[FRIAM] stygmergy, CA's, and [biological] development

Mon Oct 25 02:21:00 EDT 2021

>
> On Sun, Oct 24, 2021 at 5:00 PM Frank Wimberly <wimberly3 at gmail.com>
> wrote:
> I want to clarify what a dual space is.

 The domain of dual.space can be mapped to any other domain  :-)

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On Sun, Oct 24, 2021 at 5:00 PM Frank Wimberly <wimberly3 at gmail.com> wrote:

> I want to clarify what a dual space is.  I think it is much more specific
> than Jon thinks it is.  A vector space is a linear  space which consists of
> vectors for which addition and scalar multiplication are defined.  Scalars
> are usually real numbers but may elements of other fields such a complex
> numbers.
>
> An important example of a (finite dimensional) vector space is the set of
> n-tuples of real numbers.  A linear functional on a vector space is a
> function defined on the set of vectors the into the set of scalars.  This
> is a (0,1) tensor on the space.  The set of linear functionals is also a
> vector space called the dual space.  The vectors of the original space
> define linear functionals on the dual space as follows:  v(f) = f(v).
>
> The only other dual space of which I am aware of is the dual topological
> space which Google tells me is
>
> In functional analysis and related areas of mathematics a dual topology is
> a *locally convex topology on a dual* pair, two vector spaces with a
> bilinear form defined on them, so that one vector space becomes the
> continuous dual of the other space.
>
> I am being very succinct and may not remember these definitions
> correctly.  Jon may be speaking "metaphorically" when he talks about
> pheromone trails being duals of ants.
>
> Anyway...
>
> Frank
>
> ---
> Frank C. Wimberly
> 140 Calle Ojo Feliz,
> Santa Fe, NM 87505
>
> 505 670-9918
> Santa Fe, NM
>
> On Sun, Oct 24, 2021, 1:05 PM Jon Zingale <jonzingale at gmail.com> wrote:
>
>> """
>> The problem for me with this view is that I don't understand how seeing
>> pheromone as 'organizing itself in space' is intuitively useful.
>> """
>>
>> I suppose that even if I didn't find this view *useful*, which I do and
>> will attempt to explain momentarily, I continue to find that it offers
>> a theoretical completeness that I find aesthetically compelling. Much
>> like magnetism and electricity can appear as distinct phenomena or as
>> two aspects of an integrated whole, stigmergy points to a similar duality
>> between agent and environment, another integrated whole. Lifting to such
>> a perspective offers insights into a class of possible implementations,
>> all preserving the underlying dynamics.
>>
>> For instance, when attempting to reason about the ant-pheromone system,
>> I find it useful to view the ants as inefficient *raster-like* update
>> to the state, but of course one could also choose a less brownian,
>> less resource-limited or less discrete approach. For instance, I believe
>> it makes the analysis more clear if we instead picture a continuum of
>> ants acting on the space and begin with pheromone of very little effect.
>> Then slowly turning up the potency, we begin to see the pheromone
>> organize and as a side-effect (and as an epiphenomenon from my view)
>> the ants follow suit. To view the ants as an implementation detail, for
>> me, yields clarity into the problem, while the pheromone takes the role
>> of first class citizens in the ABM.
>>
>> """
>> Toward the end, you wrote, "I only meant to emphasize that stigmergy
>> appears to me as a local concept." I'm not sure what that means.
>> """
>>
>> By local, I mean local as it often manifests in mathematics, but I
>> gather that you would prefer a different tack. Here I am referring to a
>> pair of related concepts for me:
>>
>> 1. Excision of glider's from Conway's game.
>>
>> 2. Characterization of subjectivities (one's subjective experience, say)
>> relative to objectivity.
>>
>> When one watches Conway's game unfold, it is challenging to maintain the
>> view that gliders are not agents but simply a local patch of board state
>> in the process of updating itself as a whole. The ease with which we
>> perceive gliders as agents facilitated the discovery of "glider guns",
>> and ultimately the construction of assemblages of "glider guns" to make
>> logic gates. Further, there is a smallest possible toroidal board such
>> that one can have a glider (and only a glider) walk along the surface
>> forever. The relation of this smallest board to any other board state is
>> (in my view) an analogy, an inclusion relation.
>>
>> Localization, here for me, is a way of bracketing the baby from the
>> bathwater while continuing to acknowledge that the meaning of both is
>> in relation to a whole. There have been a number of discussions on this
>> forum (and quite a few papers by its participants) where work is done
>> to emphasize the complications associated with non-trivial mereological
>> systems, systems of parts with non-trivial structural constraints. Two
>> recent papers that come to mind are:
>>
>> 1. https://www.biorxiv.org/content/10.1101/2021.02.09.430402v1.full
>> 2. https://arxiv.org/pdf/1811.00420.pdf
>>
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