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

[Jon Zingale]

"""
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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