The mathematical physicist must simplify in order to get a manageable model, and although his concepts are of great beauty, they are austere in the extreme, and the more complicated crystal patterns observed by the metallurgist or geologist, being based on partly imperfect reality, often have a richer aesthetic content. Those who are concerned with structure on a super atomic scale find that there is more significance and interest in the imperfections in crystals than in the monotonous perfection of the crystal lattice itself.
Recently there is a tendency to pursue distortion in art, but in the case of this jar, natural deformation has raised distortion to the level of spontaneous beauty.
Generally speaking, the Western perception of art has its roots in Greece. For a long time its goal was perfection, which is particularly noticeable in Greek sculpture. This was in keeping with Western scientific thinking; there are no painters like Andrea Mantegna in the East. I am tempted to call such art ‘the art of even numbers’.
In contrast to this, what the Japanese eye sought was the beauty of imperfection, which I would call ‘the art of odd numbers’. No other country has pursued the art of imperfection as eagerly as Japan.
We love to see the process, not just the result. The imperfections in your work can be beautiful if they show your struggle for perfection, not a lack of care.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.