The Science of Discworld IV Judgement Da

SIX



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REALITY ISN’T MAGIC





Is magic real?

Most of us no longer think that, not even those who are comfortable with supernatural intervention in everyday life. Magic is superstition, unlike entirely sensible beliefs in virgin births or life after death.

Magic is a human-centred viewpoint. It explains natural events in terms of what people want to happen. Assemble the magical ingredients (which often relate metaphorically to the desired outcome, like a rhino horn to an erection), incant the magic words (words have power), and the universe obligingly changes to accommodate your wishes.

On the whole, we much prefer stories about causes, as they hang together better than magical ones. We like to be told that something happens because something else did. You have to be quick on your mental feet to avoid the seductiveness of turtle-pile explanations involving causes all the way back, though. Most of us feel more comfortable when the pile is fairly short.

Scientists prefer rational, evidence-based causality. Religious people like to rest their short pile of causes on God, which relieves them of the need to look more deeply, just as Hume advised. Ironically, science lies behind technology, which we use to remodel our world so that it seems to work like magic, as we said in The Science of Discworld. When you switch on the light, all sorts of complicated technology goes into action: electricity, conducting wires, plastic insulation, and so on. (If you think a light switch is simple, you’re not thinking about what makes it work and how it can be produced.) The electrician and the company that made the switch need to understand the technology in considerable detail, but the user does not. To them, it works ‘like magic’. If you could show an iPad to a mediaeval monk, he would probably declare it the work of the Devil. Who else could create moving pictures on a slate? He would certainly find it incomprehensible. So do almost all of its users today. We want our gadgets to work like magic, doing what we want because we want it.

In contrast, science is mostly about how things happen ‘of their own accord’. Science is universe-centred; magic is human-centred. The two viewpoints come together in technology: here the human-centred view sets our goals, while the universe-centred view helps us to achieve them. So technological magic involves a special kind of causality. Not natural causality – the workings of nature’s laws – but human causality: how we can make nature do what we want.

Our thinking about causality easily gets muddled. We don’t really understand what it is. Worry not: neither do scientists. In fact, anyone who claims to understand causality hasn’t fully understood the question.

One of the big puzzles about causality is that once you start to trace the causes of even the simplest features of the world, you find an ever-branching backward tree, with many unlikely things coming together at just the right instant to make something else happen. We rest on an infinite pile of coincidences, and the pile gets wider the further back we go. The probability of anything specific happening seems to be zero.

Dawkins starts Unweaving the Rainbow with the example of all the people that aren’t alive because they’ve never been born, the sperms that never made it to an egg for fertilisation, all the DNA combinations that were never actualised. These ‘potential people’, he says, outnumber the sands of Arabia. The ones who have been born are the tiniest of minorities.

He quotes Desmond Morris ascribing his love of natural history to Napoleon: if Morris’s great-grandfather’s arm had not been removed by a cannonball in the Peninsular War, all would have gone differently. If your parents, or your grandparents, had never met … You can see where we’re going here: the events that have actually happened are the tiniest fraction of those that might have happened.

It’s easy to sort this out for Discworld. Narrativium makes sure that things go as they ought, and if there’s a problem, there are always the History Monks to set things to rights. But Roundworld isn’t like that: when the wizards needed to produce Shakespeare all kinds of things went wrong before they got the right version of him.fn1

How do you know that you are the right version?

Let’s examine this problem: all the things that could have happened, versus the tiny fraction that actually did.

Some physicists claim to believe (we find it hard to accept that they actually do, when they get up in the morning) that there’s a very simple answer to this conundrum. All possible things happen. Each distinct choice starts off a new universe, so that the Trousers of Time are forever bifurcating; everything happens somewhere. This seems absurd, making potential events as real as actual events. It’s as if you tossed a coin a hundred times and wrote down the list of what happened: HHTTTHH and so on. Fine. But then you claim that every possible series happened ‘somewhere’, that HHHHHH, all heads, and TTTTTTT, all tails, happened too, as well as all the other possible combinations. Only … they didn’t happen in this universe, they happened in other ones. You’re stuck in the universe where HHTTTHH happened, but somewhere else, the all-tails and all-heads options came up. The newspapers there must have been full of that news, mustn’t they? Or are they perhaps in the kind of universe where unlikely things happen all the time?

This is the world of Schrödinger’s cat, alive and dead at the same time until someone takes a look. Ponder Stibbons alluded to it in chapter 1. Well, it’s the world of Schrödinger’s cat according to quantum physicists, though not according to Schrödinger, who used a cat because cats aren’t like that. But electrons are, so quantum physicists view a cat as a sort of super-electron. There is, however, a different view: that HHTTTHH was what happened, and that the other possibilities, like the other people whose sperms didn’t make it to an egg, or the other histories that didn’t result in Morris being a great naturalist, didn’t actually happen. Anywhere.

Now, there is a sense in which the classical universe is the superposition of all conceivable quantum states, and that’s what the quantum physicists are so keen to explain. But only one classical universe arises from of all those quantum alternatives – and that’s why a cat is not a super-electron. Feynman explained this in QED using light rays as an example. The classical (that is, non-quantum) law of reflection tells us that when a light ray hits a mirror, ‘the angle of incidence equals the angle of reflection’. That is, the ray bounces off at the same angle as it hit. In a classical world, there is only one outcome, determined by this simple geometric law. In a quantum world, there is no such thing as a light ray; instead, there is a quantum superposition of wavelike photons, going in all directions.

If you model the incoming ray in such terms, these photons concentrate around the classical ray in a particular manner. Each photon follows its own path; even the places where they hit the mirror can be different, and where they go afterwards need not obey the classical equal-angles law. Wonderfully, if you add up all of the waves corresponding to all of the photons – all of the potential quantum states of the system – with the right probabilities, the answer concentrates very tightly around the classical reflected ray. Feynman manages to convince his readers of this technical point (the principle of stationary phase) without doing any sums. Brilliant!

Notice how here the entire quantum superposition, of all possible states – including crazy ones where the photon follows wiggly paths, hits the mirror many times, and so on – leads to a single classical result: the one we observe. It does not lead to a superposition of many different classical worlds, like the traditional story of a world in which Adolf Hitler won the Second World War coexisting alongside one in which he didn’t, together with endless variants in which all possible choices occurred at all possible times.

Yes, but … Can we somehow pull that quantum superposition apart into many different classical scenarios, so that their superposition is the same as the quantum one? Each classical scenario would be a superposition of some of the quantum ones, and we must be careful not to use any of them twice, but is it possible? If so, our objection to the many-Hitlers universe would be irrelevant.

The most reasonable classical variations on the equal-angles scenario involve classical choices about where the incident light ray hits (which determines the angle of incidence) and what angle it comes off at (the angle of reflection). That is, we draw lots of straight lines that start at the light source, hit the mirror and bounce off – possibly with unequal angles.

Now, there are indeed photon-paths, submerged in the ocean of all possible quantum states, which mimic all of those classical paths. But if we change the point at which the ray hits the mirror, and try to synthesise that ray as a sum of nearby quantum states, it doesn’t work. To make the original set of photon-paths represent the original incident ray correctly, these paths must be assigned probabilities that are concentrated near that ray. The paths near a different ray then have the wrong probabilities to represent that alternative ray. In short, we can’t change the point at which the classical ray hits the mirror. But then, paths that reflect at a different angle aren’t classical at all; in classical physics they are impossible, because classical paths obey the law of reflection.

This thought-experiment with a mini-universe containing a mirror and a light ray seems to indicate that the quantum superposition concerned determines a unique classical state, and that it can’t be pulled apart into several different classical states. Perhaps there’s a clever way to do that, but not in the world of incident and reflected rays. In short, although this mini-universe has infinitely many different quantum states, there is exactly one superposition that obeys a classical narrative. Since that’s true for this simple mini-universe, something like it is presumably true for more complex ones. In particular, although the classical story in which Hitler lost the Second World War can be pulled apart into zillions of quantum alternatives, these states determine a single classical narrative, the one in which Hitler lost World War II. Moreover, this state cannot be pulled apart into different classical narratives by partitioning the quantum states that combine to create it.

If this argument is correct, there’s no reason to believe that the constituent quantum states are anything other than useful mathematical fictions.

The main problem underlying Schrödinger’s cat is not quantum superposition; it is our inability to model observations in quantum mechanics in a way that corresponds to actual experimental apparatus. Instead of admitting that we can’t say what happens when we observe the world, and find just one state out of many potential ones, we insist that the entire universe must keep splitting into pieces that include all possible outcomes. This is just like insisting that the entire universe revolves round a stationary Earth, instead of accepting that maybe the Earth spins instead.

Since many things did not happen when you came into being, what about those that did? Were lots of them random rolls of the genetic dice, in which one sperm carrying these genes got there and the other 200 million missed out? Or a specific cannonball took an arm off and missed all the rest … or killed other people? Were other – perhaps all – events strictly determined by what had happened the instant before, which in turn was determined by the instant before that? Do we have to choose between everything that happens being the luck of the draw, or everything being strictly causal and determinate, from the Big Bang onward, through now into the infinite future? So that only one future was ever possible?

The opening chapters of Daniel Dennett’s Freedom Evolves show conclusively that we can’t – ever – decide between these options. They aren’t real choices: determinate/indeterminate isn’t the way to go, because we can’t ever know which applies. The distinction makes sense only in a thought-experiment where we rerun the entire universe again, starting from an identical state, and check whether the same events occur both times. It is a valid distinction for how we think about our world, for the kinds of model we propose, but it’s not a meaningful statement about the world itself.

We could take examples of events from anywhere and anything, and discuss their provenance: what makes them happen. Here we will look at three. The first example shows how difficult it is to demonstrate a cause in the real physical world, because tiny events can have tremendous outcomes. The second shows how, in our cultural world, small events – or the absence of such events – can take over a social universe and bias it away from the desirable outcome. Finally, we’ll show how meddling by humans can completely change biological systems – and we’re not thinking of dodos.

In the 1960s Edward Lorenz, a mathematician and meteorologist, discovered that tiny differences in computer input for (a toy model of) weather prediction could lead to large differences in the resulting forecast. From this discovery, together with a variety of other inputs, came the mathematics of deterministic chaos. We have all heard how the flapping of a butterfly’s wings in Tokyo can cause a tornado in Texas a month later. This is a fine, dramatic example, but it considerably misrepresents causality. It suggests that only that butterfly is needed for the tornado, when actually it’s the difference made by that butterfly that changes the circumstances just slightly, and flips the balance of causality into another path, a different trajectory on the same attractor. In reality, our world is full of butterflies.

Weather is a dynamic path through the attractor that we call climate. As long as the climate stays the same, the attractor doesn’t change, but the path through it can. We then experience the same kind of weather, but in a different order. Climate change is more drastic: it alters the attractor. Now the entire range of possible weather-trajectories is different. Nonetheless, much of it still looks like plausible weather from the original attractor, because the attractor may not undergo any radical change – it need not encounter a tipping point. It can get a bit bigger, a bit smaller, or move around a little. We can’t observe attractors directly, but we can reconstruct them mathematically from observations, processed in the right way. The simplest way to detect change in the attractor is to observe data such as long-term averages of temperature, size and frequency of hurricanes, likelihood of flooding etc. Many objections to ‘climate change’ confuse climate with weather.

We wrote a long piece in The Science of Discworld III about causality, and don’t want to repeat that here. Enough to say that there is not any single cause of any event; it is almost always truer to declare that all of the preceding events contribute, than to point to one cause. However, stories do have a linear structure: A causes B causes C … The law courts are full of that kind of story, as are most novels, and pretty well all detective stories and science fiction. Even Discworld stories rely on that fictional causality for their coherence. But this is because we are the storytelling ape. A story is a linear sequence of words. It is interesting to speculate whether an advanced alien culture would of necessity concoct such false-to-fact linearly causal stories. Could one always attribute events to three or four, or ten or twenty or a thousand, causes? Or is that the storytelling ape’s way of seeing causality?

If we truly live in a deterministic universe, whatever that means, each successive state is the inevitable result of the immediately preceding state, including such minor causes as the gravitational influences of far stars, even the gravitational influences of the beasts on the planets around far stars. This picture is consistent with certain portrayals of the universe, where for some elements (spaceships approaching the speed of light are favourite candidates) what is in the future for some is on the left for others, while to the right are events-past. So every event is already ‘there’, in some frame of reference. This portrays the whole universe as a vast crystalline structure, with the future just as determinate as the past.

We find this representation as unsatisfactory as the perpetually-dividing Trousers of Time image. Historically, some of it derives from a misreading of Einstein’s concept of a world-line in relativity, a fixed curve running across spacetime and describing the entire history of a particle. One curve, calculated using Einstein’s equations, so one history, right? It’s a valid image in a world with only one particle, whose state can be measured exactly, to infinitely many decimal points. It’s not sensible for the vast, complex universe. If you start drawing a curve in spacetime, and allow it to develop as it grows, at any given stage you may have no idea where it will go next, no way to predict its future path. Einstein’s equations don’t help, because you can’t measure the current state of the universe exactly. That’s not a deterministic universe in any meaningful sense, but after infinite time you’ve got just one curve, one world-line – just as before.

Faced with a choice between two extremes, a world that is random or one that is completely predetermined, most of us dislike both. Neither matches our experiences. That doesn’t prove either of them is wrong, but it makes a key point: any theoretical model must explain our daily experiences. It may well demonstrate that deep down, things are not as we assume; however, it does have to explain how what we assume emerges from the model, even if it’s a misinterpretation of what is ‘really’ happening in the model. For example, the standard claim that science has proved atoms to be mostly empty space does not prove that the apparent solidity of a table is an illusion. You also have to explain why it seems solid to us; then you discover that empty space isn’t empty at all, but filled with quantum fields and forces. Which is what ‘solid’ means at that level of description.

So we would like to find some leeway, some choosable indeterminacy in what happens, if only to foster our illusion of having free will. We would like to think that on an appropriate level of description, what we decide to do is not simply what we have to do.

Worryingly, the great (though sometimes misguided) philosopher René Descartes would have had sympathy with this approach, but that’s because he famously divided the world into two separate aspects, res cogitans and res extensa, mind and matter. He needed res cogitans, the mind, to be freewheeling, so that it could instruct the body, res extensa. In contrast, he thought that little of the body’s influence, if any, went the other way.

Consider the accidents of history that converged on Descartes, making his world a divided one and resulting in all kinds of anomalies in the present intellectual scene, from Arts and Science departments in universities, barely considering each other to be intellectually proper, to descriptions of minds and souls in popular parlance that are, to say the least, irrational.

In Essential Readings in Biosemiotics, Donald Favareau presents a fascinating story that makes a lot of sense. He starts with Aristotle, who wrote some twenty-six essays, only six of which were translated into Latin by Boethius in the sixth century. Two (Categories and On Interpretation) were about the material world, one (Prior Analytics) was about the mind, and the other three (Posterior Analytics, Topics and Sophistical Refutations) were about law and argument. The essay that joined up mind and matter, De Anima – Life, or Soul – was not translated until the thirteenth century, so it got left out of the western world’s traditional ‘works of Aristotle’ for a thousand years, based entirely on Boethius. It was, in fact, translated from the Arabic in 1352 by Jean Buridan; all the great libraries then were in Arabia and Spain, and the Muslim religion was in the ascendant. But despite that, it was not then added to the standard ‘works of Aristotle’.

In particular, Descartes had access to Categories and On Interpretation, but not to De Anima or On Sense and the Sensible, which provided a series of beautiful bridges between mind and body. So, believing himself to be free from preconceptions, but in fact carrying only part of Aristotle’s weighty arguments in his memory, he divided mind from matter. That laid a secure foundation for this intellectual separation, right up to Norbert Weiner and Cybernetics, when feedback and machinery met.

That accident, that De Anima was not available to Descartes, or to Francis Bacon when he published the Novum Organon in 1620, which was based on the six essays translated by Boethius, changed the whole European intellectual climate for the next four hundred years. From Newton through to Einstein, physics was delimited with no thought of information. Shakespeare, Samuel Taylor Coleridge, all the way to Kingsley Amis, John Betjeman and Philip Larkin – everyone talked about machinery and industry, but only from outside.

The two worlds, mind and matter, only began to come together with Sigmund Freud and Carl Jung, who were in neither world, nor by any means in both. And then, after the Second World War, during which many scientists had been involved with communication issues, Claude Shannon began to publish papers in which information was treated as a quantitative concept. Soon after that came cybernetics, in which feedback of information interacted with amplification and other physical changes, resulting in changes to output. The safety-valve on a boiler was an early example: when the pressure got too high the valve released some steam. Weiner added room thermostats, which turned the heat off and on. Nearly all amplifiers for sound use ‘feedback’ to send the output back to the input, improving the sound quality.

Here information is used to control mechanical systems, which introduces a whole new dimension of technological magic. Hidden inside every laptop, iPhone, and for that matter, refrigerator, is a long, complex series of ‘spells’: the software instructions that make all of the general-purpose electronics carry out the specific tasks needed to make the gadget work. Programmers are today’s sorcerers.

However, no one yet thought of linguistics as having anything to do with that kind of information. Only at the turn of the millennium did Steven Pinker, a linguistic psychologist, write How the Mind Works from a neurological and linguistic viewpoint. The two sides met, productively, after three hundred and fifty years.

Pinker later wrote The Better Angels of our Nature, arguing that today’s humans are significantly less violent than they used to be. The book presents a wealth of data to support this contention. Nearly all of the reviews disagree; all of these are by people who are statistics-blind. They comment on the very apparent decline of violence in the last few centuries as if it were only apparent, unsupported by valid observations. Almost none of the comments are from positions that are modern and balanced; nearly all are from arts or science viewpoints, but not both.

Now that the division between mind and matter has been buried, or at least is on its way to the cemetery, how do we think about causality? Well, here is our second example, which splits into three related issues: day and night, the rainbow, and turning a light switch on.

What causes day and night? The answer is easy and obvious.fn2 It is a question of gravitational forces, working according to the law of gravity, and the Earth turning on its axis so that it presents different faces towards the Sun. The Earth turning, about once per twenty-four hours, is what causes day and night. Easy.

Now let’s think about a rainbow. Here things are a little more complicated. Jack sent each of his six children in to school to ask the teacher what made a rainbow. In each case the teacher gave what we’ve elsewhere called the lie-to-children response:fn3 ‘A raindrop is like a little prism, and you’ve seen how a prism breaks light up into colours.’ ‘No,’ said Jack’s children, ‘it’s the sharp bits on the prism that break up the light, and there aren’t any sharp bits on raindrops. Anyway, we understand about raindrops refracting light, we want to know why there’s that wonderful great bow in the sky.’ And all the teachers said ‘I don’t know’, variously, and two said, ‘When you find out, please tell me,’ and got great plus points for that.

The children were wrong about the sharp corner of the prism: it still refracts if you round the corner off. But they were right to focus on the shape of the rainbow, rather than its colours. Until you explain the shape, it’s not clear why the colours, emitted by millions of different drops of rain, don’t smear out.

What actually happens is quite complicated, though known to Descartes. Sunlight striking each drop gets refracted (and broken up into different colours) and then it bounces (total internal reflection) and passes out back towards the Sun, the different colours being further separated. Some fancy geometry shows that there is a focusing effect, because rays that enter the drop behave differently according to where they hit. Most of the light of a given colour comes out in a concentrated ‘beam’ at an angle of about 67˚ from the direction it went in. This angle depends on the wavelength, that is, the colour, of the light. So, if you’re standing with the Sun behind you, you see the backward-pointing coloured spray of rays from those raindrops that form a 67˚ circle in the sky. Someone standing a metre to your right doesn’t see your raindrops, but those corresponding to a different circle a metre to the right of yours.

Many years ago when the world was young, Jack was training to be a rabbi, and he grew up with a reasonably-firm conviction about God, Abraham and the covenant between them (Genesis 9 verse 13). He was delighted by rainbows, and still is. What a nice idea … but quite a complicated way to achieve it. And didn’t light get refracted in exactly that way before the covenant? Now he sees rainbows as grace notes in the physical world, apparently unlikely processes that are delightful, or the evolution of frogs, whose developmental programme has to work in wildly varying temperatures, requiring a longer genome than our own. He doesn’t implicate a god in these things, but he is grateful nevertheless. He does genuinely wonder whether humans are the only creatures that enjoy rainbows, or indeed enjoy at all. Still, rainbows were ‘there’ long before humans came on the scene. Perhaps the crab civilisation (The Science of Discworld chapter 31, ‘Great Leap Sideways’) enjoyed them.

So much for the causality of rainbows: complicated physics, but a delightful outcome.

Now we come to a really difficult bit of causality; turning a light on. You think this is simple too? Not a bit of it. You go into a room from a lighted hallway, and the switch is there. All kinds of clever neuronal things happen, sensory things and motor things, and the result is that the muscles in your arm lift it so that your finger can work the switch. You press (or turn or whatever) the switch, and the connection is made. Now alternating current can participate in a circuit that includes a lamp bulb, possibly with a filament which instantly heats up to about 3000˚ Celsius, emitting lots of heat and quite a lot of light. It might instead be a fluorescent tube, or an LED that produces light more efficiently, that is, with less heat.

We need to think about you causing your finger to press the switch – but we also need to understand how the electrical system is just sitting there waiting for you to work it.

Jack has a friend who’s an electrician, a pleasant, helpful guy that you can phone up and he’ll sort your electrical problem out. The electrician has many friends and acquaintances who are academics, and he has, at least three times, been in the following situation. Someone has rung up to ask why a socket that they have bought and put into the wall isn’t working an appliance that they’ve plugged into it. When the electrician turns up … well, he discovers that they genuinely didn’t know that there have to be wires in the wall connecting the socket to the electricity supply. They thought the socket alone would be enough.

Part of the problem is the old arts/science division, but one of the people concerned was a biologist. What is it about electricity that’s so mysterious? We don’t think the problem is electricity, or even understanding how it works. It’s about cryptic investment. There was a time, quite long ago, when there were gas pipes to many public buildings, to power the lamps so that people could work when it was dark outside, but no electric supply, yet. Jack’s mother took over the fifth floor of an old factory in Middlesex Street in the East End of London. There were rotating belts going up through the floors, turning long rods to which her sewing machines were attached, worked by great electric motors in the basement. Jack was amazed, when he went down to see these in the 1960s, that there were also remains of an old hydraulic system: water was piped to the building from a central pumping station, and returned when it had done its work, probably between the 1880s and 1910.

Such investments have been fossilised now, replaced by electric cables; but there had been a succession of power supplies to that building, invisible from outside, just made explicit by a series of bills from The London Hydraulic Power Company. The London Hydraulic Power Company had 181 miles of cast-iron pipes under London providing power to factories. Who’d have thought that we would have forgotten that? The electric cables to houses are ever so discreet now, but they used to be a pair of wires from a local transformer, draped over the gardens. They still are in many rural districts, but a lot of cables to houses are now underground in British cities and suburbs. (Less so in America and Japan.)

So it’s no longer obvious, to anyone who bothers to look, just how much investment there has been in energy distribution. Since the wires are invisible, people aren’t always aware that they are present, let alone necessary. But that hidden wiring is the reason why we have only to lift an arm to turn the light on.

Our third example, as promised, is biological, and involves the meddling of humans: orchids.

Pick up a flower and look at it. Admire its petals. There were no petals 120 million years ago, just leaves. Some of the leaves may have been coloured, to attract insects, but they weren’t petals. Leaves held their own wonders, however: they were flat areas on plants, making photosynthesis more effective. They helped to collect sunlight and to shade other competing plants. Before big leaves evolved, many plants had tiny leaves like scales on their stems; before that, plants were mostly in the seas, with flat ‘stems’ to collect more sunlight.

Petals are a trick that advanced land plants – angiosperms – use to attract insects (sometimes hummingbirds or even bats) so that they can reproduce sexually when pollen is carried from plant to plant. Originally, petals were leaves, with no reproductive role, sexual or not. But leaves have evolved into colourful arrays – which appeal to the human urge to tinker.

Look at a standard domestic rose; not the ones in hedgerows, which are often ‘normal’. The sepals, anthers, perhaps even stigmas, have all been turned into petals. The flower of a cultivated rose is a monstrous concoction that has undone millions of years of evolution by selecting genetic differences over the generations. In any plant nursery there are hundreds of cultivated varieties, of many plant species, all with monstrously enlarged petals and double flowers, in which anthers and sepals have been converted into petals. These varieties are unable to reproduce sexually and have to be multiplied by methods such as taking cuttings. We humans have exaggerated their sexual parts to such an extent that for them, sex is now impossible.

There is another side to this process. Without human intervention, orchids have evolved wondrous flowers, complex and colourful. But orchids tend to be rare, growing in remote forests in the angles between the stems of vast trees, or in tiny patches at the edges of dangerous marshes. Humans, admiring the flowers without wanting to modify them, have used a different technique to make them available, to transcend nature. They have developed a variety of sophisticated methods to multiply plants without sex, including tissue culture, by which almost any part of a plant can be made to grow into a whole little plant.

The result is a deluge of orchids. They have been multiplied to the point at which it is possible to buy living orchid plants for a few pounds at any nursery. Left to their own, in their rare habitats, these plants would not have had any significant impact on humanity. Only a few botanists would ever have heard of them. But today we see them everywhere, in huge quantities; in bridesmaids’ corsages, on restaurant tables and on windowsills. Human cultural capital, this time in the form of know-how, has caused these orchids to exist.

The same goes for trains, cars and aeroplanes. And electrical distribution systems. And washing-up detergents. And the most grotesque weaponry. We all live among the products of this cultural capital, even those of us who live ‘in the wild’, on mountains or in jungles (except for a few indigenous peoples who have hardly any contact with the outside world). Part of being a twenty-first century human is that nearly all of our surroundings have been ‘caused’ by previous investment, by cultural capital, be it artefacts or knowledge. We have taken over the natural world, and are remaking it in our own image. Nearly all of the causality that surrounds us depends on cultural capital.

In this way, we have remade our world in the image of narrativium. There is lots of hidden wiring behind the scenes, but it is deliberately hidden, so that we don’t need to understand it to work our world. If you needed a PhD to log onto Facebook, the internet would have remained what it originally was when Tim Berners-Lee invented the world wide web: a research tool for particle physicists.

Things happen ‘by magic’ because we have made them work like magic. If we want something to happen, it does.

Like turning the light on, or buying an orchid for a few pounds.

fn1 See The Science of Discworld II: The Globe.

fn2 Though not obvious to 20% of Americans, who believe that the Sun goes round the Earth, and a further 9% who don’t know: see Morris Berman, Dark Ages America.

fn3 This phrase is not intended to be derogatory, but it recognises an educational dilemma. In The Collapse of Chaos, ‘liar-to-children’ is a highly respected profession on the planet Zarathustra. The name reflects the occasional need for teachers to simplify explanations, to pave the way for more sophisticated ones later. The Zarathustrans observed that while all such explanations are true for a given value of ‘truth’, that value is sometimes small.