[FRIAM] observability and randomness

[∄ uǝlƃ]

I'm satisfied that river deltas are unrelated to the mechanism I proposed (LOUMFW). Since this is an entirely different subject, I've changed the title (and "pulled a Jon" by starting a new thread while quoting from an old thread 8^).

You mention the no onto mappings result from Lawvere. It seems to me that the lexicon of control theory might better get at the point. Observability is broken down into several sub-types, some of which are more natural to me (and simulation), like reachability and constructability. Gisin's yapping about far away digits *becoming* more definite or *changing* disposition connotes evolution, whereas the language in Lawvere connote static maps (albeit, maybe, with pathological shapes, bulbous regions that may only be reachable by wiggling one's way through little wormhole constrictions or somesuch). At least they connote that to me with tiny exposure to category theory and relatively larger exposure to control theory. My only point is maybe look to that body of work for something about observability's relationship to randomness?

On 6/23/20 6:30 PM, Jon Zingale wrote:
> For instance, in computational theory, recognition of a language by a
> machine offers a means of computing statements in the language. Machines
> are ordered by their capacity, and eventually, even Turing machines are
> limited to what they /can know/. In the section of Gisin's paper entitled
> "/Non-deterministic Classical Physics/", Gisin relies on a result from
> symbolic dynamics that I am continuing to work through. Effectively,
> the result can be summarized as saying that limited observability of
> chaotic dynamics /entails/ randomness[‡].
> [...]
> [‡] The clearest source I have for this at present is article 5, section 3
> of Conceptual Mathematics by Lawvere and Schanuel. If anyone on the
> list has further expertise or reference for this concept, your input will be appreciated.

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