ART & SCIENCE
by Werner Hahn (Art & Science Research
ISBN: 9810223633 –
Author: Hahn, Werner - Title: Symmetry as a developmental principle in nature
and art –
In www.worldcatlibraries.org you
see that – just now (07/2006) – the book is in 52 libraries of
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:
of asymmetrizing symmetry breaking and formation.
In a two-sided strategy energy is processed innovatively:
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)
SYMMETRY AS A
that symmetry is a fascinating
phenomenon which provides endless
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.
Concept and Significance of Symmetry: The Discovery of
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
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.
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).
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.
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.
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.
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" (10.3.5.4.).
- 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; 10.3.4.6., 10.3.5.3., 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 (10.3.4.2.).
- 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.).
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
"neo-Baroque"/"neo-mannerism", as well as
evolutionism"), provides a possibility for presenting and elucidating
additional comprehensive connections that previously could not be expressed
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,
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
"(...) 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.
Symmetry as a Developmental Principle in Nature and Art
TABLE OF CONTENTS
Foreword by Prof Dr. Rupert Riedl
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
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
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"
126.96.36.199. 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
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
10.3.4.1. Hypothesis: Symmetry in the Mechanism of Left-Right Division during DNA Self-Replication
10.3.4.2. Love as an Act of Symmetry?
10.3.4.3. Symmetrization Processes in the Cell Cycle: Symmetries of Repetitive DNA-Segments
10.3.4.4. Meiosis as Symmetric Process
10.3.4.5. Theory of Mutation and Theory of Symmetrization. Production of New DNA by Repetitive DNA through Symmetrization Processes?
10.3.4.6. Light as Causal Factor in Morphogeny and Morphomutability (Fucus-Example)
10.3.4.7. 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
10.3.5.1. Light as a Factor Inducing Mutability
10.3.5.2. On the Abiotic Synthesis of "Organic" Substances through Radiation and Abiotic Biogenesis
10.3.5.3. 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
10.3.5.4. 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
10.3.6.1. Omnipotent Cells as Symmetric and Sexual Structures (Male- Female Structure, Hermaphrodite Structure).
10.3.6.2. Hypothesis of the Inherently Symmetric and Potentially Bisexual Proto-Proto-Proto...Cell
10.3.6.3. Phenomenon of Gynandromorphy (Intersexuality): Living Beings with Male and Female Physical Side
10.3.6.4. 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"
10.3.9.1. A-Posteriori Asymmetries in the Vegetable Kingdom. On Laevorotatory and Dextrorotatory Screw-like Structures, Enantiomorphic Development of Blossoms, Limited Divergence and the "Golden Section"
10.3.9.2. 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
188.8.131.52. 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
184.108.40.206. Facial Perception under the "Tendency toward Symmetry" with Binocular Simple Sight and in Double-Mirror Experiments
220.127.116.11. On the Perception of "In Front" and "Behind" through Crossed and Uncrossed Anaglyphic Picture Sight
18.104.22.168. Picture Point-Cross-Sliding with Polarization Picture Sight
22.214.171.124. Crossed and Uncrossed Red-Green Double Picture Sight and Summary of Depth Inversion
126.96.36.199. 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)
188.8.131.52. Experiments on Naked Eye Spatial Picture Sight
184.108.40.206. Double-Mirror Experiments with Stereo-Picture-Pairs Supporting a Symmetrization Theory of Perception
220.127.116.11. 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
18.104.22.168. 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
Literature and Figure Sources