A friend of mine, Saiko Yoshihara, who was in the same elementary school as me in Dalian, is a semiprofessional painter joining Shinsho Fine Art Association. She held a solo exhibition in Hanamaki, Iwate, from December 3 to 20, 2015. The postcard about that event I got from her had an image of her abstract painting (Fig. 1). In this painting, she might partly have adopted the drip technique similar to the one used by Jackson Pollock. The black dots suggest the effects of earthquake disasters. She lives in the region that suffered the Great East Japan earthquake in 2011. However, the work also seems to have images of a brain and a new life to overcome the disasters. The light and tender tone in the painting emanate hopes for the future. Thus, I liked this painting very much.
Fig. 1. Painting “DUET” by Saiko Yoshihara as printed on the postcard; Copyright © 2015 by Saiko Yoshihara
One thing in this painting surprised me. It was a series of black dots starting from the lower left and going to the upper right. It is similar to experimental data plotted in the figures of my physics papers. First, I was reminded of the plot of the extrapolated range of electrons (a measure of the penetrability of electrons through material layers) [Ref. 1]. It showed the range as a function of the electron energy (simply called “range–energy relation”). I draw the figure (see Note 1) by cutting the whole region of the horizontal scales into two. Namely, I combined the two parts in a single graph using different horizontal scales at the bottom and top. This makes it difficult for laypersons to grasp the whole trend of the relation at a glance.
To make similarity easily visible, I have produced a new graph by combining two copies of the original figure. In Fig. 2, the horizontal scale extends naturally over the whole region treated. The width-to-height ratio of Fig. 2 is made equal to that of the painting in Fig. 1. Thus, we can clearly see a similarity between the series of dots in her work and those along the two adjacent curves running from the lower left to the upper right of Fig. 2.
Fig. 2. Range–energy relation of electrons in aluminum and copper in logarithmic scales. Points represent experimental data; and lines, the empirical formula we proposed.
Saiko’s painting has other series of dots that deviate further from the uppermost one as they go further to the 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 graph in my work [Ref. 2] on the backscattering of electrons. It is reproduced in Fig. 3 again with a modification to make the width-to-height ratio equal to her painting. It shows the backscattering coefficient of electrons (the ratio of the number of electrons coming back from the incident surface to the number of incident electrons) as a function of the atomic number of the absorber material divided by the energy of the incident electrons. Data for different materials lie on slightly different curves, similarly to her plural number of series of dots.
Fig. 3. Backscattering coefficient as a function of the atomic number divided by the energy of the incident electrons. Points shown by different symbols represent experimental data, and solid ones show my experimental data. Lines connect the experimental data smoothly.
Why did Saiko, who has never seen the figures in my papers, draw dots arranged like those physical data? The curves represented by her dots and experimental data in my works are of the type called “S-shaped curve” or “logistic curve.” Such a curve often appears in natural phenomena. We can also suppose that one of the natural movements of the right hand with a brush from the lower left to the upper right on a large canvas produces such a curve. Considering these, the happening of such similarity is not so strange.
Note
When we published Refs. 1 and 2, personal computers were not yet available. So, I draw the figures by hand on B4-size sheets of tracing paper.
References
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) [One of the most cited of my papers (see here)].
T. Tabata, “Backscattering of electrons from 3.2 to 14 MeV,” Phys. Rev. 162, 336 (1967) (DOI:10.1103/PhysRev.162.336, post-print available) [My thesis paper].
Notes for the revised version
This article originally appeared at https://ideaisaac.blogspot.com/2015/11/accidental-similarity-between-abstract.html on November 14, 2015, and has been one of my most viewed posts (1.69-k views). In the present revised version, I made minor changes and improved the sentences of the text.
While preparing this version, I found Saiko’s painting used here was in “Saiko Yoshihara’s Book of Paintings: Dairen & Fukushima” (Self-published, 2015) in the complete form with the title “DUET” (“Dairen” in the subtitle of the book is the Japanese reading of Dalian). The proper orientation of the painting was the one rotated by 90 degrees counterclockwise compared with Fig. 1. Further, the original work had more portions along the four sides. However, the similarity I mentioned is also applicable to the proper form of the painting by comparing it with my graphs also rotated by 90 degrees counterclockwise. In the last paragraph, I only have to attach the word “rotated” after “S-shaped curve” and “logistic curve” and change the expression “from the lower left to the upper right” to “from the upper left to the lower right.”
In the context of the Great East Japan earthquake, the word “Fukushima” symbolizes the Fukushima Daiichi Nuclear Power Plant incidents. So, the subtitle of Saiko’s book seems to imply that her paintings were much affected by that incidents. However, she must have put Dalian and Fukushima side by side for the following reason: Her place of residence was initially Dalian and, after her repatriation from the native place, was primarily in Fukushima Prefecture.
The title of the painting, “DUET,” was irrelevant to the disaster, and my impressions of the work were not the painter’s intentions. On the other hand, the title was strangely predictable, given that her work and my graphs lined up in this essay.