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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 z_n+1 = z_n² + 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.

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.

I don’t know if they call it an altar but, at one end of the room, there is a tall symmetrical gilded structure, very intricate and ornate in design.  On the floor in front of it, is a forest of objects, including statues and another ornate artefacts.   I guess they are presents from worshippers.

But here is what holds me.  In the middle of that gilded screen is a window, and inside that window, set back a little way, is a golden Buddha, illuminated by a light from behind the screen.  Its face is serene.  From certain angles it seems almost cruel.   It is at the very centre of the gilded intricate structure and at the same time behind and completely apart from it.  It looks out at the world, and is at the centre of a teeming and restless structure that resembles golden flames, yet it is itself untouched.

How unlike a Christian or Muslim god.  It is not a father demanding respect and obedience.  It is not a king or a judge who will dispense eternal reward or punishment.  It is not a shepherd looking out at its flock.   It does not dictate holy books.  Nor has it died for us and come alive again, or loved the world so much that it has gave us its only son.

Why doesn’t it care for us?  Why doesn’t it offer us help, out here on the far side of the screen, out in the world of grief and pain and dreariness and hate and wickedness?  Do our sufferings mean nothing to it at all?

But those are the wrong questions.  They are questions for a father or a son or a king, a creator apart from us and above us.  And this is not separate from us.  It is the thing that looks out from our own eyes.

I took part in a panel discussion on this recently at the British Science Festival at Bradford (along with Steven French, Una McCormack,  Shana Worthen and Katy Price).   Coincidentally  (and very usefully), my friend Prof Rowlie Wymer had delivered an inaugural lecture on this very same theme the previous day at Anglia Ruskin University in Cambridge. He plans to write a book on the subject.

On the face of it, it’s odd how often science fiction (which after all has ‘science’ rather than religion in its title) deals with religion.  But it’s a perennial theme (my own The Holy Machine being one example). Rowlie Wymer pointed out that even avowedly atheistic writers such as Stanislaw Lem or Arthur C. Clark can’t leave religious themes alone.

There are several connections.  Firstly, SF is a form of fiction that is interested in Big Questions.  It deals with people’s relationship with the universe, and not just people’s relationship with other people.   This is something it has in common with religion.   Secondly, SF is interested in how people and societies cope with new and unfamiliar environments.  It would be impossible to seriously deal with this question without considering religion, which up to and including this point in history, has provided one of the means by which people explain to themselves how they fit in.   (In Dark Eden, I show a society that is beginning to evolve its own religion).  Thirdly, SF traditionally deals in ‘sense of wonder’ which (as Rowlie Wymer pointed out) is not unlike some forms of religious experience.

We live in a world in which religious fundementalism frequently makes itself the enemy of science.  In that battle I’m definitely on the side of science.  A set of beliefs about the world that are based on accepting as literally true an old book written one or two millenia ago versus a set of beliefs based on systematically examining the evidence.  There’s no contest.  To dismiss the latter in favour of the former is just infantile intellectual vandalism.

But I don’t align myself with atheistic fundementalism either.  To reject religion in all its forms as worst than useless is, in its way, also intellectual vandalism.   It is to ignore the fact that science looks at the world from a particular perspective which is not the perspective from which we actually live our lives, and is least good at answering the messy complicated questions which most concern us as human beings (for most of us are not going around worrying about what happened in the Big Bang or the precise nature of the fundemental building blocks of matter).   There are a whole set of questions about life which cannot be answered in terms of cause and effect, cannot be answered at all, in fact, in the way that science answers questions, but which can be assuaged by stories.

Stories are pretty basic.  Every night in our sleep, our brains weave our experience into stories.  Stories are what we naturally do, not causal explanations, and religions have provided or inspired a pretty good batch of stories.

I am not defending literal-minded religion, or even religion at all, but I am saying that ultimately facts are not what our lives are about.   In order to engage with the world, and other people, we need imagination.

 

 

Most people who read or write science fiction identify a “sense of wonder” as part of the original appeal of the genre.   This was certainly true for me.  Reading SF as a teenager with an as yet unjaded palette, I enjoyed the almost spinetingling sense of strangeness that it evoked.

I think one of the things science fiction can usefully do, is remind us that, outside the tiny tiny realm which has come to seem ordinary to us  as a result of habit and familiarity, this is a very strange universe.   (Science fiction has a particular way of doing this, but you could argue that all artistic-type activity ought to be aimed at tearing away the veneer of ordinariness.)

Science fiction can however contribute itself to a kind of dulling and deadening:  a kind of inflationary process exists which is in danger of debasing the currency of wonder.   The first time you see or read about a gigantic space ship, for instance, it inspires wonder.  When you have seen the same thing repeated over and over again, it grows tedious – and just making the spaceship even bigger does not help.  As Ian Sales says:  ‘Scale is not sense of wonder, and a lot of sf confuses the two.’    I wonder if it is possible that a failure to understand this fact has led to the decline in prestige and popularity of SF?

This is a related, but not identical point, to that made by the proponents of Mundane SF who propose that science fiction ought to be more scientific, more committed to the world that actually exists, and confine itself  to futures and technologies that might actually occur.   Faster-than-light-travel and galactic empires, are really just escapist fantasies, on this argument.  They will almost certainly never happen, and to write about them as if they were possible futures is perhaps to downplay the uniqueness and importance of our home on Earth, possibly dangerously so.

I go along with the spirit of this argument, but not entirely with the letter of it.   I agree that it is important that SF should connect with the world we actually inhabit and I am not interested in SF that doesn’t (not just for reasons of principle but also because I find it very tedious).   But sticking literally to what is actually possible is not the only way of reflecting and exploring the world we  live in, and not only SF but all branches of literature work by taking some liberties with the literal truth.