# Four-dimensional progression

USD 1900

027

Oil, canvas

19.7" x 19.7" (50 x 50 cm)

Kyiv, 2013

Any sequence of numbers contains not only the set of numbers and the rule it is formed by. The very idea of a sequence referres to the fundamental concepts of time – “before” and “after”. Any numerical sequence is a kind of flow since we use such words as “at first”, “next”, “before”, “after”, “then”.

Numerical series can be represented by three-dimensional shapes, each one of them correspnding to the numbers. This is the way to obtain certain three-dimensional structure which also includes a very specific time aspect. It has the length, width, height, and time flow expressed in the order of the sequence – “before” and “after”. This structure only seems to exist all at once, stable and not changed. But the time phenomenon is there. Therefore, this structure is only partially three-dimensional. In fact, it is a four-dimensional object.

We take one of the most common number series beginning with “1”. Each successive element is twice as much as the previous one: 1, 2, 4, 8, 16, 32 etc. Just a geometric progression. We present it as a set of concentric circular shapes, their outer diameters corresponding to the numbers in this progression. Each concentric shape is divided into equal sectors. Total number of the sectors in each “ring” corresponds to the numbers of the progression, too. Two basic alternating colors can be used in order to better percieve and count. Two colours - just because the common ratio of this progression is 2.

The shape obtained is geometrically three-dimensional. But as long as it abides by the sequential order “before” and “then”, it “contains time”. Time flow is directed from the center (where “1” is located) to the edges of the image in all directions. So we can assume that this picture is a symbol of our four-dimensional world, an image of the space-time continuum...

Two-color three-dimensional segmented rings corresponding to the numbers of this progression can form interesting visual images. There can be an infinity of choice. This painting presents one of the options. The rings are arranged so that they form four “beams” directed from the center to the corners of the picture. Four rays are a hint that our world is four-dimensional. The picture is two-dimensional image of four-dimensional world.