Two-sided form, differentiation and second-order

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Kybernetes Two-sided form, differentiation and second-order observation in Escher’s artworks and Calvino’s stories Laura Appignanesi,

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Two-sided form, differentiation and second-order observation in Escher’s artworks and Calvino’s stories

Two-sided form

Laura Appignanesi Faculty of Engineering, Università Politecnica delle Marche, Ancona, Italy

Abstract Purpose – The purpose of this paper is to find a leading idea of the mid-twentieth century, demonstrating the pervasive nature of some concepts belonging to second-order systems theory. To achieve this objective, the paper looks at the art and literature of this era, to identify the principles developed by Luhmann in his late works. In particular, Escher’s drawings, Calvino’s stories and Luhmann’s concepts seem to express, in different ways, the same functioning mechanism of the complex social system. Design/methodology/approach – With reference to theoretical approach and methodology, this paper carries out an interdisciplinary demonstration by alternative modes of logos and mythos. Some of the pillars of general systems theory are examined through the logical articulation of concepts developed by SpencerBrown, von Foerster, and first of all through the late works of Luhmann, as well as through the analysis of Escher’s artworks and Calvino’s literary works. This paper interprets these artistic and literary works using cybernetic principles and systemic concepts, in particular, “two-sided forms,” “system–environment differentiation” and “second-order observation.” Findings – In general, the main finding is the similarity of fascination with paradoxes and forms, with postontological reasoning, in twentieth century. The result of the cross-reading of Escher, Calvino and Luhmann reveals the presence of what Simmel called the “hidden king”: a philosophical paradigm of an era. In mid1900s, this leading idea seems to express itself in the discoveries of biology and cybernetics, such as in Luhmann’s theory, art and literature. Escher’s drawings, Calvino’s stories and the concepts of Luhmann are projections of second-order system theory, in its constructivist value. Originality/value – The originality of this paper lies mainly in the demonstration of theoretical concepts through the alternative modes of logos and mythos. These reflections can provide a new perspective to investigate social sciences from a cultural angle. This particular approach allows a deep awareness of the theory. The concrete value is to provide a better understanding to manage complexity.

Keywords Luhmann, Cybernetics, Differentiation, Systems theory, Second-order observation, Calvino, Escher, Imaginary, Two-sided forms Paper type Conceptual paper

Introduction Douglas Hofstadter, author of the book Gödel, Escher, Bach: An Eternal Golden Braid, states in his introduction:

The author is most grateful to the anonymous reviewers for their helpful comments. Their suggestions and deep observations were priceless in enhancing the paper and stimulating new reflections.

Kybernetes © Emerald Publishing Limited 0368-492X DOI 10.1108/K-11-2017-0414

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I realized that for me Gödel, Escher and Bach were just shadows projected in different directions from some solid central essence. I tried to rebuild the central object and this book came out (Hofstadter, 1979, p. 30).

In Hofstadter’s book, Escher’s drawings, Bach’s music and Gödel’s mathematical theorems are considered as projections of something solid, which the author in fact constructed – realizing in wood the initials G, E, B and projecting their shadows onto the walls of a room. In a similar way, this paper ambitiously tries to consider Escher’s drawings, Calvino’s stories and Luhmann’s concepts as projections of the general systems theory, in its constructivist value (Figure 1). There are interesting cases of the use of languages belonging to different disciplines, which can serve as a sort of raw material for a theoretical elaboration (in fact, Luhmann draws on biology as well as cybernetics), and there are also interesting examples of the application of interpretation tools to systemic theoretical elaborations. For example, Roth translates the basic matrix structure from its Parsonian form to Spencer Brownian’s formal language, showing that new tools, such as the NOR gate marker, contain the tetralemma, an ancient matrix structure from traditional Indian logic (Roth et al., 2017). In this paper, however, the purpose is to use the expressive language of art in a logical demonstration using two different forms: drawing and literature. In fact, the imaginary can serve not only as a knowledge tool but also as a formative or demonstrative instrument. Reference can be made to Plato to identify the methodological value of the imaginary: In Protagoras, the sophist character offers two alternative ways of demonstrating a thesis: logos – the articulation of logical conceptual – and mythos – fantasy – which rather use the emotional resonance created by a tale’s narration. According to Plato, logos and mythos are equivalent methods aimed at the same goal. This paper thus begins with Escher’s tessellations, for which some of Calvino’s passages could serve as a caption, to find substantial conceptual coherence with Spencer-Brown’s “two-sided form” concept, such as that adopted by Luhmann in his late works. The analysis continues with artworks and stories that can be interpreted by other systems theory concepts. To avoid the need to take into account all the concepts of the general system theory, this paper, by way of example, will limit itself to the following: two-sided forms, system–environment differentiation and second-order observer. The aim is to identify in

Figure 1. Cover of the first edition of Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter, Basic Books, 1979

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mid-twentieth-century art and literature, the concepts developed by Luhmann as basic principles of functioning of the complex social system. In terms of its methodology, the paper presents some arguments of other authors while, at the same time, providing a genuine argument of its own. It focuses on the late works of Luhmann (1995, 1997) and on some of the follow-ups regarding the form-theoretical redescriptions of Luhmannian systems theory by Baecker (1999) in Problems of Form. In these sources, we can find concepts of observation and paradox as explanatory category, which also belong to Calvino’s stories and Escher’s artworks. In this way, these essential theoretical concepts are demonstrated by logical argumentation, as well as by the systemic interpretation of artworks and literature. In more general terms, the parallelism between the products of twentieth-century minds shows the immanent conscience of a collapsed meaning horizon and of traditional thinking in between the Second World War and the cold war. The two-sided form (fish/bird) and the two-faced city The first concept taken into consideration is that of “two-sided form.” Luhmann, in his late writings, draws from the essay Laws of Form (1969) by the mathematician G. SpencerBrown[1]. The first part of this section thus presents the logical development of the concept as it can be deduced from Spencer-Brown and Luhmann. In the second part, the concept itself is used as interpretative tool for reading artworks by Escher that can be considered graphical translations of the two-sided-form. Finally, for the first time, the writer Italo Calvino is added to the group of writers dealing with a paradoxical vision of reality grounded on systemic intuitions. In fact, the description of one of his “Invisible cities” seems to show the importance of the abstract concept we are discussing. As for mathematical demonstration, in the essay Laws of Form, G. Spencer-Brown develops a system based on differential logic. This deals with the emergence of something from nothing. Spencer-Brown defines, in an extremely formal way, the observation as applying a distinction. A distinction (or form) has two sides, consisting of a border that makes it possible to distinguish and separate both sides. Separation between two sides means that it must necessarily start from one side of the distinction (the “marked state” or “inner space”), and not from the other (“unmarked state” or “outer space”). Thus, there is an inside and an outside: each form is the outside from the perspective of the other form. The observation must indicate what is observed. Following Spencer-Brown, an observation is an operation that applies a distinction to indicate one side of the distinction, and not the other side. This operation consists of two elements: the distinction and the indication, “we cannot make an indication without drawing a distinction” (Spencer-Brown, 1969, p. 1). If the distinction makes it possible to indicate one of its two sides, the distinction cannot contain itself. The distinction itself remains unnoticeable because it cannot be indicated as one of the two sides of the distinction (Varela, 1975). Therefore, every distinction is a “blind spot,” and this blindness is assumed as a condition of the possibility of observation. We can only say that an observation is inevitably critical to its reference. We cannot begin by making a distinction without having already made a previous distinction. The first distinction is and is not the first distinction (Glanville and Varela, 1981; Kauffman, 1987). This paradox, however, does not paralyze Spencer-Brown’s calculation. The calculation begins with a simple directive that ignores the problem of “tracing a distinction” (1969, p. 3). The discussion of the paradox is subtle, as the calculation is sufficiently complex to introduce the concept of the “re-entry” of the distinction to inner space, of the form within the form (1969, pp. 56-57, pp. 69-76; cf. Esposito, 1996). Thus, the calculation is able to take into account the circularity or self-referentiality of the processes: it

Two-sided form

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Figure 2. “Two-sided form” scheme, by G. Spencer-Brown

can reflect on itself, and it can observe its observations. The calculation then “survives” to its basic paradox and, even though it cannot eliminate the paradox itself, the calculation can explain it. Thus, with Spencer-Brown, problems of self-observation and self-description become very important. From this point of view, what is omitted is a universe that is fully accessible to itself – that is, an observation that is not built. The calculation cannot establish an external perspective. The “re-entry” operation indicates the possibility of reintroducing the distinction that a system uses within its inner space, and thus the ability to direct system information processing by means of the unit of distinction which the system uses. Returning to the role of observer, it can be stated that “the fundamental cognitive operation that the observer performs is the operation of distinction” (Maturana and Varela, 1979, p. xxii; see also Varela, 1979). Consequently, the construction of the world depends on the processing of distinctions (or, in Spencer-Brown’s terminology, form). When something is observed, it is indicated as being distinct from something else: distinction allows the indication of one side of the distinction itself, and divides the world into what is momentarily included and what is excluded. In summary, a distinction in the vacuum is sufficient to create the space, where space is considered abstractly, without dimension. This implies two self-evident “laws” which, taken as axioms, allow the development of first an arithmetical system, and then an algebraic system (Robertson, 1999). Through the distinction operation, the self-reference of the system can emerge as a re-entry. Spencer-Brown interprets this re-entry as the creation of time, in the same way that distinction creates space: an inside and an outside; from one side it can indicate the other side, and vice versa (Figures 2 and 3). As for an artistic demonstration, we can refer to the artwork Bird/Fish No. 22, by M. C. Escher. In 1936, Escher visited the fourteenth-century Alhambra palace, the location of the last Islamic royal court in Spain. He was impressed by the majolica and stucco decorations, which became a rich source of inspiration for him, embodied in the numerous artworks representing plane tessellations. The word “tessellation” means a regular division of the plane, completely covered by closed forms, without overlapping or empty spaces. In Escher’s Bird/Fish No. 22, the figures of fish and birds emerge from two colors, white and red, in a contrast which can be compared to a binary code. The line that distinguishes the two chromatic areas constitutes the boundary of both forms at the same time: crossing the boundary line means entering into the shape of the fish or, alternatively, into that of the bird. Escher’s drawings develop themselves by plane tessellation – that is, through the repetition of a form. The Dutch artist’s imagery seems to replace the broken segment that divides the plane into marked and unmarked states, with a soft line dividing the red and white parts. This distinction produces a reality: if you are placed on the white side, it becomes possible to observe the red bird; if you are placed on the red side, it becomes possible to observe the white fish. The distinction and the related indication of one side of the form are therefore the basis of the creation of an observable reality.

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Two-sided form

Figure 3. Bird/fish No. 22, M.C. Escher, 1938 © 2018 The M.C. Escher Company - The Netherlands. All rights reserved, www.mcescher.com

From the fish side, you see the bird, whereas from the bird side, you see the fish: the distinction creates the system of fish and the system of birds by the demarcation of in/ out. Here is how Calvino expresses the same concept, describing an “invisible city” that one can consider a “two-sided form” without dimension (Calvino, 1974, p. 105): When you have forded the river, when you have crossed the mountain pass, you suddenly find before you the city of Moriana, its alabaster gates transparent in the sunlight, its coral columns supporting pediments encrusted with serpentine, its villas all of glass like aquariums where the shadows of dancing girls with silvery scales swim beneath the medusa shaped chandeliers. If this is not your first journey, you already know that cities like this have an obverse: you have only to walk in a semicircle and you will come into view of Moriana’s hidden face, an expanse of rusting sheet metal, sackcloth, planks bristling with spikes, pipes black with soot, piles of tins, blind walls with fading signs, frames of staved in straw chairs, ropes good only for hanging oneself from a rotten beam. From one part to the other, the city seems to continue, in perspective, multiplying its repertory of images: but instead it has no thickness, it consists only of a face and an obverse, like a sheet of paper, with a figure on either side, which can neither be separated nor look at each other.

In this tale is clearly visible the similarity of fascination with paradoxes and forms, postontological reasoning and “flat” forms – such as the Playing Cards in Alice in Wonderland, born from the mind of Lewis Carroll (1865), mathematician and writer, both logical and creative. The city called Moriana is like a “sheet of paper,” in that it lacks concreteness – it is just a concept useful for understanding the creation of something from nothing. The pivotal point is the following: “it consists only of a face and an obverse.” In other words, the operation is the distinction and then the indication of one side (the beautiful face) or the other side (the ugly face). There is a boundary, and you can stay in the light or in the dark. The other side of the form, beyond the boundary, is given simultaneously: the city (the form) qualifies itself by having two sides: the meaning emerges from the difference. As through theoretical argumentation, as through artistic representation, so it also is through literature: the basic concept of a two-sided form with a distinction between inside and outside is demonstrated.

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The differentiation of bird/fish from the environment and the invisible city’s functional differentiation Using the two-sided form, Luhmann develops the fundamental pivotal concept of general systems theory: the differentiation between system and environment. As in the previous section, this concept can now be demonstrated first of all by a theoretical argumentation. As indicated above, Spencer-Brown does not consider form to be a figure (Gestalt), but as a boundary that marks differences and forces us to clarify which part we are pointing to – and hence on which side of the form we are (Luhmann, 1997). It is important to emphasize that the form qualifies itself by having two sides, each of which identifies the other. To cross the boundary is a “creative act” and “to point” means to produce “a cut in the world, a difference” (Luhmann, 1997). The concept of form is therefore different not only from the content, but also from the concept of the context. A form can be the distinction of something from the rest, or may from its context (Luhmann, 1997). This concept of “form” as an elaboration of a distinction constitutes the theoretical premise on which the distinction between system and environment is based. Systems “observe themselves as systems-in-aenvironment,” so the system–environment distinction is used as a form of its own observations and descriptions. According to Luhmann, social systems are placed in an “environment” (Umwelt), which represents everything that is not part of the system. Human beings are part of this environment, since their psychic systems are autonomous entities differentiated by social systems. Compared to the external environment, social systems are autonomous (Ausdifferenzierung, “autonomization” or “external differentiation”). At the same time, they are also differentiated from within (Differenzierung, “internal differentiation”) into subsystems. In particular, it is possible to have ten systems: political system, economy, science, art, religion, legal system, sport, health system, education and mass media (Roth and Schütz, 2015). “In general terms, one speaks about ‘external differentiation’ or ‘autonomization’ when a system differs itself from its environment, drawing boundaries.” Then, with reference to the form, there is an inside and an outside. The system is enclosed by a boundary and the environment is outside. The autonomization of the system through the differentiation between system and environment also produces the observation of a differentiation within its environment (Umweltdifferenzierungung): for example, in the external environment of society, there are psychic systems and organic systems. Differentiation from the external environment does not depend on the system: however, it takes special forms depending on the distinctions that steer the observation of the system. In summary, every system can observe that there are other systems in its environment (Baraldi et al., 2002, p. 83): everything that comes to stand out can be described as a difference. At this point, it is important to notice the differing theoretical approach between the systems theory proposed by Luhmann and the systems theory developed by Parsons, concerning how the whole is divided into parts: System differentiation means differentiation of system/environment differences, and not differentiation by subdivision or breakdown of a whole into complementary parts. Consequently, the system cannot be seen as a whole subdivided into parts in relationship to each other.

Thus, internal differentiation “does not concern the decomposition of a ‘whole’ into ‘parts’, neither in a conceptual sense (divisio) nor in a concrete sense (partitio)” (Luhmann, 2012, vol. 2, p. 3). System differentiation therefore does not mean that everything is divided into parts and, consequently, consists only of parts and relationships between them. Rather, each system

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rebuilds the global system to which it belongs, and contributes to make it through its own system–environment difference (which depends on each subsystem). For an artistic demonstration, we can consider Sky and Water by Escher. If in Bird/Fish No. 22, the fish and birds unfold in a uniform and repetitive way, forming a sort of tapestry that could unravel infinitely, in Sky and Water, the composition becomes animated and acquires narrative effectiveness. In the middle part of the composition, the plane is divided by a chromatic dichotomy: the black parts define the shape of birds and the white parts define the shape of the fish. But moving away from the center to the upper part of the work, the birds gain autonomy and gradually detach themselves from the white background: dark shapes stand out with the clear definition of birds in flight. Similarly, moving from the center downward, the white shapes come to differ more in detail, emerging from a black background, which at the bottom becomes the sea, as the white background represents the sky. Now, by differentiation of the system (bird or fish) from the environment, a closed and structured system is obtained, a “marked space” that can observe itself (with its boundaries) in an undetermined environment (Figure 4). In sum, it seems possible in this artwork to read the basic principles of differentiation between a social system and its environment. It is important not to confuse the abstractness of Escher’s works with a realistic work. Here we are not dealing with the substance of the sea (or the sky), referred to a perspective of first order. The environment must be interpreted not as material, but as an external reference to mark the inside of the form. In other works, it is an observational device not unlike the Devil, who was created and fell to make observation of the Christian God possible (Luhmann, 1997). What happens if there is no differentiation? As Calvino says in his description of Zoe, it is not possible to realize order from noise:

Two-sided form

[. . .] In every city of the empire every building is different and set in a different order: but as soon as the stranger arrives at the unknown city and his eye penetrates the pine cone of pagodas and garrets and haymows, following the scrawl of canals, gardens, rubbish heaps, he immediately distinguishes which are the princes’ palaces, the high priests’ temples, the tavern, the prison, the slum. This – some say - confirms the hypothesis that each man bears in his mind a city made only of differences [. . .]. This is not true of Zoe. In every point of this city you can, in turn, sleep, make

Figure 4. Sky and Water I, M.C. Escher, 1938, Woodcut © 2018 The M.C. Escher Company - The Netherlands. All rights reserved, www.mcescher.com

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tools, cook, accumulate gold, disrobe, reign, sell, question oracles. [. . .]. The traveller roams all around and has nothing but doubts: he is unable to distinguish the features of the city, the features he keeps distinct in his mind also mingle. [. . .] But why, then, does the city exist? What line separates the inside from the outside, the rumble of wheels from the howl of wolves?” (Calvino, 1974, p. 34)

In the above story, when it becomes impossible to draw the “line [which] separates the inside from the outside,” it is impossible to understand the meaning itself. Calvino thus adds his personal poetic demonstration of the pivotal importance of differentiation and of the distinction between inside and outside for the meaningful existence of the closed system. The concept of differentiation in ancient languages Linguistics can help in understanding the concept of indication by distinction (although Luhmann did not take this into account). In particular, we can focus on the findings of the glottologist Carl Abel regarding the ancient Egyptian language. He observed that: In the Egyptian language, this unique relic of a primitive world, we find a fair number of words with two meanings, one of which says the exact opposite of the other (Freud, 1953, p. 185).

Abel added: Of all the eccentricities of the Egyptian lexicon, perhaps the most extraordinary is this: that, in addition to the words that unite antithetical meanings, it possesses other compound-words, in which two syllables of contrary meaning are united into a whole, which then has the meaning of only one of its constituent members. Thus in this extraordinary language there are not only words which denote both “strong” and “weak,” or “command” as well as “obey”: there are also compound-words like “oldyoung,” “farnear,” “bindloose,” “outsideinside”[. . .]; and of these, in spite of their conjunction of the extremes of difference, the first means only “young,” the second only “near,” the third only “bind,” the forth only “inside”[. . .] (Freud, 1953, p. 186-187).

In fact, these peculiarities affect many ancient languages, not only Egyptian. For example: in Latin, altus means both high and deep, and sacer both sacred and cursed; in ancient Greek, words with an antinomic meaning are many, for instance farmakon means both poison and medicine. This linguistic paradox is solved by Abel with a reasoning based on the evolution of language, which appears consistent with Brown’s (and Luhmann’s) concepts of two-sided forms, differentiation and indication. According to Abel, meaning is formed by comparison: Were it always light we should not distinguish between light and dark, and accordingly could not have either the conception of, nor the word for, light. [. . .] It is clear that everything on this planet is relative and has independent existence only in so far as it is distinguished in its relations to and from other things. [. . .] Since any conception is thus the twin of its opposite, how could it be thought of first, how could it be communicated to others who tried to think it, except by being measured against its opposite? [. . .] Since any conception of strength was impossible except in contrast with weakness, the word which denoted “strong” contained a simultaneous reminder of “weak,” as of that by means of which it first came into existence. In reality this word indicated neither “strong” nor “weak,” but the relation between the two, and also the difference between them which created both in equal proportion [. . .]. Man has not been able to acquire even his oldest and simplest conceptions otherwise than in contrast with their opposite; he only gradually learnt to separate the two sides of the antithesis and think of the one without conscious comparison with the other (Freud, 1953, p. 187). According to Abel, it is in the “oldest roots” that the antithetical double meaning can be observed. Then in the further course of its development this double meaning disappeared from the language

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and, in Ancient Egyptian at least, all the transitional stages can be followed up to the single meaning of the modern vocabulary. The original words with a double meaning separate in the later language into two with single meanings, while each of the two opposite meanings takes to itself a slight “reduction” (modification) in the sound of the original root. Thus, for example, as early even as in hieroglyphs, ken (“strongweak”) divides into ken, “strong,” and kan, “weak.” In other words, those conceptions which could be arrived at only by means of an antithesis become in course of time sufficiently familiar to the human mind to make possible an independent existence for each of their two parts, and therewith creation of a separate phonetic representative for each part (Freud, 1953, p. 188).

It can therefore be said that languages develop through the processes of differentiation, indication of one side and autonomization. Who observes the observer? The concept of the observer, which is a pillar of Luhmann’s systems theory, is introduced as part of so-called second-order cybernetics, characterized by its constructivist epistemology. The fundamental problem of cybernetics at the end of the 1960s was to redefine homeostatic systems to take into account the observer. According to Catherine and Gregory Bateson, in studying the “cybernetic nature of self and the world” (Bateson, 1972, p. 16), the observer must be considered part of the picture. Constructivist assumptions thus replace realistic assumptions. According to Gregory Bateson, our knowledge is the end and outcome of the internal processes that we use to build our inner world (perception and cognition). The inner world is a metaphor of the outer world. In an attempt to avoid the trap of solipsism, the Batesons attribute an important role to the objective constraints, claiming that only constructions compatible with reality can survive in the long run. The article “The frog’s visual cortex” (Lettvin et al., 1959) shows that a frog’s perception does not record reality, but rather builds it. The eye speaks to the brain through a language already highly organized and interpreted, rather than by simply transmitting light impulses. As a result, the frog sees just what is selected and communicated by the eye. In Autopoiesis and Cognition (Maturana and Varela, 1979), it is stated that the activity of the nervous system is determined by the nervous system itself, and not by the outside world (p. 15): the nervous system’s action is determined by its organization, and so there is a circular dynamics. In summary, a living system responds to the environment in ways determined by its own autopoiesis (or self-reproduction), and it builds its environment through the interaction domain made possible by its autopoietic organization. A living system operates within the boundaries of an organization – that is, it is operatively closed and leaves the world out. From the autopoietic perspective, no information crosses the boundary that separates the system from its environment. As in the case of the frog, we do not see the world “outside,” but only what our systemic organization allows us to see (Maturana and Varela, 1988; Maturana, 1997). In addition, “everything said is said by an observer” (Maturana and Varela, 1979, p. xxii; cf. von Foerster, 1978; Vanderstraeten, 1997). The world merely irritates the system, raising an alarm that triggers changes determined by its own organization: this process is expressed by the phrase “order from noise”. Second-order cybernetics draws on mathematical calculation to clarify the basic operations of observing systems. Observation must indicate what is observed. Following Spencer-Brown, an observation is an operation that applies a distinction to indicate one side of the distinction, and not the other side. This operation consists of two elements: the distinction and the indication; in fact “we cannot make an indication without drawing a

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distinction” (Spencer-Brown, 1971, p. 1). Thus, already in Spencer-Brown’s calculations, selfobservation and self-description problems have become important. If the distinction makes it possible to indicate one of its two sides, the distinction cannot contain itself. The distinction itself remains unnoticeable, because it cannot be indicated as one of the two sides of the distinction (Varela, 1975); every distinction is thus a “blind spot,” and this blindness is assumed as a condition of the possibility of observation. It can only be said that an observation is inevitably critical to its reference. It also introduces the concept of the “reentry” of the distinction within inner space – that is, within the form (1971, pp. 56-57, pp. 69-76; cf. Esposito, 1996). The theory then takes into account the circularity or selfreference of the processes: the system can reflect on itself, can observe its own observations. According to Spencer-Brown, what is left out is a universe completely accessible by itself – that is, an observation that is not built. The calculation cannot establish an external perspective. The operation of “re-entry” indicates the possibility of reintroducing the distinction used by the system within its internal space; there is thus the ability to direct system information processing by means of the unit of distinction used. According to the second-order cybernetics, it is the system differentiation that defines the meaning of what is observed: one must therefore observe the observer and not the objective world. “When described, the variability is represented by constancy, namely by the timeindependent describing sentences. It is when we interpret the sentences that we add the reality, the described variability” (Löfgren, 1981, p. 130). In practice, we must find the way using our own guidance. Second-order cybernetics thus reflects on the role of the observer in the observed universe. The subject–object distinction made by traditional epistemologies is abandoned, and it tries to include itself (as observers) among the objects (what is observed). The theory focuses on the descriptor’s description, the observer’s observation, and the cybernetics of cybernetics. This approach is clear in Observing Systems (1984) by Heinz von Foerster, where the title’s wordplay already indicates that systems can be observed and, at the same time, they can observe: in other words, a system can be both the object and the subject of observation. The philosophical implications are obvious: constructivism had focused on the themes of construction versus representation. But, according to the second-order cybernetics, the world cannot be objectively represented within the system. The world is built, the environment does not contain information (Von Foerster, 1984) and every piece of information is an internal construction (Von Foerster, 1999). Reality is a construction, and this construction does not correspond to the outside world; it depends instead on the distinction between the marked state (which is indicated) and the unmarked state (not shown) just imagined by the observing system. The observing system’s contribution, which allows the construction of the information, is the act of distinction. In other words, observations cannot copy, paint or represent an external reality, because it is not possible to observe a reality that exists independently from observation: But how can you look at something and set your own ego aside? Whose eyes are doing the looking? As a rule, you think of the ego as one who is peering out of your own eyes as if leaning on a windowsill, looking at the world stretching out before him in all its immensity. So then: there is a window that looks out on the world. The world is out there; and in here, what is there? The world still – what else could there be? With a little effort of concentration Palomar manages to shift the world from in front of him and set it on the sill, looking out. The world is also there, and for the occasion has been split into a looking world and a world looked at. And what about him, also known as “I,” namely Mr Palomar? Is he not a piece of the world that is looking at another piece of the world? (Calvino, 1985, p. 102)

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Palomar wonders: who is observing the scene? And how does he look at it? The very name of the character (borrowed from an astronomical observatory in California) indicates the main role of the observer: Mr Palomar observes himself as part of the world. Calvino’s selfobservation can embody itself in Escher’s ante-litteram selfie Hand with Reflecting Sphere, which represents the author mirrored on a sphere while he observes the sphere itself holding him. The observer is part of the observed object and of the observer’s observation. In this passage, which Calvino draws with quiet irony, it is thus possible to read between the lines to uncover the concept of “second-order observation” (observing the observer’s observation), which is a Luhmann’s conceptual pillar. To quote Spencer Brown:

Two-sided form

We make take it that world undoubtedly is itself (i.e., is indistinct from itself), but, in any attempt to see itself as an object, it must, equally undoubtedly, act so as to make itself distinct from, and therefore false to, itself. In this condition it will always partially elude itself. This partiality precludes any possibility of representation or mimesis and any holistic theory. It is not sufficient to say that a part is able to express or to symbolize the whole (Spencer, 1969, p. 105).

This “second-order observation” is thus unequivocally described by literary prose and artistic representation (by mythos language), where paradox is an explanatory category (Figure 5). The internal perspective of the observer is also a central issue in many of Escher’s artworks. In Escher’s lithograph of 1935, a hand holding a sphere mirrors the image of the man holding and watching the sphere itself. He is represented within a furnished room with a distant window illuminating the scene. The curved surface sends a distorted image of lines and proportions back. However, the impression is that the sphere, like a smartphone’s lens in a selfie-lover’s hand, captures the author’s image and his surrounding environment, transforming observation’s subject into his object. Moreover, the sphere takes into account the deformation caused by the medium through which observation takes place (as myopic Mr Palomar knows, in fact he has a very different view when he looks at things with his bare eyes instead of with glasses). The curved lines of furniture in Escher’s study, as can be seen on the sphere, depend on the kind of observation and not on a constructive defect. As deeply demonstrated by Luhmann, and previously by Spencer-Brown and von Foerster, observation itself has a constructive power. Calvino and Escher are not content to look at reality. They observe it in reverse, looking for it in a mirror reflection. They lie outside of the picture. When an artist appears as part of the observed object, he becomes the creator of what he is observing; a person who observes with the means available to her (such as eyes and mirrors) creates a representation of her own world: So from now on Mr Palomar will look at things from outside and not from inside. But this is not enough: he will look at them with a gaze that comes from outside, not inside, himself. He tries to Figure 5. Hand with Reflecting Sphere, M.C. Escher, 1935, Lithograph © 2018 The M.C. Escher Company - The Netherlands. All rights reserved, www.mcescher.com

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perform the experiment at once: now it is not he who is looking; it is the world of outside that is looking outside. [. . .] Having the outside look outside is not enough: the trajectory must start from the looked-at thing, linking it with the thing that looks (Calvino, 1985, p. 112).

In the section above, Calvino returns to the observation and its point of view: from inside or outside. He suggests a device linking the object and the subject of observation: a mirroring sphere, for example (Figure 6). In 1934, Escher produced the lithograph Still Life with Spherical Mirror, in which two objects on a newspaper are standing on a book. The composition’s black background gives emphasis to these objects: a metallic bird with a human face and a mirroring globe. The convex surface reflects an environment that we presume lies behind the bird-observer (the artist’s study and Escher himself drawing the picture). The mirroring surface occupies a large space and constitutes the main object of the entire right part of the artwork. But the other part does not show the reflected environment. It is reproduced by Escher only as it is mirrored on the sphere, portioned and deformed: the room and the man at desk exist only if and to the extent that the observer-bird looks at them by the means it has at its disposal, with distortions due to the curved surface. The rest, such as the true extension of the room, other furniture and objects, real reproduction without optical deformation, does not affect the artist. The true protagonist is the observing subject, which is partly mirrored in its own object of observation: it is a metallic bird with a human face, a disturbing creature, mechanical but capable of displaying an ironic facial expression, and theoretically capable of flying – that is, of obtaining further detached point of view. This is the surreal solution adopted by Escher to describe the operation of what Luhmann calls the “second-order observation”: the observation of an observing observer. The bird is out of the system (the mirroring sphere) in the outside environment. Thus, in summary, the main subject is a disturbing stylized bird that is observing something. What? A glossy globe, a convex mirror, providing an image of a room with a man sitting at the desk; the man is the creator of the entire scene, observed in the act of creating it. This is not all: in its reflected image, the observer-bird sees itself observing: this is an original picture, deformed by the curved surface and taken from a lower perspective – in fact, it allows the bird’s belly to be seen. In systemic terms, we could say that the observer

Figure 6. Still Life with Spherical Mirror, M. C. Escher, 1934, Lithograph © 2018 The M.C. Escher Company - The Netherlands. All rights reserved, www.mcescher.com

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is out of the room-system, but the latter contains the former (as mirrored by its belly’s reflection). Observation is thus an autologous operation (which contains itself) making possible otherwise difficult observations: a bird can look forward, can bend its head and look at its legs and can twist its neck and look at its tail, but without the mirror’s aid, it would never see its belly. The theme of the thing’s reversal, made possible by an unconventional point of view, was also taken into account by Calvino, who describes Mr Palomar in front of a gecko. Even this reptile, like the metal bird, seems more interesting when seen from its belly: On the terrace, the gecko has returned, as he does every summer. An exceptional observation point allows Mr Palomar to see him not from above, as we have always been accustomed to seeing geckos, treefrogs, and lizards, but from below. In the living room of the Palomar home there is a little show-case window that opens on the terrace [. . .]. Every evening, as soon as the light is turned on, the gecko, who lives under the leaves on that wall, moves onto the glass, to the spot where the bulb shines [. . .]. Mr Palomar and Mrs Palomar every evening end up shifting their chairs from the television set to place them near the glass; from the interior of the room they contemplate the whitish form of the reptile against the dark background. The choice between television and gecko is not always made without some hesitation; each of the two spectacles has some information to offer that the other does not provide: the television ranges over continents gathering luminous impulses that describe the visible face of things; the gecko, on the other hand, represents immobile concentration and the hidden side, the obverse of what is displayed to the eye (Calvino, 1985, p. 52).

Thus, Calvino translates into literary prose the theme of observation from special perspectives, as Escher does by drawings, and concentrates his reflection on the hidden side of reality, or better said, the invisible structure. Neither is the mirror theme lacking: The ancients built Valdrada on the shores of a lake, with houses all verandas one above the other, and high streets whose railed parapets look out over the water. Thus the traveler, arriving, sees two cities: one erect above the lake, and the other reflected, upside down. Nothing exists or happens in the one Valdrada that the other Valdrada does not repeat, because the city was so constructed that its every point would be reflected in its mirror [. . .]. At times the mirror increases a thing’s value, at times denies it. Not everything that seems valuable above the mirror maintains its force when mirrored. The twin cities are not equal, because nothing that exists or happens in Valdrada is symmetrical: every face and gesture is answered, from the mirror, by a face and gesture inverted, point by point. The two Valdradas live for each other, their eyes interlocked; but there is no love between them (Calvino, 1974, p. 53).

The mirror theme is a classical theological argument and is often quoted by Luhmann from the works of Cusanus. To strengthen the (historical) argument, both Calvino and Luhmann reflect on the concept of the mirror as a parasite of self-duplication between I and me (I see myself). Luhmann quotes Spencer Brown, Laws of Form, p. 105: The world (is) undoubtedly itself (i.e., is indistinct from itself), but in any attempt to see itself as an object, it must, equally undoubtedly, act so as to make itself distinct from, and therefore false to, itself. In this condition it will always partially elude itself.

A few considerations on complexity Escher’s tessellations and Calvino’s passages allow us to identify the concept of “two-sided forms” developed by Spencer-Brown as a creative act: the simple double-operation of distinction–indication creates a complex reality whose coordinates are space (inside/outside the form) and time (through the re-entry of the form in the form itself). This makes it possible to differentiate the system from the environment.

Two-sided form

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As these concepts are taken up by Luhmann in his elaboration of the general theory of functional systems, we can say: the systemic approach can be used as the interpretative key to read figurative artworks and narrative texts; alternatively, it seems possible to illustrate Luhmann’s theory through an analysis of Calvino’s text and through an interpretation of Escher’s drawings: both can be seen as projections of abstract logical theories. In fact, with lightness and irony, they penetrate under the surface of things and reveal the intimate essence of the complex reality, which appears paradoxical but simple: The Great Khan tried to concentrate on the game: but now it was the game’s reason that eluded him. The end of every game is a gain or a loss: but of what? What were the real stakes? At checkmate, beneath the foot of the king, knocked aside by the winner’s hand, nothingness remains: a black square, or a white one. By disembodying his conquests to reduce them to the essential, Kublai had arrived at the extreme operation: the definitive conquest, of which the empire’s multiform treasures were only illusory envelopes; it was reduced to a square of planed wood (Calvino, 1974, p. 131).

We can recall that Lewis Carroll (1865, 1871) first wrote the story Alice’s Adventures in Wonderland, which plays on the theme of playing cards, and then Through the LookingGlass and What Alice Found There, which focuses on the theme of chess (aside from the mirror)[2]. Continuing with the parallelism between literature and art, consider Escher’s Metamorphosis III. The artist, by simplifying the complexity of urban rendering, comes to draw an increasingly stylized chessboard without dimension, and then a pure concept (Figure 7). Metamorphosis III unrolls like a carpet and offers a seamless sequence of scenes that turn into each another until they return to the same starting image. To capture the composition’s complexity as a whole, it is necessary to limit the observational range to individual portions. It begins with a composition of perpendicular words that form a regular lattice, on which all subsequent forms are based. They then transform: first into the black and white squares of a chessboard, then lizard shapes, then honeycomb cells, then bees, butterflies, fish, birds, houses, a village overlooking the sea, and then into the chessboard again with its black and

Figure 7. Metamorphosis III, M. C. Escher, 1967/8, Woodcut © 2018 The M.C. Escher Company - The Netherlands. All rights reserved, www.mcescher.com

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white squares, and finally into the initial lattice composed of the same perpendicular words. All the variegated multiplicity returns to a simple geometric composition of black and white forms. Complexity is reduced to ordered words on an abstract plane: a simple concept is both an immanent framework of concrete reality and a generating principle of its structure. As Calvino says in Six memos for the next millennium: [. . .] geometrical composition, of which we could trace a history in world literature starting with Mallarmé, is based on the contrast of order and disorder fundamental to contemporary science. The universe disintegrates into a cloud of heat, it falls inevitably into a vortex of entropy, but within this irreversible process there may be areas of order, portions of the existent that tend toward a form, privileged points in which we seem to discern a design or perspective (Calvino, 1988, p. 69).

Conclusions With reference to theoretical background and methodology, the paper carries out an interdisciplinary demonstration by alternative modes of logos and mythos. Some of the pillars of general systems theory are examined through the logical articulation of concepts developed by Spencer-Brown, von Foerster, and first of all through the late works of Luhmann, as well as through the analysis of Escher’s artworks and Calvino’s literary works. In general, the main finding is the similarity of fascination with paradoxes and forms, with post-ontological reasoning, in twentieth century. We can say that there is a selfdescription through functional–equivalent forms in the poetic genre and in theoretical systems thinking (cybernetic and metamathematical) in that era, and the observations from the art system describe the similarities of its own productions (Calvino and Escher) in the mirror of Luhmannian arguments. As example, the paper first considered the basic concepts of the two-sided-form. After a theoretical explanation, it presented an artistic demonstration through the systemic interpretation of an image of tessellation, and through a systemic interpretation of a literary description of an imaginary city. The same parallelism between logical argumentation and the imaginary was drawn out with reference to the concept of the distinction between system and environment and functional differentiation. Later, the pivotal Luhmannian concept of secondorder observation was taken into consideration. Even in this case, the argument began with a theoretical explanation and proceeded to a systemic reading of artworks by Escher and texts by Calvino. It should be possible to continue to other concepts of systems theory and discover the rationality of the complexity in further artworks and stories by Escher and Calvino, with reference to a sort of an immanent chess in a complex context. In conclusion, the paper shows how some concepts developed by Luhmann in his general systems theory can be found in artworks by Maurits Cornelis Escher and in writing by Italo Calvino. Another oeuvre contemporary with Luhmann’s systems theory thus explains the similarity of fascination. In particular, Calvino can be added to the list of post-Second World War artists and novelists working with paradoxes and post essence arguments. As result, the paper serves to show how late Luhmannian systems thinking is less unique than it itself proclaims (by means of his delineation of his theory against the “oldEuropean Semantics”). It demonstrates how the similarity of the fascination for a collapsed meaning horizon and traditional thinking in both sociological theory and artistic products was a common trait in the twentieth century. This result may be useful for better understanding the common themes in the postwar and cold war periods of broken coherences in world concepts. In the cross-reading of artworks, literature and social theory, the presence of what great sociologist Georg Simmel called the “hidden king” of an era can be discerned:

Two-sided form

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In every great, distinguished cultural epoch, one can find a central notion which not only emanates spiritual movements but attracts them, too; maybe this era has a general conscience of that notion or future observers use to recognize it as the ideal focus for these movements in all their meanings. Naturally, each such central notion is subject to countless alternations, disguises, and oppositions; but with all that, it always stays the ‘hidden king’ of its epoch (Simmel, 1918, p. 11).

The “hidden king” is the leading idea of an historic age. Simmel’s metaphor: Brings with it narrative and imaginary associations that vividly demonstrate the intrinsic human tensions – operative at the three levels of personality, society and culture, and recurrent across the specific realms (“worlds”) of human activity and experience (economic activity, aesthetics, religion, etc.) (Andrews, 2017).

In the twentieth century, the “hidden king” seems to express itself in Escher’s drawings, Calvino’s stories and in the second-order systems theory, infused by meta-mathematical thinking. In his late works, Luhmann’s concepts reveal the theoretical structure behind visible reality, of which the paradox is an explanatory category. Theory and imaginary manifestations thus make visible the Simmelian hidden king of this era: the fascination of the logic of paradoxes. Accordingly, these reflections can provide to researchers and practitioners a new perspective to investigate social sciences from a cultural angle. Even if the topic concerns an abstract issue, it shows the pervasive nature of the philosophical paradigm in every aspect of social life. This finding allows a deep awareness of these mechanisms and their better understanding. There is no antithesis between theoretical and empirical issues; these two approaches are complementary and synergic because an effective theoretical understanding is necessary to manage concrete complexity. Notes 1. Luhmann refers to Spencer-Brown and von Foerster and extracts some elements of their theories. By proposing a unity of coherence, divergent readings of von Foerster and Spencer-Brown are imported, as Roth pointed out in the article “Parsons, Luhmann, Spencer Brown. NOR design for double contingency tables” (2017). 2. It is also interesting to underline the similarities of Calvino and Jorge Louis Borges (1960, 1964, 1998), another contemporary writer: for instance, The Library of Babel and The Mirror of Enigmas Can easily be used to show correspondences in the appropriation of paradoxical language; the sentence “the machinery of the world is far too complex for the simplicity of men” (p. 50) shows the similarity and comparability of second-order observations and limitations of temporal forms as observational devices.

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Borges, J.L. (1964), The Mirror of Enigmas, Labyrinths, Trans. James E. Irby, Penguin, Harmondworth. Borges, J.L. (1998), The Library of Babel, Collected Fictions, Trans. Andrew Hurley, Penguin, New York, NY. Calvino, I. (1974), Invisible Cities, Trans. W. Weaver, Harcourt Brace Jovanovich, New York, NY. Calvino, I. (1985), Mr Palomar, Trans. W. Weaver, Harcourt Brace Jovanovich, New York, NY. Calvino, I. (1988), Six Memos for the Next Millennium, Harvard University Press, Cambridge MA. Carroll, L. (1865), Alice’s Adventures in Wonderland, Macmillan, London. Carroll, L. (1871), Through the Looking-Glass, and What Alice Found There, Macmillan, London. Esposito, E. (1996), “From self-reference to autology: how to operationalize a circular approach”, Social Science Information, Vol. 35, pp. 269-281. Freud, S. (1953), Collected Papers, Vol. 4, Hogarth Press, London. Glanville, R. and Varela, F.J. (1981), “Your inside is out and your outside is in” (Beatles 1968), Academy of Management Journal, in Lasker, G.E. (Ed.) Applied Systems and Cybernetics: Proceedings of the International Congress on Applied Systems Research and Cybernetics, volume 2, Pergamon, New York, pp. 638-641. Hofstadter, D. (1979), Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, New York, NY. Kauffman, L.H. (1987), “Self-reference and recursive forms”, Journal of Social and Biological Structures, Vol. 10, pp. 53-72 (58-59). Lettvin, J.Y., Maturana, H.R., McCulloch, W.S. and Pitts, W.H. (1959), “What the frog’s eye tells the frog’s brain”, Proceedings of the IRE, Vol. 47 No. 11. Löfgren, L. (1981), “Knowledge of evolution and evolution of knowledge”, in Jansch, E. (Ed.) Evolutionary Vision: Towards a Unifying Paradigm of Physical, Biological, and Sociocultural Evolution, Boulder, pp. 129-151. Luhmann, N. (1995), “The paradoxy of observing systems”, Cultural Critique, No. 31, pp. 37-55. Luhmann, N. (1997), “The control of intransparency”, Systems Research and Behavioral Science, Vol. 14 No. 6, pp. 359-371. Luhmann, N. (2012), Theory of Society, Translated by Rhodes Barrett, Stanford University Press, California. Maturana, H. and Varela, F.J. (1979), Autopoiesis and Cognition: The Realization of the Living, Springer. Robertson, R. (1999), “Some-thing from no-thing: G. Spencer-Brown’s laws of form”, Cybernetics & Human Knowing, Vol. 6 No. 4, pp. 43-55. Roth, S. and Schütz, A. (2015), “Ten systems: toward a canon of function systems”, Cybernetics and Human Knowing, Vol. 22 No. 4, pp. 11-31. Roth, S., Luhmann, P. and Brown, S. (2017), “Nor design for double contingency tables”, Kybernetes, Vol. 46 No. 8, pp. 469-1482. Simmel, G. (1918), Der Konflikt Der Modernen Kultur: Ein Vortrag, Duncker und Humblot, München & Leipzig. Spencer, B.G. (1969), Laws of Forms, Allen & Unwin, London. Von Foerster, H. (1984), Observing Systems, Intersystems, Seaside, p. 304 e ss. Further reading Appignanesi, L. (2015), “Art as communication of rural identity: some photographs by Mario Giacomelli”, International Journal of Sociology and Anthropology, Vol. 7 No. 9, pp. 197-203. Appignanesi, L. and Paladini, M. (2016), “La distruzione dell’arte nel processo di trasformazione della società”, Cambio: Rivista sulle trasformazioni sociali, p. 11.

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Cipriani, R. (2012), “Per una sociologia dell’immaginario”, Sociologia della Comunicazione 44, Franco Angeli, Milano. Croce, B. and Galasso, G. (1990), Breviario di Estetica e Aesthetica in Nuce, Adelphi, Milano. Durand, G. (1972), Le strutture antropologiche dell’immaginario, Dedalo, Bari. Febbrajo, A. (1975), Funzionalismo strutturale e sociologia del diritto nell’opera di Niklas Luhmann, Giuffrè, Milano. Febbrajo, A. (2016), “Constitutionalism and legal pluralism”, in Febbrajo, A. and Corsi, G. (Eds) Sociology of Constitutions: A Paradoxical Perspective, Ashgate, Farnham. Fornasari, F. (2012), “Nulla è senza un segno: la mappa e la rappresentazione del mondo: due casi di studio”, Sociologia della Comunicazione, Vol. 44, Franco Angeli, Milano. Luhmann, N. (1976), “The future cannot begin: temporal structures in modern society”, Social Research, Vol. 43 No. 1, pp. 130-152. Luhmann, N. (1977), “Differentiation of society”, International Journal of General Systems, Vol. 8 No. 3, pp. 131-138. Luhmann, N. (1982), “The world society as a social system”, The Canadian Journal of Sociology, Vol. 2 No. 1, pp. 29-53. Luhmann, N. (2000), Art as Social System, Trans. E.M. Knodt, Stanford University Press, California. Luhmann, N. (2001), Sistemi sociali. Fondamenti Di Una Teoria Generale, trans. A. Febbrajo & R. Schmidt, Il Mulino, Bologna. Platone, a cura di G. Reale (2006), Protagora, Bompiani, Milano. Schelling F.W., a cura di Klein A (1996), Filosofia dell’arte, Prismi, Napoli. Simmel, G. (1982), La differenziazione sociale (Über sociale Differenzierung, 1890), Laterza, RomaBari. Simmel, G. (2011), A View of Life: Four Metaphysical Essays with Journal Aphorisms, Chicago University Press, Chicago. Stenner, P. (2004), “Is autopoietic systems theory alexithymic? Luhmann and the socio-psychology of emotions”, Soziale Systeme, Vol. 10 No. 1, pp. 159-185. Stichweh, R. (2000), “On the genesis of world society: innovations and mechanisms, distinktion – tidsskrift for samfundsteori (Arhus, Dk.)”, Vol. 1 No. 1, pp. 27-38. Turchi, P. (2004), Maps of the Imagination: The Writer as Cartographer, Trinity University Press, San Antonio-Texas. Wright Mills, C. (1962), L’immaginazione Sociologica, il Saggiatore, Milano.

About the author Laura Appignanesi graduated in economics and received PhD in system theory and sociology of normative and cultural processes. As a writer, she published Colori (PeQuod, 2007), 24 secoli di storie (Affinità Elettive, 2013) and Festa di fine stagione (Italic & Pequod, 2017). As a sociologist, she published many scientific articles in international journals and some chapters in miscellaneous books. She participated in the translation of Die Gesellschaft der Gesellschaft, N. Luhmann 1997 (in press). Her fields of research are systems theory, general sociology, legal sociology, sociology of territory and sociology of art. Laura Appignanesi can be contacted at: [email protected]

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