Saturday, November 14, 2015

Accidental Similarity between Abstract Painting and Physical Data

Fig. 1. Saiko Yoshihara's painting on the post card to tell about her solo exhibition.

A friend of mine, Saiko Yoshihara, is a painter joining Shinsho Fine Art Association. She is going to hold a solo exhibition in Hanamaki, Iwate, from December 3 to 20, 2015. The other day I got a postcard from her. The card was to tell about the exhibition and carried one of her abstract paintings shown in Fig. 1. In this painting she used drip technique as used by Jackson Pollock. The black dots suggest something like remains of disaster (she lives in Soma, Tohoku region, where big earthquake occurred in 2011), but there are also images of a brain and a new life, which are going to overcome the disaster. The light and tender tone of colors in the overall work seems to emanate hopes for the future. Thus, I liked this painting very much.

One thing in this painting surprised me. It was a series of black dots starting from lower left and going to the upper right. It is quite similar to experimental data plotted in figures of my physics papers. First, I was reminded of a figure in Ref. 1, which showed the range–energy relation of electrons in aluminum and copper in logarithmic scales. I draw the figure (see Note) by cutting the whole region of the vertical and horizontal scales into two and juxtaposing the different regions into one graph by the use of different scales for bottom and top as well as right and left. This made it difficult for laypersons to grasp the whole trend at a glance. Therefore, similarity appeared only in my brain.

Fig. 2. Range–energy relation of electrons in aluminum and copper in logarithmic scales.

To make similarity visible to Saiko and other persons, I have made a new graph by combining two copies of the original figure. In the new graph shown as Fig. 2 above, each of the vertical and horizontal scales extends naturally over the whole region considered. The size of Fig. 2 is made equal to that of Fig. 1. Similarity is now seen between the series of dots in Saiko’s work and the long, two adjacent curves at the middle of the new graph.

Fig. 3. Backscattering coefficient as a function of atomic number divided by the energy of the incident electrons.

Saiko’s painting has other series of dots that deviate further from the uppermost one as they go further to right. This trend is also seen in the range–energy relations of electrons for higher atomic numbers, but the deviations are not so large as in the painting. Thinking about this, I was reminded of another figure in the other paper of mine, Ref. 2. This figure, reproduced in Fig. 3 with modification to make the size equal to that of Fig. 1 again, shows the backscattering coefficient as a function of atomic number divided by the energy of the incident electrons. Data for different materials lie on slightly different curves, similarly to Saiko’s plural number of series of dots.

Why did Saiko, who has never seen the figures in my paper, draw dots arranged like those physical data? The curves represented by Saiko’s dots and experimental data in my papers are of the type called "S-shaped curve" or "logistic curve." Such a curve often appears in natural phenomena. It also represents one of natural paths of the movement of the right hand going from far lower left to far upper right on a large canvas of F100 size (162×130 cm). Considering these, it is not so strange to see such a similarity.


It was the days when personal computers were not yet available, and I draw the figure by hand on a B4-size sheet of tracing paper.


1. T. Tabata, R. Ito and S. Okabe, "Generalized semiempirical equations for the extrapolated range of electrons," Nucl. Instrum. Methods 103, 85 (1972) (DOI:10.1016/0029-554X(72)90463-6, post-print available). This is the most cited paper in my publications (see here).
2. T. Tabata, "Backscattering of electrons from 3.2 to 14 MeV," Phys. Rev. 162, 336 (1967) (DOI:10.1103/PhysRev.162.336e, post-print available). This is my thesis paper.