The last post to this blog dates back two month now. It dealt with my apparently favorite particle: the Pile object, and closed with the question, where does its z, which we will associate with the x- and y-coordinate at hand, come from?
One possible answer results in two different concepts of the symbolic. A symbol could be understood as a ’symbol for something‘ or as a ’symbol composed of something‚. Inside of a Pile system, x- and y-coordinates are composed of something (the z’s of two other such particles). At the boundary between inside and outside we construe the terminal values, whereas the values are connected to symbols for something outside the system.
Terminal values are the result of a morphism, i.e. a process joining ‚objects‘. This process joins a symbol for something and a mere number. Such a terminal value acts like a monad: the name of the beginning number of a series, from which all following numbers derived.
For example, in a binary world consisting of 0’s and 1’s, the 0 ‚is‘ a symbol for something (e.g. FALSE). Our morphism now joins this 0 with our first number, i.e. 1 (which has btw nothing to do with the 1 in the binary world outside). The 1 outside is a symbol for something (e.g. TRUE), and the 1 at the boundary of our system is a mere number, the name of the outside 0 taken inside of the system as a z (number).