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.

Monday, July 13, 2015

From Fujioka's Fluid Drop Model of Atoms to Einstein–Arakatsu Relationship

I have made a lot of exchanges with Bill Streifer (a researcher and freelance journalist on Intelligence, nuclear work and North Korea) at the Quora site from July 9 to 13, 2015. Most part of our exchanges is reproduced here by Bill's permission.

Bill: Was Prof. Yoshio Fujioka's "fluid drop" model of the atom known as ekiteki?
And if so, why?

Tatsuo: I haven't learned about Yoshio Fujioka's "fluid drop" model of the atom but guess that if he proposed such a model, it should have been called "ekiteki" model. "Ekiteki" is the Japanese word for "fluid drop" (eki=fluid, teki=drop).

Bill: Prof. Ayao Kuwaki was a Japanese scientist and a friend of Albert Einstein. When did he die, exactly?

Tatsuo: According to the information page of him in "Wikipedia" (Japanese edition), Ayao Kuwaki was born on September 9, 1878, and died on May 16, 1945.

Bill: At the end of the war, an American airman met a man who claimed to be a student of Einstein in Germany. When I learned of Kuwaki, I suspected it might have been him. But now I see that's not possible since Kuwaki died in May 1945 and the "meeting" took place in September 1945.

Tatsuo: Sure, the student should not have been Kuwaki.

Bill: He might not have been a graduate student of Einstein, but he may have attended Einstein's lectures in Germany. Can you guess who he might have been? [And he lived in northern Korea in 1945!] An Einstein scholar is not willing to guess.

Tatsuo: I have no idea about that person.

Bill: If you provide a number of possibilities, I'll check each one. Did Hideki Yukawa study under Einstein?

Tatsuo: No, Yukawa didn't study under Einstein, but they met each other for the first time in Princeton on the former's return trip from Europe in 1939.

Bill: Einstein wasn't in Germany very long. I wonder if any Japanese or Korean scientists studied under Einstein when he taught there, or even attended his lectures.

Tatsuo: The Japanese physicist Jun (Atsushi) Ishiwara seems to have studied under Einstein in Germany (石原純 - Wikipedia). Ishiwara worked as an interpreter when Einstein visited Japan in 1922.

Bill: Thanks. Did Einstein have other Japanese students or followers in Germany? Kuwaki appears to be a little too old. I'm looking for a Japanese scientist who lived until 1946 at least.

Tatsuo: I don't think that Einstein had other Japanese students or followers in Germany.

Bill: I know of another.

Tatsuo: You Know? Who is he?

Bill: Dr. Bunsaku Arakatsu.

Tatsuo: Oh, Bunsaku Arakatsu was a teacher of my teacher and an experimental physicist. So, I didn't think he had studied under Einstein. Wikipedia page for him (Japanese edition) writes that he studied in Europe (Berlin, Zurich and Cambridge) for two years from 1926. It must have been a short time during this period that he studied under Einstein. By the way, his look is similar to Einstein's in some photos of him.

Bill: Can you find any photos of Einstein and Arakatsu together? If you can, please send them to
Is your teacher still alive? If so, could you ask him if Arakatsu or Yukawa visited Konan (Hungnam), Korea during the war? By the way, Konan and Hungnam are the same place, Konan is the Japanese pronunciation and Hungnam the Korean pronunciation.
You might also be interested in knowing that my article about an Austrian chemist who worked at Konan for more than two years (1935-1937 & 1940), will appear in a book being published by the University of Vienna Korean Dept. later this summer. The name of my article is A Letter from Korea.

Tatsuo: I don't have any photo of Arakatsu.
My teacher Kiichi Kimura at Physics Department, Kyoto University died in 1992. I haven't heard of Arakatsu's or Yukawa's visit to Hungnam (Konan), Korea. However, Arakatsu was associated with another Konan. Namely, he was the president of Konan University in Kobe, Japan, after his retirement from Kyoto University. Konan of Korea and Konan of the university in Kobe are different from each other when written in Chinese characters. The former Konan is written as 興南, and the latter, 甲南.
I have not so much interest in the history of science in Korea. However, if you write about some history of physics in Japan, I would like to read it very much.

Bill: I am familiar with Kimura. I am also aware that Konan, Japan is different than Konan, Korea.

Tatsuo: May I quote our exchanges made here these days in one of my blog sites written in English? Some friends of mine might be much interested in our exchanges.

Bill: Yes, that would be fantastic. And if anyone has any questions or comments, they can contact me directly at

Tatsuo: Thanks a lot for your permission.

Bill: Stay in touch.

—A few days later we had additional exchange as given below.—

Bill: You can add this: According to page 15 of the book Uranium Matters: Central European Uranium in International Politics, 1900–1960 by Zbyněk A. B. Zeman and Rainer Karlsch, the Japanese physicist, Dr. Bunsaku Arakatsu "studied at Berlin University ... under Einstein, becoming a member of Einstein's close circle of friends."

Bill: I returned to the original document, and I am now convinced that the American airman met a Korean scientist, not a Japanese scientist in Korea in September 1945. But it's still interesting that Arakatsu was a close friend of Einstein, so all of this work wasn't for nothing.

Tatsuo: I've been on a trip to my hometown since Tuesday and am writing a belated reply. Thanks a lot for your additional information. We surely have gotten a good fruit.

(Last modified on July 29, 2015)

Saturday, August 09, 2014

Obituary: Shigeru Okabe (1923–2013)

Shigeru Okabe in 1961.

Shigeru Okabe was born in Kagoshima and studied at the seventh high school of Japan's old education system. Then, he entered the Faculty of Science, Kyoto University. He majored in experimental nuclear physics under Professor Bunsaku Arakatsu at the Department of Physics in a handicapped environment immediately after World War II and graduated from Kyoto University in 1946. In 1949, he became an assistant professor at Tottori University. There Okabe made use of the geographical advantage that Misasa hot spring with high radon content was close there to study natural radioactivity. His study of earthquake prediction by change in the atmospheric radon concentration (Ref. 1) is internationally known as the earliest of similar studies.

In 1949, he became the Chief of Radiation Source Division, Physics Department, at the Radiation Center of Osaka Prefecture (RCOP), which was just established. There he was engaged in the construction of irradiation rooms and installation and maintenance of an electron linear accelerator with the maximum energy of 18 MeV. He also pushed forward varieties of researches such as monitoring methods of electron beams, the passage of electrons through matter, photo-nuclear reactions and characteristics of solvated electrons by the use of this accelerator. During that time, he obtained Research Grant for Peaceful Use of Nuclear Technology for six years in a row, showing his high capability of planning and advancing researches. In promoting research and maintenance work, he put the right man in the right post and also took care of the division members for getting doctor's degree or an academic position at another institution.

In 1973, Okabe was promoted to the Head of Physics Department, RCOP. Shortly thereafter, significant changes in the organization of research institutes were made by the Government of Osaka Prefecture to abolish the division system and to adopt the research group system. This made it necessary at RCOP to have the system of working groups in parallel with research groups for the maintenance and operation of facilities and equipment. In such an upheaval, Okabe exhibited his prowess in research management. At the same time, he contributed a lot of review papers to journals in the fields of applied physics and nuclear energy, and also showed much influence on the development of Radiation Division, Japan Society of Applied Physics.

Okabe retired from the Head of Physics Department, RCOP, in 1981 and became professor at the Faculty of Engineering, Fukui University. While being engaged in education, he returned to the study of natural radioactivity. Making use of geographical advantage again, he studied radon concentrations in snow. He also played an active part in research committees, made outside the university, of exo-electron and radon.

In 1989, Okabe retired from Fukui University and established Radon Science Laboratory at his home, continuing his study intensively. In 1993, he published a fine art book entitled entitled Collection of Occasional Sketches. It contains about sixty watercolors and drawings made as a hobby from his school days. He was also known as a gourmet and often enjoyed going to good restaurants in Osaka and Kyoto.

Leaving the great achievements as described above, Okabe passed away on June 30, 2013, at the age of 89.


The author of this article, Tatsuo Tabata, is much indebted to Dr. Okabe for his kind supervision and enjoyable collaboration in the earlier years of the former's professional career.

(Minor modifications made November 13, 2015)

  1. S. Okabe, Time variation of the atmospheric radon-content near the ground surface with relation to some geophysical phenomena. Memoirs of the College of Science, University of Kyoto, Series A, Vol. XXVIII, No. 2, Article 1, pp. 99–115 (1956). (According to Google Scholar, this paper has been cited by 39 articles as of August 9, 2014.)

Wednesday, June 19, 2013

The Couple Talks about the Volume of the Truncated Cone

On June 7, my wife and I joined a bus trip to Exhibition of Paintings from State Pushkin Museum and Flower Festival Commemorative Park. We had lunch at a French restaurant, whose building was a nationally designated Important Cultural Property. At the lunch table, a couple younger than my wife and I took the seats in front of us. Let's call them Mr. and Ms. N. A glass containing water from the well of the restaurant and some ice cubes was prepared for each person from the beginning of the lunch course (see the photo above).

At some stage of the lunch course, Mr. N took the glass and asked Ms. N if she could guess how to calculate the volume of the solid of such a form. She said, "Add a small cone to make it a large cone. Calculate the volume of the large cone and subtract the volume of the small cone from it." Mr. N replied that it would be very cumbersome. Then, he said that the volume can be obtained as the mean of volumes of three cylinders having the same height as the solid. His voice was so low that I was unable to hear the radii of the three solids, but from the movement of his hands, I supposed that he referred to the radii of the top and bottom circles of the truncated cone and a certain mean of the two. He additionally stated that we could obtain the formula by integration of the circular area.

I had never heard of the formula for the volume of the truncated cone, and thought it wonderful that Mr. N learned it and remembered it for some reason. However, I also wondered why he who spoke of a more complex method of integration said that his wife's simpler method was cumbersome. After returning home, I calculated the volume by Ms. N's method and easily found that the third radius mentioned by Mr. N was the geometric mean of the radii of the top and bottom circles.

To see the formula and the derivation of it, visit here. The explanation is in Japanese, but readers might easily follow equations by looking at a diagram included. The third method mentioned there by the use of Pappus-Guldin theorem (also known as Pappus' centroid theorem; the second theorem is relevant here), however, might be a little difficult to understand, if you have never heard of that theorem.