The principle of paradox we call to be followed by any statement that uses semantic identity (a) to state syntactic contradiction (≠) and thus creates a pragmatic puzzle: What to do? The principle of ambiguity states the possibility of contradiction, as in any kind of dialectics. And the principle of control states that there is only one way to check for the identity of an a, which is to compare it to itself, as one is as used to do in double-entry bookkeeping as in computer sciences.

This might be called a Parmenidean instead of an Aristotelean grounding of logic if we follow Heidegger’s 1942/43 lecture on Parmenides, which tries to show that Parmenides’ notion of aletheia in fact proposes of notion of truth based not on correspondence but on agon, that is, if I may read a little freely, based on conflicts inside facts, among observers watching them, and between moments of time each of which stresses different aspects of the so-called fact.

Why might we be tempted to do so? Or, better, who might be tempted to do so? Well, a sociologist might be tempted to start this way because the only robust empirical fact he knows of is the fact that at no time in social discourse a fact is considered identical to itself. Two observers, two moments of time are enough to call forth distinctions in any fact that turn it different if not opposite to itself. Think only of men and women, young and old, novice and expert, teacher and student looking at the ‘same’ thing. There is no reason to call this, as Greek philosophers were likely to do, a corrupt state of affairs, which by considerate reasoning and sophistication could be turned into a perfect state of affairs where A = A. Indeed any reasoning and sophistication demonstrated by a Greek philosopher, first of all by Plato, showed that the seemingly corrupt state of affairs in fact is the emirically rich and instructive state of affairs.

Sociology, or, let us say, sociological theory indeed starts with the insight that there is no possible assertion or proposition in the world, which does not exist in a Yes- and a No-version, as one may answer any sentence with its opposite. Niklas Luhmann based both his theory of language on this fact as developed his principle of the functional primacy of negativity out of this fact. In human language and knowledge negation, not position comes first because the negation is logically richer since by saying that a ≠ a it states a and asks for what it may be if it is first syntactically, then pragmatically and eventually even semantically not itself. One sentence states a fact and the world it is related to, if only by negation.

A fact, thus, comes about only by negation of negation, by aligning the observer’s perspectives of ego and alter ego, and by investing irreversible time with reversibility. Thus, all three dimensions of meaning conceptualized by Luhmann, as they are the factual, the social, and the temporal, must convene and do not have to convene to call an entity or unity identical to itself.

George Spencer-Brown in his Laws of Form (1969) proposes an elegant way to write down an identity as the negation of itself:

And he proposed to interprete negation not as antinomy or contradiction, but as implication. a negated implies b:

Both propositions taken together let us define any a as being its negation within its implication of a b or anything else, which is not a. This means that a is the re-entry of itself negated by itself in order to imply something else into itself. This sounds complicated but means nothing else but definition of identity by oscillation:

If we consider the possibility not only of a mathematically unambiguous but also of a linguistically ambiguous calculus, as any sociologist would prefer to work with, we may define the social form of a by being what it is in the context of a meaning fixing it as such:

Meaning in turn, considering our Parmenidean beginning, consists of the consideration of possible negation, of the difference of the perspective of the other, alter, and of the flow of time in any future changing future into an unkown version of itself:

Three re-entries turn a as indeterminate as any sociological theory of knowledge would like to have it. We call this a calculus of a because it describes that any a is only itself if all three possibilities to negate, alter, and evolve it are checked for.

This calculus is the condition for any form of a to be found, which determines a with respect to fact, a certain culture of agreement and certain time horizons convening:

Following our Parmenidean beginning we propose the general thesis that any a proving to be robust in human knowing must first, and by that human knowing, be turned indeterminate with respect to, and by reflection on, fact, culture, and time. As formalized by Spencer-Brown re-entries fact, culture, and future are non-linear oscillators brought about by second-order observations with respect to negation, alter ego, and future.

This gives us our first catject:

Note that this does not assume aims or purposes to assure organization. As Karl E. Weick had it in his Social Psychology of Organizing (1969, 1979), sharing of means is sufficient. Organizing is done among loosely coupled, distributed, and heterogeneous elements. Hierarchies may help, but networks are more important.

We may distinguish three steps in the development of appropriate models of organizing, going from complexity to complexity.

The first model is Erich Gutenberg’s, the founder’s of German Betriebswirtschaftslehre, model of Betrieb (firm, business, enterprise). In his 1929 book (actually his habilitation) on The Firm as the Object of Management Science Theory (Die Unternehmung als Gegenstand betriebswirtschaftlicher Theorie) he pointed out that any management science must start with bracketing complexity. Bracketing, like in Husserl’s epoché (presumably a reference for Gutenberg), means acknowledgment without necessarily dealing with it. Gutenberg’s insight was that such a bracketing was in fact possible. As a matter of fact he managed to bracket it even twice.

An organization becomes a Betrieb by subjecting it to the economy, on one hand, and to technology, on the other. The first one is done by subjecting it to the rule of efficiency via a calculus of cost and benefit, the second one by subjecting it to the rule of effectivity via a calculus of means and ends. The first one founds Betriebswirtschaftslehre, the teaching of the Bewirtschaftung, exploitation, of the organization as Betrieb, the second one could have founded a Betriebstechniklehre, a teaching of the Technisierung, instrumentalization, of the organization as Betrieb. As an academic endeavor, or discipline, only the first one could successfully be established. The second one, the Betriebstechniklehre, to this day exists as a highly successful loosely coupled network of engineering disciplines.

This gives us our second model:

Note that the exploitation and instrumentalization of the organization as Betrieb has to be done not only to the organization but also in the organization, rendering illusionary any management teaching which assumes that the design, steering, and control of organization can be done via its planning from outside. In fact, any good management practice starts with looking not only at the variable of technology and economy, but also at the variable of the organization, that is, at the whole form. Paradoxically, management has to enforce and support the organization to be able to subject it to the criteria of technology and economy. Management goes beyond a calculus of cost and benefit, and of means and ends; it employs a calculus of the moderation of the calculi of cost and benefit, and means and ends, such that the organization endures, survives, and even welcomes both.

Note as well that nothing ensures that criteria of technology and economy, of engineering options and market demands comply with each other. All kinds of conflicts are to be expected. Management science to this day entertains the dream that somehow means and ends, on one side, and cost and benefit, on the other may become reconciled via a third distinction, that of top and bottom. This was also Max Weber’s dream and nightmare of one Zweckrationalität, rationality of reason, organizing both bureaucracy (of firms and government agencies) and society. Fortunately, Niklas Luhmann, in his 1968 book on Zweckbegriff und Systemrationalität (Concept of Purpose and System’s Rationality), managed to deconstruct any conceptualization of the isomorphies of means and ends, costs and benefits, and top and bottom. Ever since, organizations may be considered highly tensionalized institutions, what, to be sure, suits their viability perfectly.

Peter Drucker, by the way, followed the same reasoning as Erich Gutenberg. His 1954 book on The Practice of Management has two axioms which taken together make sure that management deals with the distinction of the economy and the organization to apply the first to the latter. The first axiom reads: “Put economic performance first.” And Drucker does not fail to emphasize that this is a question of achievement, not of knowledge, a question of practice, not of science nor of profession. And he emphasizes as well that this makes it difficult if not impossible to transfer the skills, the competence, and the experience of managers to other institutions that lack economic purpose, such as the army, the church, or government agencies, and universities. And the second axiom reads: “To obtain economic performance there must be an enterprise.” Drucker specifies this as the function of the management of managers, which calls for self-reference and for the re-entry of the distinction of management into the organization such that scope and limits of management can be determined and monitored. Already in 1954 Drucker emphasizes creativity as the skill which both separates economy and enterprise and combines them in bringing the resources of an organization to bear on a market.

The second step in the development of models of organizing in Twentieth Century (see only army, cloister, and hospital models for earlier ones) comes with the invention of the idea of strategy which is contemporary to the discovery of an open economy, certainly informed by the earlier discovery of Popper’s open society. An open economy is an economy which does not refer to politically established territorial boundaries to protect industries. Instead, it opts for competition to assure a better allocation of capital, labor, information, and organization. Michael Porter wrote several papers and books to look at strategy under conditions of an open economy and came up first with a model of five forces (later, five factors) shaping and framing any one business strategy, and then with a value chain model embedding a business within inner and outer variables defining its strategic scope. We here refer only to the five factors model and render it again as a Spencer-Brown catject, reducing its five factors to three:

which, if we give up the idea that competition is only undertaken with respect to competitors ‘out there’, resumes to:

thus showing that competition is done by rivals inside and outside and dealt with depending on the threats they come up with to shape their bargaining power.

If that model seems to be a rather limited one defining the scope of strategy with respect to variables that demand either offensive or defensive moves, leaving almost no space for an answer to the question where innovation or indeed any kind of self-ordained business evolution may come from, we may try to go into phase three of the development we here rather crudely sketch. Phase three may aptly be termed the organizational development stage of model development, which, if informed also by sociology and literature (bringing Edgar Schein together with Gutenberg, Harrison C. White, Luhmann, and Jean Paul), includes references to inner and outer variables of organizing, embedding it within networks, society, and the microdiversity of individuals:

This model comes from my paper “The Form of the Firm” (in: Organization 13 (2006), 109-142) and actually is one model of in fact two ways to organize, a classical one (read the terms to the left of the slash indicating a re-entry level) and a postclassical one (read the terms to the right of the slash). The classical way of organizing, e.g., the Nineteenth Century one, assumes a societal mandate — or ‘order’ — to define what any organization is about. It then just has to translate the mandate, helped by administration and management, into procedure. If purposes are given, means follow suit, such that the organization in Nineteenth Century could be considered the epitome of rationality (or even reason) despite the fact that it within its empirical practices swapped purposes just as easily as means. The post-classical one, as conceptualized by James G. March and others, is defined by purposes not being given but to be found and legitimated by the organization itself, introducing all kinds of uncertainty that now request to be dealt with. Classical work becomes postclassical decision, classical steering, postclassical management, classical strategy, postclassical leadership, and classical philosophy, postclassical consulting. If classical organizing believes in rationality, postclassical one is invited to embrace undecidability.

Embracing undecidability, postclassical organization distinguishes product from procedure, organization (institutionalized hierarchies), network (identities controlling identities), society (a calculus of the reproduction of communication), and individuals (people with wit, judgment, and choice, according to Jean Paul, bringing with them mindfulness, according to Karl Weick and Kathleen Sutcliffe, Managing the Unexpected, 2001), and finds values for any one of these variables within the frame of all others. The deeper the space to the left of the right side of the equation, the more determined the value to be found of the variable. Thus, individuals are and remain the free radicals of any process of organizing; and to find, explore, and exploit a product becomes the sine qua non of any process of organizing. With its product and products an organization defines its core as its exposure, and its exposure as its core.

We thus end up with a catject which somehow is the opposite of the one we started with in this post. No organizing without people, posts and programmes being the condition of how that organizing is to be done, and yet equally important no organizing without products, people being replaceable. As a Spencer-Brown catject defines an eigen-value of a recursive function, one should not be surprised of being able to look at the same process from opposite directions (and, in fact, there are more than two perspectives).

Yet, I would very much like to draw our attention to the fact that, first, Shannon, and Weaver with him, somehow managed to conceal one of the most important findings of his theory by disclaiming any interest in the semantic aspects of information and by putting up the infamous sender/receiver model of communication, and that, second, Shannon was the one who the most forcefully deconstructed his model without actually anyone seeming to take notice.

This is not to say that Shannon’s model has not been tremendously influential. Linguists like Roman Jakobson endorsed it as enthusiastically as semiotician and aesthetician Max Bense. And endless is the list of those who were shocked that anybody could approach issues like that of communication and information in terms of mathematics, let alone statistical mathematics, in the first place.

Shannon’s model, even if it is not exactly a sender/receiver model but a transmitter/receiver model, paying attention not to people but to machines, and indeed not to meaning but to signals, nevertheless is one of the most quoted and used models of the last century, matched only by the atomic model or the DNA double helix. Therefore, we have to insert it here once more:

Schematic diagram of a general communication system (Shannon/Weaver 1949, Reprint 1963: 31 and 7)

This model was introduced by the sentence that “the fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” One could write volumes about just about any one word of this sentence, and in fact Michel Serres in the five volumes of his chef d’oeuvre Hermès (Paris 1968-1980) kind of did so.

In fact it is a signal theory of communication, focusing on the question how any one message was to be reproduced at the receiver end of the channel if the channel was noisy. This is Shannon’s engineering problem, to which, as he said, “the semantic aspects of communication are irrelevant.”

Yet, the discussion that followed was too quickly focusing on the misconception of the transmitter being a sender and both sender and receiver being similar to people. In fact, if there are any people pictured in Shannon’s diagram they should figure as information source and destination.

But even then Shannon’s strike of genius, which lies elsewhere, would go and woul remain unnoticed. His trike of genius indeed is the use of a mathematics which stems from statistical mechanics. This means that the definition of information he is gaining from the notions of statistical mechanics is a relational and can keep clear of any reference to any kind of substantial or essential meaning. As he is saying: “The significant aspect [i.e., if not that of semantics, db] is that the actual message is one selected from a set of possible messages.” This means that the information is in the relation of one message received to a set of possible messages to be conceived of. Of course, that set of possible messages could not receive any special attention because it is technically given. It is the alphabet, the set of possible letters in any specific language.

Yet, as soon as one drops the notion that the set of possible messages is technically given the notion of the relation of any one message to a set of possible messages becomes very interesting. One might for instance say that the set of possible messages is socially constructed, negotiated, insinuated, and conflicted upon. All of the sudden an understanding of meaning pops up, which is mathematically informed yet hermeneutically legitimated and sociologically to be employed. Any kind of social communication would end up with producing its meaning out of the relationship between specific messages and possible sets of possible messages, the understanding of the specific message being as dependent on the possible set as the possible set on the specific message.

In fact, Shannon’s notion of information being the relation of one message to a set of possible messages would end up being a special case of the more general Spencer-Brown case of any marked state being the inside of a distinction the outside of which is the unmarked state. Here, any one communication attempts to determine the unmarked state in order to be able to understand the distinction to be drawn, and is only restricted by itself in choosing the appropriate frame for that determination.

As Michel Serres, Niklas Luhmann, and others were already able to show, the problem of Shannon’s model resides in the fact that nobody knows who should be the one to determine the identity of the message to be transmitted. It certainly is not the transmitter and not the receiver who can do that since they are separated by a noisy channel. So who is it apart from the omniscient model builder himself?

If we go from a specifically mathematical model to a generally sociological model of communication that problem becomes even more pressing at the same time, however, that it becomes addressable and even solvable. We watch without possibly being in any doubt about that two selective instances at each end of the channel, both instances relying on their frames to construct what they take out of the communication. We watch, in fact, observers. And nothing guarantees that these observers ever share their frames except, Jürgen Habermas will be releived to hear that, their somehow common interest to continue the communication. That interest on any one side, though, may have rather diverse reasons.

Shannon’s genius in fact led him to introduce the observer already all by himself, albeit only when indeed reflecting on the notion of channels containing choice, which is taken up in his second chapter in his and Weaver’s book. Again, even if rarely quoted and reproduced, the schematic diagram he is drawing is fascinating:

Schematic diagram of a correction system (Shannon/Weaver 1963: 68)

Now the observer out of a wonderful intelligence of his own is able to both gain a knowledge of M being transmitted is not identical to the M’ being received, and to correct that deviation having both the data and the necessary correcting device. Yet, who is interested in that correction is a question that is left open. The corrected M’, now M again, is running to the right out of the diagram. If there ever was a self-deconstruction of a model, here it is.

Yet, if we now combine the insight into the selectivity of any one unit taking part in communication with an understanding of that unit necessarily being an observer all by itself we end up with an understanding of communication being the production of redundancy as already Gregory Bateson emphasized. We might just add recursivity and non-linearity to bring second-order cybernetics and complex systems theory to this understanding. We might as well also bring in conversation theory which in Gordon Pask made sure that whatever happens it has to be a “sharp-valued event” for any one observer just to lead to anything which might count as the continuation and thus reproduction of communication.

Thus, communication is the recursive eigen-value of messages selected from set of possible messages by observers engaged with a network relating them to each other. All of those variables (messages, sets of possible messages, and network of observers) are selections undertaken with respect to each other such that communication in fact reveals itself to be its autopoiesis out of itself:

Any one message may start it, provided it is matched by sets of possible messages within networks of observers, which means that pretty much must already have happened.

Note that nobody did say that only human beings qualify for communication, let alone for being observers.

Luhmann nicely indicates the speculative nature of this chapter by only sketching this possible theory of culture by way of exemplifying it with reference to just three examples, writing, print, and, even more cautiously, computers, and by giving the according three forms of culture he is developing with reference to ancient society (writing), modern society (printing press), and, not his word, next society (computers) the names of great authors. To refer to great authors in sociology in general and in Luhmann in particular is unusual because great authors, that is why they are great, do not represent everyday life, thinking, and doing, and thus are empirically rather insignificant. But in this chapter, the ancient society’s culture form goes by the name of Aristotle who ‘invented’ telos, and the modern society’s culture form goes by the name of Descartes, who ‘invented’ a restless self.

The overall argument is that the introduction of any one communication medium in general, and of dissemination media in particular, overtax the existing structure and culture of a society by new possibilities to communicate such that a new structure and a new culture have to be invented in order to stay able to both reject and accept such communication. The overall rule for any society is to accept only that communication which it is able to reject as well.

We may complement this chapter in Luhmann’s book by adding the notion of structure form to his notion of culture form. If culture form is the reduction of the overflow of meaning to some selective idea of order with respect to disorder, a structure form the form that guarantees the dissemination and distribution of that overflow. Those structures are sociology’s famous forms of differentiation of society, as there are the tribes of tribal society, the social strata of ancient society, the functional subsystems of modern society, and, possibly, the networks of next society.

The most speculative part of this sceptical theory of culture is, first, the spelling out of just what overflow is produced by any one dissemination medium, let alone by other media such as any success medium of communication, and, second, the search for that figure of order and disorder which may indicate the respective culture form. Luhmann gives us telos for writing, and restless self for printing. Telos controls the overflow of symbols referring to past, present, and future produced by writing. The restless self controls the overflow of criticism referring to flyers and newspapers, books and papers presenting the reader with deviant opinions on just about anything and anybody. We may add boundaries as the culture form of a tribal society facing the overflow of reference produced by oral language, boundaries trying to control who is talking when to whom about what, and systems as the culture form of a next society facing the overflow of control produced by computers and computer networks exploiting the possibilities of electricity.

We naturally will search in vain for an author inventing ‘boundaries’ even is the ethnological literature is rich in evidence for that assumption; and Luhmann intriguingly gives names for the culture forms of ancient and modern society but not for the computer society coming up on the horizon for him as well. I tried to turn that into a riddle in an article written for the German magazine Der Merkur (July 2001) but to date nobody answered, perhaps because I did not advertise prize money for the solution to the riddle. Until further notice there may be three candidates for their appreciation as possible great authors who may have invented a culture form of next society, as there are Claude E. Shannon with ‘information’ or even ‘communication’, George Spencer-Brown with ‘form’, and Niklas Luhmann himself with ‘system’, more precisely ‘self-referential system’.

Of course it will depend on the identification of first, the peculiar overflow of meaning produced by computers interfering with communication, and, second, the culture form able to deal with that overflow, to decide on that prize.

For now (and see my selection of papers in my book Studien zur nächsten Gesellschaft, 2007, for more explanation) we may settle for a general theory of culture form which reads like this:

or:

For tribal society brought forward by the introduction of oral language we then have:

For ancient society evoked by the introduction of alphabetical writing we have:

For modern society dealing with the printing press’s products we have:

And for ‘next’ society, to use Peter F. Drucker’s term, dealing with the introduction of electricity, computers, and computer networks we have:

I am not happy with the term ‘control’ here since that is the more general term denoting the problem resulting from dissemination media that produce an overflow of meaning. I nevertheless use it because I do not have a better one right now and I like its reference to Michel Foucault’s and Gilles Deleuze’s talking about ‘control societies’, giving that term a more empirical denotation, that is linking it to the advent of the computer society.

Right now I opt for ‘system’ as next society’s most probable culture form because systems tell how production and reproduction of meaning will be possible in the ecologies of the network of people, minds, machines, and life forms of all kinds the computer society is presenting us with. Systems indeed means first-order closure of operations and second-order closure of programs. Systems theory might have been reinvented by Norbert Wiener, Warren McCulloch, Ludwig von Bertalanffy, W. Ross Ashby, Gordon Pask, Talcott Parsons, Niklas Luhmann, Humberto R. Maturana, Francisco J. Varela, Ernst von Glasersfeld, Ranulph Glanville, and quite some others in order to give us the culture form of next society.

- we may respecify it for different culture forms of different societies, each of which brought forward by the ‘catastrophe’ of the introduction of a new dissemination medium of communication, such as, most notably, language, writing, the printing press, and computers (see my Studien zur nächsten Gesellschaft, Frankfurt am Main 2007).

We then have a value definition of tribal society, brought forward by the need to control the introduction of the overflow of reference produced by language, as language, in distinction from bodily behavior, may easily refer to absent things and persons nobody in the very moment can verify. Thus, society needs boundaries as described by Malinowski, Lévi-Strauss, Turner and many others to control who is saying what when to whom:

We have a value definition for ancient society, brought forward by the need to control the overflow of symbols produced by writing and refering to a past and a future no present can control. Thus, society needs the idea of telos, as introduced by Aristotle, to control what makes sense and what not:

We have a value definition of modern society, brought forward by the need to control the overflow of criticism produced by the printing press that enabled everybody to read just about anything and to develop opinions not necessarily checked against reality. Modern society developed the ideas of equilibrium and of reason, together defining restlessness, to capture both the empowerment and the control of individuals first, and markets, publics, affairs, truths, arts, and so on thereafter:

Last not least we have a value definition of next society, brought forward by the need to control the overflow of control projects produced by conputers and computer networks based on electrical instantaneity. Grouping is brought about by systems, ecologies define the society’s grid, and networks of uncertain scope present everybody with imponderable possibilities to switch. Spencer-Brown’s notion of form defines the bias that society is bound with to produce whatever kind of coherence:

We will have to work on this sketch in the near future.

It tries to model any X as it goes second-order observed by culture, thus looking at the X as a thing in terms of a possible practice, indicating the X as a medium in terms of possible poiesis, and so on, while entertaining at least three possible mathematics to both communicate and control the variance brought to X by that kind of culture, a 1/2-mathematics of esoteric Plato, a 0/1-mathematics of Boole, and a 1/2/3-mathematics as proposed by Peirce.

I do not know what to find out by pursuing this model. It goes beyond its own modeling. But it captures a culture as it is determined by all culture theory beginning with Edward B. Burnett’s “complex whole”, going by Bronislaw Malinowski’s functional understanding of a culture balancing institutions, needs, norms, and people, and not ending with A.L. Kroeber’s and Clyde Kluckhohn’s search for a model of culture using, at least, quaternary distinctions (as in Culture: A Critical Review of Concepts and Definitions, New York 1952).

In my current lecture on the culture form of society at University of Basel I am using a more simple equation, which, perhaps, nevertheless already goes a long way to model what a value, the culture form of society par excellence, is about (again combining Mary Douglas and Harrison C. White, reading them into the culture theory of value proposed by Niklas Luhmann in his Die Gesellschaft der Gesellschaft (Frankfurt am Main 1997):

Value defines the identity of a group in terms of possible switches to other groups within the grid of a society. Any coherence is payed for with bias.

It is still one of my favorite ones since quite a deal of sociological theory, most notably Mary Douglas’ group/grid-schema and Harrison C. White’s understanding of network, went into it while once again paying tribute to Nils Brunsson’s distinction between action and talk and entertaining a possible and prominent link to evolution theory in saying that all action indeed either searches for, defends, or boasts about mating chances.

I went on to work, however, in various contexts of teaching and consulting with a different model which was published in a paper of that title, “The Form of the Firm” (Organization: The Critical Journal on Organization, Theory and Society 13, no. 1 (2006), pp. 109-142), and which had the following equation:

Apart from the six distinctions, to be read as the constants of the model, as there are product/procedure, procedure/organization, organization/network, network/society, society/individual, and individual/unmarked state, and the seven variables, namely product, procedure, organization, network, society, individual, and the unmarked state, I here distinguished between two modes of the six re-entries of the form into the form, namely a classical mode and a postclassical mode. The classical mode is Max Weber’s bureaucracy, which assumed societal orders to be fulfilled, as there is wealth to be produced by business firm, lawfulness, by state bureaucracy, health, by hospitals, formation, by schools, knowledge, by research institutes, and so on; the postclassical mode is Herbert Simon’s, James March’s, Karl Weick’s, Niklas Luhmann’s, and Nils Brunsson’s organization, which is not defined by purpose but by always searching its purpose and being uncertain about it.

At that time I was inspired more by Gotthard Günther than by George Spencer-Brown and thus tried to model markets in terms of acceptation and rejection values. Translating what I then called a difference matrix into a Spencer-Brown expression the general architecture of a market enabling, following both Harrison C. White and Niklas Luhmann (and not to forget Georg Simmel about a competition among two on behalf of a third), second-order observations, I got:

I specified that general expression as follows for product markets:

labor markets:

credit markets:

and futures markets, the infinity sign, ∞, indicating that here the whole matrix once again is re-entering itself:

The whole point has been to show how specified uncertainty (Knight’s ‘risk’) emerged from unspecified uncertainty via attempts to calculate events from events.