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

Mon Oct 25 08:39:07 EDT 2021

What??  You right brain people are driving me nuts!  😁

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Oct 25, 2021, 12:22 AM Stephen Guerin <stephen.guerin at simtable.com>
wrote:

> 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  :-)
>
> _______________________________________________________________________
> Stephen.Guerin at Simtable.com <stephen.guerin at simtable.com>
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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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