— Introduction —
The numerical configuration I painted on this artwork comes after the sequence entitled “The Universe Is Simply Perfect”, which is the result of a dream revelation that brought me to do the first painting with the digital roots of the multiplication table from 1 to 9.
In this work I removed the last row and column which mathematically complete the table with the number 9. By painting the multiplication table of the numbers from 1 to 8 we have a different result, without manipulating the digital roots, and different visual configuration which I explain in details below. Like in the previous work, the numbers 3, 6 and especially 9 remain the rulers of the whole table and it can be seen at first sight on the painting by looking at the octothorpe shape, or hash, (#).
— Mathematical Description —
I painted this square canvas where the numbers are based on the multiplication table (1 to 8) and the result is reduced to one single digit (digital root). For example 48 becomes 3 as 4+8=12 which becomes 1+2=3. Please always keep in mind this way of calculation during the whole journey.
The sum of all frontal numbers is 306 (digital root 9), we can see [Fig.1] that the sum of each single line gives result 36 (9) or 45 (9) by the darker stripes which shows the pattern composed by the rulers 3, 6 and 9. Each row and column is composed by all numbers from 1 to 8 organised in different orders (we will explore it later) with again the exception of the 3, 6, and particularly 9 that regulate and keep balance on the whole numerical and geometric composition [Fig.2].
9 is also the digital root of each single square out of the 3-6-9 lines [Fig.3]. If we divide the canvas in 9 parts, following the blue lines which I painted, we have another pattern where the four central rectangles have the same result [Fig.4], all the digital roots are again 9.
Let’s now divide the table in smaller groups and have a look at the numerical behaviour guided by the blue thin lines (#) in the centre of the artwork [Fig.5].
If we start from the upper graphics [a], which highlight the external part of the painting in the four corners, we can see how the numbers create a very precise design where the configuration we have on the top-left is mirrored on the bottom-right as well as the one on the top-right to the bottom-left in relation to the centre.
In the central part we have an intersection of 2 lines of numbers that form a plus (+) shape like in the graphics [b]. On the first one we can see the top mirrored and inverted on the bottom and the left mirrored and inverted on the right, the last graphic shows that by taking only the 2 central digits we have always 9.
Please note that the central square is composed by 27 and 72 which express exactly the whole configuration of the table – where the poles complete each other – and result always in 9 like all the other parts of the table [Fig.5].
In the graphic [Fig.6] we can observe the blocks composed by 4 numbers. Now the number 9 moved to the four corners, again the central squares are perfectly matching and the 9 is composed by the 4 and 5 reversed like in the previous combination, but also the 3 and 6 on the sides provide the same result showing an interesting sequence composed of the intersection of 3-4-5-6 (in all directions) that occupies the central part of the canvas.
Another configuration comes out from the digital roots of the minimum of 2 numbers each time, then repeating the procedure with the result until we complete the whole work [Fig.7].
After the first operation we already have a well defined design as the first and the last column are composed by the 3-6-9 (and 6-3-9) rule and, by performing the additions, we have always 9. The two central columns provide a 2, 4, 6, 8, 1, 3, 5, 7 (and reverse), if added they are again equal 9. We can find the same configuration in the second line from bottom-left or up-right of the table; as we notice the numbers are organised in growing order and separated between even and odd.
At this point there are two columns with an order 1 to 8 and 8 to 1 corresponding in a visually perfect balance that ends always with the number 9.
Naturally we have the same outcome if we perform the same calculus in vertical instead of horizontal like we did in the graphic [Fig.7].
Let’s conclude with [Fig.8] where in the first picture [a] the arrows show the growing order of the numbers, we can also see how the table is perfectly repeated on the opposite corners.
On the graphic [b] I highlighted how each digit corresponds with its opposite on the same row or column as their digital root is always 9.
The same result occurs when we calculate all numbers inside the concentric squares like shown in the graphic [c].
If we draw two diagonals so that we create an “x” shape that connects all corners and add the digits involved we have a 6+3=9 on the last picture [d].
— Final Thoughts —
I worked a lot on the concept and creation of this artwork, which I found necessary after having finished the previous painting fully composed by numbers, if the first one represents the completion this second canvas expresses the new beginning and the cycles of the universe.
On the front there are 64 numbers (6 + 4 = 10), 1 and 0 perfectly symbolise this table as they are the binary numbers used today for example in computers, formed by the negative, passive (0) and the positive, active (1). 10 is also the number that comes after 9 (the first two digits); on the other hand the digital root is 1 and stands for the start or the beginning.
This artwork is a square canvas measuring 100 x 100 cm, I painted all the numbers at the same distance so that many different operations can be performed without any visual disturbance, for the same reasons the blue thin lines and the darker thicker shadows (octothorpe shape, #) distinguish the hierarchical structure of the numbers yet leaving unalterated the visual configuration and the compactness of the work, the centre of each digit is placed at 11,1 cm – 22,2 cm – 33,3 cm etc. I also added one number 9 at the centre of each edge and four times 9 on the back of the canvas, in the exact same place as on the front, so that they have the centre distant from the closest edges as well as between each other by 33,3 cm. This way all possible directions are symbolically imprinted with the ruler 9, considering the additions on the edges and on the back we have now a total of 72 (9) numbers on all surfaces, the digital root remains the same. If we take only the number 9, we have four of them on three levels; front, in the depth and back, these three dimensions are confirmed numerically by the operation 4×3=12 (3). The sum of the 9s on each level is 9×4=36 exactly like the sum of the numbers from 1 to 8.
Contrary to the previous work we don’t have the multiplication table of the number 9, so here the morphology is totally different but the digital root is unchanged. The table is open, that means it doesn’t really finish anywhere, it is a loop that always brings back to the origin in a never ending cycle. It is important to remember that the symbol of the number 8, if written horizontally, is the symbol of infinity (∞) which is composed by a loop with no beginning and no end, the poles and the crossing lines can also be seen in the shape.
What we can clearly notice at first sight is that the table is very balanced, the exact same structure is repeated in the opposite corners (bottom-left = upper-right and bottom-right = upper-left), where already the centre with its 27 and 72 design and the adjacent frame composed by 3, 6 and 9 show the “direction”, or summarise the entire work in its core.
The numerical constellation in this canvas perfectly matches, both visually and also mathematically, in each part of the table. The whole configuration, if observed from distance, has an “x” shape and this reminds of another natural phenomenon; for example the connections between the right side of the brain with the left side of the body and the left side of the brain with the right side of the body.
This numerical configuration can be seen as a living organism or, if we prefer, a gate. By the process of observing, calculating and discovering the different mathematical designs we involve both the conscious and unconscious, we travel the cycles of life and the forces that regulate what exists and what doesn’t exists. In essence we talk the universal language.
In conclusion the whole experience of dream, visualization, calculation and realization of the artworks has been very intense and at the same time gratifying because it really came as a result of the entire work of art I have done over the years until now. This is the mathematical formula that confirms the main philosophy of all my art.
– A Poem From Cosmos –
Enamel on canvas
100x100x3,5cm
2024
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