Research Institute


                                 AS A 
                   IN NATURE AND ART

by Werner Hahn (Art & Science Research Institute, Germany )











Preliminary remark:

ISBN: 9810223633 – Author: Hahn, Werner - Title: Symmetry as a developmental principle in nature and art – Singapore : World Scientific, 1998 – xxi, 510 p., 10 p. of col. Plates : ill. (some col.) ; 31 cm – General Note: The present edition is the original version of the work (Hahn 1989: Symmetrie als Entwicklungsprinzip in Natur und Kunst) translated into English without alternations … However, Chapter 13 … has been added … so that a supplement had to be made to the subjecect index, the outhor index and the bibliography” –

Please see the Website: with book-review (Darvas: Symmetry: Culture and Science; Vol. 12, Nr. 3-4, 2001, p. 433-434). Prof. Dr. Darvas wrote: “This book is readable even for those, who have not made detailed studies in the phenomena of symmetry, asymmetry … It must be kept in reach to the desk of any researcher of the evolution and any specialist – regardless of his/her discipline – of symmetry phenomena.”

In you see that – just now (07/2006) – the book is in 52 libraries of the USA . “Search inside the book” by shows Excerpt and Index of th English version of Hahns book. See also WIKIPEDIA: English: Article Symmetry; ; German: Artikel Symmetrie;


By making structure research more causal and studying evolution with the aim of developing an Evolutionary symmetry theory (Hahn 1989, 1990, 1994, 1996, 1998) criteria can be set up explaining how constructive innovations in nature develop. It's a matter of founding a functionally oriented, dynamic bifurcation morphology as a method of a new development theory with empirical content. This method tries to describe all forms (animate and inanimate) in an evolutionary way.

I have discussed symmetry and asymmetry as basics of development involving processes ("rules", "principles") which, affecting space and time, make possible, give reasons for, determine and structure a dependant object (Großmann 1990) . The path from an empirically supported "dynamic morphology" of art with evolutionary elements led me to nature and culture with fruitful starting points for an extensive evolution theory: neo-evolutionism.

In this way the STYLE of ars evolutoria (evolutionism), including its diverse variations and its objectifying of the evolutionary art theory to a new art and nature theory, was founded. On the basis of ars evolutoria I developed the mental structure of neo-renaissance and neo-modern art (ultra-modern art, trans-modern art); later also called science art (art science). Science art revived the unity of nature and science with art, lost after the Renaissance, in accordance with the Renaissance maxim "Ars sine scientia nihil est" ("Art without a scientific basis is nothing"). I set the aesthetic postulate of L'Art-pour-la-science ("Art for science/cognition") against the dogma about the self-purpose of art (L'Art-pour-l'art). 

Pictorial examples illustrate how, as desired, out of any three dimensional structure (basal structure) related, not identical but derived, forms can be developed (via intermediate forms, bridging structures). Form change is caused by evolutionary iterations: Via symmetry/asymmetry refraction and symmetrogenesis - the autoevolution mechanism primary asymmetrization linked to symmetrization. Creative symmetrization, newly interpreted as a reciprocal asymmetry/symmetry mechanism (Hahn 1994, 1996, 1998), embodies the basis for a bifurcation morphology conceived as a dynamic process, which makes  ”phylogenetic” process: emergence, i. e. the appearance of new systems or system characteristics in evolution. The fact that today outlines for a rationally representable, comprehensive organism theory as emergence theory are beginning to appear, is shown by the following:

The dynamic evolutionary bifurcation morphology I delineated is object bound. Fulguration (creative "fluctuation") does not develop abstractly in airless space (i.e. not as "creatio ex nihilo"). Instead, evolution is portrayed as a system-optimising process, as a functional trial and error method on the basis of inner form laws. Continued repetitions of a construction rule (mathematicians call this "iteration") lead to self-similarities in my evolutionary geometry. Form change is caused by evolutionary iterations.

Through numerous examples and in several figures (in the book on symmetry; Hahn 1989/1995 and 1998) I could prove that the new evolution theorem discovered using science art can be carried over by analogy onto the form evolution of inorganic and organic systems.

Although in symmetrization symmetry can also be seen as a "similarity of parts as an expression of a whole" (Rudolf Wille), a symmetrization goes beyond this, being a dynamic process causing new self-similarities. In this process the parts of a potentially alterable totality of events are transported through a bifurcation (a fork in the path; branching, bridge or jumping points) not only into "old" parts identical in structure and function, but also into "new" parts with altered structures and functions. This development of an identity-anulling evolutionary innovation (aniso-symmetrization) through symmetry and asymmetry breaking that occurs with symmetrization must, as such, be interpreted as an asymmetry process.

Every creative symmetrization interactively contains an asymmetrical aspect which negates total similarity (iso-symmetry). I have named this asymmetry course primary asymmetrization (initial, basis, or fundamental asymmetrization). The reciprocally effecting initial asymmetrization, dissimilar to symmetrization but with complementary polarity to it, fulguratively ensures that an ordered repetition of identical forms (identical system samples or elements) is avoided without resulting in destructive, chaotic structures (disorganization). 

This fundamental, two-sided key preventing the development of arbitrariness and chaos is one unit in the structure and function of asymmetry-symmetry-linkage. It is an auto-evolutionary system in which opposites work together synergetically: "Coincidentia oppositorum" of asymmetrizing symmetry breaking and formation. In a two-sided strategy energy is processed innovatively:
1) using an active, energy consuming (instable) imbalancing process (=asymmetrization), and 2) using a synchronous (stable) balancing process (=symmetrization).

According to the Evolutionary Symmetry Theory as currently seen in the developmental conception of my Neo-Evolutionism, when form variety evolves in nature through creative evolutionary factors that gradually and/or suddenly (continuously/discontinuously) induce new quantitative and qualitative mutations, then mainly primary asymmetrization/symmetrization is active as a fundamental "opposing pair": A duo in "harmonious discord" or (seen symmetrisized) "discordious harmony", whereby the causes for the complementary encompassing, energy and matter transforming uniform system are not a mysterious, unrecognisable secret (see also my Ur-form theory / protoform theory); for futher details see Hahn 1989, 1990, 1994, 1996, 1998).

If "asymmetry" is defined analogously to Wille's short definition of symmetry as: "Asymmetry (a lack of elegant proportion, without proportion) - dissimilarity of parts as the expression of a whole", then it becomes clear that the term asymmetrization, which cannot be separated from symmetrization, has nothing to do with non-symmetrical "disformation" or "disharmony". Asymmetrization, linked to (Adorno: "versöhnt" = reconciled with) symmetrization, can be seen as natural beauty. I define natural and artistic beauty as follows:

Beauty is that which through asymmetrizations linked to symmetrizations has become symmetrical.

In the unified concept of asymmetrization/symmetrization, asymmetry can be understood as an auto-evolutionary, energy exchanging or consuming impetus that creates novel forms, movements and functions (aniso-symmetry). As such, asymmetry is not an "enemy" of symmetry, is not "anti-symmetry", and does not exist without symmetry.

Through experiments I was able to prove that for an emerging structure mutation in my art (ars evolutoria with the variations neo-cubism, pointillistic and expressionistic evolutionism, neo-barock/neo-mannerism) proportion altering transformations are, beside the architects primary asymmetrization/symmetrization, of secondary importance for evolutionary self-renewal.

The transformation mechanism, which causes form distortion, can induce harmonic "deformation" of a structure by making forms partially dynamic, but the form alteration resulting from changes in the relative measure of coordinates and angles always contains an element of invariance. Seen from a fulgurative evolutionary point of view, few truly new things are "invented" in this way.

Wentworth d'Arcy Thompson, who, in accordance with Albrecht Dürer's form experiments with the deformation of a coordinate system, described transformation metamorphosis as a "growth law" and hoped for a "dynamic morphology" to explain the "riddle of form", was well aware of this. Transformations can be interpreted as secondary asymmetrizations.

It should be noted here that the old "modern" art, art theory and institutionalized art science have yet to say anything about evolution and little about symmetry. What was said is mostly difamatory. An interdisciplinarily oriented art science should finally take up the topics of evolution and symmetry as maxims, as well as accept and attempt to further "evolutionary aesthetics". 

Evolution-oriented aesthetics goes far beyond the field of art, presenting the evolved totality of reality, in which aesthetic values appear (daily aesthetics, natural aesthetics). Antithetic to modernistic-postmodernistic cultural conservatism and on the threshold of the new new age, I am trying, on the basis of universal, synthetic evolutionary aesthetics, to induce the turnabout in the new territory of natural aesthetic thought. Questions on the sense and value (truth) of beauty and art (once again) act as a constant, innovative impetus for philosophical nature and art aesthetics.

Here the aesthetics of a Neo-New Age, which I also introduced art scientifically as neo-modern, ultra-modern, and trans-modern, encompass the study of nature and art (Goethe: Kunst als "zweiter Natur" = art as "second nature").

Anti-art or non-art ideologies, which arbitrarily dominate the present system of a totally negatively expanded/unbound field of art including the art market scene, must be a "thorn in the eye" for evolutionarily motivated, objective artist aesthetics (for example ars evolutoria), since forms of the evolutionary perception and understanding of art are relevent for natural aesthetics and primarily directed by the eye-brain system. 

Looking beyond the boundaries of various disciplines, the author demonstrates in his book (see ISBN 981-02-2363-3: 1998 World Scientific)

                     DEVELOPMENTAL PRINCIPLE 
                                             IN NATURE AND ART

that symmetry is a fascinating phenomenon which provides endless
stimulation and challenges. He explains that it is possible to readapt art to the sciences, and vice versa, by means of an evolutionary concept of
symmetry. Many pictorial examples are included to enable the reader to fully understand the issues discussed. Based on the artistic evidence that
the author has collected, he proposes that the new ars evolutoria can function as an example for the sciences. 

The book is divided into three distinct parts, each one focusing on a special issue. 

In Part I, the phenomenon of symmetry, including its discovery and meaning is reviewed. The author looks closely at how Vitruvius, Polyclitus, Democritus, Plato, Aristotle, Plotinus, Augustine, Alberti, Leonardo da Vinci and Durer viewed symmetry. This is followed by an explanation on how the concept of symmetry developed. The author further discusses symmetry as it appears in art and science, as well as in the modern age. Later, he expounds the view of symmetry as an evolutionary concept which can lead to a new unity of science. 

In Part II, he covers the points of contact between the form-developing process in nature and art. He deals with biological questions, in particular evolution. 

The collection of new and precise data on perception and knowledge with regard to the postulated reality of symmetry leads to further development of the evolutionary theory of symmetry in Part III. The author traces the enormous treasure of observations made in nature and culture back to a few underlying structural principles. He demonstrates symmetry as a far-reaching, leading, structuring, causal element of evolution, as the idea lying behind nature and culture. Numerous controllable reproducible double-mirror experiments on a new stereoscopic vision verify a symmetrization theory of perception. 


   On the Concept and Significance of Symmetry: The Discovery of  Symmetry 
   On the Term Symmetry from the Antiquity to the Renaissance 
  The Development of an Exact Concept of Symmetry through Scientific       Progress 
     On Symmetry and Asymmetry as Evolutionary Factors in Nature. The Development of an Evolutionary Concept of Symmetry 
     Evolutionary Symmetrizations in Two and Three Dimensions. On the Syntax and Semantics of Symmetrism 
     On the Problem of Organic Form Development: Can an Artist Approach the World and Its Content Only in a Metaphorical Way? 
     Evolution: Fairy Tale, Theory or Fact? Can We Experience Evolution Directly? 
     Evolutionism/Ars Evolutoria — The Theory of Light/Colour and Form, Morphogenesis, Morpho-Mutability and Morpho-Evolution as Causal Form Theory: On the Question Whether There can be a Pre-Object, Pre-Morph "Life Process of Form" in Nature and Art 
     Preliminary Proof for the Principle of Symmetrization as a Form of Movement in Space and Time 
     Causes and Processes of Morphological Evolution. Essential Facts and Interpretations 
     The Architects Symmetrization and Asymmetrization as the Bases for the Perception of Objects and Order as well as Insight-Behaviour and Cultural
     Reanimation of Modernism Using Integrating Neo-Renaissance 
     Evolutionary Symmetry Theory and Universal Evolution Theory 

Werner Hahn:
"Symmetry as a Developmental Principle in Nature and Art"    (1998)

"...where nature ceases to bring forth new forms, man commences to create an infinite diversity of forms with the help of natural things, that is with the help of nature itself."

"If nature were not so thoroughly stereometrically in its inanimate beginnings, how would it ever rise to unpredictable and immeasurable life?"

 Since 1970, using the methods of trial and error, supposition and refutation, I  have attempted to  establish formal results for my  sculptural thinking  and work  on the  foundation of nature observations.
 Using sculptural experiments with variable form-color pictorial signs, I arrived, via perception of  movements and configurations, at a procedure for constructing forms exclusively by means  of reflections ("symmetrizations") and distortions ("transformation", "asymmetrization"). These results were surprising, and attracted a great deal of attention (see the chapters 5. - 5.4.).

  A method for changing forms was discovered by means of sensory concepts (perception, experience) in two and three dimensions. This method allowed derived configurations to originate which resembled previous and intermediate forms, despite the variety of structural designations. I thus intuitively and spontaneously arrived at the following assumption (a provisional truth), which is of outstanding theoretical and practical usefulness: The symmetrical structures of spatial and temporal order in nature may reflect an important factor for evolutionary changes in nature. The hypothesis, deriving from the will to knowledge, that symmetrization and asymmetrization are the architects of evolution in the realm of natural events presented itself as downright compelling in view of quotidian understanding and especially biological background knowledge.

 Creative symmetrization can be defined as an evolutionary process which forms regulatorily derived, structurally new entities. Here, symmetrical and/or asymmetrical refraction leads to the emergence of newly structured and diffentiable mirror-image/polar equalities synthetically combined into a network. Here, compared with the old, disrupted symmetrical totality of events, the new form of symmetry can obtain a selectional advantage from the symmetrization (which is often linked with asymmetrization).
 Pictorial examples (Figs. 150 - 170; chapters 5.2. and 5.3.) illustrate how, as desired, form-related, not form-identical but derived forms can be developed from a two- and three-dimensionally structured original form (basal form) via intermediate forms (bridging forms). In the midline-orientated sensory constructions which unfold in the course of time, special, unique, and surprising things appear - spontaneously, conspicuously, and unexpectedly - through self-reflections.

 In order to examine whether the hypothesis that symmetrization and asymmetrization might prove to be true as a principle of formation and construction in nature, or whether it does not agree with reality, I began, parallel to practical sculptural work, an intensive study of the literature on problems of symmetry and evolution.
 After two manifestos, in 1971 (see 5.3.1.) and in 1972 (12.2.1.), the first part of the book entitled On the Concept and Significance of Symmetry (chapters 1. - 5.4.) was completed by 1975. In it, the content and the role of the symmetry phenomenon was placed at the center of interest. A study of the literature revealed that hitherto there had not been any general evolutionary theory of symmetry. Thus the task was to conceive of the symmetry phenomeon directly as a heuristic principle which could serve to permit a number of new insights into the laws that govern nature and culture.

 In the 20th century heretofore, symmetries were mainly interpreted, and often defamed, as "quiescence, stasis, invariability" (5.1.), and as "rigidity, pedantry, boredom, death" (3.4.). In order to free themselves from the "millenia-old burden" of the allegedly "static, rigid symmetry" (M. Seuphor), so-called modern artists and sculptors discovered the possibilities of equilibrium in the asymmetrical. P. Mondrian was thoroughly in error when he wrote, in 1924: "Symmetry characterizes things as separated; therefore, a universal formation of the universal must reject symmetry.". W. Baumeister was of the opinion that symmetry "no longer meets the requirements" of the arts today (3.4.). Without recognizing that symmetry is a fundamental principle, modern art took the path that led to abstraction. M. Duchamp was one of the few to rebel against the lack of symmetry in the form world of the avant garde: "The entire century was based on asymmetry and deformation - the "bottle-dryer" (as ready-made, W.H.) rehabilitated symmetry." (See Fig. 67.)

 I was able to demonstrate that - in contrast to the Renaissance - art and science in the modern period no longer constitute Siamese twins. Abandoning the field of natural reality, painters invented an artificial reality that no longer had any connection with the phenomena of nature. Likewise, they discarded symmetry and perspective, a process that had begun with P. Cézanne. With him, the father of classical modernism, which defamed the products of nature as "deception", there began the process of forcible dissolution of form in visible objects, a process which can be interpreted as "antirational". The pictorial composition of cubism, for instance, became more and more lacking in perspective and focal points. The art philosophy of Cézannism and cubism, with its increasing destruction of symmetry and perspective, took as its erroneous point of departure an "a priori knowledge" (D.-H. Kahnweiler) of geometrical figures: spheres, cones, cylinders, upon which - according to Cézanne -  everything in nature should be "modelled"; colors would order themselves "as great noumena, corporeal ideas, beings of pure reason, as they please", according to Cézanne, the disciple of Kant. (On the error of art philosophy, see 11.8.2., 11.8.4.)

 My discovery of a new view of symmetry as a developmental principle produced in me an encyclopedic sense of joyous discovery. Looking above and beyond the boundaries of various disciplines, I was able to demonstrate that symmetry is a fascinating phenomenon which, consciously or unconsciously, provides perennial stimulation and challenge. I recognized that today, after a long pause, it has become possible to readapt art to the sciences, and vice versa, by means of an evolutionary concept of symmetry. In view of the artistic evidence I had collected on the reality of those form-creating master builders: symmetrization/asymmetrization - with whose aid the artist no longer works according to nature, but rather in the same manner as nature itself - we can state that the new art ars evolutoria (see below) can function as an example for the sciences. The obsoleteness of classical modernism, including its theory and philosophy of art, is also revealed by its inability to keep pace with the development of theories in the natural sciences, e.g. the scientific and cultural significance of the theory of evolution, doubtless the most important single theory in modern science. The "displaced ("ver-rückt") reference system of modern painting", in which "the concepts of the sensory world are no longer valid" (W. Haftmann), has hitherto not been able even to approximate the "unity of the world" (W. Heisenberg). The "displacements" of modernism have not been able to illuminate the "meaning of existence" for enlightened and scientifically educated 20th-century man (see 12.3.).

 In Part 1 of my book (completed in 1975), I concentrated on the phenomenon of symmetry, a phenomenon which could hardly be more manifold. Here, an object of knowledge was taken up which promised to overcome the fragmentation of science into individual disciplines, and of thinking and action into specializations that had become mutually unintelligible. Symmetry, if viewed as evolutionary instead of nondynamic, appeared to me as being the Ariadne's thread that can show us the way out of the labyrinthine realms of science, out of the old and the new unclearness of our world. The concepts of symmetrization/asymmetrization could indeed be a royal road leading to a new unity of science.

 Part 2 of my book: On the Problem of Organic Form Development (chapters 6. - 7.2.2.), dealt particularly with biological questions. Here I discussed the points of contact between form-developing processes in nature and art that provide a theory of form, its development and its transformations. Emphasis was placed on the idea of symmetry at the beginnings of a dynamic, organic theory of form: Goethe, de Candolle, Darwin, and others (see 7.1. - 7.1.5.). Plant teratology proved to be a treasure trove for a posteriori symmetrizations and asymmetrizations that can be observed today (7.2.1.). It was ascertained that living nature behaves like an artist who does not permit himself to be restricted to the merely useful: The "mutation-selection theory" was surmounted (7.2. - 7.2.2.).

 The collection of new and increasingly precise data on perception and knowledge in regard to the postulated reality of symmetry then led to a further development of the "evolutionary theory of symmetry" (Evolutionary Symmetry Theory; EST) in Part 3 of my book: Evolutionism/Ars Evolutoria - Theory of Light/Color and Form, Morphogenesis, Morphomutability, and Morphoevolution as Causal Form Theory (chapters 8. - 13.). My purpose here was to present for discussion the facts and problems of an evolutionary concept of symmetry in its applicability to many fields of dead and living nature, to the liberal arts and natural sciences, and to society. It was my desire to stimulate a discussion of the Evolutionary Symmetry Theory that would transcend the boundaries of individual disciplines.

 The knowledge gained through the interaction of discoveries, new evidence (often experimental), and theoretical concepts was concentrated on the paramount importance of symmetry for understanding evolutionary events in nature and art. In many areas, this knowledge produced convincing arguments, e.g. the conviction that inter- and trans-disciplinarity in symmetry research leads to a recovery of scientific perceptional abilities which are hindered by individual disciplinary developments, by atomization into individual fields.
 Transdisciplinarity involves the development of an overarching paradigm encompassing a number of scholarly disciplines. The theory of symmetrization and asymmetrization as a theory of form, formation, and form-variation/mutation ("evolutionism", "neo-evolutionism") illustrates a transdisciplinary framework. The components of this theory (modern painting, art theory, evolutionary biology, natural philosophy, psychology, geometry, physics, chemistry, cosmology, music, etc.) are not only linked internally and closely interwoven through integration by the theme "symmetry"; in addition, the disciplines (monodisciplinary fields) are subsumed in the transdisciplinary concept "symmetry" under a supradisciplinary paradigm. Superintegration as the ideal of a unified science would be attained if all science could be reduced to a general theory of form.

 Here are only some of the results and aspects of my transdisciplinary consideration of symmetry:

- Evolution of a form is unthinkable without total disdain for,  and renunciation of, form. Dissolution of form in the sense  of a transformation of totalities via symmetrization / asymmetrization is in the service of a morphoevolution (8.1. ff.).

- Cell division in uni- and multi-cellular animal and plant  organisms can be interpreted as mirror-image symmetrization. Likewise, in meiosis and DNA doubling I recognized  symmetrizing formational processes. M. Eigen has postulated  a mirror-image symmetry in the structure of the "Ur-gene"/"proto-gene"  (

- The demonstration that changes of dimension and proportionality in ontogenesis and phylogenesis are primarily based on symmetrizations linked with asymmetrizations (10.3.4. ff.).

- Light proves to be a causal factor in symmetroclastic and symmetrogenic morphogenesis and morphomutability (see Fucus serratus as an example;,, 10.5. f.).

- The hypothesis of the inherently symmetrical and potentially  bisexual "Ur-ur-ur...cell"/"proto-proto-proto...cell". Sexuality as a mechanism for triggering form-giving symmetrization (10.3.6. ff., 10.4.4.). Love as an act of symmetry (

- Model concepts on symmetrization. Evolution from unicellular  to multicellular organisms via morphologically "primitive"  diplocells, tetrad and octet forms (10.4. - 10.6.).

- Demonstration that the master builders symmetrization/asymmetrization are the foundations for perception of objects and orders as well as discernment behavior, cultural evolution (11. ff.).

- Discovery of double-mirror sight as binocular double stereoscopic vision that can be used to develop a symmetrization theory of perception via a plethora of controllable reproducible experiments with forms and colors (11.6. ff.).

- Mirror-image symmetry as a law of form and composition, and the "principle of precision" in Gestalt psychology (11.6.5.).

- Symmetrizations as the basis of all cogitation and memory (11.9.4.).

- Experiments indicating that white visible light has a symmetrical structure (11.7.).

- Refutation of the dogmatism of "absolute and blind chance" (J. Monod). Order in chaos (11.9.6.).

- Ethicization via social symmetrization (11.9.7., 13.).

- Evolutionism as the third basic direction in philosophy, being neither materialism nor idealism (12.2.3.).

- Evolutionism as a unification of ambivalences: "great realism" - "great abstraction" (12.2.).

- Symmetry as a developmental principle in music. Foundation of a musica evolutoria (12.5.).

- The light-matter/antimatter-energy primary model ("Urform model") of evolution as a key figure in clarifying evolutionary processes, providing access to a "graphic atomic dynamics". Protomorphology and protomorphogeny which deny that the universe began from nothing, and postulate the dissolvable multiunity of the infinitely small in dynamic geometry: Ur-ur-ur/proto-proto-proto...symmetrization center, Ur-ur-ur/proto-proto-proto...geometry, Ur-ur-ur/proto-proto-proto...three-dimensionality, Ur-ur-ur/proto-proto-proto...mathematicity, etc. (12.6. and 12.7.).

 The results of my investigations thus overcome disciplinary limitations and embarrassments: The "dynamic concept of symmetry" and the method of interdisciplinary parallelizing makes it possible to attain an overarching pervasion of the "key theme: symmetry" in the fields of art, the humanities, and the natural and social sciences, a comprehensive integration and unification of the reality of art and the laws pertaining to it, together with the reality of nature and the laws governing it. This new direction in art: ars evolutoria or evolutionism, originally called "harmonic art" or "symmetrism", is, owing to its direct provision of experience, outstandingly suitable for making us aware of the fascination of symmetry as an evolutionary construction principle in nature and culture.

 Moreover, ars evolutoria is based on Goethe, who appraised art as a "true mediatrix", as the "most worthy interpretress" of natural reality (concept of style, see 11.8.). The art style evolutionism, which is directed towards the "unity of entirety", contains, as an integrative perspective, aspects of the following fundamental stylistic directions: realism (cogitation), surrealism (emotion), expressionism (sensibility), and constructivism (intuition) - all reflections of basic human psychosomatic structures - in an overall synthesis ("reanimation of modernism"; see 12.2.4., 12.4.).

 The style ars evolutoria, with the variants "neo-cubism", "neo-Baroque"/"neo-mannerism", as well as "atomism" ("pointillistic evolutionism"), provides a possibility for presenting and elucidating additional comprehensive connections that previously could not be expressed in art. 
 On the one hand, I used the expressions ars evolutoria and evolutionism synonymously as stylistic concepts in this book, but in addition, in Part 3 I achieved an actualization and extension of the 19th-century term "evolutionism" in regard to a philosophy of nature and culture. In my pictorial work, and also in my book, the scientific attitude and the artistic vision are not antithetical. Since the search for unity in nature on an evolutionary basis requires transdisciplinary points of view and hypotheses in order to obtain knowledge of the symmetry/asymmetry phenomenon, and since there are many points of contact with the Renaissance, especially with the searchers and artists Leonardo da Vinci and Albrecht Dürer, the purpose of my book is to found a Neo-Renaissance as a "belligerent movement".

 This new concept for a new style and a new epoch: "Neo-Renaissance" as a constant challenge to cultural reflection, thus designates a new beginning for a comprehensive and evolutionary knowledge of the world obtained by a union between science and art. In view of the linking and interaction of the two, my book places critical emphasis on the art and cultural history of modernism: a plea for a positive, culture-forming attitude towards art. (On the dilemma of avant-gardism, together with its "kingmakers", see 11.9.9., 12.3., 13.). I hope to establish and encourage a dialog between institutions, disciplines, and persons involved in cultural activities of the present who so far have carefully avoided taking one another seriously.

 In addition, the book is intended to lead to a new understanding and consensus between competing world views, and between the cultural and natural sciences. On the basis of the universality of the form-creating and form-changing evolutionary factors: symmetrization/asymmetrization, and in agreement with the evolutionary epistemology, perspectives also emerge for a new and progressive philosophical direction, with the goal of "social symmetrization", i.e. ethicization by means of growing knowledge (11.9., 11.9.7., 13.). The Neo-Renaissance is convinced that man and society are capable of further education and development in the direction of perfection. It advocates the surmounting of the "fragmentation of our world view" (R. Riedl) by building a bridge between nature and mind.

 Thus it is important "to have unrolled the phenomena of symmetries in their full breadth to a monumental work; whether in quanta, atoms, and crystals, or in corporeal forms, senses, and brains, or in the forms of all the artifacts that have originated from human activity. Only then will we become aware of our potentialities: the concert of relations that joins the inorganic and the organic, our sensibilities, our thoughts, and our deeds; that which reciprocally unites nature and culture in the human psyche." (Riedl; see the preface of the book).

 In the hope that artistic creation and theoretical reflection in the new movement Neo-Renaissance (science art, neo-modern art; see chapter 13) will not be understood by only a few, the present book, despite the unusual multiplicity of aspects and projects contained in it, is intended as an introduction to this new material for the interested layman. In spite of all the documentary evidence that it presents, the book is possibly too short in places. However, a presentation of all the data would have made the book even more voluminous, and thus less appealing to the large circle of readers it was written for.

 In publishing these practical and theoretical research results, I hope not only to motivate the knowledgeable reader to recognize new tasks, but also to invite him to make suggestions for improvements in, and further developments of, the material presented here.

 Although the German first edition of my book on symmetry (Hahn 1989/1995) already contained the above preface, I should still like - as a sort of epilogue - to remark the following on the English edition at hand:

 My book on symmetry, which has been called "giant opus" (Sitte), "monumental work" (Irrgang), "opus magnum" (Der Spiegel) and "masterpiece" (Nagy) ("in the footsteps of Leonardo", according to Ohff, Der Tagesspiegel , Berlin ), has meanwhile been recognized as the key work on an Evolutionary Symmetry Theory (EST). In 1991, inspired by an excellent book review (Großmann 1990), I started the "Action/Initiative EST", which in 1993 resulted in the successful "International Frankfurt Symposium Evolutionary Symmetry Theory -Self Organization and Dynamic Systems" (Hahn/Weibel 1996; see as well Gutmann 1996, Wuketits 1996).

   Because of its historical significance and since no falsification (i. e. defeat of my theories) has been presented as of yet, the edition at hand is the original version of the work (Hahn 1989) translated into English without alterations; neither in the text (chapters 1. - 12.7) nor in the figures (Figs. 1 - 689 c and the 10 colour plates) have alterations been made. However, chapter 13 with 10 sections has been added to the English edition so that a supplement had to be made to the subject index, the register of persons and the bibliography. The following key-words (see chapters 13. - 13.6.) reflect the further development of the main ideas of the basic work.:

 asymmetrization/symmetrization principle (hypothesis, reciprocal mechanism), social asymmetrization/symmetrization (asymmetrizing initiative and resymmetrization), iso- and aniso-symmetrization, initial or primary asymmetrization, secondary asymmetrization (transformation), science art (neo-modern art/trans-modern art/ultra-modern art), auto-evolution, self-organization, evolutionary aesthetics, evolutionary geometry (bifurcation morphology), evolutionary humanism, neo-evolutionism, holo-evolutionism, holistic natural theory, universal theory of evolution, ethical universalism.

In the past six years, the results of the work were widely spread, particularly in the Germanophonic regions. Meanwhile - on 14 May 1992 - I received a certificate from the President of the German patent office granting me a patent for the "mirror construction" (see 11.6.6., Fig. 434); In my book I attach particular significance to the double mirror-experiments. In view of the scientific and artistic success of my book, I would be delighted, if the reader of the English edition of the work took the same view as Professor Dr. Dr. Gerhard Vollmer did, who - after reading the book - remarked in 1991:

"(...) we have to do with a marvellous compilation, an encyclopedia full of life, full of inspiration, full of ideas, full of references, associations, relations. I feel unreserved admiration for this gigantic, lovingly compiled and splendidly got up work. Congratulations to you on the completion of the work and its richness of content. As far as my knowledge goes, there is no other work that could stand up to comparison."

My book provides a broad foundation for further discussions, cooperations, empirical studies and theoretical reflections in natural sciences, humanities, philosophy, modern art and music (see Hahn/Weibel 1995). With regard to the English edition, I hope for a similar judgment from the part of the reviewers, in analogy to the judgment of renowned chaos researcher, Siegfried Großmann (Großmann 1990):

"During 20 years of compilation, Hahn succeeded in creating an admirable book in which he traces the enormous treasure of observations made in nature and culture back to a few underlying structural principles. (...) The content is not merely contemplative, not mere curious observation, but the demonstration of a comprehensive hypothesis, devised as the result of experimental and theoretical research: symmetry as a far-reaching, leading, structuring, causal element of evolution, as the idea lying behind nature and culture. (...) The book is full of suspense and worth-while reading: symmetry as Ariadne's thread through nature and art as 'cause, source and driving force of evolutionary dynamics'. (...) Interdisciplinarity and general course of studies at their best. Literature as a link between science and art. Strongly recommendable."


I extend my gratitude to all those who supported me with advice, interest and goodwill during the many years of my research. I am particularly grateful to Professors Werner Hofmann, Rupert Riedl, István Hargittai, Dénes Nagy, Hermann Haken and Arne Wunderlin, Friedrich Wilhelm Gutmann and Peter Weibel, Rudolf Wille as well as to Dr. Franz M. Wuketits for their support and interest in my works. Cordial thanks to (university) professor Dr. Rupert Riedl, chairman of the department of zoology at the University of Vienna, for his introductory remarks to the world of symmetries; a "very readable, genuine introduction" (according to Peter Sitte in a review).

Moreover I should like to thank the publishing house World Scientific Publishing Co Pte Ltd, Singapore, for their assistance in publishing the extended English edition of my book on symmetry, which will be distributed worldwide. The book provides a sound basis for further reflexion at different levels and in various disciplines of the natural sciences as well as the cultural sciences. It would be a great pleasure to me to see this work continued - now on a global scale.

Werner Hahn
(In the summer of 1999.)

Werner Hahn: 

Symmetry as a Developmental Principle in Nature and Art


Foreword by Prof Dr. Rupert Riedl

Introduction and Thanks 

Section I

1.  The Discovery of Symmetry 

2.  On the Term Symmetry from the Antiquity to the Renaissance 

2.1.  Vitruvius´ and Polyclitus´ Theory of Symmetry - a Derivation of   the Pythagorean Concept of Symmetry 

2.1.1. Vitruvius´ "Law of Symmetry" 

2.1.2. Polyclitus´ Arithmetic Symmetries 

2.2.  The Concept of Symmetry from the Founding of Materialism and   Idealism to the Middle Ages

2.2.1. Democritus: "Cheer" through Symmetry

2.2.2. Plato: Symmetry as a Source of Beauty, Virtue and Truth 

2.2.3. Aristotle: Symmetry as a Principle of Natural and Artistic Acts 

2.2.4. Plotinus: Criticism of the Traditional Theory of Symmetry 

2.2.5. Trends to Theologize the Term Symmetry since Augustine 

2.3.  The Rediscovery and Modification of the Ancient Concept of    Symmetry in the Renaissance

2.3.1. Alberti´s "Concinnitas" and Leonardo´s "Divine Proportions"

2.3.2. Dürer: Simmetria - "Comparability ..., that is Beautiful"

3.  The Development of an Excact Concept of Symmetry through    Scientific Progress

3.1.  Kepler´s Reflections on Symmetry and Modern Use of the Word   Symmetry

3.1.1. Kepler´s Discoveries

3.1.2. On the Exact Modern Concept of Symmetry in the Field of    Inanimate Objects

3.2.  Haeckel and Jaeger: Symmetry in the Field of Living Organisms

3.2.1. Haeckel´s "Stereometry of Organisms" and "Symmetrism" Concept

3.2.2. Jaeger´s Treatment of the Symmetry Problem

3.3.  On the Emancipation of the Term Symmetry in Philosophy    (Aesthetics): Hegel - Rosenkranz - Adorno

3.3.1. Hegel: Symmetry and Natural Beauty - "Everything Intellectual   is Better than any Product of Nature

3.3.2. Rosenkranz: Overcoming the "Rigidity of Symmetry" - Organic   Totality

3.3.3. Adorno: Asymmetry in Relation to Symmetry - "Non-Identical    Objects" under the "Spell of Universal Identity" as the    "Reconciled"

3.4.  On the Discussion of Symmetry in Art Science - Symmetry in    Modern Age

4.  On Symmetry and Asymmetry as Evolutionary Factors in Nature.   The Development of an Evolutionary Concept of Symmetry

4.1.  On the Question of the Development of Symmetries in Nature -   Portmann: "Unknown Powers of Creation"

4.2.  The Development of an Evolutionary Concept of Symmetry in order   to Understand the Symmetries in Unicellular and Multicellular   Organisms and the Importance of Transformations

4.2.1. Symmetrizations in Unicellular Organisms

4.2.2. Symmetrizations in Multicellular Organisms

4.2.3. Transformations as Developmental Deviations

5.  Evolutionary Symmetrizations in Two and Three Dimensions. On   the Syntax and Semantics of Symmetrism

5.1.  Against the Defamation of Symmetry

5.2.  Symmetrizations in Planes (Two-Dimensions) Combined with other   Harmonic Changes is Construction

5.3.  Symmetrizations in Space (Three-Dimensions) and     Transformations. Comments on the Significance of Light and    Colour in Symmetrical Pictures

5.3.1. Manifesto "On the Art of the Future" (1971)

5.4.  A Letter to Prof. Dr. Werner Hofmann

Section II

6.  Can an Artist Approach the World and its Content only in a    Metaphorical Way?

6.1.  Are there Points of Contact between Different Formation    Processes in Nature and Art which Make a Theory of Form,    Formation and Form Change Possible?

6.1.1. Goethe´s Attempt to Consistently Invent Creatures "into    Infinity" that have an "Inner Truth and Necessity"

7.  Evolution: Fairy-Tale, Theory or Fact? Can we Experience    Evolution Directly?

7.1.  On the Roots of a Dynamic Organic Form Theory

7.1.1. Goethe's Conception of Metamorphosis Governing the Regular and   the Irregular in Contrast to De Candolle's Quest for "Types"   with "True" and "Original" Symmetric "Layouts" in Fauna

7.1.2. De Candolle´s Search for "True Symmetry" in Plants and the    Problem of  "Varieties" that "Are Passed On"

7.1.3. Troll´s Accusation: Darwin´s Concept of Evolutionary History   Trys to Manage without "any Principle of Meaning and Order".   Thesis: "Nominalism ... Destroyed Teleology" (Engels)

7.1.4. Portmann´s Legacy as a Morphology Scientist. How do Colours and   Patterns without Adaptation Value Originate?

7.1.5. Darwin´s "Great Theoretical Interest" in the "Law of Symmetry".   Alterations without Advantage in Natural Selection

7.2.  Ludwig´s Thesis: "Symmetry is a Marking of the Body just like   any other" - Antithesis: Symmetrizations as Powerful     "Active Guides"; Overcoming the "Theory of Mutation and    Selection"

7.2.1. Plant Teratology as a True Treasure Trove for Changes in    Symmetry which Can Be Observed today

7.2.2. Flower and Leaf Forms as the Results of A-posteriori     Symmetrizations and Asymmetrizations

Section III

8.  On the Question whether there Can Be a Pre-Object, Pre-Morph   "Life Process of Form" in Nature and Art

8.1.  On the Inconceivability of Form Evolution through Totally    Disdaining or Rejecting of Form

8.1.1. Leonardo: "Through Confusing and Uncertain Things Intellect is   Inspired to Make New Inventions" Evolutionary Action of Form in Symmetrism/Evolutionism -    Naturally Regular and not "Confusing"

8.1.2. On Klee´s Claim that there is a "Form as Genesis" 

8.1.3. Cézanne: Art as "Harmony Parallel to Nature". Can Colour-Forms   "Modulate" themselves as Noumena and such like allegedly    "Everything in Nature Models itself ... as Sphere, Cone and   Cylinder"?

8.1.4. Belief in a Synthesis of Reality/Law of Art and a Reality/Law   of Nature

8.1.5. Conception of how EVOLUTIONISM Developped: Painting as a    Science. Formational Natural Laws as the Lasting

8.1.6. Metaphysical Concept of Development: Everything Develops into   Everything (Bergson)

8.2.  The Search for the "Proto-Cell" of the Ars Evolutoria and for   the "Basso Continuo" of Evolutionary Formation

8.3.  On Morphospeciation in the Ars Evolutoria: Comprehensible    Arsspecies Division without Intentions of Coding

9.  Preliminary Proof for the Principle of Symmetrization as a Form   of a Movement in Space and Time

9.1.  Symmetrizing Proto-Motions, Proto-Centers, Proto-Planes,    Proto-Axes, Proto-Matter, Proto-Power, Proto-Form

9.1.1. Matter as an Existence Form of Motion / Motion as an Existence   Form of Matter. Hypothesis: Light-Matter/Antimatter-Energy-   Protoform-Model

9.1.2. Can the Variety of the Animate and Inanimate World be Traced   Back to Electrons, Positrons, Nucleic Protons and Nucleic    Neutrons?

9.1.3. Interpretation of Pair Building , Pair Annihilation and    Positronium as Phenomena of Prototypical Symmetrization    Processes

9.1.4. Symmetry Principles as the Key to Uniting the Four Proto-Forces   of Nature to one Interaction

9.1.5. Mass as Materialized Energy and Particle-Antiparticle    Symmetries

10.  Causes and Processes of Morphological Evolution. Essential    Facts and Interpretations

10.1.  Scientifically Systematized Concepts of Forms and Colours as a   Matter of Evolutionism

10.2.  On Proto-Proto-Proto...Symmetry and Breach of Proto-Proto-   Proto...Symmetry in the Creation of the Universe

10.2.1. On the "Manner" of a Simply Mathematical and Physical    Understanding of Natural Reality. Heisenberg´s  "World formula"   with Symmetric Claims - Turning Away from the Concept of an   Objective Reality of Elementary Particles

10.2.2. C.F. von Weizsäcker´s Idea of the "Unity of Nature" as Opposed   to "Titanism": Integration of the Aspect of Life, Consciousness   and the "Blissful Perception of Form" (Art)

10.3.  The Role of Symmetrization for the Symmetry Change in    Biological Evolution 

10.3.1. Are the "Architectural" Characteristics of Organisms Based on   the Harmony of the Light-Matter/Antimatter-Energy-Prototype?

10.3.2. Preliminary Hypothesis: The Mechanism of Thought as a Process   of Reflection, Reproduction and Symmetrization

10.3.3. Haeckel´s Biogenetic Principle: Ontogeny as the Rapid    Repetition of Phylogeny

10.3.4. On the Universality of Symmetrization, Cell Division and the   Genetic Code as Evidence of Evolution: The Changes of    Dimensions and Proportions in Ontogeny and Phylogeny are    Primarily Based on Symmetrizations Hypothesis: Symmetry in the Mechanism of Left-Right Division   during DNA Self-Replication Love as an Act of Symmetry? Symmetrization Processes in the Cell Cycle: Symmetries of    Repetitive DNA-Segments Meiosis as Symmetric Process Theory of Mutation and Theory of Symmetrization. Production of   New DNA by Repetitive DNA through Symmetrization Processes? Light as Causal Factor in Morphogeny and Morphomutability    (Fucus-Example) Polar Differentiation and "Primitive" Symmetrization. On the   Error of the Proto-Procreation Theory, Vitalism and Mechanicism

10.3.5. Search for Proto-Proto-Proto...Ancestors, Proto-Proto-   Proto...Symmetrization and Proto-Proto-Proto...Change of Genes   in the Process of a Biogenesis from Inanimate Matter Light as a Factor Inducing Mutability On the Abiotic Synthesis of "Organic" Substances through    Radiation and Abiotic Biogenesis Theory of the Symmetrization of the Proto-Proto-Proto...Cell.   On the Significance of Primeval Light Stimuli and the    Gravitational Force as Primary and Secondary Abiotic Mutagenes Eigen´s Profile of the Ancestor of all Living Beings: Mirror   Symmetry as the Structure of the "Proto-Gene". Symmetrization   Related to Asymmetrization

10.3.6. Sexuality as a Mechanism to Initiate Shape-Determining    Symmetrization Omnipotent Cells as Symmetric and Sexual Structures (Male-   Female Structure, Hermaphrodite Structure). Hypothesis of the Inherently Symmetric and Potentially Bisexual   Proto-Proto-Proto...Cell Phenomenon of Gynandromorphy (Intersexuality): Living Beings   with Male and Female Physical Side Organogenesis of the Sex - Theory of the Equilibrium of Sexual   Potentials

10.3.7. Development of the Proto-Body Cavity by Three Vertical    Symmetrizations

10.3.8. On the Mirror-Image Symmetry between Right-Handedly and Left-  Handedly Coiled Snails

10.3.9. On Asymmetries in the Animal Kingdom as well as on Mirror-Image   Right-Handed and Left-Handed Forms. Ludwig: "Bilateral    Tendency" - Weyl: "Automorphism A-Posteriori Asymmetries in the Vegetable Kingdom.  On    Laevorotatory and Dextrorotatory Screw-like Structures,    Enantiomorphic Development of Blossoms, Limited Divergence and   the "Golden Section" On the Production of Organic, Mirror-Image Right and Left    Molecules 

10.4.  Momentous Early Stages in the Evolution from Unicellular to   Multicellular Organisms ("Dipolar Symmetrizations")

10.4.1. Development of the Proto-Proto-Proto...Cell to the Proto-Proto-  Proto...Multicellular Organism via Morphologically "Primitive"   Diplocells, Tetraforms and Octoforms

10.4.2. On the Reproduction of Vegetable Unicellular Organisms

10.4.3. Sexuality in Proto-Animals: From Isogamy to Functional and    Morphological Anisogamy

10.4.4. Homology of the Bipotential of Dipolar Symmetrization and    Bisexuality?

10.5.  Ray-Induced Mirror-Image Self-Replication of DNA and Working   Hypothesis for a Molecular Theory of Kinetic Processes of    Symmetrizations

10.5.1. Model Concepts of Mirror-Image Dipolarization and     Symmetrizations for the Development of Diplocells, Tetraforms   and Octoforms

10.6.  Conclusion: Evolution as Cause, Consequence, Meaning and Nature   of Essential Symmetrizations 

11.  The Architects Symmetrization and Asymmetrization as the Bases   for the Perception of Objects and Order as well as Insight-   Behaviour and Cultural Evolution

11.1.  On the Evolutionary and Ontogenetic Development of the Human   Visual Sensory System. Acquisition of Insight-Behaviour through   the Development of the Field of Vision and Centralization

11.2.  Symmetries of the Path of Vision

11.3.  The Problem of Human Side-Dominance 

11.3.1. On the Binocular Sight of Ambivisual Persons 

11.3.2. Stereoscope Experiment to Test Eye Dominance

11.3.3. Findings from Experiments with Inversion Glasses 

11.4.  Mirror Drawing with Righties and Lefties. Enantiomeric Proof of   Eye and Hand Dominance

11.5.  Motion Experiments to Support the External Rotational    Preference of Right-Sided People and the Internal Rotational  Preference of Left-Sided People

11.6.  Test Procedures for Double-Mirror Sight as Binocular Double   Stereoscopic Sight

11.6.1. On the Prerequisite for a Fusion with Stereoscopic Effect.    Splitting of the Need for Fusion

11.6.2. Double-Mirror Sight with Non-Coloured Stimuli Structures

11.6.3. Double-Mirror Experiments with Equivalent and Non-Equivalent   Fields of Colour and Form 

11.6.4. Construction of Inverse Depth Perception. Perspective Reversal Inversion Jumps of Reverse Figures in Double-Mirror Experiments

11.6.5. Mirror Image Symmetry as a Law of Form and Rule of Structuring   and the "Pregnance Principle" of "Gestalt" Psychology Facial Perception under the "Tendency toward Symmetry" with   Binocular Simple Sight and in Double-Mirror Experiments On the Perception of "In Front" and "Behind" through Crossed   and Uncrossed Anaglyphic Picture Sight Picture Point-Cross-Sliding with Polarization Picture Sight Crossed and Uncrossed Red-Green Double Picture Sight and    Summary of Depth Inversion Double Polarization Glasses Sight

11.6.6. From Polar Double Spatial Picture Sight (2-fold Sight) to    Double-Mirror Sight as Single Spatial Picture Sight (3-fold   Sight) Experiments on Naked Eye Spatial Picture Sight Double-Mirror Experiments with Stereo-Picture-Pairs Supporting   a Symmetrization Theory of Perception Experiments for the Purpose of Analyzing the Perception of    Shifts in the Rotational Direction of a Rotating Wire-Edged   Cube

11.6.7. Double-Mirror Experiments with Fusion as Fission - Fundamental   Fission Knot Example, Corrected Perspective Illusions,    Supplements

11.6.8. On the Polar Structure of Colour Perception

11.6.9. On the Evolution of Colour Sight

11.7.  Experiments From Which the Symmetry Structure of White Visible   Light Can Be Inferred

11.8.  Art as the "True Conveyer", the "Most Worthy Interpretress" of   the Reality of Nature (Goethe: Stil [Style] ). Does the    Knowledge of an A  Priori of Stereometrical "Protoforms" Exist?

11.8.1. Cézanne´s Artistic Intentions and A Priori Idea of     Being in Comparison to Ars Evolutoria and "Natura Naturans"

11.8.2. On the Error of the Philosophy of Art of Cézannism/Cubism    with its Increasing Destruction of Symmetry and Perspective.   Neo-Cubism of Ars Evolutoria

11.8.3. Development and Significance of Perspective

11.8.4. On Colour Perception, the Conception of Space and Shape of    People Born Blind after Operation and Babies

11.8.5. Faces as Optical Triggers for Humans and Animals. Baits-Seeing   (Anthropomorphism) and Key Images in Ars Evolutoria

11.8.6. On Endogenous and Exogenous Control Factors for the     Development of Inner Portraits in Ars Evolutoria

11.8.7. On Corresponding Structural Aspects of "Gestalt"-Finding in   Mandalas of Ars Evolutoria, in Shape Creations by Children, so-  called Primitives and the Mentally Ill

11.9.  Knowledge of Nature and Art in Evolutionism in Accordance    with the Evolutionary Epistemology

11.9.1. On Amazing Similarities of "Gestalt", in Thinking and Behaviour   of Identical Twins. The Phenomenon of Mirror-Image Twins 

11.9.2. Higher Development of Consciousness and Complementary    Interaction of the Human Mirror-Image Brain Hemispheres.    Consciousness as Unitas Multiplex 

11.9.3. Observations which are Examples against the "Supernatural    Origin" of a Mind Conscious of Itself 

11.9.4. Symmetrizations as the Basis for all Thinking and Memory 

11.9.5. Lateralization of the Visual System and Cerebral Asymmetry as   Achievements of Becoming Human

11.9.6. Versus the Dogmatism of "Absolute and Pure Chance" (Monod).   Order in Chaos 

11.9.7. Reflections on Ethicalization by "Sociological Aesthetics"    (Simmel), Social Symmetrization

11.9.8. Optical Culture as a Reflection of Intellectual Curiosity and   Development of Consciousness. Necessity of an Evolutionary    Concept of Art

11.9.9. What is the Point of Art and Anti-Art? Plea for a Positive,   Culture-forming Desire for Art

12.  Reanimation of Modernism using Integrating Neo-Renaissance

12.1.  Proportional Codes of the Ars Evolutoria

12.2.  Interpretations of Legitimacy in the Ars Evolutoria.  Evolution   as the Unification of the Ambivalent Elements: "Superrealism" -   "Superabstraction"

12.2.1. Art System in the Ars Evolutoria and Biosystems. 1972 Manifesto

12.2.2. On a New-independant Definition of the Concepts Dualism,    Dialecticism, Complementarism, Polarism, and Totalitarism 

12.2.3. Evolutionism as the Third Basic Direction of Philosophy, which   is neither Materialism nor Idealism Goethe´s Concept of Levels in Symmetry as Metamorphosis-Idea.   Polarity and Enhancement as the "Driving Wheels of Everything   in Nature" - "Matter Never without Mind...Mind Never without   Matter"

12.2.4. On the Natural Continuance of Realism (Thought), Surrealism   (Feelings), Expressionism (Perceptions), Constructivism    (Intuition) as Mirror-Images of Psychosomatic, Human Fundaments   in the Ars Evolutoria

12.3.  The Concept Superunification in Evolutionism as Anti-    Reductionism. On the Dilemma of Avant-Gardism, Including    Kingmakers

12.4.  "Trasmutazione di Forme" of the Researcher/Artist Leonardo and   Dürer. On the Unity of Artists and Researchers in Renaissance   and Neo-Renaissance. Ars Evolutoria as "Neo-Baroque"/"Neo-   Mannerism"

12.5.  Symmetry as a Developmental Principle in Music. Founding of a   Musica Evolutoria 

12.6.  Philipp Otto Runge´s "First Figure in Creation" and the Light-  Matter/Antimatter-Energy-Protoform Model in Evolutionism as the   Key Figure toward Elucidation of the Evolutionary Processes   with Access to "Visible" Atomic Dynamics 

12.7.  Consequences of the Theory of Protoform in Natural and Artistic   Philosophy. Ars Evolutoria-"Atomism"

13.  Evolutionary Symmetry Theory and Universal Evolution Theory

13.1.  Holistic Natural Theory - A Community Effort

13.2.  The Creativity Principle as a Reciprocal Mechanism

13.2.1. Iso-Symmetrization and Aniso-Symmetrization

13.2.2. The Auto-Evolution System Primary Asymmetrization /     Symmetrization

13.2.3. Asymmetry seen Symmetrically

13.2.4. Transformations as Secondary Asymmetrizations 

13.3.  Universal Theory of Evolution and Biology

13.4.  Evolutionary Nature and Art Aesthetics and the Trio     Beauty/Truth/Goodness

13.5.  Understanding through a Double Reflection of the Nature of    Reality

13.6.  Social Asymmetrization/Symmetrization and Ethical Universalism

Colour Plates

Literature and Figure Sources

Person Index

Subject Index