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ART & SCIENCE |
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by Werner Hahn (Art & Science Research
Institute,
Preliminary remark: 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
the
SHORT PREFACE 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: 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. Contents: On the
Concept and Significance of Symmetry: The Discovery of
Symmetry Werner
Hahn: "...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. 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. 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. 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.). - 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. 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."
ACKNOWLEDGEMENT 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 Werner
Hahn: Symmetry
as a Developmental Principle in Nature and Art TABLE OF CONTENTS 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" 8.1.1.1. 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 11.6.4.1. 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 11.6.5.1. Facial
Perception under the "Tendency toward Symmetry" with
Binocular Simple Sight and in Double-Mirror Experiments 11.6.5.2. On the
Perception of "In Front" and "Behind" through
Crossed and Uncrossed Anaglyphic Picture Sight 11.6.5.3. Picture
Point-Cross-Sliding with Polarization Picture Sight 11.6.5.4. Crossed and
Uncrossed Red-Green Double Picture Sight and Summary of
Depth Inversion 11.6.5.5. 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) 11.6.6.1. Experiments on
Naked Eye Spatial Picture Sight 11.6.6.2. Double-Mirror Experiments
with Stereo-Picture-Pairs Supporting a Symmetrization
Theory of Perception 11.6.6.3. 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 12.2.3.1. 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 |
