Re: observability and randomness

Posted by gepr on Jun 24, 2020; 4:00pm
URL: http://friam.383.s1.nabble.com/observability-and-randomness-tp7597412p7597414.html

OK. Sorry. I should have assumed you'd already thought it through.

On 6/24/20 8:55 AM, Jon Zingale wrote:

> 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.

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