OK, so I am a dunce, and I am making my way slowly. How about this for an eye-opener.
The symbology for iterated functions happens to be the same super-position we use for indices. That is
f^3(x |-> x+1) when x=2 is
f((((2)+1)+1)+1) = 5
This is neat when we consider the tentative thoughts we have made about indices and numbers of people, link this to versions of other people’s thought, and even link it to Bateson’s insight that ratio was a first order function, shouldn’t really be considered to be part of the number line in some way, and should be mapped on the i axis. Ok, I am bodging things, but I am merely making a note for myself. What is important is that this method of symbolic representation links up algebra, function, geometry, and a few thoughts we have traced through complex mapping of functions between eg tango and social organisation, or the versions of ideas we carry around in our head. That is, the models we carry around within the psycho-ended bit of the psycho-social dynamic, and how our different versions of eg “democracy” as they related to the complex social dynamic which is in existence supported by our actions.
This is inspired by this chris post. Incredible! I’ve always wondered how julia sets link to mandelbrot set visually, and here is this kid just exploring. Marvellous.