I am not totally sure why he considers discrete models to be unable to describe initial states or state-transition programming.
AFAIU, he considers them inadequate because they rely on an external interpreter, whereas the model of reality should be self-interpreting because there is nothing outside of reality to interpret it.
Wheeler suggests some principles for constructing a satisfactory explanation. The first is that “The boundary of a boundary is zero”: this is an algebraic topology theorem showing that, when taking a 3d shape, and then taking its 2d boundary, the boundary of the 2d boundary is nothing, when constructing the boundaries in a consistent fashion that produces cancellation; this may somehow be a metaphor for ex nihilo creation (but I’m not sure how).
See this as an operation that takes a shape and produces its boundary. It goes 3D shape → 2D shape → nothing. If you reverse the arrows you get nothing → 2D shape → 3D. (Of course, it’s not quite right because (IIUC) all 2D shapes have boundary zero but I guess it’s just meant as a rough analogy.)
He notes a close relationship between logic, cognition, and perception: for example, “X | !X” when applied to perception states that something and its absence can’t both be perceived at once
This usage of logical operators is confusing. In the context of perception, he seems to want to talk about NAND: you never perceive both something and its absence but you may also not perceive either.
(note that “X | !X” is equivalent to ”!(X & !X)” in classical but not intuitionistic logic)
Intuitionistic logic doesn’t allow X∧¬X either.[1] It allows ¬(X∨¬X).
Langan contrasts between spatial duality principles (“one transposing spatial relations and objects” and temporal duality principles (“one transposing objects or spatial relations with mappings, functions, operations or processes”). This is now beyond my own understanding.
It’s probably something like: if you have a spatial relationship between two objects X and Y, you can view it as an object with X and Y as endpoints. Temporally, if X causes Y, then you can see it as a function/process that, upon taking X produces Y.
The most confusing/unsatisfying thing for me about CTMU (to the extent that I’ve engaged with it so far) is that it doesn’t clarify what “language” is. It points ostensively at examples: formal languages, natural languages, science, perception/cognition, which apparently share some similarities but what are those similarities?
AFAIU, he considers them inadequate because they rely on an external interpreter, whereas the model of reality should be self-interpreting because there is nothing outside of reality to interpret it.
See this as an operation that takes a shape and produces its boundary. It goes 3D shape → 2D shape → nothing. If you reverse the arrows you get nothing → 2D shape → 3D. (Of course, it’s not quite right because (IIUC) all 2D shapes have boundary zero but I guess it’s just meant as a rough analogy.)
This usage of logical operators is confusing. In the context of perception, he seems to want to talk about NAND: you never perceive both something and its absence but you may also not perceive either.
Intuitionistic logic doesn’t allow X∧¬X either.[1] It allows ¬(X∨¬X).
It’s probably something like: if you have a spatial relationship between two objects X and Y, you can view it as an object with X and Y as endpoints. Temporally, if X causes Y, then you can see it as a function/process that, upon taking X produces Y.
The most confusing/unsatisfying thing for me about CTMU (to the extent that I’ve engaged with it so far) is that it doesn’t clarify what “language” is. It points ostensively at examples: formal languages, natural languages, science, perception/cognition, which apparently share some similarities but what are those similarities?
Though paraconsistent logic does.