“So what about the two buttons on the right?” asked Dion, “do they also have an up, a down, and a still position?”

“Up, down, and normal. By normal we mean that it only reacts to what we do with the five other buttons. In the up position we go up the Pascal Triangle, line by line, toward the first simplex, until there is no line left, just the number 1, the only degree of remoteness known to the primitives. When an order or a grid reaches this top of the triangle, the magnitude or the formula space becomes one with the magnitude or formula space that is symmetrically the closest to it. In the down position we go down the lines of the Pascal Triangle. The oven is a limited universe and ours can only go up or down three-hundred-and-sixty-thousand-three-hundred-and-sixty lines, but it is still the best product on the market. We need so many, because sometimes…” Yusuf said, as he raised an eyebrow at the smile Dion pulled, “…when we bring a formula space to zero, some of the magnitudes flip to infinite dimensions and we have to catch them before they get there. What are you laughing at?”

“I was thinking that I will never get to hear about the set position,” the chief sighed. He emptied his cup. Yusuf thought he earned it.

“Okay. We use it to set a domain,” the born Iraqi said. “There’s three kinds: those with only powers of mass, or only powers of length or of time, those that are a combination of two, and of course we can set a domain that is a combination of the three. The point is that we create them from zero, and they push up whatever domains are already in the oven. So if we create a domain of two mass dimensions, all the others will have gone up two dimensions of mass, but they have kept their own dimensions. So a zero dimensional formula space is still zero dimensional, but this zero is now two dimensions up. We call it an indexical zero because we can point at the second dimension of mass with our index finger and say a zero resides there. Anyway, the created domain is below this zero, and this has as a great advantage that both ranked and filed magnitudes can drop below zero. You see, intersections cannot grow bigger than domains, nor can they get smaller, but they can go below zero and domains can’t because they are absolute.”

“Yes, Benjamin said so,” the chief knew. “The domain is the span between the lowest negative and the highest positive, and the two are added to get the span, not subtracted.”

“Right. So, in short, we have jacked up a zero dimensional formula space with, say, a combination of mass and time, and then we use the intersection button to make separations so as to let the magnitudes sink into our new domain. But because length is missing, not every magnitude can sink into the domain and these exceptions will stay zero. That is basically how we single out a magnitude. We may be looking for a magnitude that makes it inside our domain or one that stays outside, but basically, we can single out every magnitude in no more than seven or eight steps.”

“So you put a bucket under the horse and see what drops?”

“Basically,” Yusuf chuckled. “We actually make a whole stack of domains beneath the formula spaces, each filtering what comes out of the one before it.”

“Like a distillation plant?” figured Dion.

“Sort of.” ]]>

Tehuti wanted to chase the hound away, he smelled of death, but Atlas had said he had to be welcome somehow, or he would not have shown up inside the fence, so the elf just circled him once or twice. At one point his jaguar tail touched the hound, who had a suit and upright build, and the elf could sense something he had never sensed before. The hound belonged to someone. Not like a love or a slave, but like something that truly belonged. What he sensed was that the devil belonged to God, whom he had never heard of, since the children of man did not share that kind of information. Intuitively he said:

“You belong in a garden, but not in Andai’s garden,” and as he said it, he knew whom he was circling. This was also an inventor. “Are you the inventor of death?” he asked the hound straight out. El Djha’athangh, as he was called in this respect, ‘the angel who occupies himself with death,’ had to laugh a bit and his mind shot through the sedation, which had kind of worn off when he had chased the elf earlier. He was careful. Either the elephant or the jaguar had experienced some deep insight into the numbers, one he could not afford to miss, but the creature probably wasn’t aware of it yet. Yet he was on Earth, so one wrong word, and God would show.

As I wrote this, I realized that it was all from the second book; in fact it appears, now that I've been blending them for a week, that I am keeping most of the first book, and rewriting most of the second. But that will change halfway through the roadworks, when I am going to paste a whole chapter in. Anyway, as a new property to both the stories, the devil now actually has something to say. Tehuti (the hero of the story) finds out he laid this claim on Andai's garden (the devil being stolen from a garden himself) :

‘I pay a fool’s price. With the stirring of the stars, when the green comes up, I state the taxes according to the ground level. Given this term, I calculate the tax demand in March, at which point I brush through my hair and state the top sum. Do not worry; I have equal rights. Whose name it will fall on, says little to me. What concerns me is a simplicity in the matter of rights. Whose payment occurred here, will yet hear from me. I folded back from my rights, but I already have everything taken care of.’

Point being that the devil taxes the future. Will there be enough future left in my story? Enough for me to wonder. ]]>

“The half dimensions?” asked Deborah. She still seemed really interested. And she was. She only had some trouble understanding him because she thought there were only four dimensions; three of space and one of time. Carmine told her:

“No, not the half dimensions. Those have been a given ever since Maxwell listed them almost…or over…a hundred-and-fifty years ago. No, the other fractions were new. One eighth of a dimension and five sixteenths. The colonel taught us that what we had been doing in the motor pool was recreating the engines until the magnitudes had the dimensions we wanted. Maybe that is not odd to you but to me, who had some basic training, it sounded like nonsense. Magnitudes had set dimensions, and these were listed, like those magnitudes that Maxwell listed. He listed the electromagnetic magnitudes, did I say that? Those are the halves, or as we say: the roots. So we learned that in fact these dimensions could be shifted and that energy could have the same dimensions as force, and force the same as energy. A whole new world opened up. We listened with different ears. Yusuf was interested in the colonel’s quantum mechanics, I liked the classical approach. He taught us that for every principle detected, certain other principles, due to the way they are derived, must always appear on neighboring dimensions.”

“On neighboring dimension? Not in?” Deborah asked. Her tone was not very serious.

“No, you should see it as a table or a grid, we call it a formula space, that numbers the dimensions. We say we number them by their powers. So we rate something at or on a certain number of dimensions. And once we have rated one kind of principle, we know the other cannot be far off. ”

“Alright. And the dimensions are mass and length and time?”

“Yes, love. So a so-called least action principle was to be found one dimension away from a principle of the conservation of energy. He also taught me how to make it appear at a fraction, or a manifold of that one dimension. And then he showed us the method we had actually been using. He called it Indexical Zero Theory.”

“You lost me.”

“I know. It argues that if any magnitude may become any other, it may also become dimensionless, which was the basis of transposing forces, which is what I do.” ]]>

It is sometimes hard to throw the pearls away, when you know you have to, because after going through the logic you really find that a button should point up instead of down, and that the beauty came from a mistake, like I had yesterday, when I assumed ranked dimensions when they were rankless. By the way, the concept of a ranked dimension is just an impression I got from studying real math, though I do this just for fun. I suppose an actual mathematician would know the real word for what I call rank. Anyway, I managed to rewrite the button and the rank, and I reached the same kind of beauty only because in my mind, after seven or eight proofreadings, the whole theory has crystalized. To the extent, apparently, that even the mistakes are beautiful. ]]>

"Yes, the intersection between entropy and temperature."

"Fine, and the fifth button also has three positions," said Dion. It was all coming back to him. "One is OFF, which is for the whole oven, and if the oven is off it has the infinite dimensions of the universe. Another position is CLEAR, and in this position you raise and lower the dimensions of the domains in the oven with the first three buttons, or the intersections with the fourth button. And in the SET position, you can create a fixed domain or a fixed intersection, but you did not tell me about the SET position, because you were telling me how you rid the magnitudes of their ranks, and you did that in the CLEAR position."

"Okay. Except that I must have called the intersection button the fifth, and the off button the fourth, because that is what they are on the oven. So do you remember how I break the ranks?" ]]>

"Yes, the intersection between entropy and temperature."

"Fine, and the fifth button also has three positions," said Dion. It was all coming back to him. "One is OFF, which is for the whole oven, and if the oven is off it has the infinite dimensions of the universe. Another position is CLEAR, and in this position you raise and lower the dimensions of the domains in the oven with the first three buttons, or the intersections with the fourth button. And in the SET position, you can create a fixed domain or a fixed intersection, but you did not tell me about the SET position, because you were telling me how you rid the magnitudes of their ranks, and you did that in the CLEAR position."

"Okay. Except that I must have called the intersection button the fifth, and the off button the fourth, because that is what they are on the oven. So do you remember how I break the ranks?" ]]>

For updates on the book ]]>