analog programming

[Bruce Nevin (20190817:12:10 ET)]

Bill proposed that beginning with the Category level and up through Sequence, Program, etc. the operations in the hierarchy are binary rather than analog operations. These are rather loose terms binary and analog, in my recollection of discussions on the net. Above his Category level, a perception is either present or it is not, rather than being more or less present. A sequence has occurred or it has not; an if/then test is true or it is not; a symbol or a word is present or it is not.

I believe that what was compelling to him about this view was that it helped him to imagine a place in the PCT model for symbols and language. What he wrote in B:CP predates our understanding of collective control, and it presents a narrow view of language and meaning. Language I have written of elsewhere, and will again. The field concerned with meaning is called semiotics. Semiotics uses terms such as sign, symbol, and icon. I’ll try here to restate some fundamentals of semiotics in terms of perceptions and perceptual control.

Semiotics claims two independent founders, the linguist Ferdinand de Saussure and the philosopher Charles Sanders Peirce.

Saussure proposed that the basic unit of meaning is a sign, which has two parts, the signifer and the signified. (These are translations into English from his French, of course.) The signifier is not the person doing the signifying as one might expect; in this technical sense, the signifier is the form of a sign. An octagonal, red, planar shape with horizontally across it the letters O, P, S, and T in a certain order is a particular combination of configuration perceptions (concentric octagons and the letters) and sensation perceptions (red for the central octagon, and white for the letters and border).

The perceptions that constitute the signifier (the stop sign) is associated somehow with the very different perception that one is supposed to stop at a location that bears a certain spatial relationship to the signifier. The perception that a location is designated, and that one is supposed to stop at or near that location, is the signified.

Peirce added a third term, making three parts of a sign. He distinguished (1) the signifier (the stop sign), (2) what the perceiver ‘makes of’ the signifier (the act of stopping), and (3) the collectively controlled perceptions that a stop sign designates a location and that upon seeing a stop sign one is supposed to stop there. He divided the signified into two parts: the socially agreed rule that upon approaching a stop sign one is supposed to stop (which we called the signified, above) and the controlled consequence, actually stopping when one approaches a stop sign, which Peirce called the interpretant. (He used the obtuse term representamen for signifier and the term ambiguous term object for signified. Doesn’t seem very practical for the founder of Pragmatism.)

Peirce said that anything is a sign if someone interprets it as meaning something other than itself, and he proposed that “we only think in signs”. Peirce further analyzed the signifier (the form of the sign) into three kinds. An icon physically resembles the signified (a photograph of a fire). An index is or physically resembles evidence of the signified (smoke is an index of fire, and an icon representing smoke may be an index of fire). A symbol bears no resemblance to the signified. The relationship between the configuration 9, the word “nine” and the number nine is arbitrary, collectively controlled, socially institutionalized.

The signified is a specific perception at a particular time and place; or it could be the memory of such a perception, and such a memory is one degree of abstraction. The signifier more abstract, in that it may refer to an indefinite number and variety of particular perceptions (or memories of them). I think that Bill’s thought that control at higher levels was no longer analog, over scalar values, was in part motivated by the sense that these variables are abstract.

A tangential point that would lead us into a discussion that I’ve carried on elsewhere: Bill also thought of words as symbols. Except in very constrained situations of denotation, they are not. The correspondence of collectively controlled language structures to non-language perceptions (observed, controlled, or collectively controlled) depends only in limited ways on the denotative association of word and object (to quote Quine’s title). End of digression.

So, stepping back a PCT pace, what is going on here? The driver controls the perception of her car slowing down and stopping at or near a recognized location. The driver perceives a particular combination of configuration perceptions and sensation perceptions (red and white) which she participates in collectively controlling as a ‘stop sign’. She controls a relationship perception between the latter perception and the location on the road toward which she controls the former. The stop sign is a collectively controlled perception. The relationship between the stop sign and the location for stopping is a collectively controlled perception. The sequence “see stop sign, then stop at the location that it designates” is a socially controlled perception that is actually codified in law.

These controlled perceptions and the cascades of control loops that control them are independent of each other. The person recognizing a stop sign may not be driving a vehicle. One can recognize a stop sign as such without controlling to stop (e.g. while looking out of the window of a restaurant). One can control the relationship between the stop sign and the location of stopping without controlling to stop (e.g. controlling a perception of someone else stopping while walking across the street, or observing that the stop line has freshly been repainted on the pavement). These are differences should probably be discussed in terms of the degree that memory and imagination play a role. There’s a lot that needs to be understood, but for present purposes I’ll leave it at that.

The notion of a Program level of control is explicitly modeled on the properties of computer programs. The logic of a computer program is in the form of arrangements of program functions and symbols. Bill identified the essential distinguishing feature of a program as a branch point controlled by an if/then function. (Other functions and idioms are elaborations from this; see Abelson & Sussman, Structure and interpretation of computer programs.)

In a program, a value is assigned to global variables at run time. In our terms, this is simply the perceptual input to an input function, creating a perceptual signal which may branch to different other input functions. During the run, functions may change the value of a given variable, with global effect in every program function that employs that variable. In our terms, such a function is a control loop affecting that perceptual signal, wherever it branches. Other variables are local rather than global, which corresponds to a non-branching signal (or branching with more limited scope).

A computer program has to have variables and the assignment of values to variables in order to do the work that branching connections do in the nervous system. A computer program has to have if/then/else functions to do the work that input functions, dendrites, axons, and synapses do in the nervous system.

A great deal of writing computer programs is done by invoking general-purpose program routines that have previously been written, tested, and collected in what are called libraries. The same routine might be used by completely disparate programs, with wildly different values for its variables. However, when the program is compiled (or interpreted) a structure corresponding to that library routine is created for the sole use of that particular program. In the implemented structure, the variables cannot be wildly disparate, they are restricted to those actually pertinent to the particular program use. The symbols are not as abstract as they appear to be when you are looking at how the program is represented in a programming language.

What is the PCT analog of the library and of the general-purpose tried and true routines collected in it? Is it a capacity of the reorganization system to ‘grow’ particular arrangements of branches and synapses? Before we consider that, we should have a better idea what those arrangements are, and how complex or simple they are.

Obviously, if/then/else tests for control of myriad perceptions are not performed by only one single neural structure. And yet we make these decisions and inferences in an ad hoc way on indefinitely many and unpredictably diverse perceptual inputs. So the simpler the neural structures involved, and the more simply and naturally they develop from ordinary sequence control, the more convincing our PCT model.

My talk in Manchester will develop an approach to these questions.