[FRIAM] models, reality, etc.

[Eric Smith]

A person who works in data compression, randomness, or statistical mechanics might try to frame a description that is as operational and contains as much structural resolution in it as possible, by drawing language from the sectors of behavior and observation that are as robustly disambiguatable among people as possible. 

Main originators Kolmogorov (minimum sufficient statistics), Rissanen (minimum description length).  It would be about ensembles of the possible, the role of the actualized within that ensemble, and whether the actual can be partly identified by recognizing smaller ensembles in which it is typical, rather than starting with larger ensembles in which it is atypical by some criterion.  A description might run something like this:

1. The way the graphic is presented to the viewer (dots moving almost in lines on a deliberately blank and flat page) — taking into account that it was designed by people to make a point when viewed by people — suggests an ensemble in which the dots could be positioned anywhere (formalized in some model of randomness) and could over time trace any trajectory of their joint motion defined by nearly linear (inertial-looking) intervals with certain occasional nearly-angular reflections.

2. It happens that the actual trajectory of positions does not have nearly so much freedom.  It can be defined by maintaining four equilateral triangles the centroids of which are positioned on a rotating square, and the orientations of which rotate at a particular rate relative to the rotation rate of the square.  I don’t see right away whether there is some important relation between the two rotation rates re. tracing out the prism, or whether any ratio of the two rotation rates in some interval would produce a prism with the same topological properties and only different relative areas of the internal triangular panels.  (I suspect the latter, and also that if I weren’t so lazy, that would be easy to prove.)  It would be a little more interesting if some relative rotation rates produce “the most random-looking” motions of the dots, and in that way some combinations are special for their ability to fool the viewer by mimicking the usual computational models of random-ideal-gases-in-boxes.

3.  The specification of any trajectory within an ensemble of possible motions constrained as in point 2 is vastly shorter, involving only positions and sizes of four triangles, and two rotation rates, than the specification of a particular trajectory within an ensemble that allows any “random” trajectories in the collection suggested in point 1.  Although several different-looking patterns can be drawn on the resulting dots (only triangles, only squares, or only the prism), these patterns do not have fully independent information.  Each is a _function_ (mathematical sense) of the minimal information set identifying the trajectory, meaning that it adds no new information to what is already in that minimal set.  The fact that, if we draw triangles, we have four of them in a square, whereas if we draw squares, we have three of them on an equilateral, is a visual illustration that the same constraints are being expressed in either rendering.

My above list did not use the word “real”.  The operational description contained no role for an “observer”; it consists of defined relations of smaller ensembles within larger ones.  To the extent that there was any “observer” in the language, that was in the framing narrative that defends our choice to introduce ensemble 1 as an a priori model, based on claims of how people set up optical illusions and games to illustrate things to other people.  Whether or not that framing narrative is correct has no bearing on whether the ensembles _can_ be defined, or on our ability to state true propositions about relations between the sub-ensemble 2, the prior ensemble 1, and the specificity of the actual trajectory within either of them.  The various information measures in the ensembles do not depend on whether we choose to draw lines in the graphic to express different variable values in rendering the trajectory; that choice governs the interface between the properties of the ensemble and the consumption propensities of people looking at computer graphics, and could be considered to occupy a conversation in cognition and neuroscience.


I just got out of a starting conversational exchange with a philosopher of science who writes about emergence, and it has the same unhappy and inter-human fraught tenor as my above paragraphs.  Apologies for that.  I try to understand what ontologists believe their language carries, which is not carried in the more nuts-and-bolts language that they generally know but don’t think needs to be part of the discussion.  If we believed ourselves to be discussing the structure, oddities, and hazards of human perspective-taking, I could see their language as having descriptive value in that realm, but I think they believe it is not “only” that, but actually not that “at all”.  I think they are saying they are saying something else.  

I suppose what I am supposed to do is not worry about whether there are operational, structured languages enabling us to see clearly and speak systematically about what the dots might do versus what they do, and rather view the whole exercise as a metaphor whose elements are meant to stand in for some other relations in the ways we try to use conversation or choreographed behavior to arrive at something with reliability properties beyond those of our shifting and ephemeral perceptive gestalts.  Or maybe not that at all, and something completely different was supposed to be the point….

Eric



> On Jan 13, 2019, at 4:23 AM, Nick Thompson <nickthompson at earthlink.net> wrote:
> 
> Wow.  It's all those things at once!  
>  
> REALLY?!!!!!
>  
> What a great example!
>  
> Let me try and put it into words.  The nominalist would like to say “There is no real pattern there, it just depends on how you want to look at it.”  The realist would like to say, “Nonsense.  The patterns appear when you take into account the point of view of the observer.  Anybody who cares to take that point of view, adopt that procedure, etc., will see each pattern.  They are real patterns.”  
>  
> How do you understand it, Dave? 
>  
> Nick
>  
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Biology
> Clark University
> http://home.earthlink.net/~nickthompson/naturaldesigns/
>  
>  
> -----Original Message-----
> From: Friam [mailto:friam-bounces at redfish.com] On Behalf Of Prof David West
> Sent: Saturday, January 12, 2019 11:53 AM
> To: friam at redfish.com
> Subject: [FRIAM] models, reality, etc.
>  
> This popped up elsewhere and I thought the FRIAM group might find it interesting. I had not heard of "statistical equivalence" before. The GIF recalled to mind previous conversations about Reality (which is "real:" the dots, the triangles, the squares, ...?); models; interpretations (ala Copenhagen); even Nick's Natural Design.
>  
> davew
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