When we see the shape of a plate to draw it, we pay attention to several parts of the contour as arcs.
It is like touching an object in order to sense the shape in the dark.
Touching is the basic ability to sense an object and seeing on sense level is its evolutionally advanced stage.
We self learn on this stage logically organisable structure of shape world around us.
The other abilities are moulded imitating the learned structure.
And Picasso recognised Cezanne's excessive use of arcs very effective.
The other modern artists followed Picasso
This is the main reason why Modern art became great in a very short period of time.
Cubism was "arc-ism".
The four arcs are easily recognizable: top and down arcs and right and left ones.
Let me show how we see a plate.
Though we see innumerable oval shapes from various angles we recognise it as oval.
This way of seeing is sign-seeing: we know that the plate is a circle.
We fix a viewpoint to see an object.
In this photo image the outline is not symmetrical: the circle of the left arc is larger than the circle of the left arc; the left side of the top arc is more curved than the right side; the right side of the bottom arc is more curved than the left side.
The outline of refined artwork becomes a smooth line and the smooth line is a link of arcs.
Artwork is easily recognizable pattern for an ideal seer as musical note is for a musician.
It can be said that Cezanne's work was in the mid way of becoming purely clear pattern.
This is similar process as a folk music sound becoming pure musical sound.
There are some prints by Renaissance painters showing a device how to draw still life objects, which means that it was even for them difficult to get photographic view overcoming three-dimensional illusion.
Cezanne did not have interest to use such device; his composition is not realistic; the only realistic factor is volume, which, Picasso eventually realised, is not essential.
Then what was his advantage of not being realistic?
Cezanne could simplify the whole pattern.
As every contour became a link of arcs the whole network was easily manipulated like Cubist method
As the first Cubist Cezanne painted unrivalled harmonious artwork.
Although we see mathematical curves beautiful, we do not find such beauty in nature so often.
There must be some other factor in the beauty of artwork.
I reason that pure artwork is made of harmonious links of arcs.
In this illustration the maximum curvature is represented as a quarter-circle and straight line is a curve of a infinitley large circle.
The other curves are arcs between the two.
Any shapes can be re-constructed with arcs
Refined artworks tend to be made of a fewer arcs.
There are infinite curves between the quarter circle and the straight line.
A small portion of a large circle becomes almost straight line.
The link of them can express any line of any artwork.
This is the last version of Picasso's bull series, which is considered to be the good example of perfect abstraction.
It looks being made of arcs and straight lines only.
Once I imagined that I could draw all the lines using circular cardboard cut-outs as rulers.
Living long enough to be able to use Microsoft Drawing Tool, I could draw almost round circles easily.
The quasi-circles are good enough to make my point because we see a quasi-circle as a circle.
He painted the oil paintings as applied art for making a living.
He knew that shapes are made of arcs though he disguise the outline for practical purpose.
This Da Vinci sketch tells us that the outline is further separated into line segments and the proportion of each part becomes measurable vertically and horizontally.
As Da Vinci drew it for his own interest he did not bother to refine the line and Hokusai needed to draw realistic outline for readers; the final quality of executed line depends on the practical use.
They were the same kind to Picasso: analytical artist.
Ferdinand de Saussure distinguished parole and langue and studied the latter,
.Likewise the visual grammar seeks ideal models underneath individual works.
And Surrealists' works are made of curves which are links of arcs.
Formally every artwork is made of arcs.
In this work by Magnelli arcs make polygons with curved lines.
The second one by Balla and the third one by Mondrian are made of overlapped arcs.
In the works of Modigliani and Arp they may look different type as we tend to see the works on iconic level at first sight.
Besides, the arcs are hidden in the outline, which is why the contemporary critics failed to see the common denominator of these works: arcs.
As they could not see that all the modern artists were Cubists, they classified Modern art on sign level, inventing the isms.
It was chaotic like the time of discovery of the numerous subatomic particles in physics without recognising the parameters.
Imagine they are made of wire, their shapes can be easily recognised in the dark, which means that sense-seeing is as fundamental as tactile ability and that colour-seeing is different.
This Arp can be made of three two-arc unit.
His Caryatid series is as advanced as Webern's serial works.
It was unfortunate that the best formalist Clive Bell used the term "form" not only for shape but for colour, which is the cause that prevented unification of all art.
Even Picasso took sometime to realise that colour and tone is not essential factors.
Visual grammar is the most basic cognitive faculty based on sensing shape.
