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commented on Context Changes Everything by Alicia Juarrero

Alicia Juarrero: Context Changes Everything (2023, MIT Press, The MIT Press)

#JuarreroBook Ch. 6 Interlude: Game of Life

We’ve had problems seeing what we're meant to be seeing in the book's examples. This week we drifted off to one of our own, Conway's Game of Life. I'd like to continue a bit with that. GoL is fascinating, and helpful in contexts such as ours, see web.ics.purdue.edu/~drkelly/DCDRealPatterns1991.pdf

So can it give us informative examples of constraints? Here 3 examples for discussion

1) general mathematical relationships that express possibilities/impossibilities with respect to patterns in GoL. These seem analogous to the threshold for connectedness in J's button example (we didn't reach a definite conclusion on that..)

2) variants changing topology and/or synchronicity of updating, please see here arxiv.org/pdf/nlin/0405061

these seem possible examples of 'context' and 'constraint' to me. The way I'm seeing these is as external to the fundamental entities (squares) and their interaction rules. None of that has changed. But tweaking the temporal synchrony of updating, or having 'gaps' in the topology, alters the possibility space/the behaviour of GoL

So how would we describe these? (in what way) are they 'real'? are they causal or causal like? what explanatory role do they play? are they context dependent or independent constraints?

3) (now hypothetical) Imagine there were timing or topology parameters that made glider guns much more likely (instead of the "labyrinth pattern"). Would this be an "enabling constraint"? Would we be missing something without such a notion (by just continuing to point to the individual squares and rule set)? Are glider guns a ‘whole’ that we need for explanation etc?

[discussion on GoL started here: social.sunet.se/@dcm/112372763988712787]

replied to Ulrike Hahn's status

@UlrikeHahn @uh @dcm in analogy to Gödels Incompleteness Theorem, Rosen shows that there are limits to any formalism and that semantics depends on the system of the observer (which is part of the context, the outer semantics) of any formalism. That is, Rosen extends Gödel's proof of the incompleteness of Number Theory, a foundation element of any formalism, to general System Theory. Rosen applies Set Theory, Group Theory and Category Theory to do that.

replied to Thomas's status

@UlrikeHahn @uh @dcm Applied to GoL, a formally complete described world (pure syntax), semantics arises from the context in which the syntax is applied, even if the context is also fully described by syntax alone, there can't be a formal proof that no other context exists where more, otherwise non-deductible, systems exist (the fact that a system is fully described doesn't entail the properties of systems outside the previously analyzed boundaries).

Does that make sense to you?

replied to uh's status

@uh @dcm @dcm @SylviaFysica

some thoughts on topological/spatial constraints of 2) and 3):

- they’re difference makers, but not causes (at least not at fundamental level which isn’t causal anyway) & they can *be* difference makers precisely because they don’t interact with the fundamental rules of the game
(those rules are deterministic and there’s no space for anything else to intervene, as it were); contextual constraints can be layered on top of one another and be more or less ‘hard’ 1/2

replied to Ulrike Hahn's status

@uh @dcm @SylviaFysica BUT for example 3 of constraints facilitating formation of glider guns, we get a constraint based modification of that property (runs with glider guns will tend to go on longer than runs without). BUT to explain the “still active” property I need to invoke the glider gun, I can’t just point to the basic rule set. I can point to the constraint itself, but it’s opaque, and no explanation seems possible (?) that doesn’t go via the intermediate, high level object…. e/