Name of a good poem. But what interests me is a system that can express the magic of life, by expressing the limitations of our own knowledge. I want to formalize the the idea of the Matrix (movie), the idea we shouldn't assume the existence of anything beyond our perceptions, we don't assume the existence of anything we haven't measured or observed. Sort of a neo-constructivism, in math philosophy terms.
What happens when we do that, I am discovering, is you get a "quantum-ish" system, where the act of a measurement, or an observation, or assumption - whatever term you use - changes the system observed in some way. In my system, which is based on a stripped down probability theory, a measurement collapses a probability density function, which existed as pure potential before that event. So the argument in the video in the OP, that there exists an unlimited amount of points between any two points on the real line, isn't true in my system, all that exists is the potential to specify some point in between, an event which becomes increasingly improbable as the gap between the numbers gets smaller. Its us who builds the numbers.
So as you can see, I'm thinking about seeing us as part of the system, as co-creators of the system. Because I think that's how reality really operates. If you go watching birds, you will observe them watching you. We are part of this universe, and that should be reflected in our symbolic reasoning systems.
I will read that blog eagerly. He is in a good space. I have this idea of scaffolding, the idea of using the old math as a scaffold to define a new math. But eventually the scaffold has to be taken down, and any system has to hold based on its own axioms. So in the end you can't define this thing in terms of Hilbert spaces, you have to end up defining Hilbert spaces in terms of this thing. I for one am not a good enough mathematician to do a lot of this, my focus is on a Duke's of Hazzard simple axiom set based on information theory that normal people could get, and seeing how powerful you can make it. If I had to choose between a system that can give a few geniuses deep insight into the universe vs. one that could give everybody moderate insight, as a small d democrat I'm with the latter.
PEace and thanks for sharing Tama, I love all your posts. 
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