Hi Gemma, Thanks for your generous comments!
"when people say that if there is symmetry then there is more structure"
Yes that is what we get from a physics education. I am saying that this is upside-down. It comes from a fundamental missunderstanding of the nature of mathematics, and perhaps reality itself. I only learnt about this from hanging around the mathematician James Dolan, he is the one that explained all this to me. When a physicist says 'spontaneous symmetry breaking', they should really be saying 'spontaneous structure creating'.
"I am also not so convinced that entropy and information are opposites to each other. I feel like they may stand in a more complicated relationship."
Right, I was using the technical definition of information, from Shannon's theory. Strangely enough the only place I could find that explicitly stated that "information is the negative of entropy" was from a quote by Norbert Weiner.
"you are basically saying that AI is based on inference" - yes
"David Deutsch has written an essay..." - This sounds interesting, thankyou.
"I agree with you that language, numbers, etc ... perhaps originated as maps, but they are so much more than that."
I guess this is the distinction between control and reason. Or the duality between syntax and semantics.
"the vector-based model of meaning in natural language." - yes
"the concept of energy: it quantifies everything that a physical object can become"
Ok, that's a very interesting way of thinking about energy. In my essay I tried to avoid writing about dynamics, energy, time, thinking only of kinematics. So many mysteries to ponder...