There is this psychological type who satisfied with the potential for something to exist rather than actually doing or seeing the thing. In Meyer's Briggs test, its INTP: The theorist. Somehow that mindset permeated math too much with set theory, to the extent the theoretical objects diverged from observable reality, leading to absurdities like the infinite amount of points between .999... and 1, any one of which can never be specified or measured with a finite measuring device.
Those links are really interesting, I really enjoyed that pdf. Its the approachable writing style. Love it.
My thing has been to see if I can draw up working foundations with information theory, which means creating a lean mean version of probability theory from which everything can be derived. On reading that paper, I am pleased: The system I came up with makes all functions invertible, which was discouraging before I read that. What I'm doing that seems unique is really based on enshrining uncertainty at a fundamental level. The observer must be an integral part of the system. I'm also looking at the idea of independent random variables being equivalent in every way to separate dimensions in a space, and going really deeply into that. When you put all that together, you get a math which doesn't try to understand the universe independent of the observer, but rather as totally dependent on the observer: So inquiries into the nature of the universe are also inquiries into the nature of self.
My, that sounds hippy dippy doesn't it? Okay, example: A simplified baby's experience is represented as a two dimensional space, where one dimension is sound information events, one is visual information events. Because the two are independent, a probability density function collapse (aka information event) in sound - "mommy here!" is at first independent from visual events. But the baby's mind is learning, meaning that it is coming to a state where the vast dimensions of independent variables of primal experience are becoming correlated, to produce a space of lesser dimension in his mind. Eventually, the baby correlates the sound event with the visual event of seeing his mother, and maybe even tries to eradicate anxiety of not knowing and keep the dimension low by saying "mommy" himself at some point when she doesn't.
The point is that in a situation where the universe is described by invertible functions, the known and the knower are inseparable, and from one, you can get to the other. I think that's a beautiful thought.
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