A partition, e.g. the buckets, defines an equivalence relation which is transitive. Or is that what you said.
--- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Sun, Nov 8, 2020, 7:25 PM jon zingale <[email protected]> wrote: > Unless I am somehow forgetting some clever interpretation, I was wrong > about > the transitivity. > > Let me try to reason from an example: an experimenter defines a litany of > tests for deciding how well a collection of things can be relied upon when > treated as computational objects. For instance, an audiophile may have a > box > of capacitors that they wish to rank according to how well the caps filter > out hum without suppressing the dynamic range of the music. This process > defines a partition function on the box of capacitors. In a limiting case, > we can imagine having only two buckets, one with caps that are good enough > and the other with those that are not. In this coarse way, transitivity > holds because we either grabbed 3 caps that are from the *good enough* > bucket or we did not. > > What I think I found confusing has to do with the distance function d:: C_t > x R_t(H) -> K, with K some ring. Here, allowing the C_t param to vary has > the effect of allowing the problem dependence to vary, or as in the example > above, allowing the hum tolerance to vary. Fixing a problem domain fixes > the > C_T and this is rather instead like providing a space equipped with a fixed > origin. From that the more familiar distance function d':: R_T(H) x R_T(H) > -> K can easily be formed with nice transitivity features and all. > > Now that I am reoriented a bit, I think an interpretation in terms of > V-profunctors and the closed monoidal categories we discussed in the linear > logic discussions could be fruitful. In effect, the function d as defined > in > the paper is effectively a profunctor interpreted via a Cost quantale, > covariant in the Abstract category parameter, and contravariant in the > Physical category parameter. Dang, I hope some part of this makes any sense > :) > > > > -- > 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/ >
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