Number series

We're all familiar with our culture's ideas about space, we all have the basic vocabulary: There's length, width, depth ... Almost anyone can see that this can be expressed as a series: space₁, space₂ ...
or, dimension₁, dimension₂ ...Let's not get into the trouble the Christian calendar did though by starting with one: geeks these days start with that Arab invention, zero:space₀
space₁
space₂Einstein got people thinking of time as a fourth dimension. Hawking and others have followed suit thinking that time and space came into existence together, rejecting any idea that a God or anything else knowable by humans preceded space. Prigogine broke ranks, assuming that time is infinite. I join Prigogine's break of rank (scoffing at Hawking et alia): space came into existence within time. Space is mortal, time is not.

You may agree with this, disagree with that ... No matter what we agree or disagree on, I further assume that the truth will still be the truth, no matter what we think or say. (Mortals! While we've got the chance! To spew symbols!) Regardless, get this: these _subnumber-series are handy, vivid ... They simplify, they teach.

Let's do spatial dimensions again, with a bit of care: First (that is, 0^th), there's space₀ (location), then there's space₁, length (or width, or depth), then space₂, width (or depth, or length), and then space₃, depth (or length, or width) ... and then there's time.

Except according to Prigogine (as thought about by pk) time came before space, so it actually should go:space_-1time
space₀location
space₁length
space₂width
space₃depthwith plenty of room for Klein's (or Kaluza's) multiply-more dimensions: dimensions numbering eleven or twelve (since the early Twentieth Century!)

I first noticed how neat such series could be with Gregory Bateson's presentation of Learning_N. Learning ₀ represented a species' genetic or inherited intelligence: the insect knows how to grow its leg, its eye ... the insect knows how to move its wings ... Learning ₁ for Bateson represented the kind of learning humans are so proud of, where baby learns to say "Ma," then "Mama," then "mother"; or we learn not to touch the hot stove again; or we learn anything not in our DNA which the phenotype may retain through life, possibly teaching the "thing" learned to family, friends, allies ... Now we know that Learning ₁ is not unique to humans: the bird learns to hold a stick so that termites will grab the stick and the bird can then transfer them from the termite mound to it mandible, and from its mandible to its mouth ...

Learning ₂ for Bateson was meta-learning, learning to learn: what geniuses do (in more than one species), what schools delude themselves to think they do. (Note: that latter point is Bateson's And mine; not just mine.)

So: here, theorizing Macroinformation, I apply Number_series to levels of metainformation, drawing careful analogy with space; but now, further, I've also been presenting pk cosmology in exactly such a series: Existence₀ ...

Note: when I say "category" I mean what previous philosophers mean, but also introduce new categories. When I say "level," such as in "logical level," I mean much the same thing. Ditto when I talk about sets and subsets. Read category, level, set ... as likely references meta-differences.