Is the transfinite network isomorphic with mathematics?
Here we accept the formalist view of mathematics introduced by Hilbert. Richard Zach Hilbert’s approach formally distinguishes mathematics from the study of reality and sees it as like a game played with certain symbols and certain rules. The symbols cannot move themselves to implement the rules: all the action comes from the mathematicians (and their computers) manipulating immobile symbols according to the rules of their current game. The mathematics industry, like any other, thus comprises workers (mathematicians) who ‘do’ the mathematics and their mathematical communications which may be conversations, lectures, papers, books, models or any other means of mathematical communication. Although mathematicians are very prone to talk about continuous and infinite entities like lines and real numbers, all their communication is symbolic, that is finite and quantized. Everything that a mathematician needs can therefore be represented by finite strings of symbols manipulated according to f
