‘I’ve got a question,’ said Henry, a number theorist, a dark, slight young man, always quietly spoken and amiable. ‘About this watersoul and firesoul stuff. That’s new to me and I don’t much like the sound of it.’ He looked around. The others visibly relaxed: that was their concern too. Roy felt somewhat relieved that Henry had got in first.

   ‘You seem to have had rather more contact with the slave people than the rest of us, especially during the period you’ve just been describing. At one point you mentioned incorporating the slaves’ so-called “craft skills” into the New Beginning. Personally I can hardly wait for china and glass: clean and elegant things, instead of all that grubby rustic stuff.’ His voice was jocular. The others laughed, muttered and murmured in agreement, and Roy felt himself isolated as a person with peculiar ideas.

   Henry went on, and his voice rose to a higher pitch. ‘In the last part of the story, I got the impression that you have accepted this notion that we – the firesoul boys, as you call us – have a mental handicap as compared with the watersoul, as you call the slaves.’ There was an audible in-breath from the audience, and a corporate rising up as all their spines stiffened. ‘Now, taking that just a little bit further, I can see you coming to the conclusion that the New Beginning shouldn’t happen at all, that it would be a threat to the lovely life of the watersouls, that we’d devastate the planet all over again. What do you say to that?’ His voice had become high and rapid as it built up to the challenge which Roy had been dreading. A loud rumble of agreement rolled round the ring around the campfire.

   For a moment Roy’s mind went blank, and a lump of fear rose in his throat. ‘I have had my doubts,’ he said huskily. Their gasp was almost tangible. But uttering the few words triggered some thoughts in his own defence. ‘But none of us can be sure what the completion will be,’ he said more boldly. ‘Each of us is a product of our upbringing. You cannot blame me if I was given the opportunity to learn to respect the village people, and you were taught all along to despise them. But you cannot deny they have special powers; how else would the knowledge we now have have reached us? Could any of you reach it by yourselves?’

   Peter, the theologian, immediately rose to his feet and spoke up with his answer to Roy’s challenge, ‘The knowledge they brought to us came from God. The Mother Sages were merely the channels He used. Through them He has told us many of the laws by which He created the universe.’ Peter’s voice soared as his words flowed, and his eyes bulged and shone. Short in stature, pale-skinned and plump, yellow curls clustered sparsely on his prematurely balding head, he reminded Roy of an angel on one of the tapestries in his big house on the hill. He raised his little arms. ‘This knowledge is the word of the Creator himself, the highest and purest knowledge, sent to us as a sign that we have been chosen to fulfil His holy purpose. That is why the New Beginning was ordained. What you call ‘the completion’, I call the Covenant.’

   Roy took a little comfort from the uneasy shifting, and what he sensed were suppressed sniggers, in response to Peter’s declaration. The group’s unity was weakened by this second strange person. ‘You say that because it’s what you were taught that by your Mother Sage,’ Roy said. ‘Others of us were taught differently. Various stories were told us to convince us of our worth compared with all the other people, who undoubtedly have powers we do not possess.’

   ‘No, you are wrong. I know this from God Himself, my Mother Sage said nothing to me about God. She was a heathen, like all the slaves.’

   ‘You know, what Peter says makes a lot of sense,’ said one of Roy’s group, named James. ‘How could these ignorant peasants bring us all this highly sophisticated knowledge, unless it was through God?’ Peter beamed at him approvingly.

   ‘But saying it came from God instead of through the power of eversight doesn’t explain anything; it just replaces one mystery with another,’ Roy protested.

   ‘Maybe, but the power of God is a mystery recognised during the time of civilisation, which we are here to re-establish,’ said James.

   ‘Exactly, it’s part of the ancient pattern; it fits in. What we’ve been taught, and the sort of people we’ve become, resonate with it. That must be why Peter had those thoughts about God.’ Roy turned to Peter. ‘They came to you because they were a sub-pattern of the ancient times which resonated with the firesoul pattern. Your unconscious eversight connected you to them and then they surfaced, perhaps in your dreams.’

   ‘What is this nonsense about pattern you keep on about?’ said a man named Charles, a theoretical physicist who had joined their group to hear Jasper’s lecture. ‘You’re using a vague word of ordinary conversation as if it were a fundamental concept.’

   ‘Pattern is a model of the world that’s like common sense. I think I first picked it up from Mother Sage’s story I just told you about. Later on I read the papers about pattern that she picked up from the mathematician from the ancient times. It’s just how everything is: patterns in time and space. If you simply accept that the past is still present, which we know, don’t we, from the Mother Sages’ eversight, you can see how patterns form and change and link together. It’s like putting Jasper’s fractal geometry in a geometric space which includes time, instead of the space moving through time and changing moment to moment. And you also put consciousness inside the geometric space; then, instead of being outside observers, we’re participating in it. If you do that you get pattern.’

   The words poured out of Roy’s mind, rational thoughts about a way of being that was the opposite of reason. He panicked: he was getting trapped inside his head again, into that seductive realm festooned with logic and filled with ideal constructions, their immutable lines and surfaces extending to infinities and eternities. The soft unfolding beauty of pattern would be corrupted in that realm of absolutes; it belonged outside; he must struggle to keep alive that part of himself which knew the outward world. His senses strained for a glimpse of the moon, the sound of a night bird, but the campfire drew him in. Someone was speaking.

   ‘But you still haven’t really said anything,’ said Charles. ‘Okay, there are patterns, but seeing them doesn’t explain why they’re there. We’re either awe-struck by them, and say God created them, or we think and investigate and come up with scientific explanations.’

   ‘God created the laws of science, remember,’ interjected Peter.

   ‘But with pattern you don’t need any explanations, apart from noticing the patterns,’ Roy said, pleased with himself for saying so much in so few words.

   ‘Look, that’s silly! It’s just circular what you’re saying.’ Charles shrugged towards the others, who smirked back their agreement.

   ‘I think it’s something you either get or you don’t. I can’t really justify it logically, without distorting it.’

   ‘Why not! You’re supposed to be a mathematician.’

   ‘But maths is just the way we think. It’s patterns we create with our brains. All animals use their brains to match patterns they see with patterns they remember. It’s how they can tell food and danger and mates from all the irrelevant stuff. What Alfred does with his maps, is similar to what animals do who bury stores of food all over the place, and then have to remember a map so they can go back and dig it up in the winter.’

   Alfred himself joined in. ‘Yes, I get that. If I make a map of the sky, and join up the stars and measure the distances, that doesn’t mean there are triangles and so on in the sky. They’re just in my mind and down on the map I draw. And when you identify elliptical orbits: they are just patterns in the mind, like Roy’s saying.’

   ‘But saying that doesn’t help. I agree there are patterns, of course there are. But saying there are patterns doesn’t explain the patterns. Roy here seems to be implying that it does. Weren’t you?’ Charles challenged.

   ‘Yes, I was,’ Roy replied, and resisted the warnings of his other self in order to pursue the argument. ‘I was trying just now to explain it using the fractal geometry concept of space. If you extend the idea of patterns in space to patterns in space and time and consciousness, you can see that patterns tend to follow on, and copy each other; one moment very like the one before, and then on a larger timescale changes follow lifetimes. Patterns generate, continue for a while and then degenerate. Over even longer periods, they evolve, or complexify. Simple patterns join up to form more complicated ones. And evolution itself has a lifetime. You can see this principle in anything. And when you do, you don’t need mechanistic explanations, like science came up with in the ancient times. But you can devise a mathematics for pattern. That’s what Mother Sage’s fey mathematician did: perhaps she had eversight, or maybe she just realised, I don’t know, but she was trying to use the ideas to formulate a rigorous pattern maths.’

   He was about to launch into the theory of pattern maths when a vision suddenly appeared to him of a creature part woman, part wild beast, its two heads fused at the back, the four eyes switching from side to side as if straining hopelessly to see the other head, and flashing with love and hostility by turns. Then Roy saw that the creature had no body; the heads had eaten it. He shuddered and clutched at his own head as if to tear off his skull. But the monster and its warning existed in its own time. Outside it had never been; the talking world drew Roy back.

   ‘Wait a minute; before we get on to that,’ said Charles. ‘Let’s go back a bit. Are you suggesting that the laws of science only exist in the human mind, that they do not actually govern the behaviour of entities in the external world?’

   The monster flashed its warning, but Roy had to go on. ‘Oh, worse than that, I’m afraid.’ He gave a nervous little laugh. The argument was alluring, making him forget his fears of being trapped in the mental realm, of dragging pattern there, and of the other men’s hostility. ‘Pattern means that you can forget about distinct entities or things, as such. What we think of as particles and forces and energy fields are all interconnecting patterns. So are plants and animals, their form and perception and memories; so are people, their habits and cultures, their music, art, religion and science. Pattern is everything, everything is pattern.’ Why couldn’t I just say that? he thought. The fewer words the closer to truth, because there is no truth to discover. But he was compelled to be the part of himself who could play their game.

   He went on, ‘As an explanation, it is better than anything science has come up with, because it depends on only one axiom, which is that the universe consists entirely of conscious patterns in space and time; hence the patterns of the past are always present. Present patterns are aware of past patterns and of each other; they are influenced by a kind of resonance. All change is growth, evolution and dissolution based on following and complexifying what is already there. The only reason we have a problem with pattern is because we think the past vanishes; we don’t have eversight. But that shouldn’t be a problem: we’ve believed in forces we can’t see, like gravitational attraction, which we only know about by its effects. And gravitation can be regarded as a geometric phenomenon: so it is actually a kind of pattern.’ His rational self had quite taken over now.

   ‘Pattern of what?’ Charles asked. ‘There must be some substance these patterns are made of. And that substance would have to have some fundamental properties, so you’re back to physics as we know it.’

   ‘That would be true if there were two kinds: the substance and also emptiness, or no-substance. Then you would have to say what the substance is like, compared to emptiness. But according to the single axiom of pattern, everything is pattern. That includes the substance and the no-substance. It’s better to conceive it in terms of a single substance, which might just as well be no-substance.’

   ‘That sounds completely weird! Not scientific, is it? You couldn’t prove that.’

   ‘I suppose you could call it metaphysics: the basics of existence; the first principles of pattern as a science. All science is based on unprovable metaphysical assumptions deep down, but with classical science many of the assumptions are unstated: like the existence of things and force fields and their properties, and the idea of explanation and the laws of science. But the metaphysics of pattern is a much simpler kind, so by what they used to call “the principle of scientific parsimony” pattern is good science.’

   ‘Hmm. But even if we accept all this, what’s the point of it? Isn’t this concept of pattern so vague it’s useless.’

   ‘I think pattern could be useful, but that’s not the point. I’ve said that pattern is the only explanation, as such, but that doesn’t say we can’t use the models of science and maths. As I said, they are patterns, so they are as real as anything else. Pattern does not invalidate the laws of science, because belief in those laws is a pattern in itself. Just because pattern says our particles and forces etc. are in the mind and perhaps not in the real world, doesn’t mean that the belief in those concepts is not useful and applicable. Indeed, in the ancient times, the models of science were externalised and made real through their application in technology based on science’s models. You could say science creates a world in its own image. If it conceives an ideal geometric world it creates architecture based on ideal forms, if it conceives a mechanistic world, it creates machines. At the time of the collapse it was starting to conceive an intelligent organic world, and it created the intos technology which saved humanity from extinction. So you see —’

   ‘Green dragons in space!’

   Everyone stared at Alfred, who had stood up and thumped one fist into his palm, a gleeful expression on his face.

   ‘What?’ they chorused.

   Alfred grinned. ‘Sorry. It just took me back to when I was a boy. I’ve heard lots of you mention the wonders of civilisation and technology your Mother Sages tempted you with to keep you interested in the work. With Roy it was artificial light, aeroplanes and printing. With me it was spaceships. I’ve been a star gazer all my life. Mother Sage used to say that the intos technology could provide space explorers with artificial worlds to travel around in. The intos used to be called the “green dragon”. All the children since the emergence have been told the legend about the black dragon of necrotech and the green dragon of biotech. So: “green dragons in space”! I loved it. That’s the point of all this for me.’

   ‘Didn’t the dragon depend on solar energy, like a plant? How would it survive away from the sun?’ asked Charles. Everyone laughed at him treating Alfred’s boyhood dream as part of the serious discussion. But Alfred was happy to play.

   ‘Oh, it would milk some other source of energy. There’s energy everywhere,’ he replied confidently. ‘It’s intelligent organic, so it would work it out, like we would, only better because it’s not limited biologically to one configuration. What’s interesting from what Roy’s been saying is that the people who invented the intos didn’t use science or maths, in any conventional sense. They called what they did “intuitive innovation”. What they achieved, or rather what the intos turned itself into as it learned, was impossible by the laws of science. It only happened because science was discredited at that time: it didn’t contribute directly to the economy, my Mother Sage told me. So the technologists were allowed to try the impossible. Perhaps intuitive innovation was based on pattern: pattern mathematics even.’

   ‘Rubbish! Dangerous rubbish!’ Peter rose to his feet, his red juicy lips wobbling wetly with passionate fury. ‘The intos was a manifestation of evil; it was not based on scientific principles, which are the laws of God. It was dreamt up by power crazy technicians who denied science’s truths, tried to play God and created a monster they had no control over. The people who sought refuge inside the intos were corrupted; they became idle parasites in a Hell of disgusting fantasies. No men emerged at the end of that period, just a few pregnant women who practised male infanticide, keeping just a few young men for stud. Their descendants are these tribes of dirty peasant people who live like animals. They are totally uncivilised, have no religious faith, and absolutely no sense of purpose. They are the lowest grovelling savages, and Roy here thinks they’ve got super-human powers. He is a heretic, and a threat to the New Beginning, and we should deal with him accordingly!’

   Roy had forgotten his fears when his rational self had taken over. In desperation he tried to treat Peter’s outburst as a contribution to the discussion.

   ‘But we wouldn’t have been born if it were not for the intos. Through the intos humanity left behind the awfulness it had perpetrated: all the wars, the poverty, the disease, the deserts and the storms. It made the New Beginning possible.’ But Roy’s reply only emphasised the doubts he had admitted having, by reminding the group of the dark history of civilisation. Peter said nothing more; he did not need to.

   There was a long silence. They could hear the crackling of the fire. A wolf howled. A feeling of vulnerability arose as a collective shiver. They had forgotten the world around as they faced the campfire and each other and the reassuring power of the rational mind. Only Roy knew that this was the pattern which had given Man his original identity and, with the tamed fire itself, his dominion over nature.

   At last Alfred cleared his throat, to signal he was going to speak in his capacity of leader. ‘This has been an interesting evening. I don’t think there’s time for anyone else to go on with his story, even if —’ He paused. ‘What I suggest is we hear the rest of Roy’s story tomorrow. I know we’re all feeling a bit uneasy about Roy’s – er, unusual ideas, but I don’t want us to rush into condemning anyone before we know the whole thing. What do you say?’

   There was a sigh of relief and a murmur of assent. Roy had to join in, although he would have preferred his next turn to be after everyone else’s because he dreaded everyone’s reaction – not just Peter’s – to what he had done after Mother Sage’s death. With the system of reversing the sequence, and with twelve in the group and probably time for one or two stories each evening, it would have been half a moon’s cycle before it was his turn again. And who knows, some of the others’ stories might turn out to have similar experiences and insights to his own, which might then have to be taken seriously – and that was the reason he had joined the march, after all. But Alfred was right; they had to hear the rest of his story as soon as possible.

   With the threat of what tomorrow’s revelations would bring, Roy longed for some comfort; he was strongly tempted to disregard the convention and go to find his Fey. He lay down, but the thought of her kept him awake long after the other men had gone to sleep. The moon was full and bright above the smoke. At last he crawled slowly and carefully away.

   No one woke up, so Roy got to his feet and walked back the way the march had come. When he was well clear of the fires he came to the first sleeping huddle. The moon was full, and bright enough for him to see the women. He lifted a curtain of hair gently and peeped at the moonlit face of one of the fey’s. No, that was not her. He tried another, and then another. None of them awoke, but each stirred and cuddled up closer to a nearby body. Roy’s Fey was not in this huddle. He walked further, and skirted the next mound of bodies, drawing aside more hair. Not there either. At the next huddle, as he lifted a mass of dark curly locks to reveal a stranger’s face, the fey opened her eyes. She turned and reached up for him with both thin arms. Oh well! he sighed. Getting onto his hands and knees and wriggling his way in, he enfolded the fey’s warm back in his front. The huddle of women’s bodies closed in around him.

The morning was strangely quiet. To the astonishment of all the men, apart from Roy, there were no chattering villagers bustling around, and no tasty food arranged in baskets for each group. Roy came back from his cosy night with the feys to an uproar of complaint and anger. He could not help being conspicuous because he was with the women, and because he was carrying two basket traps, each with most of its compartments occupied with small birds and animals flapping or scuttling around. His Fey, whom he had found when morning came, walked beside him with more baskets on her head. Other feys followed with similar burdens.

   ‘Breakfast!’ Roy announced, putting down his baskets. He reached into a compartment, grabbed its occupant and dispatched it neatly with a blow from a stone on the back of its head. He held it up towards Alfred, who had walked over to see what was going on.

   Roy could see Alfred struggling to decide how to react. Anger showed in his face.

   He squatted down to Roy’s level and hissed, ‘What do you think you’re playing at? I tried to be fair to you last night and this is all the thanks I get!’

   ‘It’s nothing to do with last night. Not directly anyway,’ Roy said. ‘It’s just that I know more about the village life than the rest of you. I tried to warn you yesterday morning. The villagers haven’t enough surplus food to feed us as winter draws in. The people who came last night left traps and the feys set them. There’s quite a good catch. We can cook the meat. Look, they’re quite easy to skin.’ He demonstrated, cutting a hole in the animal’s belly with a bone knife, he pulled out its guts, then he separated the skin from the flesh and pulled the little pink body out.

   Alfred made a disgusted face. ‘I don’t think the men will want to do that,’ he said.

   ‘They will if you leaders tell them to. Anyway, it’s either that or go without breakfast.’

   ‘Why can’t the feys do it?’

   ‘They’ll do some, but it’ll be quicker if everyone joins in, and the feys won’t do the cooking, or go near the fires.’ Roy resisted asking why the feys should do all the work, but Alfred probably received that message too.

   ‘All right. I’ll see what I can do just this once. But I want to talk to you as we’re marching. We’ll have to find some way of sorting this out.’

   Roy continued to kill and skin the animals as Alfred gathered together a leaders’ meeting to discuss the emergency.

   When Alfred had gone, Jasper came up to Roy to ask what was going on. Roy explained. Jasper nodded and reached for one of the animals. ‘Show me,’ he said. Charles and two others joined them. Roy noticed Alfred glance over in their direction. After a while Alfred led the leaders to his group’s fire, where several animals were now skewered close together on a stick over the refuelled fire, the flames grilling them nicely. Roy explained the technique, and gave them a taste each.

   Then the leaders withdrew again for further discussion. They were near enough to Roy’s group for the grumbling mood to be audible. But at last they dispersed, and Alfred returned and ordered Roy and the men he had coached to go to the other camp fires and pass on what had to be done.

   The sun was higher than usual when they were ready to resume the journey. Roy took his place in the column as usual. As he strode along he realised he was feeling happy and relaxed. Nothing dreadful was going to happen during the day. His night with the feys had somehow reassured him that he was not getting stuck inside his head again. He was going to have to tell the rest of his story this evening. He would just do that when the time came, and then whatever the consequences would be would be. Until then he was not going to worry.

   Then Alfred came up beside him. ‘You’re looking pleased with yourself this morning,’ he said.

   ‘I had a good night,’ Roy smiled.

   Alfred looked embarrassed. ‘Yes, well, we couldn’t all — Be a shambles wouldn’t it? We have to have discipline, and maintain our integrity. Well, they are villagers, the feys. Not good to mix, in the present circumstances. When we get there we can make suitable arrangements. Anyway,’ Alfred said firmly, drawing himself into his leader’s role, ‘Roy, we need to talk. Now, tell me why there’s a problem with the food supplies. I really don’t see why there should be. I know you think it’s this “thinking they’re our slaves” business, and we can just exploit them. Well that isn’t my attitude. The way I look at it is this: they must want to help us, they decided to bring us all up, didn’t they? Presumably they’ll benefit from civilisation in the end. “Development” was what they called it in the ancient days.’ He looked at Roy, who frowned and opened his mouth to reply, but Alfred went on.

   ‘Anyway, never mind all that, let’s just work out the sums. There are currently about a thousand of us on the march. There are more people than that in each village who are fed all right on a regular basis. Isn’t that right?’ Roy nodded, and Alfred warmed to his argument. ‘All they have to provide for us is two meals, and then we move on. When we were living in the villages there was plenty of food for us: there’s no actual increase in numbers. There are massive food stores under the houses, filled up every winter with nuts, dried meat, dried fruit, seeds, honey, cordial – you name it. And yet you say it’s winter coming on that makes the problem.’

   For a moment Roy had doubts. Was he nursing a moral position which did not stand up? Did he really know what the village people wanted? Was he trying to protect their culture because he found it attractive, from changes they actually looked forward to? But he pushed those considerations aside; they were not the point. What about the practicalities?

   ‘I haven’t worked it out logistically; I just noticed that the baskets seemed to weigh the same each day – had done for more than a moon’s cycle, I think – and during that time twenty to thirty men would have joined us. Perhaps I jumped to the conclusion I did about the surpluses. But I think, in a way, it’s that they don’t really have any surpluses as such: only supplies to cater for accidental losses such as pest or disease damage, or spring coming late. And they practically hibernate in winter, so each person eats very little, whereas we’re marching during the day and expending energy in the evenings: mental work uses energy you know.’

   ‘Okay, I see that. But let’s work it out,’ Alfred said. ‘We need to estimate how many days’ supplies we’re depriving a village of, at hibernation levels of consumption. How much less do they eat through the winter, would you say?’

   ‘I don’t know really. Let’s say a quarter.’

   ‘A quarter less, or a quarter of?’ Alfred asked.

   ‘Of,’ said Roy.

   ‘That’s a huge reduction. Don’t they need energy to keep warm?’

   ‘Well they sleep huddled together – you’ve seen the feys, and in the winter they doze through most of the day and night. And they put on a lot of weight during the autumn harvest-time feasting, so some of their stores are in their bodies. It may even be less than a quarter, I don’t know. I’m sure it’s not more. I lived with them for more than a season cycle, so I think my impression is reliable, but they don’t actually measure or count anything; it’s all done by patterns.’

   Alfred frowned. ‘Let’s leave all that stuff ‘til this evening,’ he muttered. ‘Okay, let’s assume it’s a quarter. So what’s the population of a village?’

   ‘I don’t know if they’re all the same – I doubt it. But I did once work out the size of our village. There are about three hundred sleeping huts with six or seven in each during the summer; in winter they double up. Anyway, that works out to about two thousand. Quite a few people go to the forest after the autumn feasts. Most of the babies are born in the autumn, but they don’t eat anything, they just add to the nursing women’s consumption a bit – living off their fat really. The numbers are least in the winter, but only by fifty or so I should think. We may as well assume two thousand.’

   ‘They do live like animals!’ Alfred exclaimed, obviously referring to Peter’s outburst the previous evening.

   ‘Yes, they do live like animals. Their life is in ecological balance so that the human animal isn’t being disruptive.’

   ‘But they change the ecology. The gardens are highly artificial.’

   ‘All living things affect the ecology. That’s fine, as long as the overall balance is sustained. The people don’t disturb the soil: it’s wild underneath the gardens; and they don’t use fire, so energy is conserved within the living system. Using fire and digging the soil for farming and mineral extraction were fundamental to human culture in the ancient times. From that point of view, the village people are not behaving like humans, but more like animals. But that doesn’t make their way inferior.’

   Alfred seemed interested. ‘So is fire technology why they call us “firesoul”?’

   ‘Yes, that’s the basis,’ Roy replied. ‘Last night you mentioned the legend about the dragons. According to that, people made the black dragon of fire at the very beginning. The way I’ve worked it out is that fire is what made us human. We came from primates who had already domesticated wildfire: using fire to drive out game and later encouraging grassland for grazing animals, deliberately or accidentally, I don’t know. Be interesting to know if anyone’s looked that far back by eversight. The “soul” part refers to our minds: it was presumably gathering around the campfire which turned our consciousness inwards, hence “firesoul”. We live in our minds; it’s as if there’s another world in there, which we like better than the one outside. It’s not like that for the watersoul people. They’re not enclosed in their minds and separate from each other, they’re all rolled up together, and with the others in the past whose pattern they continue. I think that’s the way all animals are – plants too – perhaps everything. So the reason humans were so destructive was that we were not part of it all, at least, we believed we weren’t. And our lot on this march have been brought up to pick up that pattern. The Mother Sages did a good job, but they couldn’t have done it without the need for completion.’

   ‘Hmm,’ said Alfred, dubiously. ‘I suppose you have to get into the pattern way of thinking for that to make sense. Anyway, we’re getting off the subject, which was the winter stores. If we assume two thousand people in a village, that’s twice as many as we are. We need an active day’s supply each, that’s four times a hibernation day’s supply. So that only deprives them of two days’ reserves. Doesn’t seem too bad, does it?’

   Roy felt confused. He had been so sure he was right about the food. Then the people from the next village had only brought enough food for one meal, leaving the traps, just as if they had picked up his concern and made it true.

   ‘I’m not so sure any more,’ he said, ‘but perhaps we needed this to happen: it shows we don’t have to rely on the villages. That’s probably a good thing to realise because we can’t be sure there’ll be a village nearby all the way to the city. Which reminds me, I was going to ask you, where are we headed for? Where is the new city?’

   ‘I don’t know that I can answer that really,’ said Alfred. ‘I think it’s just assumed we’ll know in some way, or that we’ll choose the best situation we come across, probably on a big river, most likely at an estuary, somewhere to build a harbour and be able to use boats for transport and trade and so on. But to start with we’re just following the road, to see where it ends up.’

   ‘But this isn’t a road!’ exclaimed Roy. ‘It may not end anywhere.’

   ‘What do you mean? Of course it’s a road, and we’re going along it. We’ll get somewhere.’

   ‘When I lived in my village this “road”, as you call it, was just the second firebreak. The sections of the firebreak are maintained by different villages, and they join up, otherwise they’d be useless for stopping fire. But no one travels from one section to another; that’s not what they’re for. Just because you can go along something doesn’t mean it’s going anywhere. Perhaps the sections go all around this range of hills and join up in a great loop.’

   Alfred looked stunned. ‘But I’ve been plotting the direction,’ he said, ‘and, allowing for skirting the contours, we’re going almost directly south.’

   ‘It could be a very big loop,’ said Roy. ‘But I suppose the firebreak could stretch from one part of a coast to another. Anyway, perhaps we’ll be able to see the sea from some point, and we can leave the firebreak and make a new path through the forest. Then we’ll be glad we can set traps and prepare our own meat.’

   Alfred’s face brightened. ‘We could hunt – you know, properly.’ And he mimed throwing a spear and then aiming a bow. He looked at Roy. ‘There are big animals in the forest; those with horns or tusks. Why don’t they hunt those? Why just traps?’

   ‘They don’t have reasons for why they do things.’

   ‘I know: it’s just pattern; hunting’s not part of their patterns. But why not? There must be a reason, even if they don’t think that way. They could make the weapons surely? After all they make tools.’ He paused. ‘I know, weapons are aggressive; tools aren’t – but the trapped animals still die, so it’s just as aggressive really.’

   ‘Trapping doesn’t feel aggressive,’ Roy said. ‘It’s as if the animals give themselves. We put a little feast in each trap for the animal, and it gives in return. If you look at the traps, there’s nothing to stop the animal getting out after it’s had the food. I mean, there’s no wide open door, and it’s easier to get in than out, but an intelligent creature could find its way. But they choose not to. Anyway, that’s how I see it, although I hadn’t worked it out before you asked. But I could be quite wrong; it was just the track you were following.’

   Alfred had been looking uneasy, but then he brightened. ‘Talking of tracks! I’ve been neglecting my mapping work discussing this food business. I’d really better get on. See you later!’

   Roy watched him bound off, but carried on thinking about watersoul ways. It might simply be that running around hunting wastes energy and trapping is less effort. On the other hand, it might be fear of picking up firesoul patterns – hunting big grazing animals and later on enslaving them. The people leave them for the hunting beasts, like wolves, whose pattern has always been to control the grazers’ numbers.

   Roy’s musings were interrupted by someone hurrying from behind to join him. It was Jasper, who clearly had something urgent on his mind. ‘Roy, can I ask you something about what you were saying last night?’ he asked.

   Roy would rather have walked alone but he was grateful for Jasper’s support over the breakfast crisis. ‘Yes Jasper, what do you want to know?’ he asked.

   ‘The papers you told us your Mother Sage wrote for you, the pattern maths stuff, could I have a look at them?’

   ‘I’m really sorry to disappoint you, but we didn’t bring them with us,’ Roy replied.

   ‘But why not? I would really have liked to see what pattern maths was all about,’ Jasper said wistfully.

   ‘Yes, I’m really sorry. I’d have been glad to let you have it. The actual theory was your sort of stuff: something like an extension of Klein’s geometry groups, but going beyond topology to a completely comprehensive geometric space – like I was saying last night, including time – multi-dimensional time actually – and discontinuous space as a result – and universal consciousness. In such a geometric space, no properties are absolutely preserved, but there’s a set of soft properties and relationships; what were they now? — Oh, yes: self- and other-similarity, lifecycle, evolution and dissolution, and completion. I think I could remember most of it, given a few weeks of peace and quiet somewhere. Not much chance of me getting that, I suppose.’

   ‘Could we, could some of us, go back and pick the papers up, perhaps?’ asked Jasper.

   ‘I don’t think they’d be much use if you did. They got in a mess – that was why we didn’t bring them. I don’t think you could make any sense of them now.’

   ‘What do you mean: they got in a mess? How?’ Jasper’s voice was husky with anxiety.

   ‘They got torn up for messages and love notes; you know, the sort of thing the youngsters do in the mating games. Village people are pretty careless about property. They found the basket of paper in my room in the big house. I would have told you about that in the next part of my story.’

   ‘But that’s dreadful!’ Jasper almost wailed. ‘You heard what Alfred said: this stuff may have been the basis of the intos. I have a hunch that the New Beginning has to progress rapidly to where we left off technologically – if we’re to avoid the disasters of the ancient times.’ He said this pointedly, the implication being that if Roy’s knowledge were valuable for building a new kind of New Beginning, Roy himself would no longer be seen as a threat – except perhaps by Peter.

   It was a bizarre situation for Roy: being the only doubter, and perhaps the only one to know about a new kind of mathematics which could be crucial to the success of what he dreaded. It had not occurred to him that any maths would be that important. The mathematicians were the least necessary for the initial stages. The technologists: those who knew how to extract metal from rocks, make glass, fire clay, make tools, construct buildings, lay roads, pipe water, dispose of waste; they would build the city, and civilisation would grow and progress from there – only then would it be possible to consider sophisticated developments like the intos, and by then it could be too late. There were agronomists amongst the marchers, and those who could make agricultural chemicals and machinery, probably biotechnologists too, of the pre-intos variety, so there would be forest clearance for necrotech agriculture. There did not seem to be any gardeners on the march, apart from the feys, who did not count. The village people were all excellent gardeners, but they did not need a New Beginning; they needed protecting from it.

   Roy suddenly felt his earlier sense of well-being fade; he was tired of all the words and ideas and arguments which threatened to drive him back inside his head. He was reminded of the crisis he’d been through in the village when he’d stuck his head on the rocks as if to smash it to pieces to get free, to get outside his head into the real world. How was he going to be able to get them to see what he had been through? He was aware of Jasper saying something else, but he could not listen.

   ‘Sorry, Jasper, would you leave me alone now. I’ve got to think – about tonight you know,’ he managed to say. He saw Jasper’s hurt look, and felt for him. He seemed to have his own doubts to wrestle with and perhaps the others would see those as a threat too.

   ‘I shouldn’t say anything to anyone else about your interest in pattern maths,’ he warned, ‘and about the New Beginning depending on something that might not be available. They don’t like doubters – you could be in trouble too.’

   Jasper looked as if he might protest; probably insist on his firm commitment to building the new city – he was no doubter, certainly not! But to Roy’s relief, he said nothing and soon fell behind to join his usual group.

   Roy took the few steps off the road into the forest and squatted to empty his bowels. The stress he had been going through had upset his guts, and the liquid shit left a burning sensation. He tore up some moist moss to wipe himself. He stepped back and waited, still and quiet, to see the first response to his addition to the ecology. Some tiny flies darted down, a small frog hopped up, the flies scattered, the frog waited for their return. In time, as the stuff soaked down to the soil, creatures too small to see would take an interest. You do not have to be a scientist to know when you are joining in the processes and when you are disrupting them, Roy thought to himself. If you do not try to understand, you know all that matters.

   He willed his mind to hush. Living with rational thinkers bent on an important project, he easily reverted to that way of being. The brief escape he had enjoyed in the village seemed another lifetime away. Roy shut his eyes and concentrated on the rattling whisper of the trees at the forest edge. The sound was diffuse enough for time to linger uninterrupted by the moment. But a bird’s sudden burst of piping song broke through. Roy remembered Mother Sage telling him about the myth of naming: the belief that singling out some thing, say a bird, and giving it a name, a name for its kind, gave a human being power over what was named. But the price of that power was the fragmentation, the separation, the instant and the location, which left man lonely and, if he would admit it to himself, afraid.

   Perhaps, Roy thought, describing to the others how he had been changed would take him back to that blissful state, as near as one like himself could become to being watersoul, a ripple in the unending pattern.

12

Habitation

‘I don’t know if you can imagine how I felt after my Mother Sage died. All your Mother Sages were with you right up to the day you left for the march. They waved you on your way – I saw some of them. Then they would have gone to the forest, I am sure, since their task was done and they were old. But I expect you imagine them still alive, don’t you?’

   Roy saw pain in some of their faces, but he did not wait for anyone to comment.

That time was very terrible for me. My grief and hurt were overwhelming. Not only had Mother Sage left me, but my identity had been shattered. I had no one to talk to about my suffering, having lost the very person I would have been able to share my thoughts and feelings with. I had been trained not to show strong emotions, even to deny I had any, which must have contributed to the trauma I went through.

   The loneliness of losing my companion and guardian was emphasised because, without her, the environment she had surrounded me with began to disintegrate. Most of the servants rolled up their bedding and went down the hill. Village people don’t have any sense of responsibility; it was only Mother Sage’s influence that kept them from going off to do what they pleased. The new Fey stayed for a while. She brought me food twice a day for several days, and then she too went, and I was left to fend for myself. It is pointless now to wrap all that happened to me during that period in descriptions of loneliness and woe. I did recover myself, and I learned a great deal.

   I had a look at the papers in Mother Sage’s basket. None of it had been bound, but most of the loose sheets were in groups enclosed in folders. Several of these containing the journal she had told me about, dated by the calendar system she had devised for my benefit: days within moon cycles within season cycles numbered from when the project of bringing me up was begun. It was all written in tiny script, the lines close together and on both sides of each page. So many words! I started reading it, but I found it disturbing, not so much because it brought my loss vividly to my consciousness, but because I discovered in it another person besides the Mother Sage I had known for most of my life. This person was the one I had had a poignant glimpse of when she told her story just after she died: the watersoul woman drawn back from her going to the forest to be my guardian. The interplay between the two personalities was clearly apparent, but manifested in unexpected ways. I would have thought it would have troubled the watersoul woman to put on a pretence of despising her own people; but not so; she had the careless innocence which I later found was typical of her people. It was the personality coloured by firesoul values who was troubled by the deception.

   Putting the journal aside, I looked to see what else there was and found a small bundle of pink-dyed folders labelled ‘Pattern Mathematics – Bony Bailey’. I could not read that either because the identity I had lost was as an important New Beginning mathematician, and I wanted nothing more to do with mathematical ideas.

   There was another collection of papers which were notes about the project of bringing me up as firesoul. I certainly did not want to know any more about that terrible deception.

   While I was trying to make up my mind what to do next I took to wandering around the empty house. The drawing room and dining room had many embroidered wall hangings showing scenes from the ancient days. Some of the pictures showed what Mother Sage had called ‘classical scenes’, of gods and nymphs and mythical creatures or charming young couples tending flocks of animals amongst flowery meadows and little hills. Other pictures Mother Sage had called ‘religious’; they were less jolly. Some had been taken down. They had shown cruel torture, and had given me bad dreams. Mother Sage had been explaining the religious stories to me, but then she stopped. There were violent scenes in other pictures: plumed generals on horseback and armies engaged in battle, and huntsmen slaughtering wild beasts. They hadn’t bothered me that much, I think because they were not meant to affect you like the religious ones were.

   There was quite a different kind of picture, which had always fascinated me, hanging in my old schoolroom. It showed a city with towering buildings, wide streets teeming with vehicles, and skies streaked with gleaming aeroplanes. I remembered, when I was a boy, going to the tapestry workroom when that picture was being stitched. I suppose that at first the ‘slaves’ had ‘followed the patterns of tapestry making’, and so created close copies of tapestries they saw in the past. Only later did they make one to Mother Sage’s design.

   When I was little I used to enjoy crawling around on the floor of the drawing room tracing the pattern in the fur carpet. The village people only kill small wild animals and so the carpet was made up from hundreds of little pelts stitched together in a complex geometric design.

   The drawing room had more furniture than Mother Sage and I could ever use. There were leather-covered chairs and couches, and others of fine basketwork, with fringed and embroidered cushions. Other items were purely decorative. Displayed on basketwork tables were sculptures of wood and bone: several women in coyly erotic poses, a few fearful beasts leaping to the kill, a warrior in a plumed helmet plunging his sword into a fantastic monster. There were basketwork vases, once always full of fresh flowers, now holding dead stalks and surrounded by shrivelled petals.

   Compared with the simple dwellings of the village people my house was a palace. Like a wealthy man from the ancient times I had many possessions. I had been told as a child that these things showed how important I was, and how the ‘slaves’ had laboured long hours to make them for me, and the latter was surely true. I was to discover later that the village people make things as much for the fun of making them as for their usefulness. They were perpetually discarding and remaking, using materials which grow abundantly and are decomposed to good mulch when discarded. But nothing they make is anyone’s personal possession. And there is no ownership of houses, land or produce from the gardens. Children do not belong to anyone in particular, love and lovers belong to anyone or no one. Curiously, judged by firesoul values, the absence of property is as much carelessness as sharing; one could not say for sure that it is good or bad, it could be seen as a kind of selfishness, even cruelty, in spite of the people having no sense of the separate self to benefit from any selfish behaviour.

   But I am getting ahead of my story; my understanding of watersoul ways was meagre and uncertain before I went to live with the people. Having been reminded of crawling on the fur carpet and watching the tapestry-making when I was much younger, I thought perhaps it would help me come to terms with what had happened if I read the papers about how my upbringing was decided upon. I read through the first folder. In it were records of eversight discussions with other Mother Sages, in which they agreed on what aspects of the ancient pattern they could and should replicate for the boys.

   The most difficult issue was the use of fire. In principle, fire technology was an essential component. At first many of the Mother Sages, including my own, had expressed willingness to use fire; but they could not find ways of using it that were satisfactory. The main problem was that they could not get the other village people who were supposed to be servants to cooperate, not in lighting or using fires, or in moving big stones to make fireplaces, or in digging up clay for bricks. The Mother Sages could have had fires on the ground in the open which they lit and used themselves, but that would have distracted them from the education work, and lowered their status, which they felt ought to be between the firesoul ‘lords’ and the ‘servants or slaves’. Fire inside a house made entirely of wood was only possible with a centre fireplace on an earth floor and a smoke hole in the roof. A single great hall was a possibility, but the Mother Sages decided on a house design with several elegantly furnished rooms. So there would be no fire.

   Another important topic was whether to bring the boys up singly or to bring groups of them together at an early stage into schools. It was the problem with fire that decided this. Fire was linked to the pattern of inturned consciousness, and the isolated self. There would be no fire to reinforce and confirm this essential personality component, therefore it would be confirmed by keeping the boys physically isolated instead, apart from the mother figures, who would carefully avoid being too affectionate and physically close to their charges.

   I could not go on reading about these deliberations. It reminded me of what Mother Sage had told me about artificial environments for wild animals called ‘zoos’, which they had in the ancient times. This was in response to questions I asked about the hunting scenes on the tapestries. It seems some people were sorry that the wild animals had been killed and the wild places they had lived in destroyed, so they collected the last few animals and kept them in zoos. In order for the animals to exhibit their natural behaviour and, most importantly when there were few or none left in the wild, to mate and reproduce their kind, they had to be provided with surroundings sufficiently like their natural habitat. That was what the Mother Sages had been doing for us firesoul boys.

   Mother Sage had told me that the firesoul boys before us had faded away and died because the watersoul village was not a suitable environment for them; even so the discussions about us made me feel uncomfortable. It was as if it was us they were constructing, rather than the environment, and I suppose that was what was done to children in the ancient times. Later, when I began to think in a pattern way, I realised that what the Mother Sages were doing was tuning in to an old pattern, which was present, although its links with ongoing human behaviour had been almost entirely broken. We were the only fragments of its continuing manifestation.

   There was an account in the folder about the building of our house. The house was to be large and rectangular in shape, and durable, which required a great deal of timber. So a swathe of forest trees from the village to half way up the hill was cut down. To make the foundation of the house a number of tree trunks were cut to form piles and driven into the ground using rocks. A sturdy frame was constructed and filled in and roofed with shingle. The upper floor was rigidly boarded.

   Stone axes with long wooden handles had been made for cutting down the big trees. I had seen the axes because, after the house was finished, they were arranged on a table in a special little room which was never to be used. Mother Sage said that this symbolised that the pattern of felling and construction was completed. The episode had been disturbing for the people, who naturally followed old patterns and disliked anything new. When it was all over a healing process began. When the people wandered up or down the cleared avenue they brought pocketfuls of fruit to munch on the way. Then they pushed into the earth some of the small fruit seeds, and any of the stones they did not crack open to eat. When the house was first built the avenue must have looked like a grand drive, such as big houses used to have in the ancient times. But over the years the hillside and the area around the house became an orchard garden, which matured to harmonious balance.

   I went outside then to look at the house. I had not noticed what a bad state it was in. It was covered with moss, many of the shingles on the walls and roof were soft and rotten, loose or missing. It occurred to me what a lot of wood would be needed to keep the house in good repair. Those axes would have been kept busy felling forest trees. Supposing the whole village lived in houses like this, there would surely be hardly any forest left. I began to wonder what effect the New Beginning would have. Not only would vast amounts of timber be needed, but mountains would be demolished for rock and minerals.

   I went back into the house and into the little room where the axes were. I pulled at the handle of one of them and the whole arrangement fell down. The axe was heavy. I lugged it out and went around the back to the servants’ huts. There were six huts, sleeping six or seven people each. There were several big forest trees in amongst the huts. I took a swipe at one of them with the axe. The sharp stone blade bit in deeply, but I could see that it would take me some time to make the V-shaped holes necessary for the tree to fall. I had never tried to do it, but I guessed I could do it in an hour. I found myself talking to the tree.

   ‘I could cut you down in an hour. How long has it taken you to grow? Fifty season cycles? So the new houses have to last that long. Mine didn’t, but we’ll have technology – chemicals or something – to stop the wood from rotting.’

   I imagined the tree lying at my feet. ‘Now what?’ I asked it. ‘I’d have to cut you up. Branches off first, then into lengths, then into thin slices for floor boards and shingles. I suppose when they built my house they propped the sections up and then split them with blows from above.’ I mimed the actions. ‘My word, they must have worked hard! But of course, for the New Beginning there’ll be people who know how to get metals to make better tools, and even machinery. Then it’ll be easier: we’d have you in nice pieces in no time.

   ‘Now, how many of you will it need to house properly all the people who lived here? There were six or seven people to each of the six two-roomed huts, which is about forty people. The two of us had ten rooms between us in the big house. So we’ll need twenty houses with ten rooms. Each house needs the timber from a strip of ground the size of the avenue. My goodness, we’d have to clear the whole hillside. So what about the village?’

   I climbed up the ladder of one of the huts and onto the roof, then onto a branch of my tree, and as high as I could get. I parted the branches to look down at the village. Mentally I sectioned off the village into groups of ten huts, and grouped these in threes.

   ‘If there are six or seven people to a hut, each of those sections would house two hundred people. There are about ten such groups, so this is a village of about two thousand people. We’d have to clear the forest at least to the second firebreak,’ I told the tree. ‘I suppose there’d be other materials: stone, blocks of baked clay, perhaps even metal sections, I don’t know. But they’d have to be dug out of the ground, so the forest would be cleared anyway, perhaps just as fuel for the fire technology.’ I climbed down thoughtfully.

   Picking up the axe, I went back to the big house. I took a swipe at a section of the side wall, severing a supporting pole. A cascade of shingles slithered down to leave a gaping hole.

   ‘Much easier to destroy than to build,’ I muttered.

   I no longer wanted to be in the big, empty, rotting house that had been my childhood cage. I decided to move into one of the servants' huts, which are very small; really more like nests. I had watched when the first one was being built, much to Mother Sage's annoyance. There were plenty of rooms in the house for the servants, but they did not like them, they were too hard and square apparently. They had tolerated them for a few years, but then Mother Sage reluctantly agreed that they could make their own sleeping huts, as long as they were tucked away in the forest at the back, out of my view. But I insisted on watching the construction, and Mother Sage, grudgingly at first, explained the principles and techniques which were used.

   Down in the village there is a long slow cycle of hut-building. Oval rings of fruit or nut trees are grown from seed, so that many season cycles hence they can be used for hut frames. As they grow they are pruned so that there are branches only where they would be needed. They bear fruit meanwhile, and some never become huts.

   When the trees in one of the rings are tall and strong enough, a hut can be built onto them. Lengths of bamboo from the bamboo island, or small roundwood coppice or saplings from the outer garden, or wood from old huts are used for the rest of the frame. The thickest poles are hung from bands over the ‘V’ formed by the first branching and lashed together at first floor level. On these are built the supports for the upper floor and the roof. The walls are filled in with lightly framed woven mats. The roof is thatched with reeds. The upper floor, which is the communal sleeping area is made of tough webbing, attached to the poles at the sides and forming a bouncy floor on which are piled fur blankets and feather quilts. The lower floor is enclosed in secure panels to make a food storeroom.

   Each hut lasts about the same number of season cycles as a human lifespan which, for these people, is intentionally short. During that time, the hut would have its walls replaced and its thatch renewed as often as necessary to keep it neat, and secure against predators and vermin.

   When the supporting trees grow too big, the hut is abandoned and another one made on another tree ring.

   When the servants built their huts behind the house on the hill, they picked out a number of naturally occurring collections of young trees in the forest behind us. Some of the smallest trees were cut down to leave suitable rings, and the huts were built in the usual fashion, using the felled trees as poles instead of bringing bamboo or wood from elsewhere. At the time, my attitudes coached by Mother Sage, I shared her distaste at the idea of sleeping curled up with several others on a bouncy platform. I retired to my four poster bed in my own chamber, and Mother Sage to hers, but I fancy the house echoed with emptiness after the servants moved out.

   Now, years later, I was moving out of the big house into a sleeping hut. I collected some bedding, rolled it into a bundle for putting over my shoulder to climb the ladder, and made a cosy nest in one of the sleeping huts. I slept very soundly that night, and felt ready for anything in the morning, as if my mind had been cleansed of anxiety. I climbed out into the sunlit garden, and went to the stream to wash my body. Approaching the massive shape of the big house on my return, a thought that seemed to have come from a forgotten dream came to me, and I spoke it aloud to the house:

   ‘I wonder if we should make the New Beginning of civilisation. The village way is easy, and the people are happy. They have everything they want round about them, and they can tell what effect they are having: all living things have an effect; that’s all right as long as it all cycles. But shut inside a city with everything brought in from outside we wouldn’t know if all the forests were cut down and the land turned to deserts. Perhaps the wonders of technology would only make the destruction worse. How would we know? Could it be that busy garden villages are better than lonely cities?’

   Though the words I uttered were calmly rational, the implications for my life were shattering. The words echoed through my head, sending reverberations of such force they crushed my soul, my whole reason for being. I shuddered, screwed my eyes shut and crossed my arms around my body as if to defend myself against physical attack.

   But nothing happened. I was still there. Mother Sage had raised me for the New Beginning, and fed me with knowledge. I was approaching manhood with a life to live. I relaxed and opened my eyes. The decaying house confronted me.

   ‘How can she have been wrong?’ I asked the house. ‘And all the others like her who decided to raise firesoul boys? They were convinced the boys were being born because there was a pattern which had to be completed. Of course they assumed that it was the catastrophe brought about by firesoul technology that had to be healed and continued in a better way. But if there is no better way: if firesoul technology would always be destructive and could only be available to a very few people, with the rest miserable slaves, and with constant wars over land and what had to be stripped off the land and taken out of it —

   ‘But perhaps civilisation is worth even such a price, which must be paid again and again. And cities, and grand buildings, are merely the shell. Within the shell, the embryo grows: human creativity – art, literature, philosophy, science, mathematics – that is worth any price, surely?’

13

Pattern Mathematics

So that was how it was that at last I turned to the pattern mathematics folders Mother Sage had left for me. In it she had recorded the work of Bony Bailey, a mathematician from the ancient times. The first part was not so much mathematics as what I understood to be philosophy, since it concerned two views of how people could think. As I read it, I could sense – as if with eversight – the woman from necrotech thinking as she wrote.

Pattern is an alternative conceptual model to the ‘reason model’ of contemporary science and mathematics.

   The reason model evolved with the first human societies and civilisations. It was first of all practical and then became abstract and intellectual. Basic ideas such as number and measurement arose out of the need to assess quantities, in order to administer property, to engage in trade and to construct buildings and machinery. The large brain of Homo sapiens helped him to accumulate information: originally about the location of sources of food and other useful materials; later on about how to make things and about how to engage in co-operative activities.

   When social organisation gave rise to societies divided by class, there were people who were not engaged in the day to day practicalities of survival since their needs were taken care of by servants and slaves. They had spare mental capacity, which, for some of them, came to be employed in further study of the once purely practical ideas of number, measurement and shape. The abstract study of these ideas came to be associated with the concept of ‘explanation’: the ideas were used to conceive models of what underlay the universe, and how its divine creator had made it, assuming that the God had a mind similar to their own.

   Economy has always been a guiding principle of conceptual thought. In the case of the reason model, economy manifested as the thinkers’ search for the simplest possible ideas to form their basis for comprehension; and then combining the simple ideas, as necessary, to explain more complicated situations. The rightness of this approach was never questioned, since the goal of formulating explanations was so eagerly pursued. It did not occur to them that the result was an extreme lack of economy in the world as they saw it.

   For example, take a straight line of some arbitrary length: either a real rod of a thin material, say a precisely straight wooden stick; or a mental image of a rod. In the concrete world or in the abstract world, the rod is limited in size: we could agree that to see it that way is an economical view of the rod. But looked at from the reason model, it contains an abundance of infinities. It can be divided up endlessly to make an infinity of rational numbers. In amongst the rational numbers is another infinity of irrational numbers. The rod could be repeated endlessly to extend through an infinity of one dimensional space. It could be used to delimit an endless number of two- or three-dimensional spaces, and an endless variety of shapes and sizes. The concept of number: that purest and simplest of ideas is hugely and absurdly uneconomical in the mental world where it resides.

   If reason’s economical models and its uneconomical world had stayed inside the brains of thinkers, they would have been impotent and harmless. However, they have been externalised, made manifest in the world, leading eventually to such monstrosities as financial worlds of huge numbers and uncontrollable power and influence, computer technology and mass production, simplistic models of how crop plants grow and, in general, uniformity, repetition, loss of diversity, homogenisation of human culture and the degradation and disruption of many of the processes of life on earth.

   What then is the pattern model? Crudely speaking, it is the reverse of reason’s model. It resides in the world, rather than in the mind. It is economical in repetition: there are no identical patterns; the universe and everything in it is finite and contained within their lifetimes; no thing includes or measures, as that rod did, infinities or eternities. On the other hand, pattern accepts complexity and does not require simple explanations, or reduction into simple components. I imagine it existing in the environment of an alternative human society as intricately patterned, consciously designed, productive gardens.

   Describing the pattern model as a conceptual model is purely a device: an understanding bridge. As far as I am aware, no culture has yet come into being which employs pattern as a model. I think of pattern as the opposite of reason, and a philosophical outlook yet to be adopted. As the opposite of reason, pattern would not be the subject of intellectual exploration; it would be the unstated basis for a way of life. One cannot take the pattern model any further as an alternative conceptual model to reason’s model without accepting some form of hybrid between the two. Such a hybrid model could make the case for pattern, when no one living by pattern would bother to do such a thing. A hybrid model requires a hybrid thinker. I propose to take that role. I shall say more about reason’s model than about pattern’s because the first step is always to question your own certainties, or they will be a barrier to alternative ideas.

   One objection someone might make to the pattern model is that to be a model it must reside in the human brain. But I have said that pattern is not a model, but a way of living. So what would the pattern living people use their brains for? To see: the brain is an organ of sight. People do what all animals do with their brains: observe interesting connections in time and space: let’s call this vision in time as well as space ‘eversight’.

   A further difference between reason’s model and pattern is that rational thinkers believe themselves to be detached from the world they conceptualise about or observe in their experiments. But this detachment is always a pretence. Pattern people would have a focus of consciousness directed outwards, rather than inwards like rational thinkers. They would be curious about each other’s patterns, which would be shared rather than possessed, and they would be intimately involved in their human companions and in their surroundings. They would not be interested in a serious, moralistic, selfish, possessive or even altruistic way, but casually and for fun. Pattern consciousness would be about interconnectedness – a form of spirituality. But it would be quite different from the spirituality that is discovered through meditation, the spirituality that is called ‘the inward light’, which one could call ‘firesoul’. The pattern kind of outward spirituality could be called ‘watersoul’, to reflect a flow of transient mingling and merging.

   I like to think that I am watersoul. I feel that I am beginning a new human pattern which others may follow in the future. It was thinking about this possibility that led me to conceiving a pattern geometry.

I was intrigued that Bony Bailey used the terms ‘eversight’ and ‘watersoul’. Perhaps this was where Mother Sage had got them from, there being no words – in the ancient language sense – in the watersoul village people’s language for anything, let alone for their own nature. It was interesting too that Bony lacked the detachment of all the other mathematicians Mother Sage had contacted for the New Beginning. She wrote as a real person, which made me wonder how she looked. Mother Sage had experienced her through eversight, which meant from inside her skin, so she would not have seen her face – unless she saw her in a mirror, of course. Firesoul people had to have mirrors to develop their individual selfhood. In every room of the big house, there were shallow bowls of water to serve as mirrors for me to see myself in. I remember Mother Sage showing me myself when I was a boy: ‘See, there’s Roy in the mirror.’

   Bony called herself watersoul, so perhaps she looked like the village feys: lithe and slender with long thick hair. But Mother Sage had said that people usually cut their hair short in the ancient times. A servant has always cut mine. Men used to cut the hair on their faces close to the skin too, which village men do not do, but have long beards. I have too little facial hair as yet for that to be necessary. Mother Sage has very long hair, but she has it plaited and twisted around her head. That was a practice for older women in the ancient times, I believe.

   Perhaps Bony had permanent layers of fat – as Mother Sage told me many had in the ancient times – even more than the deposits the village people accumulate before the winter in preparation for hibernation. This was due to their unhealthy diet, consisting mainly of grass seeds and the infant milk from large animals they had tamed. And it was such hard work to get food that way that the people in cities had to employ many slaves to labour on the land, and to carry out food preparation. That is another reason not to cut down the forests when the New Beginning comes: so that there is lovely food from the gardens and forests.

   After a break for these speculations, I returned to reading about pattern mathematics.

The reason model includes the study of Euclidean geometry. The main characteristic of this geometry is that rigid bodies are preserved in all their properties as transformations are performed on them. So if a shape in a Euclidean plane, a triangle, say, is rotated about a point, translated from one position to another or reflected in a line, its shape, the lengths of its sides, the angles between its sides, and its area are not altered.

   Euclidean geometry is a firesoul pattern. As a pattern it persists. It is taken up readily by those educated in firesoul science, or the reason model as I have been calling it. But it also becomes part of the ‘common sense’ of all firesoul people. Of course, they say, a triangle stays the same shape and size if you turn it over or throw it across the room; unless it gets broken of course.

   But firesoul science, physics in particular, produces various ideas which suggest a reality full of bodies which are far from rigid and invariant. There are tiny charged particles spinning in a void, waves of electromagnetic energy, quantum fields which are particles and waves, bodies shrinking and getting heavier when they travel very fast, matter turning into energy. Surprisingly, none of these ideas caused Euclidean geometry to be abandoned; and rigid bodies are still common sense. Various other geometries have been devised: projective and non-Euclidean geometry, topology, fractal geometry, but only for specialists. Curiously, Euclidean geometry is generally thought of as two-dimensional, in spite of people believing they inhabit a three dimensional universe. No one really expects geometry to be like the real world, or vice versa, and yet they still think Euclidean geometry is ‘true’.

   A pattern-living person would need no conceptual model, but I need to understand pattern conceptually. Because I am a mathematician by training, I need to describe pattern mathematically. I know that Euclidean geometry will be useless to describe it. In the pattern world things are far from rigid, solid or invariant. Not even time behaves as the reason model assumes. In fact time is the very notion that has to be tackled first.

   Scientists are used to showing time as if it were space: draw an axis and label it ‘t’. Draw another axis at right angles and label it ‘p’ for position in all the space dimensions: lovely, just like the Euclidean plane. I do the same, but I use the whole of the plane for the present time, as if I am looking down on it.

   Now here comes the neat trick: what I see is not a solid time plane, it is discontinuous, full of holes. Through the holes I see other time planes, also discontinuous. They are stacked up, not an infinite number – pattern has no infinities – but there are plenty of them. Just to complicate matters, because pattern willingly accepts complexity in its models in order to let the world be economical, when I look through lots of the holes I am not seeing corresponding lots of locations in the planes below, but far far fewer.

   Of course I could, if I wished, draw a single line through my stack of time planes and call that the time line as the reason model represents it. That line has a tiny bit of validity as the direction of evolution or complexification, but it is not very useful, so I do not bother.

   I come next to what is in the holey time planes. I have used up three dimensions to represent my ‘plenty of’ time planes; there is no room for any geometric shapes in space dimensions. Fortunately, this is not a problem. I simply use my own intuitive model of how the world is and was, and put it ‘over there’, separate from the time block.

   I am making a big assumption in taking my own intuitive understanding of the world as how it ‘really’ is. But I am being economical with the world in doing so. Why invent an underlying real world, say one of particles, waves and forces, or an overarching ideal world, when what I know best is the world I live in.

   It may seem as if having the set of time planes and the world as it is and was is breaking the pattern principle of keeping the world simple. But reason’s model multiplies the world extravagantly by its model of time, in which the entire universe is thrown away with every infinitesimal instant of time that passes. Some versions of reason’s model, while struggling with a probabilistic quantum theory, even postulate multiple universes, representing each and every possibility, being thrown away every instant. In addition, reason’s model has an extra realm of existence: the one containing the transcendent laws of nature or science.

   But, you may argue, if my spatial universe includes what is and what was, I must have a universe for every instant too. But this is where the holes in the time planes come in. Each different pattern – leaving aside what precisely a pattern is – exists only once. Take a pattern completed in a particular time plane: that pattern exists in the time planes which span its lifetime, and nowhere else; but it shines like a sun into all succeeding time planes so that viewed ‘from above’, which means ‘as in the present’ for that plane, many many exact duplicates can be seen.

   An example will help. About three quarters of the way through the evolution of life on earth the eukaryotic cell emerged. This is a nucleated cell, which could reproduce sexually, and which made possible the explosion of variety and complexity of multi-cellular life forms which followed. By pattern theory, there is just one eukaryotic cell, complete in its eukaryotic-ness. Later eukaryotes include this one, not as copies or variants of it, but by holes in the time plane showing it as if copied, exactly or with variations. Any variations over and above the original exist in the time planes of the completion of each variation, and shine through subsequent holes to give rise to apparent copies. The billions, trillions, zillions of various eukaryotes in living beings in any present time result from the shining through time of the unique completed patterns existing in their own time.

   The pattern model described is not meant to suggest that one cell, of the many once existing, is ‘kept’, in memory as it were, to act as a model, and the rest pass away with the passage of time. The model asserts that there is and ever was only one – of each new level of differentness. Thus the pattern model is as economical with the world as possible.

   A pattern can be anything: an electron, an atom, a molecule, a simple cell, an organelle, an eukaryote, a multicellular organism, the behaviour of an organism, the relationships in an ecosystem, a planetary process, a human culture, a set of beliefs and so on. Every different pattern is based on patterns in the past, only what is different about it existing in its own time.

   Pattern theory does not include any mechanisms which make it work. All that is needed is the recognition that every pattern is aware: of itself in the present and during its lifetime, of the earlier patterns shining into it, of other patterns resembling it, of other patterns of which it is a part. Awareness includes the tendency for new variations to be slight. Most pattern, when viewed ‘from above its timeplane’ in its present, is past pattern, unchanged. New variations which do occur are not spontaneous and instantaneous differences, they arise from local circumstances and they occupy time, each has a lifetime and is compelled to complete itself.

There was a great deal more pattern mathematics, which I worked through gradually, and which often threatened to burst my mind, so different was it from what I had learned before. At the very end was some additional writing from Mother Sage herself. It seems that Mother Sage believed that part of her own self was identical with Bony Bailey: part of her was Bony Bailey shining through the holes in the pattern geometry. She called that ‘soul-sharing’. It seems that everyone shares soul: we are all composites, with very little uniqueness in each of us. Mother Sage shared the tiny part of Bony Bailey’s nature which was watersoul, but not the larger part which was firesoul. Since I am firesoul, I share that larger part, I suppose. And this is part of a common pattern of all firesoul humanity. I am all of them, and hardly at all myself. That is a hard idea for a firesoul individual to accept.

   Awareness of pattern – not in an intellectual, inwardly conscious way but in an outwardly conscious way – is a watersoul attribute. At Bony’s time, and earlier in necrotech, the only watersouls were those few people Mother Sage had told me about called fairies and witches. Were they mathematicians? I came to regard our feys as mathematicians. Twice each day I went outside the house with my gathering basket. Even with my limited vision, I could see that the productive gardens depended on an intricate and fluid geometry for their partnership with nature. Imagine being able to create designs in geometric spaces in multi-dimensional time! But Bony’s insights had approached such a vision – so it could be understood by a firesoul person sympathetic to watersoul ways. Surely that is what I was becoming. Perhaps then, there was a special role for me in the New Beginning. I could explain my concerns about big houses, and other destructive things which people had built in the ancient times. I could stop the village ways being destroyed, and help firesouls and watersouls to live together.

   I needed to test these ideas against real life. There was only one thing to do. I had to go to the village and see if, now that I was full grown, I might survive and be accepted amongst the watersoul people.

   But not yet. First I had to read carefully through every word of Mother Sage’s journal to prepare me for the role I would have in reverse of hers. She had had to sublimate her watersoul nature to live with me; now I would make adjustments to fit in with the watersouls. Hence it was several moon cycles from Mother Sage’s death before I ventured down the avenue to the village.

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