the improbable, yet elementary notes

active draft. a technical sketch. general, before special —alignment, before distraction

1. paradigm, measures, common measures, incommensurability

note: consider all set-theory as pseudo-set-theory; a means for a novice mathematician ¹ to express ideas in less time and space, than a similarly novice writer might, in prose.

all terms are tentative. corrections $\land \lor$ advice, welcome.

this reinterpretation did not begin as set-theory, nor does it depend upon it, however, it does appear to my novice eyes, to align nicely. wherever possible, i encourage an attempt to see past this particular, specific map, to the territory beyond, to which i am pointing. and a generous interpretation, to make up for inevitable mistakes of expression—these documents will be updated as necessary

note: subscript denoting type on anonymous set ok?

note: remember, this is a simplification, and an introduction

note: add Venn diagrams, perhaps?

note: while any two paradigms may appear incommensurable as an isolated pair, we will later discover that there exists a universally special paradigm, which by analysis or composition, renders all paradigms reconcilable, and as such, commensurable

2. map territory

note: this page implicates category-theory, or some other. to be introduced later

note: however, any map may be represented by another map, in which case the former is the territory of the latter; and maps exist in the universe, so when territory is considered the set-of-all universal phenomena, maps are included ²

*here, we will consider that maps are universal phenomena which are the product of interpretation ³; and as such, distinct from all universal phenomena which are not the product of interpretation, ⁴ *

so generally, and for the time being: for the map territory distinction: a map is interpreted representation; territory may be interpreted representation, or true ⁵