Georg Ivanovas From Autism to Humanism - systems theory in medicine

4. Systemic Basics

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4.2 Recursivity


Recursivity arises if a result of an operation is again the starting point of the same operation (von Foerster 1984).

The result of the limes operation might be (Zimpel 2005)

  • Infinite or stable values.
  • Bi-stable or n-stable values after a few iterations.
  • An unsolvable operation such as the division by zero.

Von Foerster emphasized especially the stable value. He exemplified such stable outcomes by extracting the square root of a number. Irrespective of the starting number (n>0), the result will always be one. The result is not determined by the operand but by the operator.

Thus, such a recursive operation leads to a result that is characteristic for the operator. Von Foerster called this phenomena eigen-behaviour of the operation.

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This is a general law. Its validity can be shown in many different ways.

Optically: When photocopies are made with a three-lens system, the result is a triple photocopy.

A recursion is when a copy is made from the copy. Already after the sixth passage we have a stable picture, a limes picture. In such a limes picture the result looks the same, regardless whether the copied object is a triangle, a square or even a word (Jürgens, Peitgen & Saupe 1989). The shape of the limes picture, its eigen-behaviour is determined by the structure of the copy machine not by the shape oft the copied item (illustration see 1).

Acoustically: If we feed a sound effects machine with a certain piece of music, the machine will transform the music according to certain principles. When the machine is recursively fed its own product the outcome will be, after some time, a stable sound, regardless whether the starting point was classical or rock music. The here presented examples are the Gnossienne No.1 by Satie and a bit of rock music by Nirvana, recursivly processed by Knut Auferman.

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A recursive system with a stable operator will develop (if there is enough time) the same eigen-behaviour independently of its original state. This process can be called trivialisation. If there is not enough time it will, at least, approach its eigen-behaviour. On the other side: Even a small change in the operator will lead to far reaching changes in time. This might explain delayed side-effects of drug therapy or how major changes can be attained by small interventions (chap. 5.3.e).

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All living is organized in a circular recursive way. Thus, physiological and biochemical processes follow the same pattern. In fact, the human cannot be understood without a clear concept of recursivity. Best known is the recursive neuronal self-organization. For example, perception modifies the neuronal connections in the visual system thus modifying perception (Chiu/Weliky 2003). Recursive processes are also the driving force in the development of all social behaviour (Zimpel 2000).

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Piaget was a forerunner in the study of recursive senso-motoric interactions. He studied the development of cognition in babies and children. He found that the different senses are interconnected: Perception interprets motion and motion interprets perception thus leading to a stable cognition (Piaget/Inhelder1966). His concepts have been further developed by von Foerster (von Foerster 1976) and Zimpel (Zimpel 2005). Lately brain research is able to demonstrate some neurological foundations of these recursive processes (Gottlieb/Mazzoni 2004). However, it is still preoccupied with rather simple connections, like sounds improving the learning of visual tasks (Seitz 2006, Smith et al. 2007).

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The development of eigen-behaviour and the process of signification are not separated (chap. 3.9). Thus, an object is not only an object an sich (as such). It is at the same time a sign for itself. Von Foerster called such a sign a token for eigen-behaviour. For a more formal deduction of this process see Rocha (1996).

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Recursive processes are difficult to understand. Actually, they are mostly misunderstood. When Science Magazine tried to explain recursivity, it chose as an example the Babutschka, the Russian puppet in a puppet in a puppet (Premak 2004). But the Babutschka is totally linear, no recursion is involved. This is a typical misunderstanding, often found in scientific papers. To generate a feeling for recursive processes and to demonstrate certain of their impacts, I would like to present a series of examples that are more or less connected with medical practice.

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One of the first to analyse recursive interactions was Bateson. His concept of schismogenesis describes a pattern that leads to discord and rift. Based on the principle of action and reaction he demonstrated that severe problems arise when a certain kind of interaction remains unchanged (Bateson 1972: 61-72). He distinguished a symmetric and a complementary form of schismogenesis. The symmetric form prevails when one party tries to go one better as the other with the same means. This is seen in an arms race, in market competition, in sport events or in the race to the moon. The film War of the Roses demonstrated it for couples.

The other form, the complementary schismogenesis, is much less sensible. It happens when the mutual reaction is somehow in opposition. This can be often observed in couples (example in appendix IV). When one partner, let’s say the wife, likes a little bit more conversation than the husband, she will talk more than he likes. As a reaction he will talk less. But this is too little for her, so she will talk more. This makes him talk even less. If this pattern continues for some time there will be a nagging wife and a frozen husband. There is no cause to be elaborated. The film Dogville showed this kind of schismogenetic pattern It also can be seen in the Stanford Prison Experiment..

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Such recursive processes are called positive and negative feedback mechanisms.

A positive feedback is the recursive loop stimulating itself leading to a cascade or an exponential development. It is seen, for example, in aggressive behaviour. Areas of the hypothalamus controlling aggression release adrenocortical hormones that stimulate this region (Kruk et al 2004). The resulting sudden explosive development of aggression is familiar to all of us. The positive feedback mechanism guarantees a quick response, crucial under many circumstances. Immune response is characterized by a whole set of comparable cascade effects. For example, immune cells multiply exponentially.

Such interactions involving a positive feedback mechanism are very sensitive to their initial conditions (Heylighen 2008: 4). In immune response “the difference between health and disease could be the ‘stochastic’ activation of a single cell, followed by positive feedback” (Germain 2001). It follows also, that positive feedback mechanisms are essentially unpredictable. Even unnoticeable changes might have an enormous impact.

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The cascade effects are controlled and suppressed by negative feedback mechanisms. They recursively inhibit their own expression. This has already be seen with the liar’s paradox and the electric bell (chap. 3.2). A typical example in medicine are the clock genes of every cell. They produce a ‘period protein’ that regulates negatively their own expression with a time delay thus producing an inner rhythm (Gelder et al 2003). Or: Osteoblasts release a substance (RANKL) that promotes osteoclast maturation and activity (Marx 2004b). In this example two partners (osteoblasts and osteoclasts) are involved to produce the negative feedback mechanism. Or: Immune cells produce the cytoplasmic protein A20 which activates a self-limiting mechanism thus preventing septic shock and other inflammatory processes (Boone et al 2004). Negative feedback mechanisms are more predictable than the positive feedback mechanisms, but they are also less controllable (Heylighen 2008: 4).

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The dynamics of complex systems typically exhibits a combination of positive and negative feedbacks, such that certain changes are amplified and others dampened.

The relation between Th1 and Th2 lymphocytes is such an example. Th1 inhibits Th2 and vice versa (Schwartz 2002). This is a feedback mechanism, although ‘negative’ as one partner impedes the other leads to an increasing difference between the two. Actually, it is a complementary schismogenetic pattern which plays a central role in the development of chronic disease. This Th1/Th2 relation is controlled by other feedback mechanisms, otherwise the system would never be stable. One of these mechanisms are the receptors of interleukin-7 (IL-7). As soon as the cell receives IL-7 it reduces its receptors on the surface (Park et al 2004), a typical negative feedback loop.

The coupling of positive and negative feedback mechanisms makes a system’s behaviour both unpredictable and uncontrollable (Heylighen 2008: 5).

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Autoimmune disease is characterized by lymphocytes which bare receptors against autoantigenes. Some of these autoreactive lymphocytes persist within the peripheral lymphocyte pool. Current evidence shows that they are controlled by other lymphocytes which are necessarily autoreactive to themselves (Kronenberg/Rudensky 2005).

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If test persons are shown two photographs and are asked which of the depicted persons is more attractive, they prefer the photograph they look at longer. The longer they look the more beautiful the person on the photo appears. People gaze at what they like and like more what they gaze at, something the authors call a cascade effect. When the test persons were not allowed to move their eyes no correlation between the duration of exposition and preference could be detected (Schimojo et al 2003). Here the interplay of recursion, movement and signification (‘beauty’) can easily be observed. The findings are in line with Piaget’s cognition theory.

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Sacks reports many cases where parts of the body vanish from inner representation through immobilisation (chap. 2.2). Only the incessant movement of the body maintains the body-scheme on the cortical level. Already after some hours limbs can be erased from the inner representation. It is the motion that creates a picture of the body, but the picture of the body is necessary to make movements. If this recursive process is interrupted, patients might be unable to move or even perceive parts of their body. They seem not to belong to the self anymore (Sacks 1984).

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Every social behaviour is based on recursive processes. A child throws leaves in the air, another child does the same. The children are thus getting connected and start to play with each other. People talking to each other take the same or a similar posture, putting the finger at the chin, crossing legs etc. This process has been called mirroring.

Mirroring has its neurophysiological equivalent in the so called mirror neurons in the frontal lobe. “These neurons are active when their owners perform a certain task, and in this respect are wholly unremarkable. But, more interestingly, the same neurons fire when their owner watches someone else perform that same task” (Motluk 2001a). However, mirroring is not restricted to the frontal lobe but includes also the function of the amygdala and of other brain structures (Gelder 2006).

This means that to a certain extend there is no difference between me and other on the neuronal level. This has been shown in many regards

Mirroring is a kind of structural coupling (chap. 4.8) between humans that exceeds previous theories of social development by learning. And it is not limited to seeing. To hear someone yawning might induce a mirroring effect in ourselves. But it is often sufficient to think of someone yawning to induce a physiological effect. That is, mirroring in a wider sense does not only exceed the distinction between me and other. It also exceeds the concepts of past, present and future. The semiotic aspect is included. This can be seen in the fact that a word like “wheezing” is able to induce asthma attacks in asthmatics (Rosenkranz et al 2005).

As families have similar brain structures (Motluk 2001b), it can be expected that mirroring is more intense between them. That is, the question whether something is inherited or acquired cannot be answered as clear as assumed. Probably behaviour is much more acquired than thought, but this behaviour is interwoven with genetic expression. It is no surprise that a recent twin research attributes only a small fraction of coincidences in the behaviour of twins to genetic disposition (Hughes et al. 2005). But such conclusions depend probably more on the frame (chap. 3.6) and on the punctuation (chap. 3.7) than on the data.

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Language is learned through a recursive process. Meaningless sounds of infants are reinforced, giving them simultaneously an intersubjective meaning (signification): “mamamama” – “Oh yeah, say ‘mama’”; or: “This is a spoon” – “ooon” - “Very good, spoooon” - “ooon”. The stable eigen-behaviour is the common language.

The acquisition of language does not necessarily follow this pattern, as children cannot be kept from learning a language even if there is no reinforcement. They do not learn the language but the whole system of semantics. Children seem to learn the frame factors and structure at first and are only later concerned with the content (Dewhurst/Robinson 2004).

But they need to be in communication. Just hearing a language (the content) without recursive interaction does not show any effect (Kuhl et al. 2003).

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Children in a deaf school in Nicaragua developed their own sign language with its own grammar (called a ‘big bang of language’) just communicating with each other. It seems that the only thing needed to generate a language is enough people to communicate. A deaf child in a family without a supporting system is not able to do this (Breuer 2000). It stays without the possibility of complex thinking. Deaf children remain in a state of debility if they do not learn to communicate (Sacks, 1989). The same is true for totally neglected and deprived children who have no ‘social input’ (Zimpel 2004).

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Communication creates abilities. Abilities create communication. It is structurally (genetically) determined to learn a language. Through the interaction with the environment a certain language is learned. It might as well be a sign language. Lately, Chomsky and colleagues gave a more specified concept of language and communication taking recursive elements into account. They differentiate between the faculty of language in a broader sense (FLB) and the faculty of language in a narrower sense (FLN). FLB is the faculty of communication, which is common in all animals and does not change through social contact. FLN is a recursive product with open-end possibilities and as such only existing in human beings (Hauser et al. 2002). Hauser and Fitch showed in experiments with monkeys that it is exactly the lack of recursive action that limits the development of language in animals (Fitch/Hauser 2004). An editorial related to Fitch and Hauser’s article asks: “Is language the key to human intelligence?” (Premack 2004). This can be definitely answered with no. Recursivity is the key to human intelligence.

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In the late sixties and early seventies there was an intense discussion about self-fulfilling prophecies. It was said and proved and disapproved and proved again that the expectations of the teachers lead to the expected behaviour in a pupil. This has been called ‘Pygmalion in the classroom’, Pygmalion- or Rosenthal effect (Gumpert/Gumpert 1968, Spitz 1999).

This effect has been defined as a “behavior that brings about in others the reaction to which the behavior would be an appropriate reaction. For instance, a person who acts on the premise that ‘nobody likes me’ will behave in a distrustful, defensive or aggressive manner to which others are likely to react unsympathetically, thus bearing out his original premise” (Watzlawick et al: 99).

It is not difficult to develop models, how it is possible that the expectations of a teacher leads to the expected behaviour: The teacher, driven by his expectation, shows a certain behaviour towards the ‘bad pupil’ that slightly differs from his behaviour towards other pupils. Even if it is only a little depreciating, the pupil will react (as it is impossible for him, not to react) and he will behave a little different than other pupils. This reaction might serve as a confirmation for the teacher that his ‘information’ of a ‘bad pupil’ was right. In their communication every recursive loop then might deepen the problem. It is a typical schismogenetic pattern.

An important, but unanswerable question is: Who is responsible? The teacher as he behaves according to the information he has got? Or is it the pupil because he does not work properly? Or is it the adviser?

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The parents’ belief is the best factor to predict a child’s alcohol consumption later. When one or both parents overestimate the alcohol consumption of their child the probability that the child will increase drinking is very high (Madon et al 2004).

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Women are bad in maths. They know that. When given a test and been told that the test might activate negative stereotypes about women's math ability, women performed worse than when they were told nothing. The effect is more prominent when men are present (Kersting 2003).

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The memory of 90 healthy older people was tested. When positive words like “guidance,” “wise,” “alert,” “sage” and “learned” were flashed during the test, memories were better and people even walked faster. When negative words like “dementia,” “decline,” “senile,” “confused” and “decrepit” were flashed, subjects’ memories were worse, and their walking paces slowed (Kolata 2006).

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Children of single parents have more problems than children with two parents. Everybody knows that. A recent study (Weitoft 2003) shows that these children have an increased risk of psychiatric diseases, suicide or suicide attempt, injury and addiction. It is a severe problem. All single parents know this burden and many feel guilty. They live in an atmosphere of uncertainty and shame. This atmosphere is the ideal breeding ground for an abnormal behaviour. It is inevitable that children in such an atmosphere behave strange. And even if they don’t, a slight abnormality that might be thought of as a normal problem of adolescence in other children is interpreted as a consequence of the single parent status. Then all kind of helpers (doctors, psychologists, social workers, teachers, kindergarten teachers and neighbours) will intervene and deepen the conflict by creating a Pygmalion effect.

Science is no help in this situation. Even if the first study about the children of single parents were false, the spreading of this ‘knowledge’ through radio, television and hundreds of newspapers, through paid and non paid helpers makes it a self-fulfilling prophecy and the second or third study on the subject will, this time correctly, find: “Yes! Children of single parents have more problems!”

With some legitimacy it is possible to state that psychological studies create the problems they find. The question how it really is makes no sense: It is an in principle undecidable question.

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It is normal to wake up several times a night, as the idea of a continuous sleep is a cultural myth (Moodallem 2007). The problem starts when waking up is seen as problem. Then, the very idea of having a problem prevents sleep (Bachmann/Steinhilber 2004). A real disease is created, when the physician gets involved and prescribes drugs. The person attains the official status of a patient, takes drugs which cannot be discontinued easily, as the rebound effect provokes sleeplessness. Actually, half of the patients with sleep disorders receive drugs like benzodiazepine (chap. 4.8) which might lead to addiction (Balkrishnan 2005).

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Breast feeding is recursive. The mother produces the amount of milk to a certain time according to the demands of the infant. The aim of helpers is often to avoid a negative impact of breast feeding onto the growth oft the child. The infant is sometimes weighed before and after drinking. Then the drunken quantity is compared with a table of reference values (established on formula-fed babies which overestimates the necessary weight increase). Afterwards the ‘missing’ quantity is administered by bottle. This prevents the mother to produce a sufficient quantity of milk, as the demand is restricted, making the gap between produced and ‘needed’ breast milk ever greater (Declercq et al. 2009). This is just another typical example of a self-fulfilling prophecy where well meant measures (weighing, schedule, positions, etc.) to prevent problems create the problems they pretend to prevent.


Footnote

(1) Illustrations by courtesy of Hartmut Jürgens. More details in H.O Peitgen, H. Jürgens, D. Saupe, "Bausteine der Ordnung - Fraktale", Klett-Cotta, 1992


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