[FRIAM] observability and randomness

[Jon Zingale]

Gisin's yapping is yapping about sequences, as are morphisms into Lawvere's
(Y^Nat, β) object. The onto-property of morphisms from X gives the tipping
point where all sequences from the perspective of Y are covered even though
X may be doing more. That Lawvere is constructing his objects in a category
of dynamical systems, he is talking about evolution of state. One of the
best treatments of control theory from a categorical perspective is in Arbib
and Manes. There, they construct observability and realizability via
free/co-free dynamics and highlight the connection the two concepts share
via duality. Similar to the point I was making about Markov being a matter
of perspective (model), while dynamics are not static in one frame they are
in another. I hope that I am not being too obvious while missing your point.
There are graph-theoretic interpretations of randomness as complete graphs,
where everything is connected to everything. One interpretation is that any
structure imaginable arises as a sub-object. Another, perhaps by assigning
non-zero transition probabilities to all the edges, would be that any state
is reachable from any other. I am not sure I am responding appropriately to
your post.

Could you tell me more about the lack of relation between river deltas and
the proposed mechanism? I remember you calling the theory LOUMFW, but I am
not sure if it is an acronym or what.

Glen says: "and "pulled a Jon" by starting a new thread while quoting from
an old thread 8^)."

Huh, it's kinda nice to have something named after me.



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