art and math have the same basis: visual grammar

Art and math have the same basis.
I do not mean that art has mathematical basis as many authors have written.
My claim is that there is the same visual-grammatical basis for all the mental activities, including math and art.
The proto visual grammar is formed by experiences which enter through the visual sense organ.
To see a picture we customarily see it on perceptual level.
When we enjoy it formally however, we forget time passing and the work being a thing in space: shape seeing is not practical.
Art seeing (shape seeing) is not perceptual seeing but sensual seeing.
Any association from seeing is the secondary activity of perception.

There is a frequently quoted topic in Hermann Weyle's book "Symmetry".
When the mathematician proved that there are only seventeen ways to cover a plane with tiles artists already had used all the possible way.
Since the time of Ancient Egypt until modern time, the patterns had been used.
This suggests that the ability to make patterns is universal.
Making the pattern solved the mathematical problem, which means that applied art can solve applied mathematical problem.
Everyone can see shapes, which  teaches him  apriori self organized system of shape.

Seeing a shape is to see the quantifiable geometrical characteristics of the shape, which have number concept.
Most noticeable characteristic is countability of shape.
String, loop, dot, cavity and coil are countable elements:

Then can the proportion represent number?

Effect of the proportion in art work has been popular; especially of golden section.
I put it aside because the length of a line segment cannot be exactly measured by sight.
It is as hard as weighing a thing by holding it or hearing absolute pitch.
What the example shows is the orderly size difference of the shapes.

The proportion can be sensed exactly in this way by the help of countable squares.
The proportional element appears at the last stage of art style; there are many art works ignoring the exact proportion.

Visual sense is the most important sense organ because it can count the characteristics of shape and  grouped shapes.

Babylonia, Maya, Ancient China, and  Ancient Egypt had similar numerical system: grouped shapes represent natural number.
The notations of the small number like 1, 2, 3 are similar in all of these ancient civilizations.
The inconvenience to write large numbers made invention of sign; each civilization has different sign.
It supports the idea that the concept of number did not come first but sensing shape made the concept of number.
The representation of number concept inevitably became same everywhere.
The same shapes of the ancient numerical system is the archaeological remnant of what ancient people had before language, which suggests that the universal grammar is not language but shape.

Before learning any sign system every child self-teaches the structural relation of shape by visual experience.
Though every child masters the basic visual grammar it is usually replaced for sign system by education.
A few grown-ups do not forget the great pleasure of seeing shape to become artist or mathematician.
Clive Bell writes,
"I wonder sometimes, whether the appreciators of art and mathematical solutions are not even more closely allied. Before we feel aesthetic emotion for a combination of forms, do we not perceive intellectually the rightness and necessity of the combination?"

There is a story that Socrates could instruct an ignorant slave boy to solve a geometrical problem.
The boy had innate ability; how old could he be?
Around ten year old since he could serve as a house servant?
There is an IQ test with shapes for the lower grader of elementary school, which means that  children of younger than ten must have the ability to see the shapes in the test.
There is some evidence to lower the age further: dozens of You Tube movie about child pianists.
It seems that three year old kids are ready to learn playing the piano, which means they can understand the musical structure.

                                                         (three year old Hiyori plays)
A child player must be curious about hearing musical structure.
Then where the curiosity and ability come from?
There must be a preceding ability: the visual sense.
All the children are curious about shapes.
My guess is visual sense has innate ability of recognizing structural system of shapes.
This structural understanding becomes the model of all the mental activity: all the other abilities are moulded on this formal system.

Shape seeing is the innate ability every child can do.
But analysing three year old child's drawing cannot show us how the child's visual sense ability is; to play the piano a child does not have to create sounds since the piano prepares all the sounds;  it is like a child who can sense a circle can draw a circle using  PC.

This visual ability remind me of Chomsky's universal grammar.
"....the theory suggests that some rules of grammar are hard-wired into the brain, and manifest without being taught.
Chomsky has speculated that UG might be extremely simple and abstract, for example only a mechanism for  for combining symbols in particular way, he calls Merge. ....the human brain contains a limited set of rules for organizing languages....all languages has a common structural basis. This set of rules is known as universal grammar."(Wikipedia)

My assumption is that the set of rules can be self-taught by the experiences of seeing shapes.

I am more familiar with Piaget, so let me quote from Wikipedia about Piaget's "The Child Conception of Space".
"Children at the earliest stage, when asked to reproduce certain geometric figures, preserved only the topological features; that is, they were accurate in terms of continuity/discontinuity, enclosure/ exclusion, inside/ outside, nearness/ farness."

I use this idea as the principle to explain visual grammar.
The topological features of shapes can construct number concept and logical system: proto visual grammar appears at this stage.

there is shape relation to show us number concept: the nearness of shapes makes a group and isolate from other groups.

The grouped shapes show the number concept and such group can be arranged in order: the lower grader at elementary school can learn counting with the picture of apples.


There is another obvious relation of shapes which can teach us basic logic.
When I say we have innate logical intelligence, I mean there is logical structure of shape and our sense experience can notice it.
Kids can draw a face with two eyes, which means they understand the number 1,2 and inside- outside relation.
I call such faculty of counting and of logic proto visual grammar, which can be developed to visual grammar.

Let me show a simple logical example: the possible position of two loops( loop shown as square).
When there are two loops one is either inside or outside of the other.

To add one to the left pattern there are three possible positions: outside of the large square; between the two squares; inside the small square.

To add one to the right pattern there are two ways: outside two squares; inside the either one of the squares.

(the same pattern is shown in blue)

There are good examples in Arp's works which show his grammatical awareness.
I listed up some examples.

Arp writes,


"....I wanted to create new appearances, to extract new forms from man.
We do not wish to copy nature. 
We do not want to reproduce, we want produce.
We want produce as a plant produce a fruit and does not itself reproduce.
We want to produce directly and without meditation.
As there is not the least trace of abstraction in this art, we will call it concrete art."

His genius picked patterns from pre-existing list of shapes.