Picasso's geometrical spirit in 1932 invented syntactical device

                         Picasso  Reclining Nude series in 1932
Picasso is said to have written the date of execution in the bottom side of the picture for the convenience of future researchers.
The catalog numbers which are based on the date can be used as the titles of the picture.
I arranged the digital images online by the title of [Reclining Nude] .
The digital image is a new medium of art in this century.
To study Picasso the titling is important because each work  is different experiment.
Each has unique design.
[Reclining Nude 32-042] which has solid balance like archaic sculpture seems to be made of simple scale.
I start with this picture as it looks obvious that Picasso used a sort of device like circle- rulers.

Picasso  [Reclining Nude 32-042] / circle-arc model /scale

The model shows that  three compositional techniques are used:
1) The design is made of limited circles. (scale)
2) There are points on which more than three circles intersect. (pivot)
3) More than three  pivots are lined. (pivot lining)
I have already explained about these three techniques.

                                   Picasso [Reclining Nude 32-042] circle-arc model
As I recognize another technique in this simple model,
 I made the largest circle(red) thicker.

                                      Picasso [Reclining Nude 32-042] largr circle-cross model
A circle with the horizontal and vertical diameters can make a unit which I call circle-cross unit.
The extended circle of the left foot can be moved down vertically to match the extended circle of the right foot .
The circle of the left arm can be moved to match the neck.

                                      Picasso  [Reclining Nde 32-042]  pink circle- cross model
Pink circle-cross units also are used  the same way.
The circle of the right thigh can be moved to match the left leg.
And sliding it to the left, it can be matched to the circle of the left arm.
The circle of the left upper arm can be moved to match the back side of the head.




In the next picture  the limbs are exaggerated.

                             Picasso [Reclining Nude 32-053]

                     Picasso  [Reclining Nude 32-053]  circle-cross model
Four different-sized circles (blue. orange, green, purple) make the basic  structure.
The largest light blue circles are the most important for the basic structure.
I made one sky blue circle deep colored to make it easier to see.
All the blue arcs are within the triangle which is made by connecting the three points (the top right corner, lower right corner and lower left corner).
Two intersecting points of the blue circles (pivots) are outside of the frame and one is on the right side.
One of the third largest green unit and two forth largest purple units are lined on the horizontal diameter of the deep blue unit.

                      Picasso [Reclining Nude 32-058]

                      Piasso [Reclining Nude 32-058] circle-cross model

                     Picasso  [Reclining Nude 32-058] /circle-cross model/lined 7 units


The basic one of the largest red circles is shown in thicker line.
Seven units of different size are lined along the horizontal diameter of  this largest circle-cross unit.
Picasso could have been great architect.
Renaissance artist could produce not only painting but also ornament, sculpture and architecture.
Understanding all the types of art is essential to become real artist.

[Reclining Nude 32-079] reminds me of gemstone: every part is packed like a bud.

    Picasso  [Reclining Nude 32-079]/ circle-cross model
The large red units make the basic structure.
All the red arcs are within the triangle that linked top right corner, bottom right corner and bottom left corner.
I colored the same red circle-cross unit in two hues (brownish red, vermilion)for explanation sake.
The two brownish red circles touch at a point: the horizontal diameters are connected (shown within the parallel purple lines).
On this horizontal line a blue unit and two yellow units are placed.
There is another pair of red circles which intersect( within the pallarel black lines).
.


The upper body starts opening like a flowering bud.

                       Picasso [Reclining Nude 32-080]

                       Picasso [Reclining nude 32-080]  circle-cross model

                      Picasso [Reclining Nude 32-080] seven different units lining


The four circle-cross units (sky blue, red, orange, purple)make the basic structure.
I made one of the five light blue circles thicker, which is basic.
The vertical diameter of the basic circle is placed on the center of the picture frame.
Three smaller units (a pink unit and two purple units) are on the horizontal  diameter of the basic circle.
The second largest red circle's tangent line is the same as the vertical tangent line of the basic circle.
One orange unit is on the vertical diameter of the red unit and another orange unit is on the horizontal diameter .

                 Sharaku(Hokusai) [Otanikoji]


Here in Japan they say that Picasso's works are like children's painting.
The majority of Japanese does not have any doubt that Sharaku was an amateur painter; a No-actor.
It seems for me that most Japanese in these days cannot see a painting formally.
We do't say that we see Manga but that we read Manga: painting is an illustration.
The lyric is more important than the sound in popular song for most of Japanese.
After finishing Japanese version of this blog, I happened to find You Tube Video [Picasso 1932: Love, Fame,Tragedy at Tate].
As the title suggests ,
any online articles about this show are  about Picasso's life and the paintig is by product of the great artist's life.
None of them are referring to formal aspect of Picasso.


Modern Art was one aspect of Modernism but unfortunately there were no serious art critics who could  equal structuralistic scholars like Jacobson or Chomsky.
I have previously classified four levels of seeing; 
1) Seeing with referential knowledge,
2) Seeing symbolically,
3) Iconic seeing,
4) Formal seeing.
Formal seeing  is innate act without referring any knowledge, which can be the base for the other three ways of seeing..
On this level the imaginative power works in the same way for Picasso and Einstein.
Art is significant because it is created on normative level.

Klee, Vasarely, Stella made the same type of polygonal mosaics (Geometrical classification of abstract art )

                                                   Klee [Village on the rocks], 1932
                                                   Vasarely [Quami], 1950
                                                   Stella [Irregular polygon], 1965
All the artworks can be classified into one system according to the geometrc structures of the work.
The upper three works are polygonal mosaics.

                                                 three works in the Irregular polygonseries
I introduce a new model called proto-shape: a polygon made of definite number of line segment with free angle and free size.

.

Both look like overlapped polygons. ( This is a seeing of iconic level.)
But on perceptional level, the two shapes can be seen as two  polygons to share sides.
The left is made of a triangle and a six- sided polygon and
 the right is made of a triangle and a eight- sided polygon.
A concave polygon  can easily be identified by paying attention to the concave.

There is only one proto-shape for any polygon without concave but several proto-shapes for concave polygons .

  The left shape can be smaller.

These are the same as proto-type.


 Concave polygons can be classified.
A triangle does not have enough sides to make a concave.
A quadrilateral can make only one concave.
Polygons with more sides can be made by paying attention to the concaves and the convexes.

        polygonal table




I used to buy many art magazines and Auctioner's catalogues in Strand for this type of Vasarely's works.
Now I find more digital works than my collection .
Without extending the polygonal table I made the nine- sided polygon by cutting off two concaves on a five- sided polygon.

The other polygons can be found in the table.

                                               polygonal distribution diagram
                                               mechanical compositional method
Vasarely seems to have used some algorithmic method.
The below illustration shows such imginary process.
1)  Draw  five six- sided polygons surrounding a five- sided polygon.
2)  Add concaves on the polygons.
3)  Move some shape parallel.


Stella and Vazarely used polygons as motif.
The polygon distribution diagram below shows that Klee used the same method.

                        klee [Village on the rocks] polygon distributio diagram
There are several many-sided polygons: three eight-sided polygons(vermillion) and three seven-sided polygons(brown).
None of them have remarkable feature as main role.
They look like the back ground of the surrounding convex polygons .
So I draw auxiliary lines to show the likely hidden parts of the polygons.

                        klee [Village on the rock]  complimentary line model
In this way I can eliminate all the concave polygons.
The convex polygons which are made with cardboard can be overlapped to make the design.
There are one hexagon and the rest are pentagons, quadrilaterals and triangles.
This basic design was constructed firstly
 and the secondary surface structure was  made by extending and overlapping the surrounding polygons.
The structural model below confirms my asumption.

                         klee [Village on the rock]  structural model of intersecting polygons
The  overlapping shapes make three dimensional illusion.
For example the two polygonal corners  are lined on a vertical line near the center, which look like steeples
and  the parts on the lower right look like eaves structure.


Finally I make two models for harmony and balance: scale model and line extension model.

                        klee  [Village on the rock]  scale model

                              

As a line segment has not only the size but the angle, I extend all the line segments

                       Klee  [Village on the rocks] extension model
The extended lines  intersect at many points, which makes the structure balanced.


The diagram of modern art movement by Alfred Barr shows that all the movements until 1935 converged to two types: non-geometric abstract art and geometric abstract art.
Most followers took this diagram as a model to fablicate more movements for extending the network of the diagram.
The importance in this diagram is that the final stage is formal: artwork became geometrically analyzable.


Without any analysis we can recognize that these three works belong to the same genre.
It seems that they were made without any direct influence though the makers had the notion of making abstract art.
The world of internet overflows with art-images which themselves are new medium of art.
But geometrical patterns can easily be classified on the level of seeing shape.
The same type of works  can be collected to study the difference of syntax.
Creating new artwork means inventing new syntactic device.

Klee's musical serialism in linear composition

Many artists who claimed that they were influenced by Klee's work understood only symbolical aspect of his painting.
Some modern composers like Boulez and Stockhausen showed interest in Klee's formal technique.
Klee did not express musical feeing but composed structures like a composer.
Though there are many writings about "Klee and music", words cannot explain the syntax of art.
I am going to use visual grammar for showing Klee's syntactic devices.

                                                          Cezanne/Picasso/Klee
Obvious stylish progress can be seen in these three paintings.
In Cezanne's landscape with buildings the linear structure is dominant.
Picasso neglected perspective and natural color, and the space looks like a structure made of cardboard.
Klee made a mosaic of quadrilaterals; all the geometric elements are quantifiable.
I made a network model.
The model neglects the size and angles of the line segments.

                     Klee CastleHill  line network diagram
These illustrations are the equivalent at the network lebel.
Naming the intersection as "dot", each point is expressed as D (N) [N=3, 4, 5: N is the number of line segments].
There are six D (5). ten D (4) and twenty D (3).
Adding the elements of size and angle, the design is made.


Any artwork is classifiable at this level.


A composition with straight line segments needs a new model to explain the syntactic device.
Any line segment can be considered to be a radius with a pair of two circles which centers are the two ends of the line segment.

                                  Klee  Castle Hill  linear scale model
The linear scale model suggests  that the balance is due to three devices;
1) The extension of some line segments pass through the dots.
2) Some circles form pivot structure.
3) Some dots are alined on the horizontal lines and vertical lines of the frame work.

                                  Klee  Castle Hill  linear scale diagram
Placing one end of each line segment on the center of concentric diagram, we can have horizontal line segments to compare.
The diagram also shows that
1)  there are twenty different size.
2)  the number of the line segments of the same size.

                                  Klee  Castle Hill  Colored line model
In this painting the size of the line segments are important.
The colored line model confirmes that the effect is based on the schematic design.
There are several regular patterns like:
1) a chain of three same sized line segments: the shortest pink ones and vermilion ones.
2) a chain of two same sized line segments: lightest pink, vermilion, yellow, yellow ocher.
3) three light blue ones are attached at a point.
They are fragment of decorative pattern.
Decorative art is not different from painting; the difference is a degree of regularity.


This model can be constructed with colored straw: cutting straws in size and connecting them with strings.
In such a model the angles and the positions are changeable but harmony remains the same.




Now we know that Klee used serial technique in 1929.
This is almost the same time when Schoenberg invented twelve tone music.
It does not mean that there were any relation between Klee and Shoenberg.
Both music and art are based on innate universal grammar.
Plato said " I would teach children music, physics, and philosophy; but most importantly music, for the patterns in music and all the arts are the keys to learning."
My assumption is that the ability for sight precedes ability for hearing.
To understand any design we must have pattern-recognition ability beforehand.
The degree of sensing outside phenomenon is not analogue but digital.
Artist's expression  therefore becomes digital.
Digitaly expressed sounds and shapes form a scale.




After knowing that artwork is made according to the grammar, it is obvious that we cannot establish art theory without examining  the syntactic level of artwork.
The critics in the last century are like people arguing about classical music without reading the musical scores.

The same universal syntactic technique that was used for Ukiyo-e and Modern art

                                        Modigliani  [Caryatid]  pivot-line model 
Art making is not  sketching an object  but  designing a shape.
When he draws a curved line he is conscious that the line is made of several line segments each of which has different curvature.
Each curve becomes an arc.
The arc can be extended to a circle.
Using the circles he can adjust the balance.
Some artists were aware that the intersection of the circles can be fixed for balanced structure.
When I made the model of Modigliani's [Caryatid] I noticed a straight line going through more than three intersections(pivots).


This time I am going to check all the models I have made.

                               Modigliani  [Caryatid]  pivot-line model
Modigliani is generally known as a portrait painter.
But some people consider that [Caryatid] series is the most important.
The model supports such taste judgment.

                              Matisse  [Dance Ⅱ]  pivot-line model
We enjoy played music.
The effect is due to the structure which is expressed on the musical note.
Matisse painted [DanceⅠ] spontaenously.
Then he constructed [DanceⅡ] with unit arcs.
He chose a few circles to make a scale.
Matisse used the device to fasten the circles: to make the whole structure he intersected the circles on several spots, most of which are lined.

               Picasso  [Woman with a flower]  pivot-line model
Searching Picasso image online we find many imitation Picassos.
The reason why we can easily find out real Picasso is
the quality difference.
And the quality judgment can be supported by the model.

                             Klee  [Support for a shield]  pivot-line model
This masterpiece is not well known.
The reason may be because there is not so much to say in this picture of string on sign level.
The model reveals how the harmony is generated.
Now we know all the greatest modern artists used the same syntactic device.

                   Sharaku(Hokusai)  [Yamashita Kinsaku]  pivot-line model
Many people believe that Sharaku was Noh-actor and only early half body portraits are significant.
It seems that they see only facial expression and fail to see the whole body.
I consider that Sharaku style is the result of Hokusai's interest in early ukiyo-e.
The quality is equal to the best early ukiyo-e painters like Totorii Kiyonobu.

            Kaigetsudo Ando  [Tatibizinzu]  pivot-line model
I have chosen Kaigetsudo because his style is most distinct among early ukiyo-e painters.
Wikipedia says about Kaigetsudo, "it is probable that many of the works attributed to him were painted by his disciples".
The taste judgment can tell us which are by Ando himself and the pivot-line model can confirm the judgment.
The study of Ukiyo-e painting can be started with structural analysis of  works.
The pivot-line model shows us how artwoks are balanced and harmonised.

Cezanne's intuitive syntax and Modigliani's intentional syntax

                                  Hokusai [Ryakuga haya-osie]
                                  Cezanne [Six Bathers]/ Modigliani [Caryatid]
For these works, the same type of harmonizing syntax was used.
Painting, ornament, sculpture and archtecture are based on the same syntax.
As we can see in [Hokusai Manga], Hokusai knew that painting and ornament are designed in the same way.
Renaissance artists were experts of all the types of art.
There is no such thing as pure art but artwork is made for some practical purpose.
Art survived even after the practical purpose outdated or forggoten because the shape remained like a shell.
We get artistic sensation by seeing visibly perceivable geometric characteristics.
We perceive them quantitatively.
Artist is an inventor of new syntax.
Most people are accostomed to see shapes on iconic level.
In figurative painting the outline is not noticed as geometric because the line is a sequence of arcs.
Unlike painting , ornament has easily recognizable symmetric structure of circles.
A good listener can only perceive the effect of the musical note but the composer  can　use the musical syntax.
A good viewer can only perceive harmonious effect  of shape but the artist can use the syntax of shape.
Klee wrote in his diary,
"I learned to understand archtectual monuments....the obvious commensurability of parts, to each other and to the whole, corresponds to the hidden numerical proportions that exist in other artificial and natural organizms.....the importance of measurement....becomes evident."

                Cezanne [Six Bathers] lithograph
This drawing above seems to have been drawn after the lithograph below.
Althogh the legs are missing the foot is in proper position.
The curvature of the lines is very clear.
Arcs are the smallest elements.
The sequence of arcs becomes a melodious line.
The closed or almost closed line is a motif.
Ornament has pivot structure for balance and harmony.
At least Cezanne knew that deliberately drawn line becomes a curve with single curvature though he was not aware that the composition was forming  pivot structure.


The litograph can be reconstructed with five circles as he had excellent sense of harmony.
The modern artists could easily recognize Cezanne's scale method.

                Cezanne [Six  bathers] arc model
The circle-arc model I made before was to show that the largest and the second largest circles make the basic composition.
This time I add the smaller circles to show that each motif is well balanced.

                Cezanne [Six Bathers] pivot model
This model shows that same colored arcs are grouped at specific parts, which suggests that he paid very much  attention on the arcs of the same circle.
To make the point clear ,I enlarged two parts.

               Cezanne left Bather
The three pink circles overlapping the body are the main structures with pivots(intersection of more than three circles).
The highest circle which is the extension of the bottom thigh has six pivots.
The middle circle which is the extension of backbone has four pivots.
The lowest circle which is the extension of the front part of lower limb has also four pivots.
When a designer trys to balance the closely grouped arcs, the extended circles of the arcs tend to form pivot structure like ornamental design.

                            Cezanne right bather in [Six bathers]
The largest circles (green) which make the arm parts is the basic.
The second largest circles (pink) are not used as a whole circle but covering partially from both sides.
Many of the smaller circles intersect at the pivots.


The holes of ancient flute are made to sound scaled tones.
A musician of flute makes scaled music.
The document says that Cezanne was very fond of visiting The Loubre and enjoyed to draw marble statues.
Cezanne's sense of harmony further developed as he painted  the same motif  for sevral months.
Cezanne discovered the harmonizing device unintentionally.
Modigliani learned Cezanne's technique of harmony.
It is almost unbelievable that Cezanne used pivot structure consciously but surely Modigliani used it
deliberately.

                              Modigliani [Caryatid] pivot model
There are  three distinctive syntactic devices in the model.
1) It is made of six circle scale.
2) The second largest circle(green) is the base of the pivot structure.
3) There are eleven lines with more than three pivots and six of them intersect at a point(pivots on radial lines).


As nobody studied  artwok syntactically, the development of Modern art stood still.
Universal Art is a masterpiece based on unique syntax.