DESMOS 1997...

"DESMOS" is a series which began in May 1997 and up until now, consists of three sculptures, sketches and computer graphics - simulations.

It is the continuation of a course of quest ("The Girl With The Ball" 1987-95, "In Front Of The Mirror" 1996-97) on the problem of the structures of Transition-Movement.

Movement-energy as a property (Content) of matter, has to participate in the formation of its geometric structure (Form-shape) and to be imprinted on it.

The synthesis is based on the antithetical connection of two regular tetrahedrons embodied in the cube.

The Edges of the Tetrahedron vibrate as chords, which at some instances are imprinted as a curve and at others as a concavity, cause and effect of the system's rotating movement. In other words, forms of electro-magnetic fields between the "Points" of the ends.

The curves tend towards the surface's curve of the conceivable sphere in which it is embodied, and essentially create the Whole System.

The work (series) searches for the geometry of the microcosm and macrocosm.

The geometry of the dynamic fields, poses the question of Movement and Change, in other words of Time.


Sketches for the preparation of Desmos No 1

Sketches in two and three dimensions


Wave=CONTINUOUS (wavelike motion of quantum)
Particle = NON-CONTINUOUS (tangent points, taps of waves where their molecular nature is shown off.)
The Point, when it is defined without dimension equals with the localization (material substance) of the mutual relationship, in the simplest (pure) form as energy.

Hence, I consider as point (or moment) "the area", the one which I shapely lay between the two horizontal lines, where Being is shown in its contrast with Non-Being.
Up: Graphic presentation in three dimensions
Below: Graphic presentation in two dimensions
POINT and MOMENT are notions that do not coincide, even though they both want to convey the smallest piece (the almost nothing - Fact) of space and time, respectively, "the non-existent that exists", to the two approaches of existence.

A POINT includes infinite MOMENTS of Universal Time. One moment realizes infinite POINTS of Universal Time.

Here we consider them identical notions.
1. MOMENT: The smallest (in duration) route of reciprocal effect - quantity of exchange of matter = reflection.

2. POINT: Area of coincidence where the difference is shown.

The positive and negative signs indicate the points where the relationship is manifested (unity and difference)(+), as well as the areas where this relationship does not exist (-).
SHAPES 1-2 : Reduction of the graphical representation of "Moment" or "Point", in simple geometrical shape, two triangles. Each triangle sets the field of the "event" of quantum particle 's vibrating movement. The straight lines indicate the polarization between the Points which set the field of the quantum particle 's movement, where its existence is manifested. In three dimensions, the formation of the tetrahedron becomes pretty obvious.

SHAPES 3-4: penetration of triangles until "integrity".

With the appearance of a independent, third, regular form, we consider that the penetration has been completed.
SHAPES 5-6 : If we join the opposite spikes of the hexagonal star also perimetrically, we get the linear representation of two regular tetrahedrons that are embodied in a cube, or the perspective representation of one regular octahedron.

SHAPE 7: Two regular tetrahedrons.

SHAPE 8: In the hart of the shape formed by the two tetrahedrons, there is a regular octahedron, provided that the eight regular tetrahedrons that protrude radially, are removed.
The three basic colors at the spikes of the two triangles and in correspondence to the regular tetrahedrons. In the second case, the fourth spike is covered by three colors.
Desmos' view from above in its pure geometrical shape.
Cube internally coated with mirrors. Computer processing. There is a clear correlation with Desmos' sectional view (above).

The self - analysis process carried out through perpetual reflections, leads to the reduction laid out above: that a cube is a composition of two tetrahedrons.

The computer 's negative imprint fully coincides with the positive one of the stereometrical shape.
Forms which correspond to the shaped reductions of the way in which Existence is displayed, offer aesthetic satisfaction and fascinate us.

The shapes that are produced from the two tetrahedrons have turned out to be symbols.

Desmos No 1

32cm x 32cm bronze sculpture

Four facets
Basic elements
1. A regular tetrahedron
2. In contrasting (reflective) relation with itself creates a cube.
3. The dynamic relation between the two (attraction - repulsion) produces rotatory motion which results (is embodied) to a sphere.

"Desmos Νο 1" height 35 cm, bronze


Sketches for the preparation of Desmos No 2
The base of the sculpture is located in its center and is expanding to all direction. The two axes are two elongated tetrahedrons.
The tops are connected with forces - fields that shape their forms and intensity.
Unlike in the sculpture Desmos No 1, here I am seeking the connection (dynamic fields) of each one of the tetrahedron's tops with the other three.
Side section:

When the fields (forces) cross, they have to put pressure, as well as penetrate each other. On the external edges the shape tends to become indefinable. The same is true for the surfaces (the skin) of the fields, which should not be clear, implying the Halo which surrounds them. On the contrary, the clarity of the tensions of the fields' form, approaching the center, is a crucial element in order to render the condensation of mass.
Center section:

Approach to the form of fields - forces.
I also deemed necessary to replace the equal distance from the center (radius) of the tops of each tetrahedron with a progressive increase by 5cm (115, 120, 125 and 130), so that the sphere into which the sculpture is embodied to be elliptical.

Desmos Νο 2

Sculpture. Dimensions 260cm x 230cm

At this phase, I preferred to make the tetrahedrons' tops semi - spherical, implying the general shape. The iron base is the graphic presentation in two levels, of the original shape's sectoral view.


Universe is tetrahedral
Sketches for the preparation of Desmos No 3
At the first phases of penetration between of two tetrahedrons, the Cube is clear.

The curvature of acmes, produces tension in the sphere.

The Halo that surrounds the event and its primordial nature, possibly carry and have preserved some elements for the state before the first event (Big Bang).
The hypothesis that the known Universe is a product of "disturbance" that occurred in something else, is now well founded.From Nothing comes nothing..

The tetrahedral structure of Universe probably carries something from the Something

"Desmos" pastel on paper, 50 x 35 cm

LEFT: regular tetrahedron internally coated with mirrors (computer processing).

RIGHT: Simulation, from Virgo Consortium, which represents the structure of the Universe in great scale. The correspondence between the logic of galaxies dispositional net and the net which is produced from tetrahedrons' acmes is obvious. A curvature of the acmes would render the images almost identical.
Mass - Energy = Matter

Non-continuous - Continuous = Movement

The moment of the Big Bang = the moment of the identification of the difference (the identification of opposites)

= the One emerges as unity identity (is being identified) of opposites

= New Whole... from Infinity to Infinity

Moment (or Beginning) of Infinity = relationship of Infinity with itself.

Beginning of Infinity = Whole: Infinity in one moment (beginning) = Something (close to nothing). The notion of Moment already means something and (from the) and nothing.

Moment as relationship with and in distinction from Nothing = something different (distinction) from all the rest. Nothing is not nothing (absence) but the indefinite Whole in distinction to the definite Something (moment).

The Dilatation of the Universe = a) a situation defined by the given internal relationships of the Universe b) Moment (definition) in relation to Nothing (the Whole) in which it is embodied. When the Point is defined as the incision of two straight lines = the minimum definition of the two straight lines. The presupposition of their existence (of the two straight lines), emerges with the Point as their minimum definition = from Nothing to Something (Point).

(The existence of two straight lines emerges from their relationship, in the form of the Point.)

The Big Bang = the Something (definite Being) after Nothing (non-definite Being).

"Desmos Νο 3"
largest dimension: 110 cm, bronze


"Desmos Νο 4" height 37 cm, bronze


This sculpture is part of an ongoing series/study including sculptures, drawings, 3D graphics simulations and texts, which began in 1997.

This effort here was to seek the most general, abstract form that organic matter could have had as it took its very first “steps,” or more precisely, the form/link that illustrates the passage of inorganic into organic matter. That is, that form which is not easily distinguished from the form of inorganic matter, but in the manner in which it is structured contains the basic elements necessary for it to be organic.
What is interesting about this form/link is that some of the elements that come together in the initially chaotic condition of interaction among the elements of inorganic matter at some stages constitute a system able to produce functions of autonomous change (autonomous motion) and autonomous reproduction. If this takes place, the general form and function of this system then becomes the basis/foundation for the manner of existence of every form and every function of organic matter, including even the function of thought.

One of the first basic elements the form of organic matter must have is symmetry. A second basic element is that this symmetry must be formed from the synthesis of at least two discrete factors in such a way that their relationship enables the system to move autonomously. And a third is that it must constitute a system of relationships whose properties enable the system to reproduce autonomously.

First step

The synthesis begins by taking the regular tetrahedron as the first factor.

The four points of its vertices denote the meeting place/intersection of its six edges (lines). In turn, its edges denote the meeting place/intersection of its four faces (or planes).

Its identical faces and the congruence of all its elements make the regular tetrahedron the simplest and most symmetrical form from which an image of the concept of space in general can be derived.

Second step

The synthesis of a tetrahedron with itself (as a second equally discrete factor of the synthesis) in their most stable symmetrical relationship gives rise to a system with its own properties.

This synthesis presents unexpected rich properties in its form, while retaining its rigorous structure as a system.

Third step

The eight vertices of the synthesis coincide with the vertices of a cube. The edges of the two tetrahedrons are diagonals of the cube’s six faces. Through this approach the cube can be considered to contain the synthesis of the two tetrahedrons like a framework (or an analysis).

Fourth step

We place the eight points of the vertices of the synthesis on the surface of a sphere and bend the diagonal edges so that their points run along the surface of the sphere.

Fifth step

Transformation of the diagonal edges connecting the vertices from straight lines into arcs suggests pulsation. The existence of pulsation, if there is no external cause, indicates interaction of forces within the system itself.

If the planes of each tetrahedron are approached as force fields that keep the points of its four vertices in a unity, then in their interrelationship the force fields of the two tetrahedrons, when they intersect (at the midpoint of the two diagonals), are negatively curved in relation to each other (repulsion). Thus a negative and positive curvature is created in relation to the straight line, whereas the eight points of the vertices of the synthesis are maintained in their stable relationship (attraction).
From this point of view, the sphere, in general, may be regarded as a composite figure created by a symmetrical system of two tetrahedrons and the autonomous motion of that system around its centre.

NEXUS as a point and a moment

The point is defined as zero dimensions, non-existent. Its existence acquires semblance, form, only as the locus of the section (relationship) of at least two straight lines.

In a situation of infinite interactions, straight-line motion is possible only if in its analysis it has the form of a spiral.
In turn, spiral motion can be achieved by an object (hypothetical before its identification) only when it is a system of relationships of at least four points.

The four vertices of a symmetrical tetrahedral arrangement, when it is moved by rotating it, correspond absolutely with the formation of a spiral with a regular frequency and a regular wavelength.

Thus the pivot on which the centre of the tetrahedral arrangement moves in its spiral motion is a straight line.
Therefore the point, even in its most abstract sense, must be a meshing of at least two systems that exist in three-dimensional space and that through this relationship define the points of space.

The point, from non-existent, acquires existence and phenomenon through the relationship/section, and hence it is the product of a process/motion.
The process of creation of the point (section/relationship) until its completion

The point, as the simplest definition (image) of the notion of space, is at the same time the image that renders one point of motion, and thus it also gives the image of the notion of an infinitely small amount of time (=moment).

NEXUS as a work of art

NEXUS has as elements of its construction those referred to briefly in the preceding pages.

The construction elements of the work are purely geometrical, in order for it to be grounded in mathematical logic.
The logic of mathematics originated from the observation of the forms of the world and their relationships. But it is obliged, by the nature of its purpose and tools, to regard the figure as a figure of the object only, apart from subjective perception, and finite. It is no accident that for mathematical thinking zero (0) and infinity (∞) are useful symbols only, whose meaning lies outside its field, in so-called metamathematics.
On the level of mathematical figures and the forms of the meaning of objects, the dominant property is aesthetic abstraction, reduction to the essential. Nevertheless, mathematical thinking makes only the abstraction the object of its knowledge.

In contrast, art makes aesthetic abstraction as a whole its object, where the forms of the world are com-posited as one form, the form of its universal nature. Within this form of universality, subjective perception is described as its active part.

The creation of the Tetrahedron on all scales.

The encounter point of two Tetrahedrons.

"Desmos" height 15 cm, aluminium

"Dynamic Tetrahedrons"
largest dimension: 11 cm, aluminium


TIME: The whole of movement and changes in a unified system.

The "tops" of the system constitute the tops of a tetrahedron. One minute counts at the same time the rotation of the Earth around its axis and around the Sun, the rotation of the solar system around the center of the Galaxy and the rotation of all the above within the Universe from and towards, one center
Time is a passive notion. It expresses the sum of the up to "now" changes. The total of the changes, collectively + causality = the Arrow of Time. Future = a notion that intuitively conceives and projects the dynamics of phenomena as the product of their causes.
The tetrahedron of the Time concerns every point of the Universe.






Mechanics of Time

The Tetrahedron of the Time

Bronze Construction. 1,30m diameter.

Space as quality is the relationship, that is given quantitatively as distance or size. E.g. the simplest "one point" sets as prerequisite the coordinates which situate it and correspond to a system that includes it. The fact that it is a section of two or more lines, defines it as a relationship or a phenomenon. Point = zero space, the non-existent which exists because it makes obvious the interaction of two systems and their relationship towards a third one, it defines space.

Time: General term that imprints the successive movements (changes) of a point in space towards a system, which is taken as Measure (e.g. rotation of the earth around its axis).

Space-time: General term that imprints the quantitative movements of bodies within their interactions and towards a system that is used as Measure.

The phenomenon of relativity does not abolish the simultaneous absolute character of Space-Time on the Universe's scale. The speed of Light as limit is sound evidence for the absolute nature of Time on the Universe's scale.


1. In the Process of Cognition

a. Art expresses and cultivates the ability of Man to think in Images. 
This intellectual ability is called Imagination

Imagination (in Humankind) is the synthesizing function of the intellect that transforms the blending of the data of experience, intuition and knowledge into a Holistic mental image.

b. In the process of understanding the partial (analysis), Science must be able to maintain the Image of the Whole in which the parts are integrated. 

This ability is afforded by Imagination.

c. The development of the Scientific Knowledge expands the horizon of experience and enhances the intuitive function. 

These compel Imagination (and Art) to change the way it "looks" at the world. 
The new "insight" reveals potential paths towards deeper scientific understanding.

2. In Technology

Technology reflects the way Man affects the material world surrounding him as well as the degree of his understanding of it. 

The material (and the way it is processed) is the body of Art. The spirit of Art is expressed through the material. 

By using the advances of Technology today, whatever they may be, Art does NOTHING MORE THAN WHAT IT HAS ALWAYS BEEN DOING. 

The prevailing view according to which Technology in nowadays building ties with Art that did not previously exist, lays too much emphasis on the Form of Art, cancels its content, and with it its function in the process of Cognition

As a result of this view, no systematic work has been carried out on the aspect of the theory of knowledge, which forms the point of departure and foundation of the Causal relation between Art and Science, despite all possibilities afforded by Technology for such work today.

3. Today, it is more than necessary for Art to acquire a solid basis in science (in view of the new conditions), in order to get rid of the wretchedness of Fashion and theSeemingly New
All that has been given in the form of cohesive insight into the History of Art or a Theory of
Aesthetics, was given by Philosophy up to the time of Hegel. 

Any subsequent endeavours by inspired movements of redefinition, in the light of the new scientific and social developments, did not have enough time to progress, encumbered as they were by the disastrous events of our century. 

After the Second World War, and particularly in the past two decades, ideological breakdown in Art has taken ominous proportions.

4. By way of indication, I will cite the views of four scientists with respect to Science:

"The role of Aesthetics as s means of successful investigation has not been sufficiently discussed." 
Roger Penrose

"The aesthetic orientation is found not only in Man but also in Nature. In fact, it is beauty and not provability that constitutes a criterion of truth in Nature. When your information tells you one thing and your instinct of the Beautiful tells you another, then leave the former and follow the later." 
Nobelist Subrahmanyan Chandrasekhar

"Art is a theory about how people look at the world. It is obvious that no-one has a detailed knowledge of the world that surrounds us. What artists have achieved is to have realized that only few things matter and then they try to find them out. Thus, they can carry out part of my own research for me." 
Mitchell Feigenbaum

"Mathematical structure, namely arithmetic analogy as the source of the harmony of sounds, is among the most amazing discoveries of humankind." 
Werner Heisenberg

5. A serious approach to the question of the relation between Art and Science cannot avoid the theoretical and experimental investigation of the following questions with the help of the new technological possibilities:

a. Does Art (Painting, Sculpture, Poetry, Music, etc.) contain Logic? 

If so, is it the same logic in all the semblances of Art? 
If so, what are its various manifestations? 
If not, do they converge? 
If so, where and how?

b. Is the Logic of Mathematics the same as the Logic of Natural Science and Nature? 

If so, what are its various manifestations? 
If not, do they converge? 
If so, where and how?

c. Is the Logic of Art, Mathematics, Natural Science and Nature one and the same? 

If so, what are its various manifestations? 
If not, do they converge? 
If so, where and how?

It is obvious that, in order to deal with the question of the relation between Art and Science, one has to answer in the affirmative the question "Is it possible to provide a satisfactory (scientifically grounded) answer to the questions above?" .

Athens, 3/3/1995

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