Neither imaginary nor real

I suppose most people can remember plotting equations onto graph paper at school.  y = x produces a straight line.  y = 2x generates a steeper line.

And then you try y = x2 and find that it generates a beautiful smooth ever-steepening curve, a parabola, while  y = 1/x generates a hyperbola, a pair of curves that get closer and closer to the axes of the graph, but never quite reach them.

The following is a bit more complicated than y = x2 or y = 1/x, but it can still be explained in a few lines, and can still be understood by someone like me, whose maths ability hit a glass ceiling at about the sixth form level.

First, you let the y axis represent ‘imaginary numbers’ (that is: multiples of ‘i’, which is the notional square root of minus one), and you let the x axis represent real numbers (i.e. the ordinary kind: 1, 2, 1.5, -1, 101, 0.3: that kind of thing).  Your graph is now what is known as a ‘complex plane’, because any so-called ‘complex number’ (that is: a combination of a real and an imaginary number) can be represented on it by a point.

Set the complex plane on one side, like pastry, for use later.

Now, consider the following formula zn+1 = zn2 + c.   It took me a while to get the hang of this, but it is a formula for generating a sequence of numbers.  The members of the sequence are labelled z1, z2, z3, z4 ….. etc, and all the formula tells you is that you generate each member of the sequence (starting with z0 = 0) by multiplying the previous member of the sequence by itself (i.e. squaring it), and adding a number of your choice designated c, which remains constant for the whole sequence.

So, if we take c as 1, the sequence we get is:

z0 = 0

z1 = 02 + 1 = 1

z2= 12 + 1 = 2

z3 = 22 + 1 = 5

….and so on

What you find is that starting with some values of c, such as 1, the sequence generates higher and higher numbers, as just shown, but for other numbers, the sequence is ‘bounded’, which is to say it oscillates between fixed points.   For instance, if you set c as ‘i’ the sequence runs: 0, i, (-1 + i), −i, (−1 + i), −i… and then the same, on and on.  Or, if you set it as -1, the sequence just bounces back and forth between 0 and -1.

So now, returning to the complex plane you set aside earlier, you mark all the points on the plane that lead to a bounded sequence in black, and you leave the other points unmarked.   And what do you get?   Well, even at first sight it’s a lot more complicated than a parabola, but that’s only the beginning of it.

It is, of course, the Mandelbrot set, and, famously, its complication is without limits.  Look at it at higher and higher magnifications, and you never reach the end of its curls and wiggles.  Home in on what looks like a smooth line, and you see tiny shapes on the surface.  Zoom in still closer, and these shapes start to resemble shapes that you had already seen at lower levels of magnification.  Zoom in still more, and on the edges of these shapes too, new curls and wiggles start to appear.  (There’s a video of it here).  It is completely bottomless.

And now remember that this infinite complexity, this mad meaningless order, is generated by a comparatively simple rule which can be described in a few lines, as I have just done. This thing is not real.  It has no objective existence in the world.

And yet it is not human-made either.  These shapes are not the product of a human mind.  They have been discovered, not created.  This thing is neither real nor imaginary.

Think about it hard enough, and I reach a boundary beyond which my mind will no longer go, but across which I sense a strange awful place where mind and matter, real and imaginary, order and chaos, are not separate things at all.

Some people find the Mandelbrot set beautiful, and I suppose it is, but for me it is the beauty of a poisonous flower.

Easter Island

I was interested by a recent debate on Radio 4 between Friends of the Earth’s Tony Juniper, and the former Tory Chancellor of the Exchequer, Nigel Lawson.   They were talking about shale gas, and Lawson’s position was simple: this stuff is cheaper than renewable energy, and therefore that’s what we should go for.   Tough, hardnosed, realistic.  Like the guy on Easter Island, who argued that wood was cheaper than other fuels, so it was just silly not to chop down the last tree.

‘But how are we going to make boats?’ someone wondered, as they were all toasting themselves round the fire.

“But I don’t like science fiction.”

“I don’t like science fiction. I like my novels to be about ‘real’ people doing real things in the real world,” was the initial reaction of Emma Higginbotham in an article about Dark Eden in the Cambridge Evening News. She goes on to say,  “I decide to read the first couple of pages and skim through the rest. But to my amazement, I’m completely hooked by page two, and devour the whole thing in a few greedy sittings.”

Phew!  (And thanks, Emma!)  But it is frustrating how many people’s initial reaction is the same as hers – “I don’t like science fiction” – because, unlike her, most people don’t have a reason to test that initial reaction and so prove themselves wrong: they don’t like science fiction and that’s that.

Why is this?  The same people would, I imagine, quite happily read a book set in the past, or in a faraway country, or an imaginary country.  They’d even happily read a book set in the future (1984), or one with science fictional elements such as time travel (The Time Traveller’s Wife), cloning (Never Let Me Go), or the extinction of human kind (Children of Men), provided it was by an author known as ‘mainstream’.  So why this squeamishness about things that say ‘science fiction’ on the tin?

It wasn’t always so.  In the 60s and 70s, bookreading households would have thought nothing of having Day of the Triffids on their shelves, or maybe a few Ballards.   My father, I guess, classes as an SF fan, since he had a whole row of SF books (Pohl & Kornbluth, Heinlein, van Vogt, Ballard…), but it was my mother who recommended books to me by John Wyndham and Brian Aldiss: it just wouldn’t have struck her that they were SF and therefore beyond the pale.  Of course even then there were harder core SF books that my parents would have regarded as outside their range, but my point is there was a permeable membrane between SF and the rest of literature, not (to mix metaphors completely) a Berlin Wall.   Somewhere between now and then, SF has come to be regarded by many as the exclusive province of Comic Book Guy.

Yes, some science fiction is poorly written, some is ‘toys for the boys’, some caters for immature, and sometimes not very attractive, impulses.   But isn’t that true of romantic fiction also?   Isn’t it true of any kind of fiction at all?  I’m not saying that I think everyone should like all science fiction, only that they should be prepared to admit the possibility that they might like some of it.

All fiction works by making stuff up, partly for fun and partly to provide a new imaginative perspective on the real world.   It seems a pity to me – and not just because it means less people will buy my stuff – that a particular kind of ‘making stuff up’, should be so readily dismissed by readers and writers.  That seems to me to be throwing away a very rich resource indeed.

Non-science fiction readers who read my books, often seem to like them to their own surprise (like Emma Higginbotham, or like the judges of the Edge Hill Prize).  I would really like to persuade more to give it a go.

Launching Dark Eden

This (approximately) is what I said about Dark Eden at the launch party last night at Heffer’s bookshop in Cambridge:

Thanks to everyone for showing up, and to Heffers and Corvus for organising this event.   And thanks to everyone who contributed to the book itself.  Special thanks to Mathilda Imlah my editor at Corvus for her input, which made this a much better book than it otherwise would have been.

Eden is a planet without a star, that’s why it’s dark.   (I believe such planets are thought to be possible by those who know about these things, and may even be more common than the kind of planet that circles round a star.)

Eden isn’t completely dark though. There is life there, powered by the planet’s own heat.   (I believe this is thought to be possible also).  The life gives out light, and everywhere, at higher altitudes, is warm enough for human life.

There is no day or night, there are no seasons. The only rhythms by which time can be measured are biological ones.

Five people stumbled on the planet in a damaged spaceship. (Interstellar travel, is something I’m not sure really is possible, but without it there wouldn’t be much of a story) . These five people spent some time on Eden, and then three of them decided to try and get go back to Earth in their broken ship. The other two decided to remain, a man and a woman – Tommy and Angela, or Gela as she’s known. They didn’t know each other before then, and Gela wasn’t sure she even liked Tommy that much, but they decided to stay and wait for help to come.

160 years later their descendants – the descendants of one not very successful marriage – are still waiting, in a single, inbred community that calls itself Family, stuck in one valley that is lit and heated by trees that pump sap down into hot rocks underground, and pump it up again.

 hmmmph hmmmph hmmmph, they go

And of course, in a forest of hundreds of thousands of these geothermal trees, those pulsing sounds all merge together, and becomes a constant hmmmmmmmmmm that is the background to everyone’s lives.

These people have never left the valley. It is surrounded by icy mountains, which, without trees, are also completely pitch dark.

The people live by hunting and gathering, using implements made of stone, wood and animal sinews. They still live in hope that one day they will be able to return to a planet full of light that none of them has ever seen. They long for that light and for the legendary wonders there, like boats that fly, and horses you can ride on, and lecky-trickity that runs along strings.

And for this reason they believe they must never leave the spot where people first landed.

The central character is a boy called John Redlantern, who decides all this is crazy, and is determined to get people moving, out of the valley and across the mountains. To achieve this he commits a terrible transgression, and from this first transgression, more follow, bringing violence and hatred into the world.

The story is told partly by John – and it is John who is telling it in the passage I’m going to read you – partly by his girlfriend Tina Spiketree (sort of his girlfriend. Monogamy is not part of the culture of Eden), partly by his loyal cousin Gerry, his clever, lame cousin Jeff and his kind aunt Sue.

Apart from being about these events on the planet Eden, I see the story as being about families and societies and about the past, and our relationship with the past, and with things that we’ve lost and have to leave behind.

In the short passage I’m about to read you, it is the middle of the gathering that Family calls Any Virsry. It’s an occasion when they sort out problems, make rules, and listen to lectures about how great it was on Earth, but it’s also an occasion when they re-enact their own story.

So. Imagine a forest clearing, under a starry sky. The trees have no leaves at all, and they are warm, or even scalding hot to the touch. They have luminous flowers, and small creatures vaguely reminiscent of earthly bats, swoop and dive among those shining flowers, hunting creatures vaguely reminiscent of earthly insects. (Though on Eden bats have arms as well as legs, and small almost human hands)

500 people are packed in round the edge of the clearing: old, young, adults, children, dressed in animal skins, many with badly deformed faces or twisted feet. They are all looking into the middle of the clearing, where there is a circle of stones – their most important relic of all – to mark the place where the landing vehicle came down from that spaceship 160 years ago. John Redlantern is among this crowd of people.

In the centre of the clearing five people have been acting out the story of how those first five people came to Eden. Two of them are playing Tommy and Angela, the ancestors of everyone present (People even swear by them now: ‘Tom’s dick,’ they say, ‘Gela’s tits’ or ‘Gela’s heart’). One of them is playing a man called Michael who is one of the three who decided to try and get back to Earth. The Three Companions as they’re called.

People swear by Michael sometimes too but when they swear by him, for reasons that you’ll soon see, they always say ‘Michael’s names.’

 **

This part of the story is called Michael and His Names, and it’s the bit that kids love the best.

‘Where is this place anyway?’ Angela asks. ‘What do you think it’s called?’

‘I don’t know,’ says Michael. ‘Let me think. Perhaps we could call it…’

He pauses.

‘It’s Eden!’ yell out all the kids round Circle, because of course any fool knows that!

Michael frowns, like he thinks he’s heard something but he’s not sure. He holds his hand to his ear.

‘Perhaps,’ he says, ‘we could call it…’

‘Eden!’ the kids yell again even louder.

‘I don’t know,’ he says, ‘it’s on tip of my tongue, but I can’t quite think of the name.’

‘Ed-en!’ the kids bellow.

Michael smiles.

‘E-den,’ he says slowly, ‘I think we could call it Eden.’

The kids all cheer.

‘Look at this,’ says Angela, ‘what’s this?’

She’s pointing to a whitelantern tree.

‘It’s a tree!’ the kids yell out, laughing. How could anyone be so dumb as to not know what a tree was?

I guess it made everyone feel good to see Angela and all of them not knowing these things we knew so well, after we’d had to listen for so long to that big big list of wonderful things they had on Earth which we didn’t understand at all. It was kind of reassuring to know that they didn’t even know what a tree was, when we were feeling useless useless for not knowing about metal and telly vision and horses and the Single Force.

‘We’ll call it…’

Michael hesitated. The kids laughed. They loved all this. I suppose I did too. I loved it but I at the same time hated it for trapping us and making us feel so helpless and babyish and small.

‘We’ll call it…’

‘A tree!’ yell out the kids.

The grownups are smiling and laughing too, and a lot of them are joining in with the kids. Everyone was tired tired, what with the wakings being changed, and the long weary list of Earth Things, and the Laws and the Genda and all, but now everyone was brightening up again.

‘We’ll call it…. a… tree!’ goes Michael, who is really a skinny little guy of forty wombs or so called Luke Brooklyn who’s mainly known in Family for being clever with blackglass.

Everyone cheers.

‘And what’s this?’ asks Tommy, looking over from Big Sky-boat which he’s trying to fix and pointing at a little jewel-bat swooping overhead.

‘What’s what?’ goes Michael, looking where Tommy pointed. The bat has gone.

‘This!’ says Tommy, pointing to another bat.

‘What’s what?’ goes Michael again.

‘This here!’ says Tommy, showing him another bat again

‘Oh that,’ says Michael. ‘Well I don’t know about that. I’ve no idea. I’ve never seen anything like it. I don’t know what to say.’

‘It’s a bat!’ yell the kids.

Michael frowns and screws up his face. He can almost hear them but not quite.

‘It’s a bat!’ they yell again.

He holds his hand to his ear.

‘It’s a bat!’ the kids bellow again.

He frowns like he still can’t hear, and he scratches his head.

Michael was called the Name-Giver because he gave us the words that we still use for all the animals and plants that live in Eden, and found out things about them like how they came up from Underworld when everything was ice, and how dry starflowers could feed our skin like Sun did on Earth. But in the Show he was also the name-hearer, because he didn’t actually choose the names. He only heard us, faintly faintly, shouting them back to him from the future. And then he took them, and gave them to the things in the world, and sent them out again to us the slow way, through the five six long generations between us and him.

‘It – is – a – BAT!’ the kids yell even louder.

He nods. He smiles.

‘I think we’ll call it a bat!’ he says, and everybody cheers.  [From Dark Eden: pages 128-131]

 * *

I hope you read the book, and I hope you enjoy it.

If you do enjoy it, please do recommend it to other people.

If you don’t, though, I advise you to keep it to yourself.  I’d hate you to show yourself up.

Dark Eden

 

Mad money

It seems so bizarre that the chairman of a largely state-owned bank, RBS, should be thinking he ought to get a £1,000,000 bonus on top of his salary that you have to pinch yourself. Even more bizarre that the government, even for a moment, should hesitate to block this. Imagine if the NHS were to announce at this point that its boss needed a £1m bonus!

But that’s how it is, and here is a petition about it.

A pebble on Mount Everest

It occurred to me while I was driving home that, if it wasn’t for Adolf Hitler, I wouldn’t exist.

I’m not sure if my parents would have met at all if it wasn’t for my father’s family moving out of London as a result of Hitler’s war, but, even if they had, it’s inconceivable that their lives would have gone down such a similar track – and I’m trying not to be too graphic here: it’s my parents I’m talking about – that the, er, same combination of genetic material would have occurred that ended up resulting in me.  That would be like throwing billions of dice on two different occasions and coming up with exactly the same combination of numbers.

It’s not just me of course.  No one else below the age of about 70 would exist either.  There surely can’t be any doubt that the disruption of lives in all the countries involved in that war was sufficient to ensure that every single one of their citizens would have had their daily timetables put out at least to the extent that, assuming they survived the war at all, they had a different set of children, if not entirely different partners.  Even in countries not directly touched by the war, people would soon feel enough of the effects of what was happening in the world outside for the pattern of their days to be altered to at least that extent.

And then – I was driving along the A14 in the dark, the lights of other cars all around me – it occurred to me that any individual in the past would have the same affect: it didn’t even have to be a history-changer like Hitler.  Go back to the 18th century, and disrupt the daily routine of one randomly chosen person anywhere in the world, and by now we’d be a completely different set of human beings on Earth.

In fact, I decided – I was now not far from the Newmarket turnoff – never mind people, a stone would do the job.  Travel back in time with a small pebble and place it on the top of mount Everest.  No one would notice any change, but the airflow over the mountain would not be quite the same.  Every moment millions of molecules would end up in different places from where they otherwise would have been, and they in turn would displace other molecules.   Quite quickly, the entire atmosphere would be differently configured from what it would otherwise have been: trivially different, but still different.

And then weather events would occur very slightly earlier or later than they otherwise would have done.  Departures would be delayed by seconds, journey times increased or decreased, so that people went to bed a few seconds earlier or a few seconds later.  And accidents would occur that wouldn’t otherwise have happened, or fail to occur when otherwise they would, and so on and so on.   And each of these events would in turn change the flow of things just like that pebble still sitting on top of the mountain, albeit now covered with snow.   And by the time a century had gone by, that one pebble would have caused an entirely different cast of human beings to be living on Earth from the ones who would have otherwise come into being and lived out their important irreplacable lives.

Not a very original thought, I know – it’s butterflies’ wings and all of that, something which has been written about many times, including by me – but it absorbed me sufficiently that I forgot where I was on the road, and turned off at the Newmarket exit rather than continuing straight on to Cambridge, delaying my arrival home, and thereby changing the course of history and the entire population of the Earth.

The Christmas Story

As a child I was sometimes taken to church at Christmas.  I saw countless nativity scenes, both 2D and 3D.  (Often, like the German advent calendar above, they linked the old christmas story to the wintry weather of Northern Europe, where the Christian holiday has subsumed an older solstice festival.)  I sung many carols (‘In the deep mid-winter, long ago, earth stood hard as iron, water like a stone….’).  I heard readings from the gospels.  I saw nativity plays, and even participated in at least one (I was a shepherd).   I was exposed to all this, but I don’t remember at any point, even for a moment, believing the story- the virgin birth, the angels, the shepherds, the wise men – was actually true.  In fact it seemed to me obvious that nobody really did, just as it was obvious to me that no one really believed in Santa.

But I liked the story.  I liked the way it came round every year, like midwinter itself, and I liked the way that we all came back to it together.   For me, it became a story about human birth: the mystery of a living being emerging into the inanimate mineral world (‘hard as iron’, ‘like a stone’), a tiny thing, dwarfed by the great inanimate universe, but yet in a way, bigger than all of it put together.  The story wasn’t true, but it brought me into the presence of a truth, allowed me to experience it not simply as a fact, but in my imagination.   It allowed me to participate in it.

The value of these stories is not just a question of their literal truth or falsehood.  This is what Dawkins and Co don’t get, useful as it is to have them yapping round in the yard to see off the fundamentalist crazies.  The fundamentalist crazies don’t get it either.

One of the most interesting writers on the complexities of the distinction between truth and falsehood is Philip Dick: it is his constant theme.  His Do Androids Dream of Electric Sheep, famously, is about real humans hunting down fake ones (the crucial difference being the capacity for empathy).   Many of the real humans in the book subscribe to an austere religion called Mercerism, and regularly commune by electronic means with the figure of Mercer himself, forever toiling up a barren hill, while rocks and stones are thrown at him.   Late in the book, this central scene of Mercerism is shown to have been faked up in a studio: Mercer, it seems, was just an actor, the hill a painted set.

But here’s the interesting part.   People carry on being Mercerists anyway.   The ones who exposed the hoax were androids, andys, fake humans.  Their mistaken assumption that, by exposing the hoax, they’d destroy the belief system, was perhaps itself evidence of their lack of human understanding, their fakeness.  Empathy and imagination, after all, are closely related things.

 

The City & The City, by China Miéville

I live in Cambridge where, every summer, hundreds of foreign teenagers descend on the city to attend the various language schools.   Often they move around in large crowds, instantly recognisable because of the standard issue language school backpacks and t-shirts.  Often they hire bikes (this city is, after all, the UK capital of bicycles), and can be seen wobbling along in groups, sometimes on the wrong side of the road, or even going round roundabouts the wrong way.

And the thing that strikes me about them is that they are not really here.   Physically they are in Cambridge, but they aren’t really present in it.   We notice their language school livery and their Latin looks and pay no further attention, dismissing them as transients who will soon be gone. They hardly see us at all.  I even tested this once.  A group of Italian boys were walking towards me, filling up the entire width of the pavement.  They needed to make room for me.  The only way I could have got out of their way was to press my back up against a wall.  But I kept walking, and sure enough one of them walked straight into me.  He looked startled, as if surprised to discover that I was actually solid.

You see the same thing with British tourists abroad.  Waiters fetch things for them, but they hardly even make out the waiters’ faces.  Physical location is only one aspect of where we are, and not really, most of the time, the most important one.  We are much more interested in other kinds of nearness.  Look at someone walking down the road, talking to a lover on a mobile phone.

In The City & The City, China Miéville draws attention to these other kinds of nearness and distance, by imagining a place where it is not just normal to ignore and discount much of what is physically present, but actually compulsory.  The two city-states of Beszel and Ul Qoma occupy the same piece of territory, and are so interwoven that, in some places, they share the same streets.   But their citizens learn from an early age to ignore the parallel city alongside their own, seeing only their own buildings, and their own people, and noticing, but then immediately ‘unseeing’, the buildings and people of the other place, whose otherness is signalled to them by small differences that they’ve learnt to instantly recognise (rather in the way that, so I’m told by people who come from there, Northern Irish folk establish almost at once whether someone is a Protestant or a Catholic) .  A person in Beszel, therefore, must not stare at, think about, speak to, or in any way acknowledge a person in Ul Qoma, even if in terms of purely physical space, they live next door to one another.  To violate this principle is to commit ‘breach’, and is a serious crime.

But this is not the same thing as saying that each city must deny the existence of the other, or that Ul Qomans and Besz must never meet.  On the contrary.  It is perfectly possible to travel from Beszel to Ul Qoma, with the necessary visas, by passing through a border post.  Having crossed over, and been issued with a visitor’s badge, a person from one city may return to the same physical spaces he normally inhabits, but as he is now legally ‘in’ the other city, he must now ‘unsee’ his own city, but may look at leisure at the sights that, when ‘back home’, he would have been forbidden to notice.  Miéville has fun with the ramifications of all this: there is even an ‘Ul Qomatown’ within Beszel, which Besz people might at first glance feel obliged to ‘unsee’, since it superficially resembles Ul Qoma.

This is one of those books (like, for instance, Christopher Priest’s Inverted World, which I discussed here previously, and like much of Kafka and Borges), which works by unfolding the implications of a single odd premise, while allowing its metaphorical possibilities, its resonances with the real world we actually inhabit, to gradually take root in our minds.   The story is a police procedural, about a Besz policeman investigating a murder which turns out to have Ul Qoman ramifications, and this provides a device by which we can gradually learn more and more about the relationship between these two states.   As the policeman attempts to solve the murder, the reader (or myself at least), is equally absorbed by the possibility of in some way getting to the bottom of the nature of this cleft city, and of the shadowy institutions, beyond the ordinary police of the two states, that maintain their separate existence, by punishing breach violations that might be as small as looking at a shop window in the ‘other’ city.

It gets a little busy and plot-driven towards the end – when it is being made to deliver the solution to the crime required by the police procedural genre, this strange imagined world does feel a little as if it is being crammed into a space that is just too small for it  –  but this is an original, clever and compelling book.  The single scene which most haunts me, is one in which the detective Borlú, during a working trip to the foreign country of Ul Qoma, walks down the Ul Qoman street that, in terms of physical space, is the street he lives in back in Beszel: he passes, but carefully unsees, his own front door.

The City & The City on Amazon UK.

Postscript

Incidentally (and this is the kind of thing that you learn when you have a Wikipedia dependency as bad as mine), there really does exist a pair of intermingled towns in two different countries.  The Belgian town of Baarle-Hertog consists of more than twenty enclaves in and around the Dutch town of Baarle-Nassau.  There are even Dutch enclaves within the Belgian ones.  See here for more.