# Recursion I

In social contexts, recursion includes the ability to take an entire situation into account and put it into a different perspective while remaining within the very same situation. This is important for evaluating different situations, allow for cultural comparisons which formulate preferences, and ultimately make selections allowing for adaption to changing contexts. In terms of modes of observation, we can refer to this as second-order observation, i.e. an observation of an observation.

In mathematic algorithms, recursion is often defined as feeding the output of a function back into it as a variable. In circuit design, this is considered feedback. There is a difference in comparison to what we can observe in social phenomena. In mathematical or technical recursion, the output value is generalized either in a data format or as a signal, in a way that allows for it to be accepted at the input stage. However, this also means that at this point, all information about the internal structure of the function which produced it is lost. Its informational value is no higher than any other input the function receives. Additional information based on the sequence of events produced and received would have to be derived in a separate part of the function.

In social phenomena, we can observe similar phenomena, where values are generalized to be used over and over again at the end and the beginning of social processes. Niklas Luhmann has described some such cases as symbolically generalized communication media, sometimes more vividly referred to as success media. They include money, power, and love, to name the three most famous examples. In these media, accumulation is generalized to the degree that money usually works as a means of payment regardless of its origin, and power over a certain situation can either be had or not, regardless of the source it references, for example god or a democratic election. Similarly, love is either there or not, but it is mostly useless to discuss the detailed reasons why love for a specific person exists.

However, social observation is also capable of processing more complex situations. In communication, it is possible to evaluate a specific operation with respect to its contexts. An example could be the sentence “normally I would not agree, but under the circumstances it has to be okay.” Such a statement is not possible if the situation is only observed and evaluated for one specific outcome. Rather, different outcomes in different contexts have to be taken into account and are compared to the actual constellation at hand. Going even further, the situation in which the communication takes place can also be observed in that manner, i.e. evaluated for its specific contexts. The situation is thereby fed back into itself, but in the mode of more complex observation, instead of generalization.

# Nothing

The notion of nothing is a rather young concept in the history of human ideas. This may be due to the apparent inability to observe the absence of everything. In mathematics, for example, Babylonian scholars first had to invent a representation for the absence of a counter, thereby laying the foundation for the number zero as used today. As a number, zero is conceptually different from other numbers, since it cannot be represented by any describable physical entity. Socially, this has been made possible by the function of negation, which allows us to state that there is something, e.g. a section of a row on an abacus, which can and often does hold counters, but in this specific observation does not. This absence is then the core of this very observation, and it serves functionally as the equivalent of zero. In fact, the number zero can be seen as a shorthand for the observation above.

This shows that it is indeed possible and, with the benefit of hindsight, relatively easy to observe an absence inside a system. All it takes is a technical abstraction of some system of observations, such as counting, and then a reference to the substrate of the system, e.g. the abacus, to show and make explicit where elements are absent. This notion of absence is, however, quite different from the notion of nothing.

In nothingness, absence cannot be made explicit by referencing a substrate, for if there were a substrate, there would not be nothing. The trick how communication deals with nothingness is recontextualization: Nothing then has a semantic boundary, so that there is a system of meaning from which nothing can be observed.

Nothing in the world.

The holistic view of an all-encompassing nothing uses the same function, when it describes the world as the inside of nothing, nothing coming into existence.

The world inside nothing.

With this in mind, observations become non-materialistic, as it is clear that there is no qualitative difference between something and nothing, no substrate to provide a grounding. Rather, nothing and some existence are an oscillatory state, where any side inevitably invokes the other.

# Self and External Reference

Sociological systems theory has established a clear distinction between self reference and external reference. Self reference is the ability of an observer to refer to himself in an observation, while external reference means establishing a relation to another identity distinct from the observer. Self reference invokes the notion of self in the world, and especially the handling of self reference and external reference within one observation is considered an important ability enabling the observer to deal with complexity arising from double contingency.

Looking at the concepts of self reference and external reference in the light of the descriptions of observations we worked out in the previous posts, the intrinsic availability of self reference has to be questioned. If we take any one observer as identical with one and only one observation, and view the notion of unity as a construction coming in after the fact of the actual observation, then we would have to place the idea of self reference also in this realm of constructions coming after the fact. If no two observers are  the same, then self reference is excluded, at least at this basic level. Here, all references are necessarily external, as no other identity can be the same as the actual observer. Even if the same reference were used, it would necessarily refer to a different observation that happened previously or will happen later.

The consideration of constructions coming after the actual observation has been theorized in the concept of second-order observations. These are defined as observations of observations, and they therefore come with the ability to create new contexts for other observations. Such a context can then be a notion of observer unity, i.e. selfhood. It can just as well include the actualization and reconstruction of another identity, such as a separate person. For a persistent notion of selfhood, it would be essential for both modes of observation to closely relate to each other, thus enabling a coherent construction of self reference. At the same time, any second-order observation is also a first-order observation, in that it also has its own unique observer, who can, at its own basic level, only make external references. These can, however, be constructions of self reference for another, external observation.

# Memory and Oscillatory State

We have discussed the availability of oscillatory (or complementary) states and of memories as contexts of an observed existence in the last post. Let us now look at their commonalities. Firstly, an oscillatory state as the complementary outside to the inside of the distinction in the focus of the observation necessarily also rests on the memory of a previous observation. As I have laid out, this is also the case if the complementary state consists of an expectation towards a potential future of the current existence.

Secondly, if we can indeed reduce any observation to fundamentally being one distinction separating its inside from everything it is not, then this must also be true for any previous observation remembered in the current one. With this in mind, the difference between oscillatory states and memories as contexts of existence becomes almost obsolete. The one remaining difference is retained in the marker that the oscillatory state is an alternative state of this existence, the existence in the focus of the observation. Thereby, oscillatory states can become a marker of uncertainty, as it is clear that they could potentially gain actual existence in the next observation.

In Chapter 11 of his “Laws of Form”, George Spencer Brown, in dealing with equations of the second degree – i.e., recursive functions -, introduced the notion of oscillator and memory functions. These notions are at the basis of our considerations, and we will return to them for further exploration.

# Momentary Observers

Considering the notions of space and time laid out before, observations can only be seen as momentary events, without any intrinsic duration in time or extension in space. This is a necessary pretense, as it is by observations, not within them, that time and space are constructed.

In this sense, only that on which the observation focuses can be said to exist, even if only for the specific observer. Everything else is context for that on which the observation focuses, either providing an alternative perspective on the existence in focus, or referencing the memory of some related entity that was observed before in other observations.

A possible alternative perspective would, for example, be the negation of that which is in the focus. In social phenomena, we often encounter such oscillatory states in which complementary views on one entity negate each other, but in a positive way that does not proceed to negate altogether the existence of the entity in question.

The other option for a context is to reference the memory of another observation. As I have mentioned, this can include expectations towards future observations as well, for they, too, have to be based on previous observations in order to project future events. Also, such previous observations were not made by the same observer. Firstly, any observation creates a discrete observer, thus ruling out the concept of unity at this basic level anyways. But secondly, they also do not have to be made by the same constructed unity, such as a person, on a more abstract level. A person is able to bind together different observations via self-reference, thus creating the notion of conciseness in recognizing existence. Memories of previous observations used as contexts can, however, also deal with external reference, e.g. the notion that some other person made a specific observation. This ability to build on the observations made by other points of reference is one of the strengths and efficiencies in society.

Therefore, any observation can be described as focused on some entity, thus attributing to it the possibility of its existence, and placing this entity in the context of alternative, complementary states of existence, and/or in the context of memories of other observations. All of this is just one event, which means it does not have a duration in time or an extension in space. For this, further observations would be necessary, which could be summoned to effectively construct such measurements.

With this, we have reached the same notion we started out with: The notion of distinction. Any observation can fundamentally be seen as just that, a distinction separating something from everything it is not.

The form of the distinction.

Everything on the outside of this distinction may be made more explicit to infinite detail, however, all of these explications will themselves be observations and thus fundamentally claim only this one distinction. In addition, all such distinctions would be decoupled as individual events, thus creating time, but never falling together. Thus, no universal existence could be claimed for them, and it could also not be referenced from any individual observation.

# Space I

I have described observation as comprised of distinctions, and in the last post, explored how time can come into existence out of the sequentiality of observations. Notably, it can be stated that observations are necessarily sequential. Any one observer is equal to what is observed, and only that which is included in the observation can be a reference at that particular point in time. This is not to say that observations can contain only one reference. Indeed, multiple references are not only possible in observations, but they are the norm, as we will see in further case studies.

Space can be described as the possibility of simultaneous existence. As with points in time, we have concepts of points in space, and also in a similar way, we can describe extensions in time as we can in space by explicitly relating different points. However, I would argue that, again similar to how time is constructed, space is also born out of the need to create continuity between observations, instead of itself being available for direct observation.

If observers are defined as part of their observations, distinct observations by one identical observer are not possible. Any one observation is always tied to its one observer, and a subsequent observation has another observer, distinguishable at least because he is making this other, subsequent, observation. The identity of both observers then has to be defined in yet another observation, taking both previous observations into account. Therefore, if no observer can make more than one observation at once, the possibility of simultaneous existence also cannot be verified in an observation. Direct observation of space is, then, impossible.

This is not to say that different existences cannot be observed in their relation, and that this relation is necessarily non-spatial. Indeed, ontological statements of the form “this is here and that is there” are rather common. However, I would argue that such statements are in fact memories of previous observations, rather than actual observations at that particular point in time. Consider how the notion of space is used as individual memory technique, where you are taught to match things you want to remember to an arrangement of places you are familiar with. You are thus asked to construct a space out of familiar relations, and then add heretofore unfamiliar references on top. A more abstract and more reduced version of this concept can be assumed as the foundation of any notion of space. The very possibility of relations is the first premise, onto which specific models of relations can be built. The places connected by such relations can then be populated by references to observations. The trick is that actual observations can firstly deal with potentially many of these relations, thus creating contexts for their subjects, and secondly they can operate as if the referenced observations were actually part of the current observation, belonging to what is going on at the moment.

I would argue that such references that are related to the subject of the current observation serve as memory functions, binding something that has been possible and probably will again be possible to the actual moment. Thereby, they serve functions of expectation as well. In the functional relation to an observation, memory and expectation are therefore indistinguishable. In order to use them differently, they have to be specified using further contexts. We will investigate such cases in detail.

# Time I

Within society, time is commonly used as an index. Some event can be said to happen or have happened at a certain point in time, or is scheduled to happen after a specific period of time. To make this reliable, time is thus considered as a steady continuum that can be referenced whenever the need arises. Einstein’s theory of relativity changed the secure notion of time, albeit without much social consequence. As society does not travel at speeds approaching that of light, the effects of relativity are negligible for social practice. And, after all, Einstein did not challenge the underlying notion of the form of time as a continuum, rather, he postulated rules as to how this continuum relates to other continua.

How, then, is time used within society? One obvious example are clocks. Their face with the constellation of its hands or digits are a communicational offer that can be referenced in further communication, even though it does need a contextual interpretation. For example, when reading a 12 hour clock, the observer needs to provide the additional information of a.m. or p.m., which he had to derive from a different source. Often, this will be clear to the observer because of the events that preceded the reading of the clock, e.g. having been to work already without a night’s sleep in between. This may seem trivial, but remember that the ability to observe such a sequence of events is a common initial step in a medical sanity check.

Clocks can be thought of as devices designed for the sole purpose of creating a defined sequence of events and counting them, such that the score is always visible on their outside. The events are mechanical or astro-mechanical movements, or samples of battery-powered oscillations of a quartz crystal, or the measured decay of atoms. Regardless of  the actual device, society is mainly interested in the score, i.e. that which we consider the actual point in time, or the delta in between different scores, which we consider a period of time. Either way, the readings used in these processes are samples of other processes designed to be read by society itself. The scores kept, even by a sun clock, are based on social conventions of number systems and of linearity in counting. Clocks can, then, be described as devices which are part of and extend their creator’s observation of what time should mean for society.

If we broaden our perspective beyond just clocks, it will become apparent that society in general is based on the sequentiality of events. Causalities are constructed because certain events follow others, with expectations towards specific sequences. Returning to the notion of distinctions, we can postulate that in general, observations of distinctions are expressed not all at once, but in sequence. Certainly, some distinctions can perhaps be observed together, contextualizing each other, but any expressions of such constellations are expected to be followed by others, just as others preceded them. In society as the autopoiesis of communication, observation follows observation, and some observations happen to reference certain scores treated as accounts of time. In this broader perspective, it would be oversimplifying to speak of clocks and the society that built them as keeping time. Instead, the events, i.e. the observations being expressed within communication, would have to be understood as the source events generating time for society. We will continue to analyze the actual functional processes involved at a later time.

# Imaginary State

Even though an observation must consist of distinctions, it is possible that the subject of the observation is not in a clear state, i.e. in a state that could be communicated as clearly distinct from everything it is not, because something else might also be the case. George Spencer Brown has referred to such an unclear state as the imaginary state. This imaginary state is defined by containing one or more further distinctions, which oscillate between their inside and their outside. Of course, they do so not by themselves, but by being observed. The classic example of such a state would be the notion of Schrödinger’s cat, locked in a box with a capsule of poison gas set to open in case the determining atom disintegrates.

While the cat is locked up, we cannot observe the cat itself directly, but only reference the notion of it existing inside the box, either dead or alive. The cat can thus be said to exist in the  imaginary state of being both dead and alive at the same time. Since being dead and being alive are separate concepts on different sides of one distinction, we have to refer to them individually when describing the cat in the box, yet, in this imaginary state, each side of the distinction dead / alive inevitably leads to the other side. Therefore, the distinction can be said to oscillate between its two sides. In order to break out of this imaginary state, we have to add another observation: We have to open the box and look inside to determine whether the cat is alive or whether it has been poisoned.

The same concept of the imaginary state can be applied to social situations awaiting decisions, for example the outcome of a trial, or the reaction to a job application. Until we observe the decision and thus the choice for one side of the distinction at stake, the situation is in an oscillatory, imaginary state, regardless of how much we analyze it. It can be noted, then, that indeed none of the outcomes exists while the imaginary state lasts. A trial is not lost nor won until the verdict is spoken, and a job application is neither accepted nor rejected until the decision is made explicit. Also, the expression of any such decision has to be in accordance with expected and usually regulated social processes: The trial verdict has to come from the judge or jury, and the decision on the job application must be backed by the organization offering the job.

Returning to Schrödinger’s cat, this premise results in the somewhat unintuitive conclusion that, in communication, neither a dead cat nor an alive cat exist inside the box. Only the cat in the imaginary state can be said to exist. In communication, the decision for either the dead or the alive cat is not reached until the box is opened and the box-opener signals his observation of the outcome. In any case, though, is the outcome expected to match the design of the experiment. For example, a dead cat and an unopened poison gas capsule are not expected. The experiment would then have failed, and the description of the entire process would need to be readjusted. This would again require additional observations framing the design of the experiment and its expected outcomes.

If we assert that none of the sides of a distinction in an imaginary state actually exists on its own, we will then have to take into account both sides of the distinctions in question whenever observing such a situation. We will come back to this when we take a closer look at the concept of the reentry in George Spencer Brown’s calculus.

# Reality I

Looking at reality as being composed of distinctions means having to accept that it is created by observers. One may find it plausible or not that a distinction exists while not being observed, but for the argument, this is without consequence. After all, whenever it is being noticed, this is by observation, and by observation only. The inverse can be postulated as well: Any observation necessarily notices distinctions. In the simplest case, any observation states that there is something that is distinct from everything it is not, for otherwise, this entity could not be said to exist. This “being said to exist” can be described as isomorphic to Heidegger’s “Dasein” (e.g. in his “Sein und Zeit”), i.e. an entity being brought into the world by the claim that it exists, against the backdrop of the possibility of its existence.

Without distinctions, nothing in the world could be distinguished from anything else, and in the end, not even the world itself could be described within itself as a concept, thereby becoming inexpressible. There would not be a word “world”, because as a word, it can only exist in relation to the system of words that is language, which in turn can only exist within communication. Thus, even the syntactic existence of “world” as a word rests on the premise of distinctions, before even considering the semantic value of the notion it references.

Any distinction is, then, necessarily an observation, just as any observation must be at least one distinction. In communication, distinctions are never expressed individually, but rather come in more complex arrangements, some of which we will analyze later. This is because such an observation cannot be expressed without its social embedding, e.g. its form as a message, for example being spoken instead of written, and by whom in which situation, and so on.

A reality composed of distinctions then has to be also a reality entirely created by observations. However, as reality itself is distinct from everything it is not, it can ultimately also only be existent when observed. Reality is what it is only from the perspective of this ultimate observer, because it is there that the distinction is drawn between those distinctions which belong to reality and those that do not. Any distinctions not taken into account by this observer are therefore left out of the concept of reality as seen from this particular ultimate observer’s point of view. “Ultimate” may sound like a claim of absoluteness, but the contrary is intended: Any observation of reality is an “ultimate” observation in that at the moment of its coming into being, it contains everything this observer is subsuming on the inside of the distinction of reality from everything it is not. However, the observation is “ultimate” in that it is itself positioned outside of communication. It can be referenced in communication, but it is impossible to express all of the distinctions included on the inside of the distinction in communication, because this expression itself would have to be included as well. If we accept this necessity and state that “reality is all this, and the expression that reality is all this”, we are missing this very statement on the inside of our distinction. We would have to state that “reality is all this, and the expression that reality is all this, plus the expression we just made that reality is all this, and the expression that reality is all this”. At this point, we would be missing the latest statement, have to include it, miss the next latest statement, and so on. Therefore, we can assert that, if the “ultimate” observation of reality is indeed possible, it can at least not be expressed in communication. Therefore, it is again without consequence in the argument whether such an “ultimate” observation exists or not. We may as well neglect it for its social nonexistence, and accept that any social concept of reality is inevitably incomplete.

# Why Observers?

With the realization in mind that a notion of a multitude of non-person observers in society is rather unintuitive and requires in-depth explanations in most cases (one of which I attempt in this blog), why would we even start such a complicated endeavor in the first place? Why not just stick with the seemingly obvious notion of statements about the reality of society?

My personal answer is that the attempt is motivated by the concern that if observers remain unobserved, the notion of objectivity becomes plausible. This can lead to a situation where statements are postulated as equally binding for every possible addressee, without requiring any responsibility from the originator of the statement. In this blog, I will analyze such statements in an attempt to make explicit some underlying social structures which point back towards the observer of a statement that was supposed to be objective. Of course, all of this has already been explained to us by Heinz von Foerster. Yet, unimpressed, society and primarily language endorse statements that claim to be objective, and they also mostly neglect the social preconditions on which such statements are built.

This is not intended as a naive attempt to change the way society behaves. Instead, the focus is on adding another observer perspective, no more important than any other, but one that is directed towards the social functioning of the preconditions that lead to statements in society. The observer is, then, the ultimate precondition for a statement, yet he fascinatingly manages to stay out of the picture in many social phenomena. Presumably, this paradox is no accident, but indeed servers powerful social functions. We will come back to this later.