the theory of the formal arts and the formal aesthetics > thesis

THE THEORY OF THE FORMAL ARTS AND THE FORMAL AESTHETICS.

"Man is a remarkable animal" (J. Ernest Nicole "Psychopathology" 1930).

ART is a remarkable phenomenon of mankind.

"Human beings built their cultures, nervously loquacious, on the edge of an abyss"

A principal intention of this research was to study what is known as ARTS through the whole history, from the very beginning of Spiritual Beauty, to the present state of Materialistic Design and by realigning of what is found, with the latest ideas in mathematics, physics, psychology and cosmology, in order to make a distinction between the concepts of "natural" and "universal" in arts, because the classical arts and the modern abstract arts are still undefined properly.

When I began, some thirty years ago, feeling that such study is needed to be done as a logical continuation of the ideas of Kandinsky, I found myself on new terrain which I had to explore after revising the phenomenon of culture. I had to discover the missing principles of 'great depth' and 'beauty' which can be used as foundations of the 'Theory of the Formal arts' and the 'Formal aesthetics' with its "universal beauty" compared to "natural beauty" of the classical arts. The general idea was already noted, in simple words, by one of the great classics Delacroix in his famous joke that the real "subject" of a painting "depicting conversation of the king with the other royalty on the picnic" is only "red and blue spots on green background" It was missing the more general natural definitions of "color", "object" and "space" with "time" as a universal definition of "order, number and position in motion".

The primary idea was the admiration of the structural simplicity of how Life or Nature on Earth and the whole Universe is built by only 4 abundant chemical elements, while the other elements are used for complexity in regions of less levels of free energy available. In mathematics "four" represents the cardinal directions, the base number of the plane, the "four-colors theorem" for 2Dimensional regions, the smallest composite number... Life on Earth is based on Carbon with 4 valences, and it needs only 4 of nucleobase types in DNA and RNA and about 20 of different chemical types of organic molecules. This alphabet of biochemistry is hardly longer than our verbal alphabet. All alphabetical forms have similar structural properties: they consist of about 24 to 30 signs (26 signs in English language), which are used to represent the sounds of spoken languages. Life is the parasitic and more complex phenomenon depending on the Universe and its own existence due to miraculous coincidences of a great number of parameters in one tiny point: Earth in the Void. "Life is not characterized by any special properties but by a definite, specific combination of these properties" (Bernal). An atom, DNA, a living cell, an organism ...any language, music, mathematics and generally all associations in mind reflect the principle of composition as combinations of a few simple elements, to many patterns, governed by a few laws of the whole.

Language is not only the medium for communicating our ideas to one another but it also has a function as an instrument of thought, where words are the instruments by which we form all our abstractions and trains of thoughts, by which we fashion our ideas. The mastering of a language inquires sense and a taste of COMPOSITION which, like "the spirit from the vastly deep", emerges not when we call on it but when we are immersed in the Void of subconsciousness spiritually. The natural languages we use mystify us with the common logic of Nature like "the whole is bigger than its part", "a+b=b+a" and "It is possible to draw a straight line from any point to any other point", "things are as they are because they were as they were". It is not considered as "true" in the Universal mathematical logic with its formalized languages.

"241. So you are saying that human agreement decides what is true and what is false?" -- It is what human beings say that is true and false, and they agree in the language they use. That is not agreement in opinions but in a form of life. (Philosophical Investigations, Ludwig Wittgenstein) ...and the Forms of Life are not only defined by languages, nations and cultures but they are principally different from the Forms of Universe as seen in pure mathematics.

Different concepts of space and time in theology and later in physical sciences are hidden in any historical art development and we see the striking difference between prehistory artifacts, icons by Rublev, paintings of the Renaissance, Classical period and modern abstract art of Kandinsky with the revolutionary changes of all underlying assertions and definitions, not recognized or defined yet. A mind of a priest, an artist and a scientist is always influenced by its communications with other minds through reasoning and intuition. Culture changes can be understood if we recognize not only the physical evolution, but also the spiritual and the psychological evolution of humanity. "Changes in consciousness call forth changes in external, social and technological life. Conversely, external changes cause further changes in consciousness." K.Rudnicki

Specialization is also constrictive, it gradually increases in complexity but is "saying more and more about less and less" and other direction of research by analyzing, to greater and greater abstractness and logical simplicity is "saying less and less about more and more" in order to discover the underlying principles which are hidden without any notion. It is always useful to study any phenomenon, as art for instance, in the most large reference frame possible - cosmology and theology of the Universe.

We have to follow the gradual idealization of space and time through the history of civilizations in order to distinguish a model and the principle on which that model is founded historically;

1.The Indian cosmological principle (the Prehistory period of Humanity).

Fig.1. The oldest Megalithic image on stone. Note that the concept of a "straight line" is not known yet and the place of worship was a round or curved labyrinth, still in use today by remote tribes and often seen in the first drawings of children. The oldest text known to us is the Bhagavad Gita which was written down only in post-Christian times from oral works in Sanskrit, a language that has not been spoken aloud for thousands of years and tells of Indian cosmology of the times-

"Krishna: See me than, O son of Earth/ As One in the plurality of forms, /As a more heavenly Nature, various/ And countless as the stars of heaven are.

Regard as a unitary Whole/ The whole world, with all its forms./ It is my body, I myself its spirit;/And everything that is, is all in me."

2 The cosmological principle of antiquity (the Mystical period of Humanity)

Fig.2.Giovanni di Paolo. 1445. "The Creation".

"The people of the Middle Ages would never have comprehended the idea of a "museum", which was invented only in the modern period. Beauty - according to the Medieval man - is so necessary that it must be a part of reality, a part of life; it cannot be separated from everyday life, but in a certain way must "inform" (in the literal sense of "giving form") everyone's existence.

What was developed in this form of life- the common logic of thoughts, the definitions (severances or borders between forms and their order) of words in other words; for instance six primary classes of categories: The first class represents ideas derived from the most general abstract relations among things, such as existence, resemblance, quantity, order, number, time, power. The second class refers to space and its relations such as motion, change, place... and so on. It was already recognized that Time has a higher order than Space. For instance, "time" measures in universal units of a solar year (a second, a minute...) from observations of the "Heavens" and the "space" measures in different natural units of human body (a meter, a foot,..) which belong to the "Earth".

3. The Copernican cosmological principle of the Renaissance (the Logical period of Humanity) was the first truly scientific principle still in use today by cosmologists with few additional generalizations. It states: "As seen from any given planet, the universe looks approximately the same". The Earth is not a special celestial body. This view maintains that if we look only at sufficiently larger spaces, the average physical parameters must be the same everywhere. Scientifically speaking it is believed that the Universe is both homogeneous and isotropic in order to make some mathematical calculations possible. We do know that it is arbitrary and conventional for simplicity's sake- heterogenic and anisotropic Universe is the case -"A principle of discontinuity," then, is inherent in all our classifications, whether mathematical, physical or biological..."(D'Arcy Thompson). We also know that the Universe at its initial stages had the greatest density and the probability of disturbances in uniformity was much higher than today, as much the same like first stages of Life on the Earth greatly differ from today. We have to accept great simplifications for our theories and revise them for new conditions of an ever changing Life and Universe, and art is not an exception.

The Renaissance was not the uniformed period -it started from degrading medieval Spirituality of the early Renaissance and ended up in the development of modern materialism. Renaissance was the cradle of natural science with observations and experiments learning how to form scientific hypotheses and theories. This is the main principle of sciences and mathematics as the special language of science- great simplification of pure materialistic reality. Scientists distinguished Idea from Conception, Concept, and Theory respectably. This is the point when the Church has separated Religion and Science, Spirit and Matter and founded the first "true" Universities (relative modern time and definitions accordingly) in Europe. We got "schools"," authorities"... to believe in, instead of God. All my citations and list of sources in the article are the remains of that period still in use today. I have stressed "belief" since God was not expelled from Science but took His shelter behind "axioms", "intuition"," the unknown" and "extraterrestrial"...generally "imagination" inside every mind of every human, independent from borders, races, nations ...and even mental distortions.

Fig.3 "Creation of Adam".Michelangelo.1512.

Art got new concepts of space, separated from time, as three Euclidian coordinates though the vertical one with special property due to gravity on the Planet which is not applied for the open space in Universe. Leonardo da Vinci (1452-1519) who is the inventor of it said-"Perspective is nothing else than THE SEING OF A PLANE BEHIND A SHEET OF GLASS, smooth and quite transparent, on the surface of which all the things approach the point of the eye in pyramids and these pyramids are intersected on the glass plane". He called perspective "the bridle and rudder of painting" together with increasing haze and blueness with increasing distance and shading in drawings to represent the orientation of objects.

Brunelleschi and Leonardo formulated the "perspective" system as axioms of the classical arts based on this pure materialistic approach of Euclidean "reality" to the flat "illusion" of fresco and canvas for materialistic reasons of "likeness":

1. Conventional linear perspective (Euclidian geometry).
2. The gradient of texture, becoming coarser in the foreground.
3. The relative size of familiar objects.
4. Obscuring of distant objects by nearer ones.
5. More distant objects are higher in the visual field.
6. Decrease of contrast with distance. (From "Mechanics of the Mind" by Blakemore, 1977.)

The very short turbulent period between Classical arts and Modern arts around the year 1900 (impressionism, cubism,.. surrealism ) clearly demonstrate how great artists struggled to defeat one or few "classical axioms" from the list not realizing the underlying concept of space and still having the "illusion" of a 3D world depicted on the 2D "reality" of a canvas. It should be mentioned here that icons and frescos appeared historically before canvas by theological reasons- Truth must have the solid base. Canvas appeared as degradation of the theological principle to material approach.

4. The Modern cosmological principle (The Modern period of Unification and Uncertainty)- the First Great Unification in physics was the doing of Newton who united the concept of gravity and inertia. The Second Great Unification in physics was done by Maxwell who united concepts of electricity, magnetism and light as different manifestations of the same phenomenon. Note that "phenomenon" or "substance" and logic itself was inherited by sciences from Thomas Aquinas. Einstein united the concepts of mass (gravity and inertion) and energy in physics with the concept of the space-time continuum (in physics and geometry). All three geniuses deeply believed in God.

Euclid geometry was the first to be revised. "geometry...is not concerned with the relations of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves" (Einstein).

Many possible kinds of geometries of the Universe become possible where Euclid geometry took its place as the simplest one on the scale of a rigid table. Euclidian space-flatness is the idea between convexity and concavity. "Curved lines" of the prehistory come back in new context with new content.

Fig.4 The concept of curvature: Euclidean model and the different mathematical models of the Universe.

Time used to be known by our ancestors to flow irregularly as biological rhythms of living organisms on Earth with Moon, under Sun together with Universe as a Spiritual Whole, it is now considered as biological or natural time. Scientists first changed it to the uniform flow of time as the time concept of the Newtonian variable "t" in the set of equations for calculations and later changed it for the "sidereal time" and then for "ephemerid time" or atomic time relative to distant stars to make it even more uniform for GPC, computers and rockets. This atomic time in which we are living today has no inner connection to the rhythms of the earth and its living organisms. The time concept today is simply a different set of laws for different applications. Humans are sacrificed for machines to get physical comfort and they are getting more mentally damaged by the illusion of materialistic progress.

Einstein moved on to the concept of the space-time continuum, depending on velocity and energy of moving matter, in 1916. The fact that mass depends on velocity was not known to Newton at the scale of our world, since the effect of the relation could not be observed except at the scale of macro world of Universe with its speed of light propagation. Subatomic particles were discovered inside the micro world of atoms. All these worlds could be described by different sets of laws and forms. We have to put aside the mathematical explanations of the space-time continuum and proceed to its applications for the simplest case of 2Dimentional continuum in order to establish the Theory of the Formal Arts for 2D canvas.

Fig. 5. The comparison of two theories with two mathematical "models" for 2-Dimensional surfaces based on the same "cosmological principle" of "continuity."

We keep in mind that we are dealing with Theories as products of the different states of Mind separated by different historical periods. Many theories like "phlogiston theory" failed to obscurity but not the ones from Newton and Einstein. They are not in any contradiction since they were developed for different "scales" of Nature and Universe and both theories are used today with the same aim- to predict future events with experience of the past. Newton's theory predicted the next appearance of Galley's comet by its calculations but failed to explain and predict events on the much larger scale of galaxies. Einstein's theory predicted the light rays bending their trajectories near massive objects like stars. Both theories are "true" in this sense. Do we have the same kind of "predictions" in art? Michelangelo's answer to a complaint of his noble client concerning poor "likeness" between the client and the portrait was: "Nobody will be interested in it after 50 years have passed". Was it the prediction of photography? I do not know but many great masters of the past are known for such "visions" through the ages. Rodin was busy with "unrecognized objects" of Kandinsky, Delacroix predicted modern art and Rothko. Intellect is not measured by tests nor by memory but by "visions" of future, the further the best. Usually such visions clear the past as well as the future-it is as if the reader from the 3D world "sees" the process P on the Fig.5 crossing the flat surface Sn in a point "p" but the flat philosopher from surface Sn sees the appearance of the point "p" in his flat World "ex nixilo" as a miracle. The theory of Einstein has many mathematical models due to the concept of space-time continuum depending on the curvature of surface Se (see Fig,4). When the scale of the space-time continuum is very small and the curvature is near zero we get the Newton theory inside the Einstein theory as a special and simple solution. The most important feature of the Einstein theory is the concept of "order". Space-time could be imagined as a sort of "jelly" where any deformation keeps the ordering. Suppose the territory of Belgium with its railways, roads and stations, with all the inhabitants with their rulers and clocks ... was made from jelly. This Jelly is a "continuum". You might compress or expand the jelly as much as you want without spaces having been lost or torn away but since you and your instruments are the jelly it is impossible to register any changes. You depart from one station and arrive to the other without any changes noticed or registered. The order is preserved in the same way as the continuum. The shape is put in the Nature by the observer, when he has chosen his system of coordinates (mesh-system) but the absolute form independent of any observer is ordering. Form is Order which is absolute and independent from any deformation.

"According to convention there is 'sweet' and 'bitter', 'hot' and 'cold', and according to convention there is order. In truth there are atoms and a void". Democritus (400 BC).

On Fig.5 the model of Newton is included in the model of Einstein as a very special case of our Solar system with a special star and a planet, with the Moon as a satellite in a very stable region of unstable and not homogeneous Universe. The miraculous coincidence of too many unrelated parameters in case of the Earth is still considered as valid proof of the God’s existence and His Design.

Any discontinuity we call a "singularity"- it simply means that no theory can be used here yet. The theory of Newton with Euclid geometry is still in use today in arts, though without it being recognized. In this theory the world appears as having gravity, perspective, proportions, shapes, straight lines and common logic. The theory of Einstein revised all the concepts of the theory of Newton into one concept, that of the "space-time continuum" with "imaginary time" as one of the parameters in a new set of equations.

Kandinsky was the first in the arts to realize the importance of new ideas. Abstract arts become fully conceptual with sharp distinction between shape and form, being commonly misunderstood. Form is a generalization of shape, since each horse has its own individual shape, but there are a large number of possible shapes that have THE FORM OF A HORSE. Knowledge of THE FORM OF A HORSE allows us to distinguish it from other animals. Knowledge of THE SHAPE OF A HORSE allows us to distinguish it from other horses. We see very many shapes of natural objects on the planet being reduced and classified according to much less than their natural forms, but their universal forms are pure abstract theoretical concepts. We will touch on the form of life later on and we will see that it is a structure. We see now that Spiritual Beauty of visions and revelations were gradually changed by humanity to materialistic "ideal proportions" from the Old Greeks to the concepts of shape and form in classical arts. We accepted them as canon. They should be distinguished from the concept of shape and form in abstract arts. It is more a general concept where previous ones took its place according to classification and order.

Fig.6 "Composition 7" Kandinsky. 1913

"To each spiritual epoch corresponds a new spiritual content, which that epoch expresses by forms that are new, unexpected, surprising and in this way aggressive... We are fast approaching the time of reasoned and conscious composition, when the painter will be proud to declare his work constructive. This will be in contrast to the claim of the Impressionists that they could explain nothing, that their art came upon them by inspiration. We have before us the age of conscious creation and this new spirit in painting is going hand in hand with the spirit of thought towards an epoch of great spirituality" (Kandinsky).

Kandinsky started and left for us the theory, the system and the simple indefinable propositions or axioms on which the system could be based both intuitively and logically. His innovations were to introduce a space of a canvas as true 2D space "now" (present moment of observation) without mentioning the mesh system being Euclidean or not, with 2D "forms" floating through the surface by their own laws. The laws were not defined. Space and time were simply combined, not fused. Kandinsky defined form as an "unrecognized object". He placed no distinction between shape and form. Colors were treated symbolically with emotions attached to musical tones. It was a great step ahead in arts and he already had foreseen that "abstract art" calls for other kinds of emotions not named yet. He named his works "compositions" with numbers but without classification.

"Here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were Three-Dimensional representations of his Four-Dimensional being, which is a fixed and unalterable thing". H.G.Wells, The Time machine. We might proceed to the Theory of the Formal Arts.

Fig.7 General Assumptions of the Theory of the Formal Arts for the 2-Dimencional Universe of a painting.

This is the Universal Principle and one of the possible Models of the "Universe", based on explanations of Fig.5. The flat Universe is actually a continuum with all possible coordinate systems already chosen. Any process could be imagined crossing the chosen continuum or even discontinuity of Universe. A process has its Form- Order depending on the Idea expressed in symbolic logic of a few simplest Elements- a Dot, a Line, a Cut, a Set. This order is of a Degree. Only 4 basic Colors of dots, lines, cuts and sets represent Curvature and Energy of Forms-blue color has the min. curvature and max. energy then green, yellow and red color respectably. There are two kinds of imperfections or Singularities- white and black ones on Fig.7-so we have 6 distinctive elements with Order of a Kind. The chosen process could be imagined as formal ordering of the particular specialization and development with all possible kinds of singularities which are "fixed" on Universe as Sections. For example 5 first sections represent many kinds of processes- the forming of a cell, a community or an organization, an Idea...to a certain level and the rest might have different "fates" like the sequence of star formation. The general Idea is as follows: "from dust to ashes". First section on Fig.7 represents the primordial stage of a cluster, Section 2 represents first "lines" from primordial elements without distinction by color, Section 3 represents differentiation of lines and color elements, and so on. An artist may choose any structure known and unknown, for example to show the pure Void from the primordial elements. Note the gradual changes of "density" from Section 1 to Section 5 respectable. It is important to keep in mind the process in the Universe as a Whole.

Fig.8 "The hidden logic of the Universe". Oil/canvas, 100 by 190 cm. 2018.

Above the general schema of classification for the developing form-order is shown as an example for presentational purposes. From the primordial cluster in the right down corner on Fig.8 to the left up one of the possible sequence of classes are presented as structures. Those structures could be imagined in many possible ways. A more detailed system of “axioms” and “laws” of Form is available in more detailed text. The great advantage of the Theory is that you may choose any number of the elements with any axioms declared and the formulated laws of composition together with your own space-time definitions, and any Universe is possible. Just follow the White Rabbit through the Hole of Topology and any Universe is possible.

There is no separate Time from Space nor Objects separated from Space-time. Everything is one SPACE-TIME CONTINUUM in 2-Dimentional Forms changing constantly together, like dreams without recognition, like something never again to be repeated, like a river of events without a past, present or future. Pure Universal Beauty of the cosmic Void has been cleared from what we knew before.

The Formal Aesthetics deal with the Beauty not in a natural way (the Earth and different cultures on it) but in the universal way, independent from any observer and the term Sublime is more fitted. Unfortunately, some mathematical ideas have been deeply involved in this concept presented in more detailed text. Sublime is the beauty for arts and mathematics.

Any visual effect for a human should be regarded as belonging to psychology, philosophy and physics all mixed up inside the brain of the observer in sensations, perceptions and interpretations.

"What I believe, I believe merely because I am the kind of person I am. That in its turn is determined by heredity and environment, over which I have no control." Macmurray. 1933.

"Mathematics is a pure theory of forms, which has as its purpose, not the combination of quantities, or of their images, the numbers, but objects of thought." Herman Hankel. 1867.

Sources:

1. Thomas Aquinas. "On Being and Essence".
2. Locke. "Concerning Human Understanding".
3. James Maxwell. "Discourse on molecules".1873.
4. William James. "The varieties of Religious Experience".1901.
5. Jagadis Chunder Bose. "Response in the Living and Non-living". 1902.
6. Bertran Russell."The principles of Mathematics" 1902.
7. Wassily Kandinsky."Concerning the Spiritual in Art and Painting in Particular"1912.
8. Albert Einstein. "Relativity theory". 1916.
9. D'Arcy Thompson. "On Growth and Form".1917.
10. Eddington. "Space Time and Gravitation". 1920.
11. Ernest Nicole. "Psychopathology". 1930.
12. Erwin Schrodinger. "What is Life?" 1944.
13. J. D. Bernal. "The origin of Life". 1967.
14. G. Spencer Brown. 'Laws of Form".1972.
15. J. Colin Blakemore. "Mechanics of the mind".1977.
16. Konrad Rudnicki. "The Cosmologist's Second".1991.
17. Raymond Tallis. "Psycho-Electronics".1994.
18. 18. Richard L. Gregory. "Mind in Science". A History of Explanations in Psychology and Physics.1981.

© Valery Konevin 2019