This work does seem to be relevant, up to 𝜀-equivalence, to many of the fibers in recent threads :) As the authors point out, the question of deciding which diagrams 𝜀-commute is the business of experimental science à la EricC's commentary on the history of chemistry. Also, the ideas expressed in this paper appear to point in a similar direction to the (model-theoretic) ideas I was attempting to land in the *downward-causation* discussion from last week. Lastly, the thesis is related to questions of how extensional (or purely-functional) computation arises from the intentional (maximally-stateful) variations of a substrate. So, thanks.
𝜀-equivalence itself is interesting because it comes with a *competence constraint* that prevents it from being a transitive relation, that in general a =𝜀 b ^ b =𝜀 c ⊬ a =𝜀 c is crucial to the theory. In other words, while there may be a wide range of arm shapes that can be used as bludgeons, one can evolve themselves out of the sweet spot. Dually, the 𝜀-equivalence condition provides a route to modeling *exaptation*, via modal possibility. As p's belonging to the Physical domain vary, images in the abstract theory vary into or out of 𝜀-equivalence with values belonging to other problem domains. In particular, if we imagine that the R-map in the paper is *actually* a structural functor as it seems to imply, we can imagine another functor R' which specifies yet another problem space. Natural transformations then, up to 𝜀-equivalence, provide a model of exaptation. Because of the experimental nature of 𝜀-equivalence, I suspect we would slowly discover an underlying Heyting algebra which would extend to a topos via studying relations on sieves of 𝜀-equivalent structures. This approach would formalize *how far from competent* a structure is wrt *proving* a particular computation. -- 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/
