#### Indexical Zero Theory

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, June 10th, 2012 at 07:30 AM (1142 Views)
Here's a glimpse of what I am about to publish to this week:

“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.”