Round and Round We Go:

In today’s post, I am looking at a simple idea – Loops, and will follow it up with Heinz von Foerster’s ideas on second order Cybernetics. A famous example of a loop is “PDCA”. The PDCA loop is generally represented as a loop – Plan-Do-Check-Act-Plan-Do…, and the loop is represented as an iterative process where it goes on and on. To me, this is a misnomer and misrepresentation. These should be viewed as recursions. First, I will briefly explain the difference between iteration and recursion. I am using the definitions of Klaus Krippendorff:

Iteration – A process for computing something by repeating a cycle of operations.

Recursion – The attribute of a program or rule which can be applied on its results indefinitely often.

In other words, iteration is simply repetition. In a program, I can say to print the word “Iteration” 5 times. There is no feedback here, other than to keep count of the times the word was printed on screen. On the other hand, in recursion, the value of the first cycle is fed back into the second cycle, the output of which is fed into the third cycle and so on. Here circular feedback is going on. A great example of a recursive function is the Fibonnaci sequence. The Fibonacci sequence is expressed as follows:

Fn = Fn-1 + Fn-2, for n > 1

Fn = 1, for n = 0 or 1

Here, we can see that the previous value is fed into the equation to create a new value, and this is an example of recursion.

From the complexity science standpoint, recursions lead to interesting phenomenon. This is not an iterative non-feedback loop any longer, where you come back to the same point again and again. With recursion, you get to circular causality with each loop, and you enter a new state altogether. Each loop is directly impacted by the previous loop. Anything that leads back to its original starting point doesn’t lead to emergence and can actually lead to a paradox. A great example is the liar paradox. In a version of this, a card has a statement written on both sides of a card. They are as follows:

  1. The statement on the other side of this card is FALSE.
  2. The statement on the other side of this card is TRUE.  

This obviously leads to a paradox when you follow it along a loop. You do not get to a new state with each iteration. Douglas Hofstadter wonderfully explained this as a mirror mirroring itself. However, with recursion, a wonderful emergence can happen, as we see in complexity science. Circular causality and recursion are ideas that have strong footing in Second Order Cybernetics. A great example of this is to look at the question – how do we make sense of the world around us? Heinz von Foerster, the Socrates of Cybernetics, has a lot to say about this. As Bernard Scott notes:

For Heinz von Foerster, the goal of second-order cybernetics is to explain the observer to himself, that is, it is the cybernetics of the cybernetician. The Greek root of cybernetics, kubernetes, means governor or steersman. The questions asked are; who or what steers the steersman, how is the steersman steered and, ethically, how does it behoove the steersman to steer himself? Von Foerster begins his epistemology, in traditional manner, by asking, “How do we know?” The answers he provides-and the further questions he raises-have consequences for the other great question of epistemology, “What may be known?” He reveals the creative, open-ended nature of the observer’s knowledge of himself and his world.

Scott uses von Foerster’s idea of undifferentiated coding to explore this further. I have written about this before here.

Undifferentiated coding is explained as below:

The response of a nerve cell encodes only the magnitude of its perturbation and not the physical nature of the perturbing agent.

Scott continues:

Put more specifically, there is no difference between the type of signal transmitted from eye to brain or from ear to brain. This raises the question of how it is we come to experience a world that is differentiated, that has “qualia”, sights, sounds, smells. The answer is that our experience is the product of a process of computation: encodings or “representations” are interpreted as being meaningful or conveying information in the context of the actions that give rise to them. What differentiates sight from hearing is the proprioceptive information that locates the source of the signal and places it in a particular action context.

Von Foerster explained the circular relationship between sense data and experiences as below:

The motorium (M) provides the interpretation for the sensorium (S) and the sensorium provides the interpretation for the motorium.

How we make sense depends on how we experience, and how we experience depends upon how we make sense. As Scott notes, we can explain the above relationship as follows:

S = F(M). Sensorium, S, is a function of motorium, M.

M = G(S). Motorium, M, is a function of sensorium, S.

Von Foerster pointed out that this is an open recursive loop, since we can replace M with G(S).


With more replacements for the “S”, this equation becomes an open recursive loop as follows:


Scott continues:

Fortunately, the circularity is not vicious, as in the statement “I am a liar”. Rather, it is virtuous or, as von Foerster calls it, it is a creative circle, which allows us to “transcend into another domain”. The indefinite series is a description of processes taking place in sequence, in “time”, with steps t, t+1, t+2 and so on. (I put “time” in quotes as a forward marker for discussion to come). In such indefinite recursive expressions, solutions are those values of the expression which, when entered into the expression as a base, produce themselves. These are known as Eigen values (self-values). Here we have the emergence of stabilities, invariances. The “objects” that we experience are “tokens” for the behaviors that give rise to those experiences. There is an “ultimate” base to these recursions: once upon a “time”, the observer came into being. As von Foerster neatly puts it, “an observer is his own ultimate object”.

The computations that give rise to the experience of a stable world of “objects” are adaptations to constraints on possible behaviors. Whatever else, the organism, qua system, must continue to compute itself, as a product. “Objects” are anything else it may compute (and recompute) as a unitary aspect of experience: things, events, all kinds of abstraction. The possible set of “objects” it may come to know are limited only by the organism’s current anatomy and the culture into which she is born.

I have written about this further here – Consistency over Completeness.

Heinz von Foerster said – The environment contains no information; it is as it is. We are informationally closed entities, which means that information cannot come from outside to inside. We make meanings out of the perturbations and we construct a reality that our interpretative framework can afford.

I will finish with a great observation from the Cybernetist philosopher Yuk Hui:

Recursivity is a general term for looping. This is not mere repetition, but rather more like a spiral, where every loop is different as the process moves generally towards an end, whether a closed one or an open one.

Please maintain social distance and wear masks. Stay safe and Always keep on learning…

In case you missed it, my last post was Observing with Your Hands:


  1. M. C. Escher Spiral
  2. Second Order Cybernetics as Cognitive Methodology. Bernard Scott
  3. A Dictionary of Cybernetics. Klaus Krippendorff

One thought on “Round and Round We Go:

  1. As always, I like your virtuous approach. I’ll add that “vicious” and “virtuous” cycles induce each other re- and pro-cursively too.
    Furthermore, coding-and-decoding codes itself into it-self-(de)coding codes. Therefore, as was proved fromally by Shannon, every coding system, given enough time (!), develops itself into an “error”-correcting code. Off course “error”, as the coding has to be “undifferentiated” and cannot distinguish itself between good (virtuous) and bad (vicious) “errors’. Probably why genetic coding codes both DNA (“double” helix) and (small letter)-RNA. And some even proposed that DNA coding responded to the “erroneousness” (de)coding introduced by RNA-viruses.

    In a long shot: as Adam “named” (or “coded”) all the plants and animals in the garden of Eden, he – as Eve noticed -, introduced “the knowledge of good and bad” and they therefore expelled themselves out of Paradise. (Funny, us using the word ex-spelling in English in this context; In Dutch, the word is “verbanning”, which comes from “ban”, also meaning “word”, being expelled by words).

    Here I see the “erroneousness” in the (grammatical) structure used in our language: we “hide” self-reference of expressions in speaking (everything I say, is being said by me, to paraphrase Maturana and Varela). We’re trained to do so, because we prefer a consistent (true/false, good/bad) use of language over a complete (and “inconsistent”) one. We have to maintain an illusion, or fiction, that we know what we’re talking about when we say we understand something.


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