The producer-product relation, and coproducers in systems theory

In appreciating the systems sciences, it can be important to appreciate distinctions around the producer-product relation and coproducers.  A system — which is conceptually bounded by observer(s) defining a boundary — does not exist independently of its environment.  A system may draw on inputs or resources in its environment.  Changes in the environment may be associated with reactions, responses or proactive reformation (i.e. changes in structure(s)) or transformation (i.e. changes in structure(s) and function(s)).

The most rigourous description of these distinctions is in Ackoff and Emery (1972), but this is a derivation of Ackoff’s original dissertation, and relatively difficult to read.  I happened across a more readable, and helpful summary in Ackoff (1981).

The Machine Age’s commitment to cause and effect was the source of many dilemmas, including the one involving free will. At the turn of the century the American philosopher E. A. Singer, Jr., showed that science had, in effect, been cheating.  It was using two different relationships but calling both cause and effect.  He pointed out, for example, that acorns do not cause oaks because they are not sufficient, even though they are necessary, for oaks.  An acorn thrown into the ocean, or planted in the desert or an Arctic ice cap does not yield an oak.  To call the relationship between an acorn and an oak ‘probabilistic’ or ‘non deterministic causality,’ as many scientists did, was cheating because it is not possible to have a probability other than 1.0 associated with a cause; a cause completely determines its effect.  Therefore, Singer chose to call this relationship ‘producer-product’ and to differentiate it from cause-effect. [pp. 224-225]

Singer went on to ask what the universe would look like if producer-product is applied to it rather than cause-effect.  One might think of Singer‘s question in this way: an orange, when sliced vertically, yields a cross-sectional view that is very different from the view revealed when it is sliced horizontally.  Yet both are views of the same thing. The more views we have of a thing, the better we can understand it.  Singer argued similarly about the universe.

As Singer and Ackoff and Emery have shown, the view of the universe revealed by viewing it in terms of producer-product is quite different from that yielded by viewing it in terms of cause-effect.  Because a producer is only necessary and not sufficient for its product, it cannot provide a complete explanation of it.  There are always other necessary conditions, coproducers of its product. For example, moisture is a coproducer of an oak along with an acorn.  These other necessary conditions taken collectively constitute the acorn’s environment.  Therefore, the use of the producer-product relationship requires the environment to explain everything whereas use of cause-effect requires the environment to explain nothing.  Science based on the producer-product relationship is environment-full, not environment-free.

A law based on the producer-product relationship must specify the environment(s) under which it applies.  No such law can apply in every environment, because if it did no environmental conditions would be necessary.  Thus there are no universal laws in this view of the universe.  For example, we have learned more recently that the law that everything that goes up must come down is not universally true.  (Unfortunately, some things that we have put up with the intention that they do not come down, nevertheless have done so.)  Environmentally relative laws can use probabilistic concepts in a consistent and meaningful way.  In an environment in which all the necessary coproducing conditions are not specified hence may or may not be present — it is not only meaningful but it is useful to speak of the probability of production. For example, we can determine the probability of an acorn producing an oak in a specified environment in which some of the relevant properties are not known. Therefore, the probability determined is the probability that the unspecified but necessary environmental conditions are present.  [p. 225]

To get further clarification, I referred back to Singer (1959) (which was edited posthumously by C. West Churchman, Ackoff’s doctoral supervisor and colleague).  More than two decades earlier, the ideas were explained in Singer’s Chapter 18, “The Producer-Product Relation”.  Part of the challenge was to understand “biocentric sciences” — which would include human social systems — in a way that is different from physics.

If the physicist’s argument for indeterminism is historically episodic and humanly limited in the public competent to debate it, not so the biologist’s, or to come at once to the general case, the “biocentric scientist’s”.  “The general case,” we say, for we recall a previous chapter to have subsumed under the generic term “biocentric sciences” a number of special studies of which biology was one.  Denotatively, these sciences are concerned with all that makes up the domain of life, its organs, instruments, social groupings.  Connotatively, they are concerned with no bodies which the physical leaves unobserved, but they recognize in the objects of their study properties the physicist disregards; namely, the properties called functional.  Now, the attribution of functional properties to the components of the biocentric world is world-old and world-wide; and the recognition of certain difficulties in the way of adjusting objects possessing functional properties to any kind of mechanical imagery is as ancient as human reflection on matters of common experience.  Of these difficulties, the principal ones may be noted in an anticipatory way, at least to the extent of giving name to certain traditional worries.  [p. 273]

First, functional properties seem to be as “inherent” in the subjects possessing them as are those structural properties, configuration, volume, velocity, mass taken by the physicist to be invariant with variation of environment.  Yet no account need be taken of these inherent properties, as data required for the physicist’s predictions and explanations — in short, for his adjustment of observational data to a mechanical imagery between whose momentary distributions a cause-effect relation exists.  How, then, adjust such observations of natural objects as recognize in some of these objects functional properties, to an imagery that has as yet no way of distinguishing the representation of an object that does from the representation of one that does not possess functional attributes?  [pp. 273-274]

In the second place, the constituents of a biocentric world seem to be subject to no such completely determining laws as are the points of a mechanical image, but what “norms” they do conform to allow them a certain indetermination, illustrated in the “spontaneity” of life in general, the “freedom” of man in particular. How can things exhibiting spontaneity of action, freedom of behaviour, be embodied in the details of a natural system that can be adjusted point by point to an image whose constituent points are completely devoid of functional attributes, and completely determined by law as to their changes of position and attribute?

Thus we come to a rough picture of the quandary in which the mind of the historic past has found itself entangled.  Without function and freedom, how give meaning to life?  With function and freedom, how conform life to mechanism?  Without mechanism, how relate cause and effect?  Without cause and effect, how understand anything?  Throughout a long past, the mind has tried numerous devices by which to resolve its perplexities.  None has received the sanction of any preponderance of thinkers; none shows evidence of growing in favor more conspicuously than its rivals.  It is left for each who sees the difficult to seek his own way of extricating himself.  [p. 274]

This leads to making the distinction between cause-effect and producer-product.

… the present study proposes to distinguish two relational terms ordinarily used quite interchangeably; the one a cause-effect; the other a producer-product relation.  [p. 275]

To begin with an example of the latter relationship, used in a sense our analysis intends to preserve — imagine the inheritor to an old estate points to a sizable oak, remarking that his oak was said to be the outgrowth of an acorn planted by his grandfather a hundred years ago.  With what conditions of mechanical imagery would his statement have to conform, if it was to be accepted as true?  That is, in what kind of mechanical image of the natural system of which this oak forms part, would one find two details, one, the image of that acorn, the other, of this oak, such that, of the two objects imaged, the first was to be recognized as a producer of the second; the second, a product of the first? [pp. 275-276]

Evidently, in a mechanical image of any “sufficiently closed” natural system in which a present oak and a past acorn had their respective places, the acorn would be represented in some detail of a point-distribution imaging that natural system as it was a hundred years ago; the oak, in some detail of distribution imaging the system as it is today.  Of these two distributions, the first would be cause of the second, the second, effect of the first.  Now, if between an acorn and an oak so imaged, a producer-product relation is to be recognized, two requirements will have to be met; under the determining law of any mechanical imagery to which that natural system is adjustable, the presence of that acorn image in the cause will have to be (i) a necessary; but (ii) an insufficient condition to the presence of that oak-image in the effect.  Thus, the grandson speaking in our example would be the first to agree that his statement could not be true, if either of two other statements were false; the first asserting that had his ancestor not placed an acorn in the indicated then-and-there, no oak would have stood in the indicated here-and-now, the second asserting that though his ancestor had placed an acorn at the time and place indicated, there might still have been no oak where the present one now stands. We are not asking, for the moment, what evidence the speaker would have to gather to confirm his belief that both these statements were true; but only, what evidence would have to establish, if his original statement was to be accepted.  [pp. 276-277]

We ask, then, what formal conditions would this mechanical image of a given natural system have to fulfil, if the acorn-image in the cause and the oak-image in the effect were to represent two natural objects, of which the existence of the first was a necessary but insufficient condition in the existence of the second?  To arrive at an answer, the present study follows a procedure which might be called, the method of virtual replacements (reminiscent of the principle of virtual displacements familiar to the literature of analytical mechanics).  A simple symbolism lets us follow the application of this method more accurately and more graphically than would an account couched entirely in verbal phrase.  Presenting the problem and its solution in terms of the acorn-oak illustration already before us, it will be easy to generalize the method and its result to apply to any two objects of which the first is shown to be the producer of the second.  [p. 277]

I’ll skip over the formalistic language, for a summary some pages later.

In terms of formal properties thus defined

the cause-effect relation is	the producer-product relation is
reflexive	non-reflexive
asymmetric	asymmetric
transitive	transitive
the relations cause-effect and effect-cause are mutually reciprocal	the relations producer-product and product-producer are mutually reciprocal

So classified, the two relations are seen to share all formal properties, save one:  cause-effect is; producer-product is not a reflexive relation.  [p. 289]

The language above can be unpacked so that:

• the cause-effect relation is reflexive, i.e. cause is necessary and sufficient (if and only if) to the effect; yet
• the producer-product relation is non-reflexive, i.e. producer is necessary but not sufficient to the product.

In the context of systems theory, the system and its environment can be coproducers of an output (and an outcome).  In drawing a system boundary, we don’t need to include every coproducing element inside … and probably shouldn’t try, as we could miss an element necessary to a product.

This ties in to a prior blog post where I had written (as point 4) that “An offering can be either an output of coproduction, or input into coproduction”, referring to (Ramírez and Wallin 2000).

References

Ackoff, Russell Lincoln, and Frederick Edmund Emery. 1972. On purposeful systems. Aldine-Atherton. [preview at Google Books]

Ackoff, Russell L. 1981. Creating the Corporate Future: Plan or Be Planned For. New York: John Wiley and Sons.  [preview at Google Books]

Singer, Edgar Arthur. 1959. Experience and reflection. Ed. C. West Churchman. University of Pennsylvania Press.  [preview at Google Books]