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Caspar Riga

Indexical Zero Theory

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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.”

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  1. Gkarlives's Avatar
    Out of context, this one is a little hard to follow and maybe a little to technical for your average SF reader. I couldn't winkle out what you were referring to other then number sets that may have some physical context, but there was nothing firm for me to connect with, just my thoughts.
  2. Queen Pandora's Avatar
    [I]GAAARRGGH!!![I] My brain's on fire!
  3. Caspar Riga's Avatar
    Brains on fire does not seem like such a bad reaction, since most of the theory pertains to fire engines. In the story, Dion, who is the chief of a reservation, has three talks with Benjamin and Yusuf. This was the final talk. The book mostly has normal conversations, but there is one thickset appendix at the end that should make clear how it all works. But then again, at the start of it, I strongly discourage the reader to read the appendix. Of course, it is meant to sound exotic, but it also has be consistent. I hope that people accept that Benjamin and Yusuf talk this way when they are going on about the garage, and that it is a kind of poetry.

    You can sample the book at , but I don't think you can sample the appendix.
  4. Caspar Riga's Avatar
    To see how readable it is, I've searched for the first occurrence of the word 'dimension' in the book. Here's the passage:

    “And the snozzle?” asked Marvin. A snozzle was the name for a nozzle on an airport crash tender, which could blast such a fine jet of water that it could pierce through the fuselage of a burning plane. Benjamin had fitted one that could cut with laser-grade precision. Marvin worried that he might have put a static charge on the water, which would not go well with gas fumes, but Benjamin hadn’t. He kept the jet thin by adding a sound to the water.
    “Now, as for daily maintenance,” Benjamin told the commissioner, “if another old mechanic, or an electro technician, tries to measure the torque, or read the current, tell him he should not look for the magnitudes, but the coefficients. Because those are the ones that change. Magnitudes just give errors. Or zeroes. Unless they bought their gear…”
    “…from Eddy Zero?” Marvin guessed.
    “Right,” said Benjamin, “then the numbers will appear as magnitudes, and you can track their compound dimensionality.”
    “Those are the revised numbers you listed in the maintenance log?”
    “Yes, and in the folder I gave you,” Benjamin said. As they stood up from their table, he advertised the fact that each year he had an option to buy four brand new fire engines, straight from the factory. Which he could equip with all sorts of alternative propulsion. Marvin made no promises. He took Benjamin and Dion to the hangar where the rigs were parked, and had them filled with water and foam, so he could test them outside.