The Science of Discworld Revised Edition

by Terry Pratchett

  It would take forever to build thousands of trial circuits by hand, so he employed a ‘field-programmable gate array’. This is a microchip that contains a number of very tiny transistorized ‘logic cells’ – mildly intelligent switches, so to speak – whose connections can be changed by loading new instructions into the chip’s configuration memory.

  Those instructions are analogous to an organism’s DNA code, and can be cross-bred. That’s what Thompson did. He started with an array of one hundred logic cells, and used a computer to randomly generate a population of fifty instruction codes. The computer loaded each set into the array, fed in the two tones, looked at the outputs, and tried to find some feature that might help in evolving a decent circuit. To begin with, that feature was anything that didn’t look totally random. The ‘fittest’ individual in the first generation produced a steady five-volt output no matter which tone it heard. The least fit instruction codes were then killed off (deleted), the fit ones were bred (copied and recombined), and the process was repeated.

  What’s most interesting about the experiment is not the details, but how the system homed in on a solution – and the remarkable nature of that solution. By the 220th generation, the fittest circuit produced outputs that were pretty much the same as the inputs, two waveforms of different frequencies. The same effect could have been obtained with no circuit at all, just a bare wire! The desired steady output signals were not yet in prospect.

  By the 650th generation, the output for the low tone was steady, but the high tone still produced a variable output signal. It took until generation 2800 for the circuit to give approximately steady, and different, signals for the two tones; only by generation 4100 did the odd glitch get ironed out, after which point little further evolution occurred.

  The strangest thing about the eventual solution was its structure. No human engineer would ever have invented it. Indeed no human engineer would have been able to find a solution with a mere 100 logic cells. The human engineer’s solution, though, would have been comprehensible – we would be able to tell a convincing ‘story’ about why it worked. For example, it would include a ‘clock’ – a circuit that ticks at a constant rate. That would give a baseline to compare the other frequencies against. But you can’t make a clock with 100 logic cells. The evolutionary solution didn’t bother with a clock. Instead, it routed the input signal through a complicated series of loops. These presumably generated time-delayed and otherwise processed versions of the signals, which eventually were combined to produce the steady outputs. Presumably. Thompson described how it functioned like this: ‘Really, I don’t have the faintest idea how it works.’

  Amazingly, further study of the final solution showed that only 32 of its 100 logic cells were actually needed. The rest could be removed from the circuit without affecting its behaviour. At first it looked as if five other logic cells could be removed – they were not connected electrically to the rest, nor to the input or output. However, if these were removed, the circuit ceased to work. Presumably these cells reacted to physical properties of the rest of the circuit other than electrical current – magnetic fields, say. Whatever the reason, Thompson’s hunch that a real silicon circuit would have more tricks up its sleeve than a computer simulation turned out to be absolutely right.

  The technological justification for Thompson’s work is the possibility of evolving highly efficient circuits. But the message for basic evolutionary theory is also important. In effect, it tells us that evolution has no need for narrativium. An evolved solution may ‘work’ without it being at all clear how it does whatever it does. It may not follow any ‘design principle’ that makes sense to human beings. Instead, it can follow the emergent logic of Ant Country, which can’t be captured in a simple story.

  Of course, evolution may sometimes hit on ‘designed’ solutions, as happens for the eye. Sometimes it hits on solutions that do have a narrative, but we fail to appreciate the story. Stick insects look like sticks, and their eggs look like seeds. There is a kind of Discworld logic to this, since seeds are the ‘eggs’ of sticks, and prior to the theory of evolution taking hold the Victorians approved of this ‘logic’ because it looked like God being consistent. The early evolutionists didn’t see it that way, and they worried about it; but they worried a lot more when they found that some stick insect eggs looked like little snails. It seemed silly for anything to resemble the favourite food of nearly everything else. In fact, it seemed to be a flat contradiction to the evolutionary story. The puzzle was solved only in 1994, after forest fires in Australia. When new plant shoots came up out of the ashes, they were covered in baby stick insects. Ants had carried the ‘seeds’, and the ‘baby snails’, down into their subterranean nests, thinking they were the real thing. Being safely underground, the stick insect eggs escaped the fires. In fact, baby stick insects look, and run, just like ants: this should have been a clue, but nobody made the connection.

  And sometimes evolution’s solution has no narrative structure. To test Darwin’s theories thoroughly, we should be looking for evolved systems that don’t conform to a simple narrative description, as well as for ones that do. Many of the brain’s sensory systems may well be like this. The first few layers of the visual cortex, for example, perform generalized functions like detecting edges, but we have no idea how lower layers work, and that may well be because they don’t conform to any design principles that we currently can recognize. Our sense of smell seems to be ‘organized’ along very strange lines, not at all as clearly structured as the visual cortex, and it too may be lacking any element of design.

  More importantly, genes may well be like this. Biologists habitually talk of ‘the function of a gene’ – what it does. The unspoken assumption is that it does only one thing, or a small list of things. This is pure magic: the gene as a spell. It is conceived as being a spell in the same sense that ‘Cold Start’ in a car is. But a lot of genes may not do anything that can be summed up in a simple story. The job they evolved to do is ‘build an organism’, and they evolved as a team, like Thompson’s circuits. When evolution turns up solutions of this kind, conventional reductionism is not much help in understanding those solutions. You can list neural connections till the cows come home, but you won’t understand how the cows’ visual systems distinguish a cowshed from a bull.

  1 The quantity of bacon per trotter is on average slightly more than quarter of the amount per head.

  TWENTY-SEVEN

  WE NEED MORE BLOBS

  RINCEWIND WAS FINDING, now that he was back at what appeared to be his real size, that he was coming to enjoy this world after all. It was so marvellously dull.

  Every so often he’d be moved forward a few tens of millions of years. The sea levels would change. There seemed to be more land around, speckled with volcanoes. Sand was turning up on the edge of the sea. Yet the sheer vast ringing silence dominated everything. Oh, there’d be storms, and at night there were brilliant meteor showers that practically hissed across the sky, but these only underlined the absent symphony of life.

  He was rather pleased with ‘symphony of life’.

  ‘Mr Stibbons?’ he said.

  ‘Yes?’ said Ponder’s voice in his helmet.

  ‘There seem to be a lot of comets about.’

  ‘Yes, they seem to go with roundworld systems. Is this a problem?’

  ‘Aren’t they going to crash into this world?’

  Rincewind heard the muted sounds of debate in the background, and then Ponder said: ‘The Archchancellor says snowballs don’t hurt.’

  ‘Oh. Good.’

  ‘We’re going to move you on a few million years now. Ready?’

  ‘Millions and millions of years of dullness,’ said the Senior Wrangler.

  ‘There are more blobs today,’ said Ponder.

  ‘Oh, good. We need more blobs.’

  There was a yell from Rincewind. The wizards rushed to the omniscope.

  ‘Good heavens,’ said the Dean. ‘Is that a higher li
feform?’

  ‘I think,’ said Ponder, ‘that seat cushions have inherited the world.’

  They lay in the warm shallow water. They were dark green. They were reassuringly dull.

  But the other things weren’t.

  Blobs drifted over the sea like giant eyeballs, black, purple, and green. The water itself was covered with them. A scum of them rolled in the surf. The aerial ones bobbed only a few inches above the waves, thick as fog, overshadowing one another in their fight for height.

  ‘Have you ever seen anything like that?’ said the Senior Wranger.

  ‘Not legally,’ said the Dean. A blob burst. Audio reception on the omniscope was not good, but the sound was, in short, phut. The stricken thing disappeared into the sea, and the floating blobs closed in over it.

  ‘Get Rincewind to try to communicate with them,’ said Ridcully.

  ‘What have blobs got to talk about, sir?’ said Ponder. ‘Besides, they’re not making any noise. I don’t think phut counts.’

  ‘They’re various colours,’ said the Lecturer in Recent Runes. ‘Perhaps they communicate by changing colour? Like those sea creatures –’ He snapped his fingers as an aid to memory.

  ‘Lobsters?’ the Dean supplied.

  ‘Really?’ said the Senior Wrangler. ‘I didn’t know they did that.’

  ‘Oh yes,’ said Ridcully. ‘Red means “help!”’1

  ‘No, I think the Lecturer in Recent Runes is referring to squid,’ said Ponder, who knew that this sort of thing could go on for a long time. He added hurriedly, ‘I’ll tell Rincewind to give it a try.’

  Rincewind, apparently knee deep in blobs, said: ‘What do you mean?’

  ‘Well … could you get embarrassed, perhaps?’

  ‘No, but I’m getting angry!’

  ‘That might work, if you get red enough. They’ll think you want help.’

  ‘Do you know there’s something else here besides blobs?’

  Some of the blobs trailed strands in the faint breeze blowing across the beach. When they tangled up on a blob gasbag, which put some stress on the line, the little blob on the end let go its grip on a rock, the line gradually shortened, and the gasbag bobbed onwards with its new passenger.

  Rincewind saw them on a number of blobs. The blobs did not look healthy.

  ‘Predators,’ Ponder told him.

  ‘I’m on a beach with predators?’

  ‘If it really worries you, try not to look blobby. We’ll keep an eye on them. Er … the Faculty is of the opinion that intelligence is most likely to arise in creatures that eat lots of things.’

  ‘Why?’

  ‘Probably because they eat lots of things. We’ll try a few big jumps in time, all right?’

  ‘I suppose so.’

  The world flickered …

  ‘Blobs.’

  … flickered …

  ‘The sea’s a lot further away. There’s a few floating blobs. More black blobs this time.’

  … flickered …

  ‘Well out at sea, great rafts of purple blobs, some blobs in the air …’

  … flickered …

  ‘Great steaming piles of onions!’

  ‘What?’ said Ponder.

  ‘I knew it! I just knew it! This whole damn place was just lulling me into a false sense of security!’

  ‘What’s happening?’

  ‘It’s a snowball. The whole world’s a giant snowball!’

  1 Wizards seldom bothered to look things up if they could reach an answer by bickering at cross-purposes.

  TWENTY-EIGHT

  THE ICEBERG COMETH

  THE EARTH HAS been a giant snowball on many occasions. It was a snowball 2.7 billion years ago, 2.2 billion years ago, and 2 billion years ago. It was a really cold snowball 700 million years ago, and this was followed by a series of global cold snaps that lasted until 600 million years ago. It reverted to snowball mode 300 million years ago, and has been that way on and off for most of the last 50 million years. Ice has played a significant part in the story of life. Just how significant a part, we are now beginning to appreciate.

  We first began to realize this when we found evidence of the most recent snowball. About one and a half million years ago, round about the time that humans began to become the dominant species on Earth, the planet got very cold. The old name for this period was the Ice Age. We don’t call it that any more because it wasn’t one Age: we talk of ‘glacial-interglacial cycles’. Is there a connection? Did the cold climate drive the naked ape to evolve enough intelligence to kill other animals and use their fur to keep warm? To discover and use fire?

  This used to be a popular theory. It’s possible. Probably not, though: there are too many holes in the logic. But a much earlier, and much more severe, Ice Age very nearly put a stop to the whole of that ‘life’ nonsense. And, ironically, its failure to do so may have unleashed the full diversity of life as we now know it.

  Thanks to the pioneering insights of Louis Agassiz, Victorian scientists knew that the Earth had once been a lot colder than it is now, because they could see the evidence all around them, in the form of the shapes of valleys. In many parts of the world today you can find glaciers – huge ‘rivers’ of ice, which flow, very slowly, under the pressure of new ice forming further uphill. Glaciers carry large quantities of rock, and they gouge and grind their way along, forming valleys whose cross-section is shaped like a smooth U. All over Europe, indeed over much of the world, there are identical valleys – but no sign of ice for hundreds or thousands of miles. The Victorian geologists pieced together a picture that was a bit worrying in some ways, but reassuring overall. About 1.6 million years back, at the start of the Pleistocene era, the Earth suddenly became colder. The ice caps at the poles advanced, thanks to a rapid build-up of snow, and gouged out those U-shaped valleys. Then the ice retreated again. Four times in all, it was thought, the ice had advanced and retreated, with much of Europe being buried under a layer of ice several miles thick.

  Still, there was no need to worry, the geologists said. We seemed to be safe and snug in the middle of a warm period, with no prospect of being buried under miles of ice for quite some time …

  The picture is no longer so comfortable. Indeed, some people think that the greatest threat to humanity is not global warming, but an incipient ice age. How ironic, and how undeserved, if our pollution of the planet cancels out a natural disaster!

  As usual, the main reason we now know a lot more is that new kinds of observation became possible, propped up by new theories to explain what it is that they measure and why we can be reasonably sure that they do. These new methods range from clever methods for dating old rocks to studies of the proportions of different isotopes in cores drilled from ancient ice, backed up by ocean-drilling to study the layers of sediment deposited on the sea floor. Warm seas sustain different living creatures, whose death deposits different sediment, so there is a link from sediments to climate.

  All of these methods reinforce each other, and lead to very much the same picture. Every so often the surface of the Earth begins to cool, becoming 10°–15°C colder near the poles and 5°C colder elsewhere. Then it suddenly warms up, possibly becoming 5°C warmer than the current norm. In between big fluctuations, there are smaller ones: ‘mini ice ages’. The typical gap between a decent-sized ice age and the next is around 75,000 years, often less – nothing like the comfortable 400,000 years of ‘interglacial’ expected by the Victorians. The most worrying finding of all is that periods of high temperatures – that is, like we get now – seldom lasted more than 20,000 years.

  The last major glaciation ended 18,000 years ago.

  Wrap up well, folks.

  What caused the ice ages? It turns out that the Earth isn’t quite as nice a planet as we like to think, and its orbit round the sun isn’t quite as stable and repetitive as we usually assume. The currently accepted theory was devised in 1920 by a Serbian called Milutin Milankovitch. In broad terms, the Earth goes round the sun in an elli
pse, almost a circle, but there are three features of the Earth’s motion that change. One is the amount through which the Earth’s axis tilts – about 23° at the moment, but varying slightly in a cycle that lasts roughly 41,000 years. Another is a change in the position of Earth’s closest approach to the sun, which varies in a 20,000-year cycle. The third is a variation in the eccentricity of the Earth’s orbit – how oval it is – whose period is around 100,000 years. Putting all three cycles together, it is possible to calculate the changes in heat received from the sun. These calculations agree with the known variations in the Earth’s temperature, and it seems particularly likely that the Earth’s warming up after ice ages is due to increased warmth from the sun, thanks to these three astronomical cycles.

  It may seem unsurprising that when the Earth receives more heat from the sun, it warms up, and when it doesn’t, it cools down, but not all of the heat that reaches the upper atmosphere gets down to the ground. It can be reflected by clouds, and even if it gets to ground level it can be reflected from the oceans and from snow and ice. It is thought that during ice ages, this reflection causes the Earth to lose more heat than it would otherwise do, so ice ages automatically make themselves worse. We get kicked out of them when the incoming heat from the sun is so great that the ice starts to melt despite the lost heat. Or maybe the ice gets dirty, or … It’s not so clear that we get kicked into an ice age when less of the sun’s warmth reaches the Earth – indeed the slide into an ice age is usually more gradual than the climb back out of it.

  All of which makes one wonder whether global warming caused by gases excreted from animals might be partly responsible. When gases such as carbon dioxide and methane build up in the atmosphere, they cause the famous ‘greenhouse effect’, trapping more sunlight than usual, hence more heat. Right now, most scientists have become convinced, the Earth’s supply of ‘greenhouse gases’ is growing faster than it would otherwise do thanks to human activities such as farming (burning rainforests to clear land), driving cars, burning coal and oil for electricity, and farming again (cows produce a lot of methane: grass goes in one end and methane emerges at the other). And how could we forget the carbon dioxide breathed out by people? One person is equivalent to half a car, maybe more.