Thanks, Everett, for re-evoking this dropped thread.
I don’t see that PCT deals with point-like models. Please explain.
Temporal extent is essential. Perceptual input must change or it ceases to be perceived. This is one possible instigator of Warren’s postulated ‘novelty engine’.
‘Multifunctionality’, ‘computational saturation’ (eh? new one on me), polycomputation. Massively parallel processing. Yes, there is a one-many relation of error output signal to reference input functions (RIFs), and a many-one relation of perceptual input signals to a higher-level perceptual input function (PIF). However the fact of control constrains which of the parallel paths may be engaged in an active control loop closed through the environment at any one time.
The arts typically close loops through imagined configurations (‘concepts’ for example) concurrently with closing loops through the environment. Dancers studied the expressive movements of physicists lecturing about particle physics and developed them in ways that the physicists approved, Feynman diagrams have been essential for a long time, and a reorganization of the periodic table by Vaughan Pratt is deeply informative.
(Vaughan explains this more fully here, including a movie. “In five steps, HIDE, HUND, FLIP, BEND, SHOW, it continuously transforms the IUPAC Periodic Table to to what I call the Indian Periodic Table, IPT for short.” He shows how Pythagorean ratios in the table are related to the various analog proofs of the Pythagorean theorem with tangrams.)
There can be genuine ambiguity even in a loop closed through the environment. An example is the demonstration of counter-control with the rubber band demo where the subject controlling knot over mark is made to write letters or some other configuration controlled by the demonstrator. Clearly attention of the subject is limited to one while the demonstrator can concurrently attend to both and the subject has the possibility of noticing both (but for either of them as for an observer it is usually just one at a time although unlike the Necker cube one perception can be in peripheral vision). So from there we go to disguised intentions (deniability) and subconscious intentions (Freud, Jung, and many others). Investigations of hypnotic phenomena afford more explicit control to this (see Collected Writings of Milton H. Erickson).
Each elementary control unit (ECU) is in the environment specified by its perceptual inputs, and for it nothing else exists. In a system of cascading hierarchical control that means the perceptions passed to it by systems at the level below. Configuration-control ECUs do not perceive balls, mice, cabbages, and kings; ECUs at levels above the category perceivers live in a world of such configurations. (There is your touchstone of ‘observer’, perhaps.) The variables in this sort of environment are all signals controlled by control systems.
Bill drew a boundary around the nervous system, an interface with the somatic environment as well as an interface with the ‘external’ environment. Many of the variables in the internal environment are controlled by control systems which are not in the nervous system, and levels of neurochemicals are signals controlled both somatically (by other organ systems) and neurally (by neurons). In ‘The war of the sparks and the soups’ (book recommended by my wife’s neurosurgeon) Bill rather ignored the soups. And obviously there are also variables in the external environment which are controlled by control systems which are outside the skin of the person perceiving and interacting with them. As to that boundary, consider Bateson’s example of the blind man making his way down the sidewalk with his cane. Is the boundary at his fingers, at the tip of the cane, somewhere between? On to the surgeon using a Waldo, drone pilot, etc.
The analogy is not to computer code but to the elementary machine functions in a computer.
Here’s a reprise from 2021:Programming and PCT - #2 by bnhpct
All programming languages are merely human-friendly language-like intermediary forms which are transformed to these fundamental operations. The transforming is done by a compiler, by a (compiled) interpreter, or the like.Broadly, there are arithmetic operations, logic operations, and operations related to storage, input, and output. Those of greatest interest here are the Boolean logic operations, of which the primitive set are AND, OR, and NOT. All the other Boolean operators can be built from (or decomposed to) combinations of these.
Texts on this, on switching theory, and so forth, carry this down to switching of bits in bytes, at the level of machine code.
I abandoned this hapless project because there is such a mismatch between bit-switching in a digital computer and the analog interactions of neurons.
Paraphrasing in summary now:
The elementary functions in an analog computer are very different from the elementary functions in a digital computer. They are summation, scaling, integration, and multiplication of the analog quantity (e.g. rates of firing or voltages). More complex functions built from these include function-generating modules. Shannon specified a general-purpose analog computer (GPAC) with five types of functions, and this was subsequently simplified to four: adder, multiplier, integrator, and a unit which outputs a constant k.
There are various ways for an analog circuit to yield a digital or binary-choice value (as for categorial choice), such as a Schmitt trigger (comparator with hysteresis induced by positive feedback)Schmitt trigger - Wikipedia or Martin’s flipflop and polyflop structures.
So the question is to what extent the structure of PIFs is genetically determined and to what extent it is determined by (a) the environment of perceptual signals created and controlled at the developmentally antecedent level, and through the hierachy below by (b) properties of the environment beyond the peripheral sensors.
We can define a configuration as an invariant function of a set of sensation vectors, thus implying particular computing properties common to these different input functions: They abstract invariant relationships so that the third-order signals will change only if sensation vectors on which they are based change in certain ways. Kinesthetically, this might mean that a hand-body configuration would be perceived as the same despite varying levels of effort and despite changes in orientation of the connecting arm relative to the body. Visually, it might mean perceiving the separation of two points as constant regardless of the direction of the line joining them in space and regardless of the amount or color of illumination. (B:CP 2005:122)
This is a general-purpose function. We can define a transition as an invariant function of a set of configuration values so that the fourth-order signals change only if third-order signals on which they are based change in certain ways. A configuration is the same regardless of changes including rotation and translation. A transition is perception of such a change (singular) as such. Like a configuration, it has boundaries, a beginning and an end, but these are not temporal boundaries. Just as the boundaries of a configuration are made of edge perceptions, the boundaries of a transition are configuration perceptions. Indeed, there can be a transition from one configuration to another, though it is perceived as ‘the same’ albeit changed in shape (not so different from e.g. rotation of a configuration).
A relationship is an invariant function of two (sets of) configuration values; and so on. What differs is not the general-purpose analog function, but rather the inputs that are brought into a unitary signal by that function.
The primitive function of the cerebellum, analog computation for orientating the body and configuring it by orienting its parts, serves not only for perception and control of other physical configurations [objects] in the environment but also at higher levels of the hierarchy for non-physical ‘configurations’ [concepts] which can be represented by physical configurations such as tangrams and Feynman diagrams. The “invariant function of a set of” perceptual signals of order n defines a ‘configuration’ of them at order n+1. The architecture of the cerebellum seems fit for this, and all cortical functions seem to send signals on a loop through the cerebellum on their way to the thalamus and thence back up to the cortex. These pathways through the granular layer and the Purkinje layer could map inputs and outputs in both directions. I delved into this for my “Go Configure” presentation to the 2022 IAPCT conference.
I am going to have to concentrate intensively on the Achumawi language for the remainder of the month, which my NSF grant pays me to do; conference activities and householder responsibilities have interfered greatly with that and amends are overdue. Not to mention holidays coming. But I’ll try to keep an eye on discussions and check in later.