behavioral sciences Article

What Can Synergetics Contribute to Embodied Aesthetics? Hermann Haken Institute for Theoretical Physics, Center of Synergetics, Pfaffenwaldring 57/4, Stuttgart University, D-70550 Stuttgart, Germany; [email protected] or [email protected]; Tel.: +49-(711)-685-64990; Fax: +49-(711)-685-64909 Received: 9 August 2017; Accepted: 30 August 2017; Published: 2 September 2017

Abstract: I deal with perception and action (e.g., movements) using results from synergetics, a comprehensive mathematical theory of the self-organized formation (emergence) of spatial, temporal, or functional structures in complex systems. I illustrate basic concepts such as order parameters (OPs), enslavement, complexity reduction, circular causality first by examples of well-known collective, spontaneous modes of human behavior such as rhythmic clapping of hands, and so forth, and then by face recognition. The role played by OPs depends on context. In the case of face (or pattern) recognition an OP represents the concept of an individual face (action of mind) and it enslaves the action (firing rates) of neurons (body). This insight allows me to interpret syndromes as order parameters playing their mind/body double role. I present criteria for the identification of OPs and discuss their general properties including error correction and remedy of deficiencies. Contact is made with a recent paper by Sabine Koch on embodied aesthetics. My approach includes the saturation of attention at various time scales (ambiguous figures/fashion). Adopting a psychological perspective, I discuss some ingredients of beauty such as proportionality and symmetry, but also the importance of irregularities. Keywords: pattern recognition; order parameters; aesthetics

1. Introduction While the readers of my paper are surely familiar with what behavioral science is about, this need not be so concerning synergetics and why it may be of interest to behavioral science. Synergetics (“science of cooperation”) [1,2] is an interdisciplinary field of research that deals with complex systems that can spontaneously produce spatial, temporal, or functional structures (Figure 1). The considered systems are composed of many individual parts that exchange energy, matter, and/or information among each other, as well as with the surrounding of the total system (Figure 2). These systems acquire their structures by self-organization, that is, without any specific interference from the outside, say, by a sculptor. Synergetics is grounded in mathematics (dynamic systems theory, theory of stochastic processes, phase transition theory, and information theory) and has developed its own specific concepts. Synergetics has found numerous applications in physics, chemistry, biology and, in particular, behavioral science, for example, movement coordination and recognition of faces, facial expression and of movements. Thus, a common ground between behavioral science and synergetics is—I think—the study of the relations between a specific “behavioral pattern” as a whole and its individual constituents. The whole may be a social group and the individual constituents persons, or the whole may be a human brain and the constituents its neurons, just to mention two examples that are relevant for my paper. The central aim of synergetics is to cast these relations, based on realistic models, into a mathematical form which allows quantitative treatments. As it has turned out there is a clear-cut correspondence between a conceptual approach that can be

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conceptual approach that can be verbalized, and a formal mathematical treatment. In my paper I will Behav. Sci. the 2017, 7, 61 of 13 conceptual approach that can be verbalized, a formal mathematical treatment. my paper will present conceptual approach. My paperand is organized as follows. Section 2 hasInlittle to do 2Iwith present the conceptual approach. My (embodied) paper is organized as necessitates follows. Section 2 has little to do with synergetics. Nevertheless, I state that aesthetics a definition of beauty, but synergetics. Nevertheless, I stateforthat (embodied) aesthetics necessitates a definition of beauty, but argue why and there no criteria beauty. Section presents concepts ofconceptual synergetics, starting verbalized, a are formal mathematical treatment. In3my paper Ibasic will present the approach. arguewell-known why there are no criteria for beauty.human Sectionbehavior, 3 presents basic concepts ofwith synergetics, starting from examples of collective and then dealing face recognition My paper is organized as follows. Section 2 has little to do with synergetics. Nevertheless, I state from well-known examples of collective human behavior, and then dealing with face recognition and that movement (embodied)coordination. aesthetics necessitates a definition of beauty, but argue why there are no criteria and movement coordination. SectionSection 4 deals orderbasic parameters and while Section 5 returns to the question for beauty. 3with presents concepts ofembodiment, synergetics, starting from well-known examples of Section 4 deals with order parameters andThe embodiment, while Section 5 returns towith the question of beauty and its psychological consequences. concluding Section 6 makes contact a recent collective human behavior, and then dealing with face recognition and movement coordination. of beauty and itsKoch psychological consequences. TheHer concluding Section 6 makes contact with a recent paper by Sabine [3] order on embodied aesthetics. paper also contains references that Section 4 deals with parameters and embodiment, while Sectionnumerous 5 returns to the question paperserve by Sabine Koch [3] on embodied aesthetics. Herofpaper also contains numerous references that may as background information for parts my paper that deal with beauty and/or of beauty and its psychological consequences. The concluding Section 6 makes contact with a recent may serve asI assume background information for parts with of my paper that deal with beauty and/or embodiment. that my readers are familiar her paper so that I do not duplicate these paper by Sabine Koch [3] on embodied aesthetics. Her paper also contains numerous references that embodiment. I assume that my readers are familiar with her paper so that I do not duplicate these references. may serve as background information for parts of my paper that deal with beauty and/or embodiment. references. I assume that my readers are familiar with her paper so that I do not duplicate these references.

Figure 1. A flower is a typical example that exchanges energy and matter with its surround. Figure 1.1.AAflower is ais typical example that exchanges energy and matter with its surround. aitstypical example that exchanges energy and matter with itsInformation surround. Information isflower stored in genes. is stored in its Information is genes. stored in its genes.

Figure 2. Scheme of a system that forms structures. Figure 2. Scheme of a system that forms structures.

2. What Is Beauty? 2. What Is Beauty? Nature abounds aboundswith with objects we perceive as beautiful, such asanimals, flowers, animals, objects thatthat we perceive as beautiful, such as flowers, landscapes. Nature abounds with such objects that such we as perceive asarchitecture beautiful, and suchweasmay flowers, landscapes. We lookartefacts at beautiful artefacts paintings, sculptures, architecture anddelighted weanimals, may by be We look at beautiful as paintings, sculptures, be landscapes. We look at beautiful artefacts such as asbeautiful, paintings,such sculptures, architecture we and may be delighted poetry music. We may perceive movements as as beautiful, such asof the elegant trotstill of poetry andby music. Weand may perceive movements the elegant trot aand horse, delighted by poetry music. may perceiveAt movements as beautiful, such the elegant trot of amore horse, still more the dancing of people. a more abstract level, mathematicians speak theand dancing ofand people. AtWe a more abstract level, mathematicians speak ofas beautiful formulae, a horse, and still the dancing At And a more abstract level, mathematicians of and physicists maymore consider their lawsofaspeople. beautiful. more generally, people are delightedspeak by new

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beautiful formulae, and physicists may consider their laws as beautiful. And more generally, people are delighted by new insights, or discoveries. Yet, a scientific of aesthetics and itsaembodiment insights, or discoveries. Yet, a scientific study of aesthetics andstudy its embodiment requires definition of requiresWhenever a definition of beauty. Whenever I met the art historian Sir Ernest who Gombrich (1909– beauty. I met the famous art historian Sirfamous Ernest Gombrich (1909–2001) had studied 2001) who had studied psychology, I asked him: What are the criteria for beauty? Each time he psychology, I asked him: What are the criteria for beauty? Each time he replied: There are no criteria for replied: Why? There Surely are no there criteria beauty! Why?for Surely several reasons that. that Hereappears I want beauty! arefor several reasons that. there Here Iare want to discuss onefor reason to me discuss reason thatend, appears me most likely.for Tothe this end, letand us consider forget “beauty” for the to mostone likely. To this let ustoforget “beauty” moment an ambivalent momentsuch andas consider an ambivalent picture such as Figure 3. picture Figure 3.

Figure 3. Vase or faces?

Figure 3. Vase or faces?

Our perception oscillates back and forth between the interpretations “vase” or “faces”. In 1920, Our perception oscillates backKöhler and forth between the interpretations “vase” or “faces”. In 1920, the Gestalt psychologist Wolfgang [4] proposed an explanation: When we have recognized an the Gestalt psychologist Wolfgang Köhler [4] proposed an explanation: When we have recognized object, our attention for this object fades away and we are able to recognize the other object, and so on andetailed object, our attention for this of object fades away we arebyable to recognize the other and (a mathematical model this process was and presented Ditzinger and Haken [5]). object, While here so on (a detailed model this processinwas presented by Ditzinger and Haken [5]). the switching timemathematical between percepts is aoffew seconds, other cases it may be much longer. A typical While here the switching time between percepts is a few seconds, in other cases it may be much example is provided by fashion. First a new style is created, which is followed by an ever increasing longer. Aoftypical examplethey is provided fashion. a new style is an created, which is followed by number people—until get boredby and requireFirst a new style. Thus excitement/boredom cycle an ever increasing number of people—until they get bored and require a new style. Thus an results. This deep-rooted human trait is well reflected by the Latin proverb “variatio delectate” or by excitement/boredom cycle results. This deep-rooted human trait is well reflected by the Latin poetry, for example, by Goethe’s Faust: “Werd ich zum Augenblicke sagen: Verweile doch! du bist so schön! proverb “variatio by poetry, by Goethe’s Faust: “Werd ichthe zum Augenblicke Dann magst du michdelectate” in Fesseln or schlagen, dann for willexample, ich gern zugrunde gehen!/When I say to moment flying: sagen: Verweile doch! du bist so schön! Dann magst du mich in Fesseln schlagen, dann will ich gern zugrunde Linger a while—thou art so fair! Then bind me in thy bonds undying, and my final ruin I will bear!” gehen!/When I say a while—thou art so fair! Then bind me in thy bonds undying, In Section 5,toI the willmoment discussflying: whatLinger that means for some ingredients of beauty. However, more and my final ruin I will bear!” importantly, we must be aware of at least one conclusion for the relation between therapist and client: Section 5, I will discuss that forAnd, somedoes ingredients beauty. more DoesIn their understanding of whatwhat beauty is means coincide? it persistof (e.g., does However, boredom arise?) importantly, must we be aware of at least one conclusion the relation betweenoftherapist In the presentwe context may interpret “beauty” in a widefor sense as the property an objectand or client: Does their understanding of what beauty is coincide? And, does it persist (e.g., does boredom happening that causes good feelings, excitement, delight, harmony, etc. in the recipient. arise?) In the present context we may interpret “beauty” in a wide sense as the property of an object 3. Concepts Synergetics or Basic happening that of causes good feelings, excitement, delight, harmony, etc. in the recipient. Synergetics deals with complex systems, that form spatial, temporal, spatio-temporal or functional 3. Basic Concepts of Synergetics structures by self-organization. In the present context, a number of insights gained by the mathematical Synergetics deals can withbecomplex systems, that of form spatial, temporal, spatio-temporal approach of synergetics visualized by examples spontaneous collective human behavior. or functional structures by self-organization. In the present context, a number of insights gained by the

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Behav. Sci. 2017, 7, 61 4 of 13 mathematical approach of synergetics can be visualized by examples of spontaneous collective human behavior.

(a) Formation Formationofofspatial spatialstructures structures(patterns) (patterns) (a)

Consider Considerswimmers swimmersinina aswimming swimmingpool. pool.If Ifthere thereare arefew fewswimmers, swimmers,they theymay mayswim swimquite quite independently independentlyofofeach eachother otherininvarious variousdirections directions(disordered (disorderedstate). state).If Ifthe thenumber numberofofswimmers, swimmers, that thatis,is,their theirdensity densityincreases increasesbeyond beyonda acritical criticalvalue, value,ininthe thedisordered disorderedstate statethe theswimmers swimmersimpede impede each other so much that they acquire an ordered mode, namely, they swim in each other so much that they acquire an ordered mode, namely, they swim incircles. circles.This Thismay may happen is, without withoutany anygiven givenorders orders from outside. First, swimmers happenspontaneously, spontaneously, that that is, from thethe outside. First, few few swimmers begin begin swimming in circles, and more swimmers join them (Figure swimming in circles, then then moremore and more swimmers join them (Figure 4). 4).

Figure4.4.Transition Transitionfrom fromdisorder disordertotoorder: order:swimmers swimmersinina apool. pool. Figure

Anyone Anyonewho whoenters entersthe thepool poolisisautomatically automaticallyforced forcedtotojoin jointhe thecollective, collective,ordered orderedmotion. motion. Spatial patterns are well known in the animal kingdom: flocks of birds, schools of fish, to mention Spatial patterns are well known animal kingdom: flocks of birds, schools of fish, to mention but but two examples. two examples. (b) Formation of temporal structures (patterns) (b) Formation of temporal structures (patterns) When, after a concert, the listeners get enthusiastic, quite often the following happens: While When, after aof concert, get enthusiastic, quite often the following happens: While first first the clapping handsthe is listeners quite irregular, suddenly few people start clapping their hands the clapping of hands is quite irregular, suddenly few people start clapping their hands rhythmically rhythmically until very quickly the whole audience claps rhythmically. A further example is until verybyquickly whole audience rhythmically. A can further example is provided by people provided peoplethe walking across anclaps elastic bridge that oscillate. Then quite often they walking across an elastic bridge that can oscillate. Then quite often they synchronize their pace so to synchronize their pace so to enhance the oscillation of the bridge. They enjoy feeling the resonance! enhance theofoscillation the bridge. They enjoy feeling the resonance! An example the animalofkingdom is provided by the rhythmic blinking ofAn fireexample flies. of the animal kingdom is provided by the rhythmic blinking of fire flies. (c) Formation of spatio-temporal structures (patterns) (c) Formation of spatio-temporal structures (patterns) Spectators in an arena may spontaneously form a “la ola” wave. First, along some line, people stand Spectators up, others at side follow and then thoseform who got upola” first,wave. sit down. In this way people in their an arena may spontaneously a “la First, along some line, generate a “wave” running around the arena. These simple examples may allow me to formulate people stand up, others at their side follow and then those who got up first, sit down. In this general concepts of synergetics. way people generate a “wave” running around the arena. These simple examples may allow me to formulate general concepts of synergetics. (1) Control parameters

They fixedparameters quantities that are externally or internally prescribed. In the example (a) the (1) are Control control parameter is the density of swimmers; in the examples (b), (c), it is the internal They are fixed quantities that are externally or internally prescribed. In the example (a) excitement of the participants. When a control parameter exceeds some threshold, the old state the control parameter is the density of swimmers; in the examples (b), (c), it is the internal of the total system is abandoned and replaced by a new one. In other words, excitement of the participants. When a control parameter exceeds some threshold, the old (2) thestate old of state unstable. thebecomes total system is abandoned and replaced by a new one. In other words, (3) Close to such instability “points” the formation of a new structure (pattern) is triggered by (2) the old state becomes unstable. some spontaneous events (e.g., rhythmic clapping of hands of only few people).

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(3)

Close to such instability “points” the formation of a new structure (pattern) is triggered by 5 of 13 events (e.g., rhythmic clapping of hands of only few people). (4) The new ordered state is characterized by an order parameter. It plays a double role: (4) The new ordered state is characterized by an order It plays a double it describes the macroscopic state and it prescribes theparameter. action of the individual parts.role: it describes the macroscopic state and it prescribes the action of the individual parts. (5) Slaving principles. (5) Slaving principles. One or few order parameters determine (enslave) the behavior of the individual parts (Figure 5) (e.g., swimmers follow the circular motion, listeners join parts the (Figure collective One or few order parameters determine (enslave) the behavior of the individual 5) hand clapping). (e.g., swimmers follow the circular motion, listeners join the collective hand clapping).

Behav. Sci. 2017, 7, 61spontaneous some

examples may indicate there aregrades different of the “strength” of TheseThese examples may indicate that therethat are different of thegrades “strength” of “enslavement”. I have discussed the sociological implications of the “enslavement” notion I have“enslavement”. discussed the sociological implications of the “enslavement” notion at various occasions, at various occasions, because sociologists strongly criticize notion that because many sociologists stronglymany criticize this notion stressing that this humans arestressing free in their humans are free in their decisions. decisions.

Figure 5. Slaving principle: One or few order parameters determine behavior of parts.

Figure 5. Slaving principle: One or few order parameters determine behavior of parts.

(6) Complexity reduction (6) Complexity reduction Instead of describing the actions of the numerous parts it suffices to deal with the Instead of describing the actions of thereduction numerous suffices to pattern) deal withrecognition, the order order parameter(s). Complexity is parts crucialit to face (or parameter(s). Complexity is crucial to among face (or pattern) recognition, movement movement control, andreduction sensory/motor action, others. control, and sensory/motor action, among others. (7) Circular causality (7) Circular causality This concept is rather counterintuitive because it contradicts our understanding of the This concept is rather counterintuitive because it contradicts our understanding of the conventional cause—effect relation. However, in the case of self-organization the order conventional cause—effect relation. However, in the case of self-organization the order parameters enslave the individual parts, while the parts through their joint action, generate parameters enslave the individual parts, while the parts through their joint action, generate the the order parameters. However, just think of the hand clapping: each participant hears order parameters. However, just think of the hand clapping: each participant hears (perceives) (perceives) the collective hand clapping, but at the same time she/he produces this effect. the collective hand clapping, but at the same time she/he produces this effect. Visualization of the “Behavior” of Order Parameters Visualization of the “Behavior” of Order Parameters In quite a number of cases the “behavior”, or precisely speaking, the dynamics of order parameters Invisualized quite a number of cases the “behavior”, or isprecisely can be by an attractor landscape. An example providedspeaking, by Figurethe 6. dynamics of order parameters can be visualized by an attractor landscape. An example is provided Figure 6.its motion On the abscissa, we plot the size of the considered order parameter, OP. Weby represent On the abscissa, we plot the size of the considered order parameter, OP. represent its (dynamics) by the motion of a ball that rolls down a grassy hill so that it may come to We rest at the bottom motion (dynamics) by the motion ofmay a ball rolls down grassy hillofso that it mayofcome to rest at of the valley. The ordinate, called V, bethat identified with athe height the position the ball. the bottom of the valley. The ordinate, called V, may be identified with the height of the position of the ball.

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Figure 6. Change of order parameter landscape with increasing control parameter. Figure 6. Change of order parameter landscape with increasing control parameter.

Figure 6. Change of order parameter landscape withindicating increasing control parameter. Figure 6.1 represents a situation where the OP is zero, a structureless or disordered state (think of the irregular motion of swimmers in a pool). When a control parameter is increased Figure 6.1 represents aasituation where isiszero, indicating aastructureless orordisordered wherethe theOP OP zero, indicating structureless disordered (e.g., Figure density6.1 of represents swimmers), situation in the mathematical model the bottom of the valley becomes quite flat. state (think of the irregular motion of swimmers in a pool). When a control parameter isisincreased state (think of the irregular motion of swimmers in a pool). When a control parameter increased (Figure 6.2). Since the ball is subject to random fluctuations (“kicks”), it moves randomly (e.g., density ofofswimmers), ininthe mathematical model the bottom of the valley becomes quite flat. (e.g., density swimmers), the mathematical model the bottom of the valley becomes quite flat. considerably away from the position of OP = 0. This effect is called critical fluctuations and is a (Figure 6.2). Since the ball is subject to random fluctuations (“kicks”), it moves randomly considerably (Figure 6.2). Since the ball is subject to random fluctuations (“kicks”), it moves randomly precursor to phase-transitions where a new structure appears (Figure 6.3). That is to say that with away from theaway position ofthe OPposition = 0. This effect called critical fluctuations and is a precursor considerably from OPnew = is 0.valleys This effect is that called critical and istoofa further increase of the control parameteroftwo appear entail two fluctuations new stable values phase-transitions where a new structure appears (Figure 6.3). That is to say that with further increase of precursor phase-transitions where a new structure appears (Figure 6.3). Thatthis is tomeans say that the OP, of to which only one can be realized. In the concrete “swimmer model” thatwith the the control parameter newparameter valleys appear thatvalleys entail two newthat stable values thestable OP, ofvalues whichof further increase thetwo control two new appear entail two of new swimmers now of swim clockwise or anticlockwise. The observation of critical fluctuations of the only one can be realized. In the concrete “swimmer model” this means that the swimmers now swim the OP, ofofwhich onlymay oneplay can be In role the concrete “swimmer model” this means that the behavior patients an realized. important in neurology (e.g., in a number of cases such clockwise or anticlockwise. The observation of critical fluctuations of the behavior of patients may swimmers now clockwise anticlockwise. observation of critical fluctuations the fluctuations may swim be indicators of or evolving epilepticThe seizures). The attractor landscape modelofmay play an important role in neurology (e.g., in a number of neurology cases such fluctuations may be of indicators of behavior of patients may play an important role in (e.g., in a number cases such serve to discuss “saturation” effects. According to Tschacher [6], the slope of a valley may represent evolving epileptic seizures). The attractor landscape model may serve to discuss “saturation” effects. fluctuations be indicators of as evolving seizures). The attractor landscape model may the degree ofmay intentionality acting control epileptic parameter (Figure 7a). According to Tschacher [6], the slope of a valley may represent the degree of intentionality acting as serve to discuss “saturation” effects. According to Tschacher [6], the slope of a valley may represent control parameter (Figure 7a). the degree of intentionality acting as control parameter (Figure 7a).

Figure 7. Vanishing of attractor. (a) Nonvanishing slope indicating degree of intentionality; (b) Slope Figure 7.after Vanishing of attractor. vanishes completion of task. (a) Nonvanishing slope indicating degree of intentionality; (b) Slope vanishes after completion of task. Figure 7. Vanishing of attractor. (a) Nonvanishing slope indicating degree of intentionality; (b) Slope When the corresponding task has been fulfilled and the control parameter is zero, the slope vanishes after completion of task. When the corresponding task has been fulfilled and the control parameter is zero, the slope

vanishes (Figure 7b). Attractors that vanish while the corresponding OP is built up have been termed vanishes (Figure Attractors that vanish while the of corresponding OPofisambiguous built up have been quasi-attractors by7b). Haken [7], in particular in the context the recognition patterns. When the corresponding task has been fulfilled and the control parameter is zero, the slope termed quasi-attractors bycorresponding Haken [7], invalley, particular inincreases the context of the recognition of ambiguous First, in the presence of the an OP beyond a critical size (the conscious vanishes First, (Figure 7b).presence Attractors that vanish whilevalley, the corresponding OP is built up have been patterns. in the of the corresponding an OP increases beyond a critical state) until the valley and with it the OP vanish. After some time the valley is reestablished. size (the termed quasi-attractors by Haken [7], in particular in the context of the recognition of ambiguous conscious state) until the valley and with it the OP vanish. After some time the valley is patterns. First, in theand presence of the corresponding valley, an OP increases beyond a critical size (the 4.reestablished. Order Parameters Embodiment conscious state) until the valley and with it the OP vanish. After some time the valley is To elucidate the role of order parameters in embodiment, we consider the example of face reestablished. recognition. In this case, an observer is able to recognize a face though it may be partly obscured.

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4. Order Parameters and Embodiment To elucidate the role of order parameters in embodiment, we consider the example of face recognition. In this case, an observer is able to recognize a face though it may be partly obscured. To elucidate the role of order parameters in embodiment, we consider the example of face Behav. Sci. of 13 He/she is 2017, able7,to61complete this percept in his/her mind and associate a name with this face. Thus 7face recognition. In this case, an observer is able to recognize a face though it may be partly obscured. recognition is conceived as action of associate memory, or, on a more abstract level, as the He/she is able to complete this percept in his/her mind and associate a name with this face. Thus face completion of a set of incomplete features (data) to a set of complete features (data) according to recognition as percept action of associate memory, or, ona aname more abstract level, the He/she is ableistoconceived complete this in his/her mind and associate with this face. Thusasface stored prototype patterns [8]. completionisofconceived a set of incomplete to aor,set complete features recognition as action of features associate(data) memory, onofa more abstract level,(data) as theaccording completionto An example is shown in Figure 8, where the family names are encoded by letters. The stored prototype patterns [8]. of a set of incomplete features (data) to a set of complete features (data) according to stored prototype individual patterns are represented by their pixel grey values. The grey values of any shown image An[8]. example is shown in Figure 8, where the family names are encoded by letters. The patterns (Figure 9, left hand side) are encoded as neural excitations that are transmitted to the neural network individual patterns are represented theirthe pixel greynames values.are The grey values of any shown image An example is shown in Figure 8,by where family encoded by letters. The individual of the brain (Figure 9, right hand side), where they are further processed. (Figure 9, left hand side) are encoded as neural excitations that are transmitted to the neural network patterns are represented by their pixel grey values. The grey values of any shown image (Figure 9, of the brain 9, rightashand side), where they are transmitted further processed. left hand side)(Figure are encoded neural excitations that are to the neural network of the brain (Figure 9, right hand side), where they are further processed.

Figure 8. Example of stored (or learned) prototype patterns. Figure 8. Example of stored (or learned) prototype patterns. Figure 8. Example of stored (or learned) prototype patterns.

Figure 9. On the left-hand side, a scheme of an image with pixels. In the right upper corner, the family Figure On the left-hand a scheme of an image with pixels. In the upper corner, the name is9.encoded by a letter.side, On the right-hand side, a schematic drawing of aright neural network. family name is encoded by a letter. On the right-hand side, a schematic drawing of a neural network. Figure 9. On the left-hand side, a scheme of an image with pixels. In the right upper corner, the family namerecognition is encoded byprocess a letter.isOn the right-hand side, a schematic drawing of a neural The pattern modeled by a pulse-coupled neural network that network. I have dealt

The pattern recognition process is modeled by a pulse-coupled neural network that I have dealt with elsewhere elsewhere in In In thethe context of my paper,paper, the following results are relevant: with ingreat greatdetail detail[9]. [9]. context of present my present the following results are The pattern recognition process is modeled by a pulse-coupled neural network that I have dealt As it turns out, consistently with the mathematical treatment of the network, we may ascribe an order relevant: As it turns out, consistently with the mathematical treatment of the network, we may with elsewhere in great detail [9]. In the context of my present paper, following parameter ξ k to each pattern k=1,··· ,5 (Figure 8). When patternthe (Figure 10) is results offered are to k mathematical = 1, ⋅⋅an,5incomplete ascribe an order parameter ξconsistently to each pattern (Figure 8). Whenofanthe incomplete pattern relevant: As it turns out, with the treatment network, we may k the network, a competition between the order parameters evolves that can be visualized as motion of an orderpoint parameter to each pattern k = 1, ⋅⋅ ,5 (Figure 8). When an incomplete pattern aascribe representative (ball) inξan k attractor landscape.

(Figure to the network, a competition between the order parameters evolves that can be Behav. Sci. 10) 2017,is7,offered 61 8 of 13 visualized as 7, motion of a representative point (ball) in an attractor landscape. Behav. Sci. 2017, 61 8 of 13 (Figure 10) is offered to the network, a competition between the order parameters evolves that can be (Figure 10)asismotion offeredof toathe network, a competition the order parameters evolves that can be visualized representative point (ball) between in an attractor landscape. Behav. Sci. 2017,as 7, motion 61 8 of 13 visualized of a representative point (ball) in an attractor landscape.

Figure 10. An incomplete pattern.

This competition is eventually won order parameter that “enslaves” the individual An an incomplete Figure 10. by pattern. neurons of the network so that a complete pattern emergespattern. (Figure 11). Figure 10. An incomplete This competition competitionisiseventually eventually won byorder an order parameter that “enslaves” the individual This won by an parameter that “enslaves” the individual neurons This competition is that eventually wonpattern by an emerges order parameter that “enslaves” the individual neurons of the network so a complete (Figure 11). of the network so that a complete pattern emerges (Figure 11). neurons of the network so that a complete pattern emerges (Figure 11).

Figure 11. Completion of pattern by synergetic computer (modelling brain activity). Figure 11. Completion of pattern by synergetic computer (modelling brain activity).

To putFigure it cautiously: these of results suggest that the order parameters play a double 11. Completion patternstrongly by synergetic computer (modelling brain activity). role—they represent perceived object, by that is, action of mind. Simultaneously they enslave the Figure 11.the Completion of pattern synergetic computer (modelling brain activity). To itit cautiously: these results strongly that the collective action of neurons: a body-action (Figure suggest 12). To put put cautiously: these results strongly suggest that the order order parameters parameters play play aa double double role—they represent the perceived object, that is, action of mind. Simultaneously they enslave the To put it cautiously: these results theSimultaneously order parameters a double role—they represent the perceived object,strongly that is, suggest action ofthat mind. theyplay enslave the collective action of aa body-action (Figure role—they represent the perceived object, that 12). is, collective action of neurons: neurons: body-action (Figure 12).action of mind. Simultaneously they enslave the collective action of neurons: a body-action (Figure 12).

Figure 12. The two sides of a coin (the order parameter). Figure 12. The two sides of a coin (the order parameter).

My approach strongly supports Spinoza’s view that mind and body (matter) represent the two Figure 12. The two of a coin (the order Quite parameter). sides of the same coin (which I identify withsides an order parameter). clearly, this view is in contrast Figure 12. The two sides of a coin (the order parameter). to Descartes’s view on the dichotomy between mind and body. So far, I have represented the example of visual patterns. My approach holds also for movement or behavioral patterns. In all these cases, the prototype patterns may be learned or can be of an archetypical nature.

My approach strongly supports Spinoza’s view that mind and body (matter) represent the two sidesMy of approach the same strongly coin (which I identify with view an order parameter). Quite clearly, this view in supports Spinoza’s that mind and body (matter) represent the istwo contrast to Descartes’s view on the dichotomy between mind and body. So far, I have represented sides of the same coin (which I identify with an order parameter). Quite clearly, this view is in the example of visual patterns. holds also for movement or So behavioral patterns. In all contrast to Descartes’s view onMy theapproach dichotomy between mind and body. far, I have represented these cases, the prototype patterns be learned canfor bemovement of an archetypical nature.patterns. In all the example of visual patterns. My may approach holds or also or behavioral Behav. Sci. 2017, 7, 61 9 of 13 parameter concept alsoorfor dynamics (of people theseSince cases,the theorder prototype patterns may beholds learned cangroup be of an archetypical nature.or animals), it might be an speculation to ascribe someforkind of mind also (of to groups, some kind of Since theinteresting order parameter concept holds also group dynamics people or animals), it consciousness to collectives, so to speak. While in psychology we can verify the concept might be an interesting speculation to ascribe some kind of mind also to groups, some kind of Since the order parameter concept holds also for group dynamics (of people or animals), it might personal individual introspection, thispsychology “tool” is absent in It isconcept important consciousness to collectives, so to some speak. While in we some cansociology. verifyof the of be an interestingby speculation to ascribe kind of mind also to groups, kind consciousness to note that the role (meaning) of order parameters (OPs) depends on the context. To underline this consciousness by personal individual introspection, this “tool” is absent in sociology. It is important to collectives, so to speak. While in psychology we can verify the concept of consciousness by statement, consider movement patterns produced by a human with coordination between to note that the role introspection, (meaning) of order parameters (OPs) onhis/her theiscontext. To underline this personal individual this “tool” is absent independs sociology. It important to note that limbs bodyofmotion. An explicit(OPs) example is provided by experiments of Kelso [10], who statement, consider movement patterns produced by aon human with his/her coordination between the roleand/or (meaning) order parameters depends the context. To underline this statement, instructed subjects tomotion. moveproduced their index in parallel at a slow (Figure 13). limbs and/or body An explicit is provided by speed experiments of Kelso who consider movement patterns byfingers aexample human with his/her coordination between limbs[10], and/or instructed subjects to move their is index fingers parallel at aofslow speed 13). body motion. An explicit example provided byin experiments Kelso [10], (Figure who instructed subjects to move their index fingers in parallel at a slow speed (Figure 13).

Figure 13. Kelso’s experiment: Spontaneous change from parallel to antiparallel (symmetric) Figure 13. Kelso’s experiment: Spontaneous change from parallel to antiparallel (symmetric) movement movement index fingers with increased speed.change from parallel to antiparallel (symmetric) Figure 13. of Kelso’s experiment: Spontaneous of index fingers with increased speed. movement of index fingers with increased speed.

When the prescribed speed was increased more and more, quite involuntarily the parallel When was more more, quite movement switched to anspeed antiparallel, symmetric one.and This spontaneous switch wasthe modeled by Whenthe theprescribed prescribed speed wasincreased increased more and more, quiteinvoluntarily involuntarily theparallel parallel movement switched to an antiparallel, symmetric one. This spontaneous switch was modeled by means of answitched order parameter dynamics in an approach Haken, Kelso, Bunz [11]was thatmodeled has become movement to an antiparallel, symmetric one.by This spontaneous switch by means ofofan parameter inincoordination. an Kelso, Bunz [11] that paradigmatic in the field ofdynamics movement InHaken, this model, the order can be means anorder order parameter dynamics anapproach approachby by Haken, Kelso, Bunz [11]parameter thathas hasbecome become paradigmatic in the field of movement coordination. In this model, the order parameter can identified as relative phase thecoordination. index fingers.InInthis further experiments by Kelso and his paradigmatic in the field of between movement model, the order parameter canbe be identified as relative phase between the index fingers. In further experiments by Kelso and coworkers as and the theoretical work ofthe myindex group, we could demonstrate that acoustic perception, identified relative phase between fingers. In further experiments by Kelso andhis his coworkers the work we demonstrate acoustic movementand coordination, and activity ofmy thegroup, CNS (central nervous system) that are by only two coworkers and thetheoretical theoretical workofof my group, wecould could demonstrate thatgoverned acousticperception, perception, movement coordination, and activity of the CNS (central nervous system) are governed by only order parameters [10]. and activity of the CNS (central nervous system) are governed by onlytwo movement coordination, two order parameters [10]. OPs [10]. govern at the next level perception and action, each represented by the orderThese parameters These govern at theatnext level perception andelements action,and each represented the corresponding corresponding OPs, which intheturn “enslave” the participating perception and TheseOPs OPs govern next level perception action, eachinby represented by the OPs, which in turn “enslave” the elements participating in perception and the elements participating elements participating in action (Figure 14). corresponding OPs, which in turn “enslave” the elements participating in perception and the inelements action (Figure 14). participating in action (Figure 14).

Figure 14. Order parameter hierarchy.

5. Criteria for OPs and Syndromes For a conceptualization and mathematical modeling we need criteria for OPs. Quite generally, OPs refer to the total system. In particular, they refer to the coordination (spatial, temporal, functional) between the parts of the studied system. Moreover, a time-scale separation holds. That is to say,

Figure 14. Order parameter hierarchy.

5. Criteria for OPs and Syndromes

5. Criteria for OPs and Syndromes For a conceptualization and mathematical modeling we need criteria for OPs. Quite generally, OPs refer to the total system. In particular, they refer to the coordination (spatial, temporal, For a conceptualization and mathematical modeling we need criteria for OPs. Quite generally, functional) between the parts of the studied system. Moreover, a time-scale separation holds. That is OPs Sci. refer the total system. In particular, they refer to the coordination (spatial, temporal, Behav. 2017,to 7, 61 10 of 13 to say, OPs change slowly, whereas parts change fast. This can be checked by means of their reaction functional) between the parts of the studied system. Moreover, a time-scale separation holds. That is time to perturbations. Additionally, while a change of OPs causes a change of the behavior of the to say, OPs change slowly, whereas parts change fast. This can be checked by means of their reaction parts, a change of a part (or a parts minority of parts) This has practically no effect means on the OPs (justreaction think oftime the OPs slowly, whereas change checked of their timechange to perturbations. Additionally, whilefast. a changecan of be OPs causes by a change of the behavior of the hand clapping example!). The while joint aaction of of anOPs order parameter and thebehavior slaving of principle is toparts, perturbations. Additionally, change causes a change of the the parts, a change of a part (or a minority of parts) has practically no effect on the OPs (just think of the visualized in Figure 15. ahand change of a partexample!). (or a minority parts) has practically no parameter effect on theand OPsthe (just think of the handis clapping The of joint action of an order slaving principle clapping example!). The joint action of an order parameter and the slaving principle is visualized in visualized in Figure 15. Figure 15.

Figure 15. An order parameter governs a whole configuration of individual parts. Figure Figure15. 15.An Anorder orderparameter parametergoverns governsaawhole wholeconfiguration configurationofofindividual individualparts. parts.

In particular, we may ascribe measurable values vl , l = 1, ⋅⋅ , N to the individual parts. An

v1,s⋅⋅ particular, we ascribe measurable values vl ,l=1, to individual parts. An order . ,Ifthe is incomplete, orderIn parameter governs a whole configuration (“pattern”) In particular, wemay may ascribe measurable values vl ,ofl···=,N Na configuration to the individual parts. An parameter governs a whole configuration (“pattern”) of vs. If a configuration is incomplete, the order the order parameter servesafor a complete configuration or it is errors (e.g., of texts). It v s to . Ifcorrect a configuration is incomplete, order parameter governs whole configuration (“pattern”) ofable parameter serves for a complete or it is ablesystems. to correct errors (e.g., It can serve can serve for synchrony betweenconfiguration the parts in oscillating Some time agoofI texts). suggested that an the order parameter serves for a complete configuration or it is able to correct errors (e.g., of texts). It for synchrony between the parts in oscillating systems. Some time ago I suggested that an order v s order parameter represents a syndrome, where the represent a set of manifestations that may can serve for synchrony between the parts in oscillating systems. Some time ago I suggested that an parameter represents a syndrome, where the vs represent a set of manifestations that may belong to belong to mind or body (Figure 16). order parameter represents a syndrome, where the v s represent a set of manifestations that may mind or body (Figure 16). belong to mind or body (Figure 16).

Figure 16. A syndrome plays the same role as an order parameter. Figure 16. A syndrome plays the same role as an order parameter.

Figure 16. A syndrome plays the same role as an order parameter. Again, a syndrome may serve for completion of manifestations and synchrony. Order parameters may even “govern” interpersonal relations, for example, in an alliance between client and therapist. A central question concerns the quantification of emotions and their measurements. Well-known examples are measurements (observations) of skin resistance, heartbeat, blood pressure, “goose skin”, eye movements, but also analysis of facial expressions (e.g., Ekman classification) or/and of gestures, and speech characteristics. EEG, MEG, fMRI measurements allow the study of brain activities,

Again, a syndrome may serve for completion of manifestations and synchrony. Order Again, a syndrome may serve for completion of manifestations and synchrony. Order parameters may even “govern” interpersonal relations, for example, in an alliance between client parameters may even “govern” interpersonal relations, for example, in an alliance between client and therapist. A central question concerns the quantification of emotions and their measurements. and therapist. A central question concerns the quantification of emotions and their measurements. Well-known examples are measurements (observations) of skin resistance, heartbeat, blood Well-known examples are measurements (observations) of skin resistance, heartbeat, blood pressure, “goose skin”, eye movements, but also analysis of facial expressions (e.g., Ekman Behav. Sci. 2017, 7, 61 skin”, eye movements, but also analysis of facial expressions (e.g., Ekman 11 of 13 pressure, “goose classification) or/and of gestures, and speech characteristics. EEG, MEG, fMRI measurements allow classification) or/and of gestures, and speech characteristics. EEG, MEG, fMRI measurements allow the study of brain activities, especially of their localization and correlations. By these and other the study of brain activities, especially of their localization and correlations. By these and other especially(e.g., of their localization and correlations. By these and methods extra-cranial methods extra-cranial excitations) specific areas could beother identified, for (e.g., example, nucleus methods (e.g., extra-cranial excitations) specific areas could be identified, for example, nucleus excitations) specific areas could be identified, example, accumbens (enjoyment), accumbens (enjoyment), amygdala (disgust,forfear). The nucleus data can be supplemented by amygdala personal accumbens (enjoyment), amygdala (disgust, fear). The data can be supplemented by personal (disgust, fear). IThe data can supplemented personal ratings. While I think it is atorleast ratings. While think it is at be least plausible to by consider intrapersonal ratings as (more less)plausible reliable, ratings. While I think it is at least plausible to consider intrapersonal ratings as (more or less) reliable, considerthat intrapersonal ratings as (more or less)questionable reliable, I believe interpersonal ratings are highly Itobelieve interpersonal ratings are highly due that to the qualia problem. Based on I believe that interpersonal ratings are highly questionable due to the qualia problem. Based on questionable due to the qualia problem. Based on quantification, promising models of psychological quantification, promising models of psychological processes have been developed by Schiepek et al. quantification, promising models of psychological processes have been developed by Schiepek et al. processes have been by Schiepek et al. [12], Tschacher et al. [13] and others. [12], Tschacher et al. developed [13] and others. [12], Tschacher et al. [13] and others. 6. Some Some Basic Basic Ingredients Ingredients of of Beauty Beauty 6. 6. Some Basic Ingredients of Beauty Though II have of of criteria forfor beauty (Section 2) there seemseem to beto at be least Though havestressed stressedthe theabsence absence criteria beauty (Section 2) there at some least Though I have stressed the absence of criteria for beauty (Section 2) there seem to be at least ingredients of beauty that have endured over the centuries. One aspect is proportionality, the other some ingredients of beauty that have endured over the centuries. One aspect is proportionality, one the some ingredients of beauty that have endured over the centuries. One aspect is proportionality, the symmetry. other one symmetry. other one symmetry. In the the latter (Figure 17), 17), translation translation symmetry symmetry (Figure (Figure 18) 18) In latter case, case, there there may may be be mirror mirror symmetry symmetry (Figure In the latter case, there may be mirror symmetry (Figure 17), translation symmetry (Figure 18) or rotation symmetry (Figure 19). or rotation symmetry (Figure 19). or rotation symmetry (Figure 19).

Figure 17. The human face is highly mirror symmetric. Figure Figure 17. 17. The The human human face face is is highly highly mirror mirror symmetric. symmetric.

Figure 18. Examples Examples of patterns produced by the translation of a square. Figure 18. Examples of patterns produced by the translation of a square.

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Figure19. 19.AArosetta rosettaasasan anexample exampleofofrotation rotationsymmetry. symmetry. Figure

The connected by by repetitions. repetitions.Interestingly, Interestingly,these thesesymmetric symmetric patterns can Thelatter latter symmetries symmetries are are connected patterns can be be observed in many self-organizing systems ranging from fluids over macroscopic chemical observed in many self-organizing systems ranging from fluids over macroscopic chemical reactions to reactions plants What and animals. What is the psychological impact ofThey such regularities? They plants andtoanimals. is the psychological impact of such regularities? strengthen confidence, strengthen us calm. This is the in human line with the consciously idea that the mind, they make confidence, us calm. Thisthey is inmake line with the idea that mind, or human unconsciously, consciously or unconsciously, is all the time trying to unearth (general) rules that allow to is all the time trying to unearth (general) rules that allow it to extrapolate, that is, to foresee, whatitwill extrapolate, that is, to foresee, what will be next. Obviously, regularities facilitate this process. be next. Obviously, regularities facilitate this process. Incidentally, however, (too much) regularity Incidentally, however, much) needs regularity generates boredom! Thus, an artwork needs generates boredom! Thus,(too an artwork “surprises”, namely, breaking of symmetry (as exemplified “surprises”, namely, breaking of symmetry (as exemplified by Picasso’s faces), irregularities, by Picasso’s faces), irregularities, unusual combinations of elements, and so forth. The weights of order unusual combinations of elements, and so The weights of order and disorder, expectation and and disorder, expectation and surprise areforth. changing in the course of time, though each epoch seems surprise are changing in the course of time, though each epoch seems to prefer a specific balance to prefer a specific balance between order/disorder. Clearly, my remarks have some consequences between order/disorder. Clearly, aesthetics—for my remarks have on therapies based on on therapies based on embodied somesome clientsconsequences it may be preferable to strengthen the embodied aesthetics—for somethe clients it may be preferableaspect. to strengthen the “order/regularity”, for “order/regularity”, for others, "excitement/variation” others, the "excitement/variation” aspect. 7. Conclusions 7. Conclusions In my paper I have tried to give a brief outline of the concepts and results of synergetics. In my to paper I have conditions tried to give a brief outline of theparameters) concepts and results According it, external (represented by control may lead of to asynergetics. qualitative According to it, external conditions control lead to a behavior qualitative change of the macroscopic behavior (represented of a complex by system. Atparameters) least at thesemay instances the of change of the of afew complex system. At least at these(“enslave”) instances the of the system is macroscopic governed by behavior one or very order parameters that govern thebehavior individual the system is governed by one or very order parameterscycle that is govern (“enslave”) the individual parts via circular causality. In this way,few a perception-action governed by an order parameter. parts via circular In this way, a perception-action is governed byon anaction orderor parameter. This implies that causality. this cycle can be initiated by the impact of cycle a control parameter perception, This implies thatThis thisorder cycleparameter can be initiated bycan thebeimpact of a control parameter on action or or both of them. approach immediately transferred to the circular model perception, or both of them. This order parameter approach canbetween be immediately transferred to the of embodied aesthetics by Sabine Koch [3], where the interplay person and art (mediated by circular model embodied is aesthetics Koch [3], where interplay betweenAsperson and impression andofexpression) now (in by mySabine approach) governed bythe an order parameter. it seems to art (mediated by impression and expression) is now (in my approach) governed by an order me, in this way the “re-invokation of the old concept of the ‘soul’ in order to grasp the holistic aspects parameter. seems to me, in this way the “re-invokation of theInold thetherapist ‘soul’ in acts order of the arts”,As (asit suggested by Sabine Koch) may be substantiated. theconcept process,ofthe as to grasp the holistic aspects of the arts”, (asproviding suggested by Sabine Koch) may besosubstantiated. In the “control parameter” by his/her incentives, specific surrounding, and forth. In conclusion, process, therapist actsThe as order “control parameter” his/her incentives, specific a warningthe should be added: parameter conceptby is seductive because of itsproviding seeming generality. surrounding, andcare so forth. a warning should So always some must In be conclusion, exercised when applying it. be added: The order parameter concept is seductive because of its seeming generality. So always some care must be exercised when applying it. Acknowledgments: The author thanks Wolfgang Tschacher for a critical reading of the manuscript.

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Acknowledgments: The author thanks Wolfgang Tschacher for a critical reading of the manuscript. Conflicts of Interest: The author declares no conflict of interest.

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7. 8. 9. 10. 11. 12. 13.

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