the theory of the formal arts and the formal aesthetics
THE THEORY OF THE FORMAL ARTS AND THE FORMAL AESTHETICS.
"Man is a remarkable animal" (J. Ernest Nicole "Psychopathology"
ART is a remarkable phenomenon of mankind.
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
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
of the parts of the
universe in regions of less levels of free energy available. In mathematics
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
combination of these properties" (Bernal). An atom, DNA, a living cell, an
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
trains of thoughts, by which we
fashion our ideas. The mastering of a language inquires sense and a taste of
like "the spirit from
the vastly deep", emerges not when we call on it but when we are immersed in
the Void of
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
"things are as they are
because they were as they were". It is not considered as "true" in the
mathematical logic with its formalized
"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
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
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
changes can be understood if
we recognize not only the physical evolution, but also the spiritual and the
evolution of humanity.
"Changes in consciousness call forth changes in external, social and
Conversely, external changes
cause further changes in consciousness." K.Rudnicki "The cosmologist's
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
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
1.The Indian cosmological principle (the Prehistory period of
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
"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."
The form of life at that epoch was mind and languages in its
primordial state like the surviving humans who were
scattered over the earth in small communities. They considered what we perceive
with our physical senses as an illusion
or "maya" veiling revelations of the cosmic God-being which were true by
intuition. No idea, no model or principle, no
concept, no scientific truth, proof or even observation existed yet -just heaven
and earth in a formless state of a
void. Space and time did not exist yet, nor sensuality nor spirituality
(Rudnicki). This state of mind shines through
old Mesopotamian myth in Genesis but now God is One;
" 1, In the beginning God created the heavens and the earth.
2 Now the earth was formless and empty, darkness was over
the surface of the deep, and the Spirit of God was hovering over the waters".
But what is seen by our mathematicians today -the first act
of creation as severance-"...a universe (in mathematical
sense) comes into being when space is severed or taken apart...By tracing the
we represent such a severance, we can
begin to reconstruct,...the basic forms underlying linguistic, mathematical,
physical, and biological science. We can
begin to see how the familiar laws of our own experience follow inexorably from
the original act of severance... Although
all forms, and thus all universes, are possible, and any particular form is
mutable, it becomes evident that the laws
relating such forms are the same in any universe. It is this sameness,
the idea that we can find a reality which is
independent of how the universe actually appears, that lends such fascination to
the study of mathematics. That
mathematics, in common with other art forms, can lead us beyond ordinary
existence, and can show us something of the
structure in which all creation hangs together, is no new idea." G, Spencer
Brown. "Laws of form", 1969.
Note the particular moment how any severance, any idea, any
theory comes to Mind "out of nothing" much the same as
Universe itself is believed to exist "ex nihilo". The whole knowledge is based
on the immediate experience and both are
changing each other as a whole process. We deal with our ideas, not with reality
for example "emptiness" as human
condition of mind is considered bad in Western culture while it is good in
Buddhist philosophy as the Tao of "pure mind"
or the "Mirror of the Universe"
2 The cosmological principle of antiquity (the Mystical
Humanity) or geocentric model of the universe was
stated by Claudius Ptolemy and it regards the Earth as a special celestial
body, us as individual human beings and
humanity, as Christians for instance, seen as a center surrounded by spheres
of active, spiritual beings. Everything was
His Spirit, the Image of Him penetrating and forming Universe according to
His design. "Words" and languages had
different meanings at that period of time in a different form of mind
the Spiritual principle used for different
mental models in this early stage of humanity. Art, science and
were not differentiated yet and the "knowledge"
could not be learned in any institution or under any authority but on the
contrary it could only be personally
experienced spiritually by revelations and visions (Rudnicki). Beauty, Truth
and Omnipotence, which later became the key
concepts of arts, cosmology and theology respectably, were the different
forms of the Spirit. Nothing was learned but
all was believed and no proof was needed. Form was 'Spirit' or 'Idea' and
Matter was the stuff of which things are made
of and how it is all arranged in composition. God has no
One. Aquinas defines God's nature as follows:
God is eternal, unchanging, immaterial and free from all
also insists that these truths are all
essentially negative- they tell us what God is not like but do not give any
insight in his nature. The art of the Middle
Ages had no gravity, no perspective, no shadows, no proportions, no
time-space separation, no objects of reality but it
had the Spiritual Beauty of the Whole created by God. No signature or
authority was needed...Humanity got the idea of a
"straight line" and square form of a temple orientated in Nature with the
distinction of 4 directions such as North-
South and East-West crossing each other at the point of observation.
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
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.
The modern idea of a "museum" is instead based upon the
notion that beauty is a
product of a particular intellectual
elaboration of the subject, an elaboration which begins with the premise of a
detachment from life, as if the true
artist must necessarily alienate himself, detach himself and emancipate himself
from life in order to immerse himself in
a sort of delirium of the imagination in which the purely intellectual
construction would play not only a leading role
but an exclusive role. In short, it is a conception of art which is detached
from everyday life, relegated to a sort of
"background" to be seen and subjected to judgment only by the elite.
In comparison, during medieval Christendom there was an
obligation to make
things beautiful; even useful things had to
be beautiful; beauty itself had utility. (Written by Il Cammino dei Tre
Sentieri). Here we have to stress the key point
of the future separation of Art and Design during the Modern Period.
What was developed in this form of life- the common logic of
definitions (severances or borders between
forms and their order) of words in other words; for instance six primary
of categories: The first class
represents ideas derived from the most general abstract relations among
such as existence, resemblance,
quantity, order, number, time, power. The
second class refers to space and
relations such as motion, change,
place... and so on. It was already recognized that Time has a higher
Space. For instance, "time" measures in
universal units of a solar year (a second, a minute...) from
"Heavens" and the "space" measures in
different natural units of human body (a meter, a foot,..) which
3. The Copernican cosmological principle of the Renaissance
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
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
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
uniformity was much higher than today, as
much the same like first stages of Life on the Earth greatly differ from
We have to accept great simplifications
for our theories and revise them for new conditions of an ever changing Life
Universe, and art is not an exception.
The Renaissance was not the uniformed period -it started from
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.
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
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
of God. All my citations and list of
sources in the article are the remains of that period still in use today. I
stressed "belief" since God was not
expelled from Science but took His shelter behind "axioms", "intuition","
unknown" and "extraterrestrial"...generally
"imagination" inside every mind of every human, independent from
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
Universe. Leonardo da Vinci (1452-1519)
who is the inventor of it said-"Perspective is nothing else than THE SEING
PLANE BEHIND A SHEET OF GLASS, smooth
and quite transparent, on the surface of which all the things approach the
of the eye in pyramids and these
pyramids are intersected on the glass plane". He called perspective "the
and rudder of painting" together with
increasing haze and blueness with increasing distance and shading in
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
and canvas for materialistic reasons of
- Conventional linear perspective (Euclidian geometry).
- The gradient of texture, becoming coarser in the foreground.
- The relative size of familiar objects.
- Obscuring of distant objects by nearer ones.
- More distant objects are higher in the visual field.
- Decrease of contrast with distance. (From "Mechanics of the Mind" by
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
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
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
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
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.
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
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" or "levels" 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.
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
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
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
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
"According to convention there is 'sweet' and 'bitter', 'hot'
and according to convention there is order. In
truth there are atoms and a void". Democritus (400 BC).
Any discontinuity we call a "singularity"- it simply means that
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
Abstract arts become fully conceptual with
sharp distinction between shape and form, being commonly
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
Knowledge of THE SHAPE OF A HORSE allows us to distinguish it from other
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
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
"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. 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.
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, now or future. Pure
Universal Beauty of the cosmic Void cleared from
what we knew before.
The Formal Aesthetic deals with the Beauty not in a natural way
(the Earth and different cultures on it) but in the
universal way, independent from any observer. Unfortunately, some
mathematical ideas have been deeply involved in this
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.
- Thomas Aquinas. "On Being and Essence".
- Locke. "Concerning Human Understanding".
- James Maxwell. "Discourse on molecules".1873.
- William James. "The varieties of Religious Experience".1901.
- Jagadis Chunder Bose. "Response in the Living and Non-living". 1902.
- Bertran Russell."The principles of Mathematics" 1902.
- Wassily Kandinsky."Concerning the Spiritual in Art and Painting in
- Albert Einstein. "Relativity theory". 1916.
- D'Arcy Thompson. "On Growth and Form".1917.
- Eddington. "Space Time and Gravitation". 1920.
- Ernest Nicole. "Psychopathology". 1930.
- Erwin Schrodinger. "What is Life?" 1944.
- J. D. Bernal. "The origin of Life". 1967.
- G. Spencer Brown. 'Laws of Form".1972.
- J. Colin Blakemore. "Mechanics of the mind".1977.
- Konrad Rudnicki. "The Cosmologist's Second".1991.
- Raymond Tallis. "Psycho-Electronics".1994.
© Valery Konevin 2019