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. -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
