Here Madame Keyne took Pryn’s arm firmly. At another moment the gesture would have seemed simple friendship, but now it seemed protective. Caught up in a political massacre and menaced by a street hoodlum, Pryn could not help thinking that whatever danger still waited for her here was probably intriguingly minuscule. Indeed, it had much the same air about it as the scarred Fox’s straying hand – something that, however unpleasant, could be gotten through, at least with Madame Keyne’s help. Yet once it were gotten through, what might lie beyond it seemed just as great a mystery as the one her initial arrival had presented. For better or for worse, she found herself putting aside fear in favor of curiosity.
The red brick path they walked up was the one Pryn had mounted with Madame Keyne that morning. As they reached the sudden and surprising stone hut at the top, Ini finally shrugged away from Jade. It was only then that Pryn pulled her own arm from Madame Keyne’s and called ahead: ‘But why did you want to kill me?’
With her calm and questioning smile, Ini turned. ‘I saved your life yesterday.’ Suddenly she sat on the grass, locking her arms about her knees, swaying. Today I thought to throw a life away – yours? But why not.’ Ini frowned at Jade. ‘I told you I don’t like to kill women! I told you that. And you wanted me to do it anyway! But I didn’t care.’
Jade’s attention had gone from the Liberator’s headquarters behind to the cityscape before them. Now she looked back at Ini – whose eyes, over the same seconds, had fixed on some deliquescent city in the clouds, its destruction, before high winds undetectable here at the ground, hugely attenuated by size and distance.
‘I must talk to you,’ Madame Keyne repeated. ‘I must talk to you all. And I don’t believe any of you are listening.’ She lowered herself to the stone bench against the hut’s back wall. ‘But I will talk. It’s my own garden. That’s the least I should be allowed to do in it – to talk.’
Because she felt nervous, Pryn sat, too, on the grass – somewhat away from Ini.
Jade still stood – there was room for her on the bench.
Madame Keyne looked as if she expected Jade to sit beside her. But Jade swayed, nervously, looking at Ini, looking at the city again.
‘I am sending you away, Pryn.’ Madame Keyne said. ‘You understand, now, I must.’
‘Yes …’ Pryn nodded.
‘This evening,’ Madame Keyne continued. ‘You must go to the Liberator for me and ask him my question. When you bring me an answer, I shall give you a gold piece – or, at any rate, its equal in small moneys. A girl your age shouldn’t be showing gold about, trying to get it changed. Then I shall put you on the road again to continue your travels. Jade, Ini, do you hear? She is my ambassador to the Liberator – not my new secretary. And when she completes her mission, she shall go!’
‘She will really leave?’ Jade asked. ‘You really will send her away? Why can’t she leave now!’
‘If I do send her away, now – ’ The smile came to Madame Keyne’s face with another emotion that seemed more serious than either curiosity or amusement – ‘will you send away your Ini – ?’
‘Oh, Rylla, will you persist in … Oh, I can’t! I mustn’t! I won’t! You know how I feel about Ini. I would simply die if I had to – ’
‘Cease this!’ Madame Keyne half stood. ‘Cease!’ She took a breath and dropped back to the bench. ‘You do not have to send away your Ini. And I will send away Pryn, I tell you. This evening.’
Radiant Jade blinked about the clearing. ‘Then let me return to the house. I cannot stay here. I am exhausted by all this …’
‘While I, no doubt, am invigorated …! Of course you may go,’ Madame Keyne’s voice had become somewhat shrill. ‘Why should you stay longer? You have everything you want.’
‘I? I have nothing! And you would ask me to give up even that. You have all the power, Rylla. All of it. I? I only want one thing.’ She turned suddenly to Pryn. ‘I want you gone!’ (Pryn flinched – but from surprise; fear, as it seemed to have more and more these days, had almost left.) ‘And I want you gone now …! But I can’t have that, can I?’ She turned, listlessly, away. ‘So. Once again, Rylla, we shall do it your way.’ Jade walked off along the red brick.
‘Oh, yes! I understand!’ Madame Keyne’s voice went even shriller. ‘You are too distraught to hear anything I might have to say now! You’ve heard what you wanted to hear. Now you’ll wander off into your own fantasies which, in spite of all our attempts at sanity, we find ourselves conforming to more and more each day – ’
‘Please, Rylla …’ Jade said, not looking.
‘You have what you want. Why must you do anything else? Now you leave us with the responsibility of carrying out your desires – ’
Jade suddenly drew herself up and turned back angrily. ‘What do you want me to do?’
‘What do I want you to do …?’ Then Madame Keyne sighed. ‘I want you to do what you always do: whatever you want. You may go.’
Her anger again losing focus, Jade turned – again – to walk away on the red brick path, between shrubs, flowers, trees …
‘Madame Keyne,’ Pryn said after a moment, uncertainly, glancing at the still seated Ini. ‘I’m happy to do your mission for you. Before, I didn’t know whether you believed I could or not.’ She felt oddly distanced, almost light-headed.
‘Before,’ Madame Keyne said, ‘neither did I.’
Pryn frowned. ‘Are you … really that interested in the answer the Liberator will give about his allies?’
‘I am interested in the answer,’ Madame Keyne said. The question, however – no – does not interest me.’ She sighed. ‘But you must still go. At the far corner of my garden there is a break in the wall. I told Ini about it once, and I believe she has been working up her courage to try it. This evening, when it grows dark – ’
sIni suddenly ceased her rocking, released her knees, and said: ‘She is a silly woman, isn’t she, Madame Keyne?’
‘Jade?’ Madame Keyne turned on her bench to regard the seated murderess. ‘Oh, I call her that in anger. But not really. I don’t think she’s silly at all.’
‘She’s very upset now.’ Ini pulled her feet beneath her. ‘She’s very unhappy and confused.’
‘Oh, I don’t know.’ Madame Keyne shook her head. ‘No. I rather doubt it.’
‘You know how she feels about me.’ Ini pushed herself to her feet. ‘It would be best if I went to her.’
‘No.’ Madame Keyne mused. ‘Going to her now might not be the worst thing you could do. But it’s definitely not the best.’
Ini brushed grass blades from her hip, then turned off along the red brick. ‘I think, though, I will go to her …’ She strode off down the path.
‘I really think – ’ Madame Keyne picked up the knife from where she’d placed it beside her on the bench and turned it about – ‘our little Ini would like to be a caring person. But it’s so foreign to her nature, she can only imitate the gestures. And she’s bewildered at the idea that one or two such gestures might better serve the impulse behind them by being indulged only after reasonable forethought.’ She looked up. ‘Are you glad to be leaving us?’
‘I … suppose I am. Still, I wish I were leaving with more certainty as to why I had been brought.’
Madame Keyne put the knife down in her lap. ‘I shall make a bargain with you. I’ll tell you why you were brought here if you’ll tell me why you came.’
‘Why I came? But you sent Ini to bring me! And I was on the bridge with that man – ’
Madame Keyne raised her hand. ‘No, my dear. Those brutal and barbaric notions with which my secretary keeps order in my life and in hers may someday overwhelm our peaceful and placid civilization. Till then, however, we can admit that they are only stories.’ Madame Keyne frowned. ‘Or could it be that in the mountains around fabled Ellamon they believe that there are great powers and small powers and that the great ones always win and the small always lose, and thus smallness can be counted for nothing? No. Not if the fab
les I’ve heard about the weak and wondrous dragons are to be believed. My dear, sometimes I believe we shall soon lose all contact with magic. When that happens, civilization will have to be written of with other signs entirely.’
‘But what is this magic you are talking about again?’ Pryn demanded. ‘You said it was power. But you don’t seem very powerful now …’
‘And yet I speak of magic, claim to know it, claim to have it …’ Madame Keyne sighed. ‘Once I had a friend. Her name was Venn – one of those brilliant women from the Ulvayn islands. I met her here in Nevèrÿon when I was much younger. She had quite the most astonishing mind I’d ever encountered. I was rich and she was poor – but riches or poverty, neither one really concerned Venn. She traveled throughout Nevèrÿon and finally returned to her island. When I was older, I visited her there several times, and she took me around with her to see the tribes that lived in the island’s center, describing to me their ways and customs – she had lived among them once, even borne a son by one of their hunters. She walked with me at night by one of the famous boatyards where they build those ships that are the wonder of Nevèrÿon’s seas, pointing out over the fence which, among the skeletal hulks, were modeled from her own designs. On a rise above the island-edge village, her little shack was a storehouse of marvels. Once, when she was first here, she gave us a marvel to keep. It stays in this hut – oh, but that must have been thirty years ago. No, forty. Ah – !’ She touched her fingertips to her cheek. Bangles jangled to her elbow. “More than forty years ago – because I couldn’t have been fourteen yet. Really, she gave it to my father, though I’ve always thought of it as mine. It was back when this was the barbarian inventor Belham’s hut. I keep it in here.’ Madame Keyne suddenly stood. ‘Would you like to see it?’
‘Yes – !’ Pryn said, though it was, of course, the name of her great-aunt’s onetime friend that prompted her answer, rather than the divagation on the unknown island woman. Pryn stood and followed Madame Keyne around the hut’s corner to the inset planks. As Madame Keyne took a metal key out of her purse, Pryn’s mind tumbled with images both about her aunt and from her aunt’s tales. Madame Keyne inserted the key in the lock, turned it, jiggled it back and forth a few times, turned it again. She pulled. Grating on the stone sill, the door slid open. And Pryn, moving behind her, was momentarily sure, if only on the most tenuous evidence of a sign not even written but mentioned, that she would find within something of her home, if not her vanished father!
Of Models, Mystery, Moonlight, and Authority
The central thesis of this chapter is that usually, when we speak of ‘information,’ we should use the word ‘form,’ The scalar measure of information (e.g., energy and entropy in thermodynamics) should be geometrically interpreted as the topological complexity of a form … Thus energy appears as the complexity relative to the largest system in which the given system can be embedded, and is the complexity which retains its meaning in every interaction with the external world; it is the passe partout parameter and so contains the least information about complexity … Another example can be cited from biology: plants take in through their chloroplasts the grossest complexity of light, namely energy, whereas animals extract, through their retinas, the correlation of forms, or the information that they need to obtain their food, and thus their energy.
Let us now deal with the technical difficulties of defining the complexity of form.
RENÉ THOM
Structural Stability and Morphogenesis
Pryn followed Madame Keyne over the worn doorstep. Grilles high in the corners let in light. On a large table by one wall, Pryn made out what first looked like piles of something green; other colors, here and there, flecked about it. In the middle of it was a … house! … a toy house! Pryn blinked. And toy trees! And toy statues! Around it all ran a stone wall, about eight inches high.
Pryn exclaimed: ‘It’s … your home!’
‘And my garden,’ Madame Keyne pointed out. ‘And my wall. And my waterfall. And my bridge. And my fountains – watch!’
Madame Keyne went to the hut wall, where various containers and conduits were fixed. Standing on tiptoe, she checked if one were filled. She examined another, then pulled a small lever.
Pryn had gone up to the table’s edge. The model’s precision was, indeed, magical, as if one might find the break in the wall at the corner – or the rotten bars at the stream entrance. On one tree-shaded rise Pryn saw a tiny stone hut, a path of tiny red bricks winding up to it and a tiny bench against its back, its wooden door indeed set ajar, so that she had to imagine two diminutive female figures had just stepped over its threshold, one of whom, even now, at a miniature table’s edge, leaned over a tinier rise, atop which stood a tinier hut, its tinier door ajar, and over whose tinier threshold had just stepped –
A splashing made Pryn look up.
On the far rise, water sluiced through the arched grate (had the bars rusted through? The water covered them, and Pryn couldn’t tell), ran along the stream bed, moved out along the four brick-lined tributaries to fill one, then two more, then the last of the brick-rimmed pools.
Water reached the falls and broke on fish, dolphin, kraken, and octopus. It swirled the rocks between the banks at the falls’ bottom. As it swept beneath the bridge, one, then two more, then the last of the fountains at the bridge’s corners sprayed, left and right, into the little stream. Water wound by bowers and benches, beneath overhanging branches of shade tree and willow, around the house, divided in three at a stone clearly carved for the purpose, and rushed on.
‘Did your … friend make this?’ The delicacy of the model was as close to magic as Pryn could conceive.
Madame Keyne pulled another lever. A contraption on the wall, with angled paddles, began to turn. ‘No. This, actually, was made by Belham – he was the inventor of the fountain and the architect for many gardens about Sallese and Neveryóna, you know.’
Pryn breathed. ‘Oh … !’
Leaves on the miniature trees fluttered; miniature willow fronds above the stream began to flitter fishbone shadows over the water in the sunlight barred by the high grilles. Waves of darker green played across whatever had been used to imitate grass.
‘A map of the garden … ?’
‘Yes,’ Madame Keyne said. ‘You might say that. Did you see the fountains?’
‘Oh, yes! They work, too! That’s wonderful!’
‘Have you determined how they work?’
Pryn frowned. I just assumed that … up there, the water in those four pools runs down through some kind of pipes to the four fountains on the bridge below the falls … ?’
‘Can you say why the fountains spurt into the air – instead of merely dribbling out in an uninteresting spill?’
‘I suppose – ’ and, to be fair, Pryn had seen the fountains through the gates around the grounds of the Suzerain of Vanar’s High Hold and had even once delivered lunch to an uncle and cousin who had been called in with a work crew to repair one in much the same manner as Clyton had repaired Madame Keyne’s – ‘it’s because the tributary pools are so much higher. The water remembers its higher position and leaps up … to regain the level of the source!’ That is what she’d heard her greataunt say.
‘A good explanation! Almost the exact words of the barbarian who built it – so exact, I am tempted to think that brilliant and tragic man spent time in your own neighborhood. But no matter.’ Madame Keyne folded her arms, it was when Belham was building these fountains and working in this hut that Venn first came from the Ulvayn islands to visit my family. Belham had finished this model, but was still supervising the workers at the falls itself. He showed Venn his model, here; and she spent a long time examining it, coming back to look at it by herself, and generally playing with it when the barbarian was not actually using it for his measures. Sometimes she would go right from here to examine the bottom of the real falls down below. (Belham thought she was a very eccentric woman and often complained about her inquisitiveness.) Finally
she told my father, “I am going to build you something.” And she moved in here for several days, during which Belham fumed and stayed in the main house with us. After perhaps a week, she had built – ’ Madame Keyne turned away from the miniature garden – ‘this.’
Pryn turned with her, to confront the shadowy construct on the far side of the hut.
Madame Keyne stepped across the dusty flags.
Pryn, after a moment, stepped after.
On a stand, that put it about eye-level, sat a large bronze bowl. Leaded to the bowl’s side was a copper tube that curved down and around to end at the edge of another large bowl set on a lower part of the stand; the second bowl’s bronze rim came just below Pryn’s knee.
‘What will happen if I fill up the top bowl with water?’ Madame Keyne asked.
‘Water, I suppose, will run out the tube and down and around and into the bottom bowl.’ Pryn spoke with confidence but tried to preserve margin for any correction that might turn out to be the mysterious point of it all.
‘Just as in the fountain,’ Madame Keyne confirmed. ‘And, as with the fountain, the water remembers its higher position and tries to leap back up. However, you will notice that the tube leaving from the upper bowl does not leave from its bottom, as do the pipes from the tributary pools; rather it leaves from low on the bowl’s side. And in the bottom bowl, the tube end does not point straight up, as in a fountain, but spills in – also from the side. Now look more closely in the top bowl.’
Pryn stepped up to peer over the top bowl’s rim; it had been filled with some kind of plaster, from which a shape, with all sorts of grooves, gullies, and irregularities, had been gouged. The plaster had dried – it looked as if a single hand had, in one motion, scooped out the hollow.