Ripheus23

Gödel coordinates

It is possible to use transets and operations thereon to represent an equation that maps onto the set of an ecograph's indices. For example, to represent the index of reduction, you take 0 [not the integer zero, but the use of the classical symbol of zero to represent a special transet function [related to the concept of integral zero]] to the power of 0 as many times as a reduction takes place. For example, the Form of Adventure's index of reduction is 1, so it is assigned the transet of 0 alone, whereas Apollyon's index of reduction is 3 so it has 0^(0^0).

For historical reasons, these are referred to as Gödel coordinates.

The color transet

Part of cartoglyphy, the theory of the color transet is that there are glyphic variations on the known semiotics of the transets grounded not in differences in iterations of shapes but also on variations in the colors used to draw the glyphs in physical space. Whether physical reality is intrinsically "greater" than the sphere of the aleph-numbers and their transets, is not known, so the theory of the color transet remains unproven in general [although there are some applications related to coloring problems in mathematics, that testify to a possible chromatic index for aleph-numbers; see also aleph-color.

• Aleph-color. The theoretical aleph-number whose internal determination of symbolic use involves colors. The idea is that colors are, in some strict sense, numbers, just like integers or fractions or irrational decimals, or whatever; see also Dorothy's staircase.
• Dorothy's staircase. Also known as Cantor's rainbow. Assuming that aleph-color is an n-aleph.n indexed transfinite number, it is possible to represent an exotic staircase using the transfinite variable z, and the transet of 0, in relation to the indeterminate glyphset for aleph-color. A large amount of contemporary staircase theory concerns attempts to prove the existence of Cantor's rainbow in such a way that the numerical index of aleph-color becomes apparent in the process. See also Munsell color sphinx.
• Munsell color sphinx. A bizarre ecometric (possibly metrometric) lifeform with the appearance of a sphinx whose head is not an ornamented human's but a physical-matter copy of the Munsell color solid. They can be found in the ecometric realm guarding mysterious staircase-demiplanes believed to be possible physical incarnations of Cantor's rainbow.