculations, to see if examples fit our hypothesis. If all goes well, we call it a theory and try it out on many other examples. To the extent that these examples get wider and wider – from the famous applefn2 to the Moon, to planetary orbits, then to the discovery that large heavy spheres attract each other very slightly in the laboratory, and that galaxies seem to have gravitational interactions with each other over vast distances – we can then elevate the theory to the status of a law.

That brings us back to the Large Hadron Collider and its dramatic discovery of the Higgs boson, a long-sought fundamental particle that sorts out the masses of the other sixteen particles in the ‘standard model’ of particle physics. What was once wild surmise has now become respectable orthodoxy, and the standard model has now taken a giant leap towards becoming a law of nature. However, it hasn’t yet attained that status, because the current state of knowledge leaves some alternatives open.

At the end of 2011, if you were an optimist, the Higgs was barely visible, a statistically insignificant bump on a graph at an energy of about 125 GeV (billion electronvolts). By the middle of 2012, the same bump had achieved five-sigma significance, meaning that the chance that it was spurious was less than one in two million. On 4 July 2012 CERN, the European laboratory that administers and runs the LHC, announced the existence of the Higgs.

Well, a Higgs. Higgs-like. Sort of Higgsy. (A theory called super-symmetry, currently popular among mathematical physicists, predicts at least five Higgses. Maybe this is just the first.) The observations did fit the predicted behaviour of the Higgs, a specific theoretical construct, but some key properties of the real particle have not yet been measured. No one can be certain that those will fit too, until suitable data have been collected. But now the particle physicists know where to look.

Journalists, true to form, insisted on referring to the Higgs as the God particle, for no very sensible reason except sensational headlines. The name comes from the book The God Particle: If the Universe Is the Answer, What Is the Question? by Nobel prize-winning physicist Leon Ledermann. However, he wanted to call the Higgs the goddamn particle because of all the trouble it was causing. His publisher brought God into it.

This is always a dangerous tactic. It is presumably why some people with religious objectives imagine there is a link between the Higgs and their concept of God – just as some previously imagined that Stephen Hawking’s use of ‘the mind of God’ in A Brief History of Time was a theological statement rather than a metaphor. The ‘God particle’ name must surely be what inspired some hopeful doorstep missionary to claim (as reported in New Scientist) that scientists now believe in God. The evangelist’s reason – ‘They’ve found Him in the Large Hadron Kaleidoscope’ – is a dead giveaway.

Pity about ‘kaleidoscope’, of course, but that slip pales into insignificance compared to the claim that scientists now believe in God because they’ve observed the Higgs. It’s like citing the photon to prove they’ve seen the light.

Ian, being a mathematician, rather likes the standard model cake with Higgs icing, although he’d have been even happier if the Higgs had turned out not to exist, as Hawking once predicted. That would have been much more exciting. Jack, a biologist, has more misgivings. He is worried that the evidence for all fundamental particles depends on specific interpretations of the data, and the manner by which they are obtained. It’s not easy to observe a new particle: you don’t just look for it and see it, like in the old days. In particular, you spot a Higgs by the company it keeps. It doesn’t hang around long enough to be observed in its own right; instead, it decays into a complicated shower of other particles. So you have to look for the kind of shower that a Higgs would produce, and infer the presence of a Higgs.

By analogy, consider a piano, as observed by pianologists: creatures that have great facility with sound, but can’t see a piano or feel what shape it is. How would they find out what this musical instrument is made of?

Let’s allow them the ability to throw things at it. Hurling small stones would be rewarded, from time to time, by a musical note. We know this occurs when a stone hits a key, but pianologists would detect only the music. By collecting data, they would find a range of notes, with a nice mathematical structure. Clearly a piano is made from twangons of various frequencies. Experiments at higher energy would reveal a new and rather different ‘pianicle’: the slamon. (We understand that you get this by slamming the lid shut.) Now it’s got more complicated. Soon the pianino has joined the list, along with the muano, the tauano and much else.

Instead of making everything simpler, new data at higher energies has just muddied the waters. So how do pianologists propose to resolve the many theoretical issues involved? They obtain large government grants to create collisions of even higher energy. This requires erecting an LHC (Large Hotel Collapser) forty storeys high, and pushing the piano out of a top-floor window in the time-honoured fashion of visiting rock stars. The results are impressive, but hard to interpret. Careful analysis decomposes the resulting sound into a cacophony of a hundred or so different twangons, several variants of the slamon … and a bit left over. This bit, obtained by deducting from the overall sound every known component, is of course the long-sought proof of the existence of the Bigg Bashon – which journalists insist on calling the Thud pianicle, a name given to the sound created when a piano encounters a hypothetical field … or maybe a car park.

This proves that a piano has mass.

Because the procedure that confirms the new pianicle is so complex and error-prone, several billion pianos need to be launched into oblivion before the results become statistically significant. They are, and the discovery is published, months after the first experiment hit the headlines.

The big question here, which is where Ian and Jack tend to differ, though not by a lot, is whether particle physicists are misinterpreting the nature of matter in a similar way to pianologists resolutely failing to understand a piano. Bashing things to see what happens can break them into constituent parts, but it can also excite new modes of behaviour that can’t sensibly be thought of as components. Are particle physicists really finding out what matter is made of, or are they just causing it to behave in ever wilder ways?

Less facetiously, think about how we analyse sounds themselves. Scientists and engineers like to break a complex sound into simple ‘components’, sinusoidal vibrations with specific frequencies. ‘Sinusoidal’ refers to the mathematical sine curve, the simplest pure sound. This technique is called Fourier analysis, after Joseph Fourier, who used it to study heat flow in 1807. The sound produced by a clarinet, for example, has three main Fourier components: a vibration at the dominant frequency (the note that it sounds like), a slightly softer vibration at three times that frequency (the third harmonic), and an even softer vibration at five times that frequency (the fifth harmonic). This pattern continues with only odd-numbered harmonics, until the components reach such a high pitch that the human ear can’t hear them.

The sound of a clarinet can be synthesised, digitally, by adding together all of these Fourier components.fn3 But do those components ‘exist’ as physical things? That’s a moot point, even though we can pull the sound apart into those ‘things’ and reassemble them. On the one hand, we can detect them by applying the right mathematics to the sound that the clarinet emits. On the other hand, a clarinet does not emit pure sinusoidal tones at all, at least not without an awful lot of fiddling about to damp out unwanted components – in which case it’s not exactly a clarinet any more. Mathematically, a clarinet’s vibrations are best described by a nonlinear equation, which generates the complex waveform only, not its individual Fourier components. In that sense, a clarinet does not generate the components and then add them together. Instead, they come as a single, indivisible package.

You can learn a lot about the sound a clarinet makes from these mathematical constructs – but that doesn’t imply that the constructs are real, just that the mathematical technique is useful in its own right. A similar method is used to compress the data in digital images, using grey-scale patterns in place of sound waves – but in the real world the image is not formed by adding these components.

Are physicists just picking up mathematical constructs – in a sense, creating them by the way they analyse their data – and interpreting them as fundamental particles? Are fancy high-energy particles real, or artefacts of complex excitations in something else? Even if they are, does this make any important scientific or philosophical difference? Now we are venturing into questions about the nature of reality, of which the most crucial is whether such a thing exists at all. We aren’t sure of the answers, so we’ll content ourselves with raising the questions. But we suspect that several different interpretations of the same physics may be equally valid,fn4 and which one is best depends on what you want to do with it.

Evidentially, the Higgs is a small bump on an otherwise smooth curve. With the mind-set and traditions of particle physics, it is interpreted as a particle. What’s interesting to us is how the bump becomes the object of attention, while the much larger quantity of data representing the smooth curve is relegated to the background.

A more familiar example has the same features. Our view of the solar system, with all the planets, all the asteroids and comets, behaving as they should, would be upset if we spotted a spaceship rocketing about but thought it was just another regular body. It would be a malefactor, not obeying the law of gravity. Indeed, the law tells us what is natural, so the spaceship becomes an anomaly.

Think of all the fuss about the Pioneer anomaly, an unexplained deceleration discovered when observing the spacecraft Pioneer 10 and Pioneer 11. These were the first space probes to reach the outer planets of the solar system, from Jupiter to Neptune. Because of the gravitational pull of the Sun, their speed continually decreased, but they were travelling fast enough to escape the solar system entirely, given enough time. However, when they were at about the same distance from the Sun as Uranus, observations showed that they were slowing down a little bit faster than gravity alone could explain – by about one billionth of a metre per second per second. After much head-scratching, an analysis published in 2011 showed that this effect could be accounted for by the way the craft were radiating heat, which created very small pressure effects.

Here, the underlying physical law, that of gravity, sets up the scenery: the backdrop against which the spaceship becomes a story. Pan narrans cannot help but see the spaceship as the most interesting item, because it doesn’t fit the story – it seems not to obey the law.

Our minds seem to have evolved to place extra weight on exceptions. The prolific science fiction and popular science author Isaac Asimov wrote: ‘The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka” but “That’s funny …”’ Law-abiding planets and comets are banal, unable to catch our attention. In the same way, we find the law-abiding mass of humanity essentially boring, so our stories are about witches and malefactors. Among Discworld’s characters, the witch Granny Weatherwax and the sweeper and history monk Lu-Tze catch our attention. It’s the exceptions to the law that make the law useful.

Are laws like that of gravity unique, special statements that are in some sense universally true? Would aliens come up with a theory like gravity, or is there something peculiarly human about falling apples, which leads our peculiar minds on to lunar orbits and solar systems? Is there perhaps a quite different way to describe solar systems?

Similarly, when Thomson started playing with cathode ray tubes, he had no idea that he was separating a beam of electrons, breaking up atoms. If we had started from some other particle than an electron, and we had gone on to find a zoo of others, would we have described the same zoo? Or would we have come up with a different zoo, which nevertheless describes the ‘real world’ as accurately as the one we’ve got?

Physicists, by and large, think not; they believe that there really are these particles out there, and that any scientific endeavour would find the same zoo. But the zoo you find depends on the theoretical model you use to direct the search. Ten years ago they had a different zoo, and in ten years’ time …

To expand on that point, consider the development of quantum mechanics. The relevant law here is the Schrödinger equation, which describes the state of a quantum system as a propagating wave. However, it seems to be impossible to detect this wave, as such, experimentally. Observations of a quantum system give specific results, and once you’ve made one observation, you’ve interfered with the hypothetical wave. So you can’t be sure that the next observation refers to the same wave. This apparently inherent indeterminacy has led to some extra interpretational features of the theory: that the quantum wave is a wave of probabilities, telling us what the state might be, and how likely any given choice is, but not what the state is; that measurements ‘collapse’ the wavefunction to a single state, and so on. By now this interpretation has become close to received gospel, and attempts to find alternatives are often dismissed out of hand. There is even a piece of mathematics, Bell’s theorem, which allegedly proves that quantum mechanics cannot be embedded within a broader deterministic local model, one that does not allow instant communication between widely separated entities.

All of the above notwithstanding, Pan narrans has problems with quantum indeterminacy. How does nature know what to do? This is the thinking behind Einstein’s famous remark about a (non-) dicing deity. Generations of physicists have become accustomed to the problem – the mathematics says ‘it’s just like that’, and there’s no need to worry about interpretations. But it’s not quite that simple, because working out the implications of the mathematics requires some extra bolt-on assumptions. ‘What it’s like’ could be a consequence of those assumptions, not of the mathematics itself.

It’s curious that we and Einstein use, as our icon for chance, the image of dice. A die (singular) is a cube, and when it is thrown, and bounces, it obeys the deterministic laws of mechanics. In principle, you ought to be able to predict the outcome as soon as the die leaves the hand. Of course there are modelling issues here, but that statement ought at least to be true of the idealised model. However, it’s not, and the reason is that the corners of the die amplify tiny errors of description. This is a form of chaos, related to the butterfly effect but technically different.

Mathematically, the probabilities of the die landing on its various faces derive from the dynamical equations as a so-called invariant measure. One chance in six for each face. There is a sense in which the invariant measure is like a quantum wavefunction. You can calculate it from the dynamical equations and use it to predict statistical behaviour, but you can’t observe it directly. You infer it from a repeated series of experiments. There is also a sense in which an observation (of the final state of the die) ‘collapses’ this wavefunction. The table, and friction, force the die into an equilibrium state, which might be any of the six possibilities. What determines the observed value of the wavefunction is the secret dynamics of a rolling die, bouncing off a table. That’s not encoded in the wavefunction at all. It involves new ‘hidden variables’.

You can’t help wondering whether something similar is happening in the quantum world. The quantum wavefunction may not be the whole story.

When quantum mechanics was introduced, chaos theory didn’t exist. But the whole development might have been different if it had existed, because chaos theory tells us that deterministic dynamics can mimic randomness exactly. If you ignore some very fine detail of the deterministic system, what you see looks like random coin tosses. Now, if you don’t realise that determinism can mimic randomness, you can’t see any hope of connecting the apparent randomness observed in quantum systems with any deterministic law. Bell’s theorem knocks the whole idea on the head anyway. Except – it doesn’t. There are chaotic systems that closely resemble quantum ones, generate apparent randomness deterministically and, crucially, do not conflict with Bell’s theorem in any way.

These models would need a lot more work to turn them into a genuine competitor for conventional quantum theory, even if that’s possible. The Rolls-Royce problem raises its head: if the test of a new design of car is that it has to outperform a Roller, innovation becomes impossible. No newcomer can hope to displace what is already firmly established. But we can’t help but wonder what would have happened if chaos theory had appeared before the early work in quantum mechanics did. Working within a very different background, one in which deterministic models were not seen to conflict with apparent randomness, would physicists still have ended up with the current theory?

Maybe – but some aspects of the standard theory don’t make a lot of sense. In particular, an observation is represented mathematically as simple, crystalline process, whereas a real observation requires a measuring device whose detailed quantum-mechanical formulation is far too complicated ever to be tractable. Most of the paradoxical features of quantum theory stem from this mismatch between an ad hoc add-on to the Schrödinger equation, and the actual process of observing, not from the equations as such. So we can speculate that in a re-run of history, our ‘law’ for quantum systems really could have turned out very different, giving Schrödinger no reason to introduce his puzzling cat.

Whether our current physical laws are special and unique, or a different set would work just as well, there is something more to say about laws in general. And about their exceptions, and especially about transcending them. By that word we don’t mean that the laws are disobeyed. We mean that they become irrelevant because of a change in context, like the way a jumbo jet transcends gravity by using air-flow past its wings.

We’ll take Ohm’s law as an example, because it appears to be simple.

Matter is basically of two kinds with regard to electricity: either it’s an insulator, or it’s a conductor. If it’s a conductor, Ohm’s law applies: current equals voltage divided by resistance. So, for fixed resistance, a greater current requires a greater voltage. However, resistance need not be fixed, and this possibility lies behind some natural anomalies, like the way that lightning changes the insulating gas of the atmosphere into a conducting ionised path for the lightning strike, or ball lightning, which essentially folds up into the surface of a sphere. Being anomalies, these phenomena are automatically interesting. We can also play tricks with variable conductors of electricity, starting with thermionic valves (vacuum tubes) in the 1920s and continuing with semiconductors like transistors. The computer industry is built upon this trick.

The discovery of superconducting alloys – no electrical resistance – near zero Absolute temperature was a very interesting anomaly, which, as new alloys have been found that exhibit no resistance at higher and higher temperatures, promises to give us a whole new energy technology. The interesting items are those that differ from the Ohm’s law picture: the witches, the spacecraft.

Ohm’s law is intimately involved with stories about electricity distribution. By describing these problems, and their solutions, we can show how leaving the law to ‘work its will’, but changing the context, can completely alter the situation. From there we can go from Feynman’s position – that laws determine the context as well as the content of natural events – to a more progressive view.

Electricity distribution to households is made difficult by the resistance of the cables, which causes a lot of electrical energy to be dissipated from the transmission lines as heat. Ohm’s law implies that the same amount of power can be transmitted, with lower losses, by making the voltage higher and the current lower. However, this would supply homes with very high-voltage electricity, and accidents would be fatal.

The trick is to use alternating current, back and forth fifty or sixty times a second. Transformers can change the voltage of alternating current, so it can be high for transmission and then reduced to not-very-lethal values when it gets to our homes. Today we could stick to direct current, using modern electronics to change the voltage, but that option wasn’t available when the distribution system was being created. We’ve now invested so much in alternating current systems that we can’t easily change them, even if that turned out to be a good idea. This trick dodges the Ohm’s law problem of resistance, hence energy loss. Even now, more than a third of the energy can be lost in long transmission lines, but that’s still far more efficient than the 70% loss delivered by the low-voltage direct current systems of the 1920s. By changing the parameters, by going to low-current high-voltage alternating current, we can to some extent change the rules.

Too many physicists seem to have a mind-set that considers physics to be all of reality, simply because it is concerned with all the basic structure of matter. In The Character of Physical Law, Feynman says:

The same kinds of atoms appear to be in living creatures as in non-living creatures (sic); frogs are made of the same ‘goup’ as rocks, only in different arrangements. So that makes our problems simpler; we have nothing but atoms, all the same, everywhere.

In the same book, he says:

Probably the most powerful single assumption that contributes most to the progress of biology is the assumption that everything animals do the atoms can do, that the things that are seen in the biological world are the results of the behaviour of physical and chemical phenomena, with no ‘extra something’.

Like Feynman, we don’t think that there’s an ‘extra something’, an élan vital (‘life force’) that drives life. No, it’s much simpler than that. Organisms have evolved, and whereas at the outset of life they were very limited, mostly ‘doing what their atoms did’, as Feynman would have it, they acquired new properties, like cell division. They got a workable heredity, they acquired eyes and the nervous systems to use them. They moved up out of physico-chemical systems, just as we’ve moved up out of the law of gravity. Organisms have new tricks, exploiting new contexts. For instance: birds, despite being heavier than air, can fly.

We’re not saying that what birds do is inconsistent with the ‘fundamental’ physical laws for the matter out of which they are made. That would be very close to making Descartes’s error, postulating that mind and matter are two different things. In fact, flight is entirely consistent with physical law. The force of gravity, acting on the atoms that make up the bird, must be counteracted by the lifting forces generated by the wings as they move through the air. If not, the bird won’t fly. Ditto jumbo jets. Our point is that flight is not something that you can naturally deduce from the fundamental laws. Molecules can’t fly, but birds – made from molecules – can. A molecule can fly if it’s included in a bird. Context makes a big difference. Life has acquired a multitudinous list of complex systems, each resulting from natural selection, to lift organisms out of ancient incompetences into new competences.

The goup in a frog isn’t a bit like the goup in a rock. The atoms may be much the same, but the different arrangements, to use Feynman’s words, completely change how you expect frog goup to behave. Similarly, the atoms in a person or a penguin or a packet of soap powder are in different arrangements. To understand the bird, the frog, or the soap powder, it’s not enough to know about the underlying atoms or subatomic particles. It’s how they are arranged that matters. In fact, they could be made of rather different stuff, but if it were arranged to carry out similar functions, you’d still end up with effective birds, frogs and soap powder.

It’s the arrangements that make the magic, not the goup.

Atoms in different arrangements have different properties: an atom in a piece of rock is probably one of millions in a crystal array, and is essentially a permanent part of that array. An atom in a living creature is probably part of a very complex network, changing atomic and molecular partners all the time. Moreover, this changing system is not typical of the unaided activities of matter obeying the fundamental laws, despite being consistent with those laws. It has been selected over many generations so that it works, so that it does something. And the something that it does, while not having any ‘extra something’ in Feynman’s sense, contributes to the life of the organism that it’s part of. It may even be part of a virus, destroying the organism, but it’s still enmeshed in all the processes that make up life.

Life has lifted itself out of the simple laws of nature, where it started, and is now a whole complex world, at least as different from that origin as a modern aeroplane is from a flint axe. The scene at the beginning of the film 2001, where the ape throws up a thighbone and it morphs into a space station, is a lovely illustration of just that kind of evolution. And that transformation is minor, compared to how life has transcended its origins.

Let’s look at it from a different perspective. The material world, the world of physics and chemistry, has many continuing processes, from the unimaginable physics in the middle of stars to the freezing and thawing of ethane and methane on Saturn’s moon Titan. Stars explode, scattering the elements that have formed within them into the cosmos, and planets condense from that mixture, according to the laws of physics and chemistry. Then, perhaps in the deep ocean near the rift in the ocean floor from which highly reduced compounds are pouring, some anomalous chemistry sets up a hereditary system. It may be a mixture of chemical processes that is in some sense heritable, it may be RNA, it may be a pre-metabolic system … But it’s the beginning of a story, a narrative that has lifted itself out of the frame of the laws, and is about to transcend them. Spaceships and witches are in its future.

As life first starts, it’s not remarkable. It proceeds more or less according to the rules of physics and chemistry, according to the laws. Then it begins to compete, perhaps for space, or for particular chemicals, or for membranes that are fatty layers on clay. Those systems that work better lift themselves out of the laws, into a tiny simple narrative that says ‘A does a little bit better than B or C, so there’s more of it in the future …’ Come back in a million years, and the oceans are full of A, while there’s no C to be found. And by then, A has diversified into A1 and A2 and A3. Now, lurking – a good narrative word – in the depths is Q, which loves to include A3 in its system. So later we have QA3XYZ, and the system is well started.

It’s all gone according to the laws, for sure; but there’s a mite of competition, selection of this over that. Come back in a million years, or perhaps six weeks, and there will be a bacterial cell that has lifted itself into a story …

The laws facilitate such changes, but they don’t direct them. They are merely history, with all the living stuff transcending them in every direction. Come back in 3000 million years, you’ll find a mess of Burgess Shale organisms. Come back 580 million years later still, and you’ll find a physicist denying that any of this is important. But the action transcends the laws: it’s the spaceships and witches that drive the narrative.

Life originally emerged from non-living systems, with laws, but it has gone on to complicate itself out of all recognition. Biology isn’t just physics and chemistry with knobs on. It’s a whole new world.

Within that world, one of its beasts has acquired language, imagination, and a penchant for stories: a special, wholly new thing in the cosmos. Narrativium has escaped from Discworld into Roundworld; now some things do happen because there is a creature that wants them to.

Perhaps there are many such creatures, all over the place; perhaps as many as one species per hundred million stars. But we should be very careful indeed, just in case we’re the only one.

Just one story in the whole cosmos.

Everywhere else, only laws.

fn1 A little too promptly for some scientists, who complained that the results were announced before being peer-reviewed for journal publication.

fn2 Although often thought to be a myth, this story has some basis. Newton often said that he had been inspired by the fall of an apple. Wikipedia states: ‘Acquaintances … such as William Stukeley, whose manuscript … has been made available by the Royal Society, confirm the incident, though not the cartoon version that the apple actually hit Newton’s head.’

fn3 For a dominant frequency ω, the combination sin(ωt) + 0.75 sin(3ωt) + 0.5 sin(5ωt) + 0.14 sin(7ωt) + 0.5 sin(9ωt) + 0.12 sin(11ωt) + 0.17 sin(13ωt), going as far as the 13th harmonic, is pretty convincing to the human ear.

fn4 In the science fiction novel Light by M. John Harrison, aliens living around the Galactic Core have invented six different space drives, each based on a different theory of fundamental physics, several of which are known to be wrong. All of the drives work fine. In Roundworld, our theories of aerodynamics are approximations that ignore atomic-scale structure, yet aircraft fly perfectly well. Lies-to-children often work.