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The Szgany system?'
Yes.
'Do you mean, how do we count? But surely all creatures count the same?'
Not so. A bird has only two numbers: the number One and a number larger than One. If it has an egg in its nest it has an egg. If it has two eggs, three, or four, it has more than one. So how do the Szgany count?
'We count in fives, the number of fingers on a hand,' Nathan told him. 'We make gates,' (he showed the other a picture), 'like so:'
I, II, III, III The Thyre have the same system, Ethloi replied, but as for me, I count in Tens! The picture he displayed to Nathan's mind was of two gates struck through.
Nathan frowned. 'But that is simply a count of the fingers on two hands. Is there a difference?'
Oh, yes, the other answered. The difference is simplicity! Now look:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
The numbers he showed to Nathan were not these but symbols of his own, which had these values. Nathan studied them a while - sufficient that he understood that the last of these numbers was the equivalent of four gates - and shook his head. 'A different shape for every number? Simplicity? But this seems to me a complicated thing.'
Ethloi was frustrated (a great many mathematicians are), and sighed. But in a moment: Now tell me, he said, how do you divide?
'Divide?'
How many of these: I I, are there in this.'J.-H'T + I ?
'I I I,' Nathan answered at once.
And how many of these: J-H"T in this: III?
Again Nathan frowned. 'There are only parts,' he shrugged.
And again Ethloi sighed. As I supposed: you ca
It was Nathan's turn to be frustrated, and: 'I know enough to divide a large orange between friends,' he blurted. 'Because it has segments!'
Yes (the nod of a wise although incorporeal head), and so does my system. Infinitesimally small segments, and infinitely large numbers. Just as I count upwards in tens, so I may count down into the single unit. Into tenths, and tenths of tenths! But listen, about your orange: what if it has eight segments and there are only six friends?
Then two of them are lucky!' Nathan's thoughts were sour now, because it was beyond him. Already he was tired of this.
Ethloi felt it in him and shook his head. Numbers are not easy, Nathan. Oh, I could show you a great many -and a great many tricks to play with them, too - but without an explanation they are only symbols. Such knowledge won't come instantly but must be learned. And somehow I don't think you will make a good pupil.
'Show me some more numbers anyway,' Nathan begged him. 'So that I may at least consider them.'
Ethloi did as Nathan requested and sent his calculations rolling across the screen of the youth's mind. Decimals, fractions; a little basic algebra and trigonometry; calculations to determine the size of the world, the distance to the moon, the sun, and the stars. It was impressive, but it wasn't shocking. Nathan might not understand it, but he knew it for pretty rudimentary stuff compared with some of the things he had seen.
It did have something of an effect upon him, however; for as if conjured by this lesser display, now he felt the numbers vortex churning within his mind like some incredible mathematical dust-devil, just waiting to blast these intruding calculi to infinity. Ethloi detected nothing of the latter through his effort of mental projection, but he did note the Necroscope's unguarded thoughts: his apparent lack of regard for the display. And the images he transmitted to the screen of Nathan's mind were shut off at once.
Very welJ, Ethloi growled then, now Jet's see what numbers you have dreamed.
'Usually they come to me when I'm asleep,' Nathan told him. 'But my time here grows short. And when you produced your numbers for me, I ... I felt my own inside of me, almost as if they waited to be summoned.' He closed his eyes. 'Perhaps I can call them up.'
What happened then was ... swift as thought! The numbers vortex seethed with power; it sucked mutating calculations into its core as quickly as they formed on the rim; incredible metaphysical equations were fired in bursts from its rotating wall, like shooting stars in a meteorite shower! Until: Shut it off! Ethloi groaned.
Nathan did so, opened his eyes, said: That is what I have dreamed.' He took no pride in it; he only wanted to understand it, desperately. And Ethloi read that in his mind, too.
But how can you have such a thing, without understanding it? His question was in the form of an awed whisper.
'Just as I have feelings,' Nathan answered, 'in my heart and in my head, without understanding them.'
Ethloi nodded slowly, and said, Aye, and perhaps you have answered your own question. For as telepathy is in the Thyre - come down through the bJood of Gutawei the Seer, the First Remembered, and spread by his children, and theirs, throughout all the Thyre - so the numbers vortex is in you. It seems as much a part of you as your blue eyes and yellow hair. And spawned in some awesome ancestor, it came down to you the same way as they did!
'I inherited it?' This was much the same as Rogei had told him. 'But from whom? Not my father for he was an ordinary man.'
Then from that same ancestor who gave you your deadspeak, Ethloi answered.
'But my deadspeak is a talent while this ... is a curse!' Nathan shook his head. 'It plagues me! I can't fathom it!'
Ethloi was obliged to agree. Not a/1 inherited things are for the good, it's true. In me it was my father's poor hearing, which turned me deaf in the end, much as he was deaf before me. A small trouble: I had my telepathy.
The numbers vortex baffles you then?' Nathan was disappointed. 'You don't know what it does?'
What it does? Numbers are, Nathan. They don't necessarily do things. And yet... I sensed something behind it, yes. What it was, I can't say. Perhaps the vortex is a key.
'A key? To what?'
To a door, or to many doors. I sensed them there, in your mind. Doors to far, far places - even to far times! -all of which lie in the swirl of the vortex.
'But first I must understand the numbers?'
And control them! Ethloi nodded. When you can bring them to heel, like a hunting dog - show them ordered on the screen of your mind, as I showed you my puny figures - then the key will be yours.
Nathan was silent for long moments. Everything Ethloi had said was much as he'd long suspected. The numbers vortex hid a key which he must find. And then he must find the door in which to turn it. But as yet he was like a babe in arms who wanted to run before he could walk.
Ethloi remained silent, waiting.
And finally Nathan sighed and said, 'Perhaps you should show me some more numbers, and explain to me your system. I'll probably make a poor pupil, as you rightly said, but who knows? Something might sink in. Anyway, I have to start somewhere.'
He stayed for an hour until, head reeling, he could take no more ...
Nathan slept one more time, ate a strangely tasteless, silent meal with Atwei, then told the elders he was leaving. They came down to the river route to see him off. Quatias, who was still spry, volunteered to go with him to the next colony just eight miles away. But in a garden of yellow flowers, where hazy sunlight fell dappled through leaf and vine, he begged a moment's privacy with Atwei. She gave him a slender silver chain and a locket, which he opened. Inside, a tight coil of jet black hair. 'It is a custom of the Thyre,' she told him. 'A secret thing which siblings do when they are parted.'
He drew her to him and kissed her forehead. 'And this is how a Szgany brother parts from his sister.' Then he hung the locket round his neck and said, Til never forget you, and I thank you for this lock of hair from your head.'
'My head?' she said, lifting a coarse eyebrow. 'Ah, no, for that would be unseemly!'