Great conversation, to which I can add little more than a few comments as I feel I am scrambling to "catch up", at least with the "fusion" of multiple things I already (thought I) understood but which are converging in this topic/discussion:
EricS wrote: > Steve, hi and thank you, > > Luckily, I actually was at that talk, so didn’t have to backfill. > > I don’t know what I think. I have been aware of Karl’s work through > various enthusiasts for it over the years, but there is such a > firehose of volume that I wasn’t willing to start, for a “free energy > principle”. I agree that it is good he talks about inference and what > I take to be causal reasoning in systems with feedbacks. > > I guess I would still like to hear the answer to the question Cris > Moore asks: what are you adding, Karl, beyond what Judea Pearl was > already doing by putting boundary states between interiors and > exteriors in Boolean networks, to define criteria of conditional > independence? I don’t know that Karl ever gave an answer to that in > which I saw a crisp statement of content. > > To the extent that I thought I roughly followed the talk, that > particular talk seemed to be concerned with what can be said about > steady states, and a kind of “holographic” manner in which the > dynamics either within or outside the boundary may be encoded in > timeseries of states on the boundary (the Markov blanket). I think this statement is the first time I've felt I penetrated this use of "holographic"... the dimensional compression as key rather than the pervasive distribution. As for my own understanding, I am used to thinking in terms of the plenoptic function *with* phase. I believe that holographic in this context is a subdimensional (e.g. 2d holographic plate) sampling of that field and the subsequent ability to reconstruct a little (or a lot) about the entire full-dimensional plenoptic field from that. The Markov Blanket seems to be a nice topological dual to the geometric (in holography). > In that respect, the idea seems similar to what the Chaos Cabal back > at UCSC (Farmer, Packard, Shaw, Crutchfield) did with “geometry from a > timeseries”, arguing, for example, that one could reconstruct aspects > of spatial structure in a turbulent flowfield from samples of velocity > at a single point in space, but over extended time. It does seem that > there would need to be some kind of trapping condition: that state > information not be able to flow to infinity at finite rate forever, so > that eventually any states however remote would get reflected back > onto the (finite, by construction) boundary. Thus the subdimensional sampling/collapse point above. I think the Chaos Cabal characterization of "geometry of timeseries" you bring up here is related to SG's dual-field (meta) theory in formation? > I have not tried to think carefully about what kinds of information > capacity limits should be needed for that to be possible, and it isn’t > something I have ever studied from those who may know a lot about > those questions. The notion of finiteness and “reflecting back” seems > similar to me, to the way total internal reflection operates in > Anderson localization. I don’t know what-all has been done to make > mappings between information dynamics on Boolean networks, and > continuum or peudocontinuum systems such as Anderson-localizing > insulators. Wow! Half a dozen ideas/references triggered here... topological/continuum duals... > I found Karl’s talk a bit frustrating; it did not have the feel of a > talk that was mostly concerned with presenting a tool and putting it > in the listener’s hand to understand and use. It was again the > firehose, with a sort of faux-bashful admission at the beginning that > he always tries to put everything he knows into every talk, and will > therefore not finish the narrative he starts. Too many strings of > notation without explaining how the reader should know what idea it > was after or how that was reflected in the notation. Having also > committed that laziness in talks, I am in no position to throw stones, > but listening to Karl makes me want to be more conscientious the next > time I have to present something. Is such a "lazy talk" not also "holographic" in the sense that the full complexity of the ideas is projected onto a set of slides and a verbal narrative (and a few gesticulations) for the "receiver" to reconstruct some subset? > But maybe it’s all okay. It may be that what he is doing establishes > a useful kind of holography principle, mapping currents and state > fluctuation statistics from a volume (which could perhaps be > indefinitely large) back onto the finite boundaries of interiors in > that volume. If indeed the whole state space is infinite, but the > information dynamics is trapping, then there should be some kind of > large-deviation behavior, such as occurs in reliable coding theory, > talking about how more remote volumes, carrying ever-less probability > to be occupied, will take longer and longer to have their > contributions to fluctuations in the overall state reflected back onto > any finite boundary in the interior. This equivalence-of/interchangeability-with a hyper-volume to a finite boundary (rather than a planar or similar, non-bounding) subdimensional is the crux (I think) of what i've been ignoring in the "holographic" metaphor in this context. I was being (overly) literal... somehow the complement to or contradiction-of Glen's accusation of excess meaning in metaphors? Maybe my overly *literal* binding *is* excess meaning in the mapping, though I started this stream-of-consciousness with it as a poverty-of-meaning (i.e. a non-closed surface when a bounded surface was required?) > > Any results of that kind, however, would probably be available only > for steady states. Dynamics would offer a variety of cases growing > exponentially in the volume, and I don’t see how they could ever be > tamed by projection onto a finite interior surface. As far as I could > tell, be only discussed the steady-state case in his talk. This is an open (in my mind) question which I look forward to hearing more elaboration of in this forum. > > Sorry I do not know how to answer anything of substance. It would > take a long slog through a lot of reading. Maybe someday…. I > wouldn’t want to discourage somebody else from doing it. Useful to me, even if my "reflection" of what I heard here might sound like incoherent noise.... I had to write it, even if I might not actually hit <send> before I hit <delete> > > Eric - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
