I was at a beach house in Santa Cruz the last few days with my family. While I was there I worked on some Q & A about the transfinite aktuals that I started thinking about a couple of weeks ago.
[Ocean reflections in the sea lion hole of the Santa Cruz wharf; those white lines are reflections of the railings. Looks amazingly like a CA.]
Q: What is the structure of spacetimescale?
A: The basic intuition is that reality looks different at varying scales and that interesting new features appear endlessly. You can zoom up or down, transfinitely finding unending novelty.
I speak of a spacetimescale continuum to indicate that scale is as fundamental a dimension as space or time. This follows if matter is infinitely divisible. For if there is no smallest feature of the world that can serve as a unit length, it’s necessary to specify the scale at which one is observing the world. There is no privileged lowest level to serve as the default scale. Therefore we need to work with the full spacetimescale continuum.
The Planck length (about 10 to the -35 meters) has sometimes been regarded as a lower bound on scale. But I prefer to think of the Planck length as simply a particularly interesting location on an endless scale axis. What’s above the Planck length is dual to what’s below—in the sense that we find equally many scale levels on either side. We can think of the size N above matching a reciprocal size of the order 1/N below. In my SF, I refer to the sub-Planck-length region as “the subdimensions†or as Subdee, and I call the creatures in this realm subbies.
I’m supposing that the scale dimension is transfinite in both directions. For instance, there’s alef-null and alef-one above and below I have 1/alef-null and then 1/alef-one. More than that, in keeping with my notion that space is an Absolutely Continuum, the scale axis is Absolutely Infinite.
We can call the beings up above the transfinite levels alefites. And if we push down to transfinitely small levels we have subalefites.
[I dialed up my camera’s ISO to 3200 and took this spooky night picture of the empty cottage across the street.]
Q: What are the bodies of aktuals such as the harp and the pitchfork?
A: I am writing about some transfinite beings called aktuals, where the name comes from Georg Cantor’s discussions of “aktual Unendliche†or “actual infinities.†The harp and the pitchfork are aktuals.
Rather than having my aktuals be transfinite in space or time, I’ll have them be transfinite in scale. A given aktual might be in contact with us and the subbies, also with the alefites and the subalefites.
To begin with, think of an aktual as a scale cylinder. By this I mean a bounded region of spacetime viewed at every scale up and down. My usage of “cylinder†here echoes the familiar geometric notion of a cylinder as a plane region that’s extruded into the third dimension.
I’ll suppose that the aktual’s body cylinders extend through every level of scale, that is, an aktual’s body is an Absolutely Infinite scale cylinder.
I think of there being an Infinity = Zero wraparound, as in my novel White Light. The wrap is at Absolute Infinity, also known as Ω, which wraps to 1/ Ω, which is the same as 0.
An aktual instantiates a wraparound of this nature. An aktual is a worldsnake Ourobouros biting his/her tail. So an aktual could, strictly speaking, be viewed as a scale torus rather than a scale cylinder.
[Stagnaro’s restaurant on the SC wharf. Kind of a Hopper scene.]
Q: Do aktuals overlap?
A: The scale cylinders of two aktuals have to overlap, for otherwise, there’s only room for one aktualized being on a planet, one aktualized cell in an individual’s body, and so on. If there were no overlap allowed, and if the harp and the pitchfork were to be distinct beings, then their avatars at any given spacetimescale cross-section would have to be an Absolutely Infinite distance apart.
This said, it may be that there’s only one aktual on Earth, at least to start with. This would be good for the story. It’s just my character Jayjay to start with; he’s different. And at the end of the novel Hylozoic, everyone gets aktualized, which leads to the third novel, Transfinite, of the series that starts with Postsingular in October, 2007.
A physical change has to happen during aktualization, your body has to actually match the patterning of Gaia and the patterning of at least one of your cells—although I suppose eventually all your cells could be aktualized to match you.
[Playing with the twins’ monkey blanket.]
Q: Say more about the limited intersection of an aktual with the spacetime of a particular scale level.
A: The harp and the pitchfork only intersect our spacetimescale in a limited zone.
These manifestations within our spacetime are incarnations or avatars of the higher aktual beings. Aktuals’ avatars are subject to the vicissitudes of cause and effect; they can’t walk through walls; they don’t have infinite intelligence.
The avatars don’t in fact know what the eventual outcome of their efforts will be. They hope that fresh regions of spacetime will aktualize in the near future. Their goal in visiting us is to promote these transformations. In fact the process works even though they couldn’t plan the details.
The aktuals have worldlines that form loops within the joint continuum of our Lobrane and the parallel world called the Hibrane. I’m thinking of closed causal loops for the sake of both tidiness and paradoxicality.
The higher self of the full aktual isn’t something accessible to any of its avatar cross-sections, save in an emotive way: an unspecific sensation of metaphysical profundity that has no actual content.
