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

[Russ Abbott]

Thanks for the thoughtful reply. I regret to say that my mathematics sense
has declined to the point where I am unable to follow a lot of what you are
saying.

About ants, you wrote, in one view "ants are a thing and the pheromone
memory is not *in* them. I see this as a particular choice of basis, one
where a decision is made about what is or is not part of the ant and
what is or is not part of the environment."  This is the standard view.

"On the one hand, we can perceive the ants as performing a search,
but just as easily, on the other,  perceive the "search" as pheromone
organizing itself in space, (the ants playing the part of a local update
rule),
that is, one can argue that the ants are a function taking pheromone in
space back into pheromone in space. Such a process begins with
pheromone potentially everywhere and ends with it organized along
some geodesic."

The problem for me with this view is that I don't understand how seeing
pheromone as "organizing itself in space" is intuitively useful. In
agent-based modeling, only agents are capable of action. Ants are agents;
pheromone is not. But then, you aren't reversing these roles. Under this
perspective, ants are still agents in that they implement an update rule.
So as an agent-based model, it's now not clear to me what the difference is
between these two perspectives. I'm putting this in terms of agent-based
modeling since stigmergy is understood in those terms, and not in terms of
arbitrary mathematical functions.

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. Is it fair
to say that your point is that it is possible to express dynamical system
in mathematical terms and ignore the notion of agents? I wouldn't disagree,
but doing so loses the fundamental value of stigmergy, which has to do with
communication between agents.

-- Russ Abbott
Professor Emeritus, Computer Science
California State University, Los Angeles


On Thu, Oct 21, 2021 at 2:36 PM Jon Zingale <jonzingale at gmail.com> wrote:

> """
> I know these are supposed to be not-very-serious examples, but to take
> them at least somewhat seriously would you elaborate a bit? Let's focus
> on the bucket filling with water. Are you saying that this can be cast
> as a stigmergic interaction? How so?
> """
>
> Sure, though perhaps stigmergic-adjacent, like an automaton that is one
> stack shy of a Turing machine. I am struggling with your question for a
> number of reasons that I can only hope to successfully convey. I am
> guided by two related images:
>
> 1. The problem a flatlander faces when attempting to establish that they
> are in fact on the surface of a projective space, that locally all looks
> nice and flat, but bracketed "out-there" at infinity is an inaccessible
> "twist".
>
> 2. The observation that while a stream function and a potential function
> (ψ, φ) appear to be distinct, and spookily related, the picture is
> quickly clarified when one sees these two functions as different aspects
> of a single analytic function (φ + iψ)[∆]. For our purposes, I imagine
> generalizing ψ and φ to endofunctors on behavior. Some of what this buys
> is the wiggle room to allow the behavior spaces to be of different kinds
> than one another and for the duality not to need to be strict inverses,
> instead pseudo-inverses or adjoints.
>
> Consider the classic stigmergic ant-pheromone system. The *indirect*
> coordination of ants is mediated by pheromone *in* the environment. This
> is the picture of a system where ants are a thing and the pheromone
> memory is not *in* them. I see this as a particular choice of basis, one
> where a decision is made about what is or is not part of the ant and
> what is or is not part of the environment. I see this as a localization
> and a factorization of a complex whole. On the one hand, we can perceive
> the ants as performing a search, but just as easily, on the other,
> perceive the "search" as pheromone organizing itself in space, (the ants
> playing the part of a local update rule), that is, one can argue that the
> ants are a function taking pheromone in space back into pheromone in
> space. Such a process begins with pheromone potentially everywhere and
> ends with it organized along some geodesic.
>
> This point is usually a tripping point that leads to endless pedantry[!]
> in the form of asking whether or not the ants, themselves, lack memory.
> For one factorization of what an idealized ant *is* they have no memory,
> from another they do. A useless misunderstanding from my perspective.
>
> Moving on, let's take a lead from Nick and consider a thermostat system
> (or some other governor in its context). There we have the coordination
> of atoms in a coiled bimetallic strip with a switch that is hooked up
> to a furnace that vents into a room with the bimetallic strip...
>
> Again, we perform some arbitrary localization, placing the "twist"
> either inside or out, the twist here perhaps is the thermal capacity of
> the room acting like a leaky memory. From one perspective, the atoms in
> the bimetallic switch change their behavior indirectly, via the furnace
> and the room. Alternatively, we could have chosen to make *the agent*
> the furnace and made the following parallel:
>
> (termites)
> 1. Some termites build a little bit of mound here and then there
> 2. A mounding threshold is met, and then
> 3. A "switch" is flipped in behavior of the termites that follow, or the
> mound's form signals to future termites, and
> 4. The termites are now set to go off to do some other task.
>
> (furnace)
> 1. A furnace builds up the temperature in the room bit by bit.
> 2. A temperature threshold is met (via the coil), and then
> 3. A "switch" is flipped in the behavior of the furnace, or the coil's
> form signals to the furnace, and
> 4. The furnace is now set to another task (quiescence)
>
> More generally, I am not very clear on what makes stigmergy so special.
> My joke with the buckets is to suggest that nearly everywhere we see
> dynamical wholes, we can probably find a localization and a factorization
> yielding a stigmergic perspective. In the bucket case, I wanted to take
> a step further than the thermostat situation and suggest a non-leaky
> memory, a non-governing system, one where the dynamics clearly switches
> mode never to return.
>
> Apologies for this muddled rant, I probably should have taken a lead
> from Marcus and coded up some examples in a functional reactive style.
> Really, I only meant to emphasize that stigmergy appears to me as a
> local concept and that it might be useful to characterize the notion in
> the language of endofunctors and natural transformations.
>
> [∆]: https://math.mit.edu/~jorloff/18.04/notes/topic6.pdf
>
> [!]: In my earlier post, I wanted to throw a bone to the realists by
> suggesting that there might be something to the idea of privileging some
> bases more than others from the perspective of an induced computational
> complexity. It is easy to make termites without mounds and hard to make
> mounds without termites, a choosing of basis by optimizing a trapdoor
> pairing. I haven't thought this through very carefully, so maybe I
> should have left this part out, OTOH, a forum is a great place for pure
> speculation and gum flapping.
>
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