POINT | LINE | PLANE | SOLID, Hazar Marji by Hazar Marji

PYTHAGORAS, EUCLID, KANDINSKY

Content

04 Pythagoras 12 Euklid 16 Kandinisky 32 Conclusion 33 Reference

PYTHAGORS “There is geometry in the humming of the strings. There is music in the spacing of the spheres.”

Pythagoras The Math God 570-495

All start from centuries before, the beginning of the philosophical thought which appeared in the Greek colonies, more specific in the west part of it. Type of new movement started to arise within the area. Holding the idea of artistic, conservative and ethical aspect, these new thoughts were intersected with the Greek of Ionian which had the idea of sense, versatility and curiosity. New school with new vision start to grow, the Pythagorean School start to spread the ideas and work more in the math-side and connecting all the result with an ethical religious purpose. The entire member used secret sign, personal clothes restrictions’ in certain situation.

This school totally agreed with the rule of: • Number is the essence and the basic of all things • Number stand in the relation between prototype ans substance • The odd, even, odd-even the new number kind. This school under the chairmanship of Pythagoras of Samos applied the Doctrine of Numbers to all the element that surrounded us, but it was obvious that they used numerical and geometrical theory as quantities, with abstraction from the biases, without determining if the contents were material or immaterial. “Every Body is an expression of the number four, the surface is three, because the triangle is the simplest of figure; the line is two, because of its terminations; and the point is one. Ten is the perfect number, because it is the sum number from one to four*” * Turner, William. History of Philosophy. Boston, USA, 1903.

The Music Philosophy Rule Starting from the previous quotes, the statement shows that the number theory came from a strong root. Digging deeper; research reveal that the Greek knowledge was gained from the philosophical and therapeutic aspects of the Egyptians music form. This music had a lot with the Hermes God who created the first lyre with stretching strings on a turtle shell. Still this lyre holds a hidden mystery of the secret symbol of the human creation. The body of the instrument representing the physical form, the string the nerves, and the musician the spirit; playing upon the nerves, the sprit thus created the harmonies of normal functioning which, however, become disordered if the nature of man were defiled*. * Crowley, Aleister & Sturges, Mary d’Este. BOOK 4. Ordo Templi Orientis. 1969

Pythagoras was concerned about this lyre and the harmony creation. One day by chance he was thinking how to achieve that and apply it to his math theory, suddenly he hear a hammering sound on a metal piece came out from the brazier shop. Pythagoras listens carefully to the sound of small and big hummer and he estimated the resulting harmony and disorder from the combination sounds. This was the first idea he had about the musical intervals and it’s connection to the diatonic scale. Stepping forward, Pythagoras apply his finding on what we all now know “Pythagoras Tetractys” or “The Pyramid of Dots”, which illustrate the relation between the doctrine number and the music . He gave each number its own characteristic No.1 is the generator of all number, No.2 is the opinion, No.3 is the harmony, No.4 is the Justice...etc. The Holiest number of all is ‘Tetracty” or “Ten’. This led him to another philosophy which is the” Music of the Spheres”.

The Tetractys This math theory suggests that the number science practice something called number worship. Pythagoras drew triangle because it is the simplest shape of all figure. He divided this shape into two parts, the first one which is the first 3 dots which present the spiritual nature of the universe. This threefold white light in their turn present the godhead which contain all sound and colour. The second part represents the inferior world which consist of the remains dots. In this part Pythagoras also divided it into another two parts the three dots for the nature power and the lower four dots for the relationship, and this part of the tetracty had a strong relation with the Pythagorean colour theory. If we look to the tetractys we can see that the sum of each dots number in one row lead us to the number TEN which is the perfect number. The tetracty play a strong and effective role when we will talk about the Musical Universals.

Music of the Spheres From the discovery of geometric elements which respond to the number, Pythagoras had the theory of the spheres, and was convinced that the whole universe was based on numbers, and everything moved according to mathematical equation which corresponded to musical notes and produce symphony. This vision introduc-

es the relation between earth and the fixed stars which in their turn work in diapason with each other. Pythagoras divided the sphere into a vast number of creation part depending on the arrangement, the movement and the position of these part. He assigned tone, harmonic interval, a number, a name, a colour and a form for each part. At the first start this was the most abstract logical way, and then it reversed to be the most geometrical solid. His sphere emphasis on the nature law and it is relation with the music science. Therefore, the music as medicine appears, as it influences on the mind and the body, and play an important role with the sense and the emotion. The sphere from a Pythagorean view consist of the upper part which is the absolute sprite (heaven), and the lower part which is the absolute mutter (earth), and this work with his previous tetracty theory. As a conclusion every element in the nature has its individual keynote with the concept of the relationship between music and form. As Goethe say â&#x20AC;&#x153;architecture is crystallized musicâ&#x20AC;?.

The Colour Philosophy In the Pythagorean tetractys the supreme symbol of universal forces and processes are the theories of the Greeks concerning color and music. As mentioned before the first three dots present the heaven at the same time this represent the white light which in his turn create the spectrum colour. The colour and tones are the active power, the arrangement of this spectrum colour related to the musical tone of the tetractys.

THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS THE THEORY OF ELEMENTAL MUSIC

* http://www.sacred-texts.com/eso/sta/ sta19.htm

EUCLIDS “There is no Royal Road to Geometry, or laws of nature are but the mathematical thoughts of God.”

Euclid Father of Geometry 323–283

Euclid starts his life between the Greek mathematicians. He learns a lot, and search a lot. His most famous achievement was known as The Elements, which is something he did not discover by himself but he took it, simplified it to the basic simple elements part. What he did is only present what the previous Greek had into single, logical coherent framework making it easy to use and easy to reference. Euclid defines the geometry science to be the figure inside the space. This figured space can be one dimension, two dimensions and three dimensions. In this description he used the mathematical theory of mirrors and reflections for dividing the geometrical figures into parts with a given ratio. These dimensions consist of:

• Point He defined it to be non-dimensional object, it is only a define the position, and no thickness. • Line Is the one dimensional space, it has length, in some cases it can has breath or thickness this transform it to another figure. Line start from one point and end with different point called the Straight Line, and he described it by the movement (point move in the same direction), and the other line type is the curved line, which is consists of several straight line, the difference here is the movement of the point change its direction continually. “If we suspend a weight by a string, the string becomes stretched, and we

say it is straight, by which we mean to express that it has assumed a peculiar definite shape. If we mentally abstract from this string all thickness, we obtain the notion of the simplest of all lines, which we call a straight line”. • Surface Is the two dimensional space figure with length and breadth, this surface transform to shape the plane which is the three dimensional shape. • Plane Figure It is a combination of points, of lines, or of points and lines together in a plane If a figure be formed of points only it is called a Stigmatic Figure; and if of right lines only, a Rectilinear Figure. Points which lie on the same right line are called Collinear Points. A figure formed of collinear points is called a Row of Points Figure.

KANDINSKY “The true work of art is born from the ‘artist’: a mysterious, enigmatic, and mystical creation. It detaches itself from him, it acquires an autonomous life, becomes a personality, an independent subject, animated with a spiritual breath, the living subject of a real existence of being.”

Kandinsky Abstraction Father 1866 –1944

Starting from his life time line, it seems that Kandinsky lived within a family with a very famous business family. This aspect plays a strong role of his life decision to become an artist which comes against his family wishes. Starting from the point of achieving his dream Kandinsky start to have his own art approach and his own art vision. He starts as an artist who draws under the effect of impressionist’s movement 1985. He was affected by Monet’s and Wagner. But all of this change to start new path of completely different kind of art. The Abstraction, Kandinsky started to change his ideas and painting, from the very clear obvious paint into a composition depend on the line and form. This strong change came from

the influence of many things in his career life, such as the germen graphic artist Franz Stuck, the Phalanx art group, the Blue Reiter. One idea these people and group assure is the associative properties of colour, line, composition, and the romantic theory of colour throughout using various sources such as Goethe and others. In 1912 the first theoretical foundation of abstract appears, by publishing “Concerning the Spiritual in Art” by Kandinsky, which turns the idea about art upside down. The artist said “the purposes (and therefore, means) of nature and arts are essentially, organically and according to the laws of the Universe are various - and equally great, and equally strong and the creative process is a self-expression and self-development of spirit”* . During the World War I Kandinsky paint many pictures all of them had the same strong spirit of geometrical elements, to serve the simplification process, and because of the strong effect of the Moscow art atmosphere.

This kind of abstract geometry reveals the analysis of colour and form and its relation to the sprite that each element inside the composition has. The other movement refuse what Kandinsky believe in, and one of his replay to the that was “Just because an artist uses ‘abstract’ methods, it does not mean that he is an ‘abstract’ artist. It doesn’t even mean that he is an artist. Just as there are enough dead triangles (be they white or green), there are just as many dead roosters, dead horses or dead guitars. One can just as easily be a “realist academic” as an “abstract academic”. A form without content is not a hand, just an empty glove full of air”*. Dealing with the deep analytical study of separating the elements of the picture, Kandinsky was influenced by the Bauhaus school. He worked with individual geometrical elements to be his foreground biases, he prefer to deal with cold colour harmony and he agreed that the circle is a sensual symbols for the perfect form. He defence his way of thinking that people

who cannot feel the romantic part of the elements and it relation to the whole composition is something bad for them, cause each elements in the art work has its own specific sprit that add the beauty to the whole. Abstract art is totally anew world disconnected from the real world, with it is own beauty aspect and it is inner spirit which goes with the same direction of the world of nature.

* * http://www.wassilykandinsky.net/ * http://www.wassilykandinsky.net/work-170.ph

Colour Theory In this chapter we can trace the relation between Kandinsky, Pythagoras and Euclid. Kandinsky was interested in the idea of colour meaning which the artist can benefit from to transmit the message of the painting. The colour itself and the music helped him to achieve a concert idea about colour theory which helped to explain what the colour means and what the same colour represent. Fascinated by the power of music on the emotional part, he aimed to have the same feeling within the piece of art. Kandinsky was inspired by the work of Wagner and Scriabin which allowed him to live the spiritual experience within art and music. This amazing experience gave Kandinsky the passion to create a table of equivalencies feelings and shapes in colour. So a certain colour is resemblance with a certain form,

both have the same characteristics. A dull shape like a circle deserves a dull color like blue. A shape with intermediate interest like a square deserves an intermediate color like red. A dynamic, interesting shape like a triangle deserves an energetic, luminous, psychotic color like yellow. Stepping forward Kandinsky explain that the colour has two effect on the human being. The first one is related to the purely physical part (the eye). This effect has the short sensation duration, for that it leaves no lasting impression on the soul because it was not affected, so it is easy to forget once the eye is turned away. For this physical effect, he divided it into two categories relating it to the object experience. Familiar Object: the effect of the colour is superficial. While the new object has deep impression on the soul and this become wider until it reach our inner soul. After this effect happened in our mind store the experience we had. The same with colour, at first, it makes only a superficial im-

pression upon a soul hardly developed to sensitiveness, an impression which disappears shortly after it has been evoked. Even the simplest effect varies in quality. The second one is the psychic effect or the elementary effect which appear when the spiritual part develops causing in deep reaching emotional feeling. The emotional vibrations caused from our inner channel derived from observing the colour very carefully. This is the power of the colour that previously illustrated in Kandinsky colour theory approach exactly like the music. This effect can be direct or achieved by the association. Association mean when we relate a certain colour with a previous experience we lived in for example light yellow would make a sour feeling, because it is associated with the lemon. As a conclusion the colour hide enormous power and thought that is still undiscovered, and by it turn affect our human body as physical organs. Kandinsky describe his theory “Color is the keyboard, the eyes are the harmo-

nies, the soul is the piano with many strings. The artist is the hand that plays, touching one key or another, to cause vibrations in the soul.*”.

* https://www.goodreads.com/quotes/search * http://ekaterinasmirnova.wordpress.com/2012

Form and Colour The last quotes from Kandinsky illustrate his opinion about the sensation abstract art. He agreed with Goethe opinion which says that all painting must have one general foundation; this means that the only way will help the art work to grow in an abstract sense, and at the end reach a purely artistic composition. Heading from the idea of general foundation, Kandinsky claim that the artist need two elements to create the composition: Colour and Form. The relationship goes this way, colour in painting must have certain subjective characteristic (inner) and must have a limited surface (boundary) help to separate this form from the other colored form within the whole composition. The harmonically relation between these elements help the reader to observe the art work effect.

The value of a specific colour is emphasized with the form applied to it. This connection has the conflict when a form does not fit to the colour used by the artist. But still has the possibility to create new harmonic aspect. Form, therefore, is the expression of its inner meaning which led us to prove that form of harmony reflects the vibration on our soul which is the most important need we have. Despite all variations which form offers, it will never exceed two exterior borders: â&#x20AC;˘ One form serves limitation with the purpose of deriving from it some material object, that is, to superimpose the material object onto a surface. â&#x20AC;˘ The other form remains abstract, that is, it represents no object of reality but in itself is a fully abstract being. The abstract shape is un-precise helped to awake our expression power, which create the idealization (the effort of beauty the organic form) and the stylization which dismiss the incidental details.

Music Effect Music and Kandinsky this is for sure take us to illustrate the relationship with the great composer Schoenberg. As mentioned before, Kandinsky was fascinated by the power of music, and stepping from that he start to draw the map between art work and music. The importance of this great composer, that both of them had the struggling to find their own voices, the inner necessity within an indifferent social environment. Both love exploring the possibility, try to reach the human consciousness, find the idea of the inner world. Both think and prepared very well for making new revaluation against the tradition based on the knowledge some old aspect artistic method and the knowledge. The most important shared character is that both of them work to embodied Gesamtkunstwerk (Total work of art/ ideal work of art, universal art work), that means that the art work make use

of all art form and avoiding traditional form of beauty to cover powerful feeling in the work. The yellow sound by Kandinsky and the hand of fate by Schoenberg have things in common: • Extreme contrast, and changing emotional state • Consistently employ particular tone colours for the main elements of the work(painting or opera performance) • Relationship between words, images and sound.

* * http://www.wassilykandinsky.net/work-170.php

â&#x20AC;˘ POINT

The Elements Going back to the elements of Euclid we can see the same elements also used by Kandinsky. But he divided the elements into the basic elements and the secondary elements. He investigate each phenomenon by itself (use the isolation) and the mutual effect of them upon each other (use the combination), and the general conclusion.

Kandinsky starts his vision by tracing each element by itself. Starting from the smallest form which is the point, he said we cannot say it is the smallest one because it has the ability to grow and cover the entire ground plane. So according to that he clear the point in the art work must assume a certain proportion, to occupy a certain area of the plan, and it should have a certain boundaries to help distinguished it from other element that surrounded it. The most important aspect of the point that the artist should have is consider the relation between the point size and the plane size, and the point size and the other form size on the same plane. Moving one Kandinsky explained in his book that the point has two fixed fact:

The Size: Is the feeling that the point give when it goes out from the boundary. We can acknowledge that the point reach it external boundary by the feeling it shows. A new phrase appears The Double sound by a Single Form. This means that the multiplicity and complexity in the expression of this point can be reached by chancing the size to serve the power and depth of the abstract from expression, or do some measurement in the numerical terms to help have a concert precise concept about the form. The Material Form: This mean the shape that the point have to express itself, this illustrate that it has unlimited number of shapes, it can be jagged, it can be sharp, it can be developed to any free shapes.” The point digs itself into the plane and asserts itself for all time. Thus it presents the briefest, constant, innermost assertion: short, fixed and quickly created.”

However, we can see that Kandinsky repeat what Pythagoras mention about the absolute and the matter, he said that the existence of element with one colour in not ready exist and those such elements are a complex of nature, everything is relative and we don’t know the absolute. Point holds two concepts inside according to his vision: • The External Concept: that means that the graphic form consider as an element by its own tension which is the movement that the form had within it is boarder. If this tension dies the art work also die. He concludes that the work of art is the sum of all the tensions the forms create within the same plane. • The Inner Concept: This measure the time in painting. The arrangement goes two directions one for the painting space and the other for the music tone. This point is still a question need to be answer.

Natures: The nature form for the space for example is in reality small space particles and carries the same relationship to the abstract point.

* Finally, point is the temporally the briefest form at the same time the basic element which create the sound in the composition. The point eccentric structure creates the absolute sound and the sound of the given location on the plane. In case of repetition it gave more complexity. These kinds of complexes are applied on our daily life environment such as: *â&#x20AC;&#x201A; Kandinsky, Wassily. Point and line to Plane. Translated By Howard Dearstyne And Hilla Rebay,1926

Architecture: Gothic building points are sharply emphasized by using religious meaning. Also in Chinese building this point used to achieve the clarity as a curve end with the point.

Dance: As all of us now the Ballet Dance Art. Going back to the classical one, the main concept of this art is the point. The rapid running on the toes illustrate a trace of point

* Music: points can be produced in music with all sorts of instrumentsâ&#x20AC;&#x201D;especially the percussion instruments. The piano however, enables the creation of finished compositions exclusively by means of the combination and the sequence of tonal points.

One Force line type:

• LINE Line is a secondary element created by the movement of the point. This happened on two cases:

(Straight Line, Free Straight Line): • Horizontal Line, represent cold form, so coldness and flatness are the basic sound. • Vertical Line, represent warm form, so warmness and flatness are the basic sound • Diagonal Line, represent both the cold and the warm, create the inner sound: centric and a centric.

Applying one force: This foreceis in one direction this creates the first line type which is the straight line warding the infinity and the tension of this line is the most concise for endless movement. Applying two forces: • A single repeated action which create angular line • A simultaneous action which create curved lines

Two forces line type (curved line): • Curved geometric wave • Curve free wave

• PLANE Also as the line, plane considers being a secondary element, it is the place where the content of the art are received. If we analysis its contents it has two cold elements (two horizontal line) and two warm elements (tow vertical line). This element achieves the balance aspect by giving two double sounds that conclude the objective sound of the basic plane. Kandinsky believed that the plane is a living thing, and has a fixed relationship between the above elements and the below elements on it. Therefore, every artist feels the breathing of the still untouched plane, and feels the responsibility toward this plane and gives it the life, by receiving the right elements in the right order which help the characteristic to appear strongly and clearly to the people who receive the art work. These characteristics according to the art work plane are:

Above • Looseness, give density to the upper border of the basic plane • Lightness, give the inner quality and every weightier form grows heavier and shows strong sound • Freedom, give the light movement of the elements Below • Condensation, give density of the atmosphere • Heaviness, give the ability for the smallest individual area to become closer and sustain the larger and heavier form. • Constrain, give the limited movement.

Left The equal to the above, with the difference of degree applied with the characteristics. More restricted. Right The equal to the below, with the difference of degree applied with the characteristics Applying this kind of theory employsâ&#x20AC;&#x2122; the inner sound tension, which is some is somehow related to our imagination, like the right sided people are more developed and freer while the left side people are more inhibited and bound.

RAISING FORCES OF FOUR SIDES OF SUQER

PRIMARY FROM AND COLOUR RELATION

PLAN FORMATION

CONCLUSION

As a result of this research it seems that Pythagoras, Euclid and Kandinsky all of them work as one team to assure the idea of the elements focusing on the relationship between each one of these elements. All of them consider the music to be the primary elements that help to reveal the inner power of the work whether it is a math equation or a piece of painting. We can draw a very clear line between all of people

who thing about the feeling and how it make all the idea stronger as Plato when he describe the beauty and it is aspect. They consider each part as a living being, that should be exposed by it is own expression. The artist is the tool that gives the breath to these elements, therefore not everyone have this creativity and strangeness to give the idea within the simplest most abstract composition. Different time period, same mind of the revolutionary idea, this one of the most common shared thoughts. Pythagoras think about the universe, aimed to achieve something logical depend on the science not history story. Then Euclid came simplify what was suggested by Pythagoras, to make it more abstract and less complicated. Finally, Kandinsky represent the idea of logic and science inside his art work, using the simplest shapes and form which behind all of them a science prove and aim, emerging that with our own experience which variety upon us.

BOOK

REFERENCE

• Lupton, ellen and Miller J.Abbott. Lupton, Ellen .ABC’s of the Bauhaus: The Bauhaus and Design Theory. Princeton Architectural Press, editor: J. Abbott Miller, 1996. • Whitford, Frank. Bauhaus. 1991 • Kandinsky, Wassily. On the Spiritual in Art. 1944 • Turner, William. History of Philosophy. Boston, USA, 1903. • Crowley, Aleister & Sturges, Mary d’Este. BOOK 4. Ordo Templi Orientis. 1969 • James, William. The Principles of Psychology. www.Abika.com • https://www.goodreads.com/quotes/search • Kandinsky, Wassily. Point and line to Plane. Translated By Howard Dearstyne And Hilla Rebay,1926. • Lang, Peter. The Art Theory of Wassily Kandinsky, 1909-1928: The Quest for Synthesis. 2010.

WEBSITE • http://www.schoenberg.at/index.php?option=com_content&view=article&id=351&Itemid=543&lang=en • http://www.storyofmathematics.com/greek_ pythagoras.html • http://www.britannica.com/EBchecked/ topic/310922/Wassily-Kandinsky/3833/Munich-period • https://www.goodreads.com/quotes/search • http://www.artchive.com/artchive/K/kandinsky.html • http://www.sacred-texts.com/eso/sta/sta19. htm • h t t p : / / e k a t e r i n a s m i r n o v a . w o r d p r e s s . com/2012.htm