#transfinite numbers

[aromantic-ghost-menace]

How fucked up do you guys think it would be if one labelled the chapter number for moment of clarity neither infinity or "???" there, but just straight up "Chapter TREE(3)"?

Like fuck it! Let's not make it an implied high number you may be able to imagine or guess or even a vague far away abstract infinite one. Nope, let's just instead take one of the most absurdly highest numbers we could define, whose size is so absurdly big that you struggle to comprehend it, yet it is still a finite and specific number that does exist.

A transfinite number if you will.

Like have that be the case and just sit down and realize, how fucking high of a mindbogglingly number that is just digits wise alone, then realize that we're talking about the number of chapters and therefore worlds that are over now and just how much fucking time therefore had to pass to make it all happen.

And now understand that this is the scale conceptual gods like the long quiet and the shifting mound do effectively work with as if it was nothing, whether they do so consciously, subconsciously or not.

[noosphe-re]

In mathematics, transfinite numbers are numbers that are “infinite” in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.

Wikipedia

[robertsmithsonlibraryandbookclub]

Untitled Project: Robert Smithson Library & Book Club [Cantor, George, Contributions to the Founding of the Theory of Transfinite Numbers, 1955] Oil paint on carved wood, 2018

[mathisart]

Representation of the ordinal numbers up to  ωω

Ordinal numbers are a generalization of the natural numbers { 1, 2, 3, .... } that abstract the idea that numbers can be used to order collections of objects.  (This is in contrast to cardinal numbers, which abstract the idea that numbers can be used to tell size, or how many things are contained in a collection.)   ω is the smallest infinite ordinal; that is, it is the smallest number that comes after every natural number.  Likewise,  ω + 1 comes after  ω, and so on; after every ordinal of the form  ω + n for a natural number n comes  ω * 2, and so on as in the diagram.

[geopolicraticus]

Bergson and Epsilon Zero

The drawing above is my attempt to illustrate my intuitive understanding of Epsilon Zero, the limit of the transfinite ordinal sequence (although here conceived as an extension of how far we might go with the Banach-Tarski paradox). I wrote about this in A Visceral Feeling for Epsilon Zero. 

It occurred to me today that my crude drawing resembles a description of evolution from French philosopher Henri Bergson's once famous (now neglected) book, Creative Evolution.

Bergson opened chapter II of Creative Evolution thus:

The evolution movement would be a simple one, and we should soon have been able to determine its direction, if life had described a single course, like that of a solid ball shot from a cannon. But it proceeds rather like a shell, which suddenly bursts into fragments, which fragments, being themselves shells, burst in their turn into fragments destined to burst again, and so on for a time incommensurably long.

Bergson is, essentially, describing a fractal in this passage, though he doesn't yet have the term or the concept, which had to wait for another Frenchman, Benoît Mandelbrot.