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.

Note

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.

Reference

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.

Boy of Age 16 Asks Me about Relativity, etc.3. Space and Time

Diagram showing space and time in space-time. Here space is depicted as a two-dimensional entity in three-dimensional spacetime. Time from the observer's viewpoint is represented as a vertical line. Image by K. Aainsqatsi (Own work) [Public domain], via Wikimedia Commons.

A friend of mine on Twitter, Aaron (a pseudonym), is an overseas, 16-year old boy, who seriously admires Albert Einstein and wants to become a physicist. He continually writes me (Ted, also a pseudonym) questions about the theory of relativity and related topics, and I am sending answers. In this series of blog posts, those questions and answers are reproduced with modifications. I am not an expert in the fields of physics related to relativity. So, my answers might contain errors. If you find any error, please do not hesitate to write a comment for the benefit, not only of the boy and me, but also of other readers.

Aaron: Will there be time, if there is no space?

Ted: Your question does not seem to be a valid one in physics. Physics is the branch of natural science to study matter and its motion through spacetime; and these, i.e., matter, motion and spacetime, are inseparable from space.* From this viewpoint, physicists are not expected to think about the circumstance in which there is no space. In treating a complex problem, physicists often assume a simplified model of the situation, but elimination of space would make the problem non-physical.

However, the following should be noted in relation to your question: Approaches to quantum gravity, being studied for uniting quantum mechanics with general relativity, suggest the possibility that space and time are not fundamental entities but emergent phenomena (see, for example, Ref. 1). If such is the case, the phrase in your question, "there is no space," would have physical meaning in the sense that equations of quantum gravity would dispense with space and time variables.

* Especially in the theory of relativity, space and time (to say precisely, imaginary time) are treated symmetrically, and it can happen that part of time duration of one observer is part of spatial length of the other observer.

Reference

1. Luboš Motl, Emergent space and emergent time, The Reference Frame (2004).

(Originally written on February 23, 2011)

On the Day I Shouted His Name ... (2)

Inoue wrote more than 60 dramas as well as many novels and essays. I have read none of them but have the book of collected photos, "Hisashi Inoue's Dalian*" [1], edited by Inoue and his theatrical troupe Komatsuza. Opening the book, I found Inoue's essay entitled "Dalian, the Dream Town." Reading this essay for the first time, I learned the relationship between Inoue and Dalian from it. I guessed that the photos in the book should have been part of collected data for a drama. However, the relationship had started much earlier. It was when one of his best friends moved to a primary school in Dalian and sent Inoue a picture card of Dalian in the winter of 1943. (I also moved to a primary school in Dalian in September 1944; namely, the friend of Inoue's and I had a similar experience. I bought this book to look at images of old Dalian dear to me.)

On the basis of his thought about Dalian, Inoue made a drama entitled "Enshō and Shinshō." Komatsuza made the first performance of this drama in 2005. It is about this story: Raconteurs Kokontei Shinshō and San'yutei Enshō went for performances in Manchuria** during the war time and were induced to stay in Dalian because of Japan's defeat. They had to do different and difficult jobs to live there for 600 days before coming back to Japan.

The last passage of Inoue's essay is as follows: 'The word "Dalian, the Dream Town" that entered deep in me as a child would not disappear until my death while its meaning is changing." One of the changes was due to his concern about Chinese people who had to live on the outskirts of Dalian when the city was part of Japan's borrowed land. Here we find Inoue's pacifism that made him one of initial members of the Article 9 Association.

Praying for his peaceful sleep in heaven, I wish to follow his footsteps in the efforts to keep Article 9*** of the Constitution of Japan and extend the renunciation of war all over the world.

Notes

* Dalian is a beautiful port city in the Northeast China. It was in the region of the land borrowed by Japan until August 1945, the time of Japan's defeated in the second World War.

** The historical name of the present Northeast China.

*** 1) Aspiring sincerely to an international peace based on justice and order, the Japanese people forever renounce war as a sovereign right of the nation and the threat or use of force as means of settling international disputes.

2) In order to accomplish the aim of the preceding paragraph, land, sea, and air forces, as well as other war potential, will never be maintained. The right of belligerency of the state will not be recognized.

Reference

1. H. Inoue and Komatsuza, ed., Hisashi Inoue's Dalian (Shōgakukan, 2002).

Effects of Chinese Classic Literature on H. Yukawa's Work

The following is the outline of my talk to be delivered at Himeji Kyoyukai meeting on February 18, 2010, in Himeji.

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The Nobel-winning physicist Hideki Yukawa developed the theory of elementary domains for particle physics together with his coworkers in his later years [1, 2]. In the preface of a book [3], he writes that the important factor that led him to the idea of this theory was the words of the Chinese poet Li Po (701­­–762), "Heaven and Earth are hotels for everything, and days and nights are travelers of hundreds of generations." He also writes that scientific research and literature are not separate things for him.

Yukawa also writes in a textbook on particle physics [4] that Li Po's words mentioned above was one of the motivations that brought his unconscious idea about the elementary domains to his consciousness. While being rather lengthy for introducing the concept of the elementary domains in a textbook, the paragraphs including the above words are considered the valuable record of Yukawa's processes of thinking.

In his lecture on experimental nuclear physics, Kiichi Kimura, a classmate of Yukawa's at Kyoto University, told us that some words in the Taoist book Zhuangzi might have been a hint on Yukawa's meson theory that brought him the Nobel Prize. I do not remember the words Kimura quoted from Zhuangzi. In his 1961 essay [5] on Zhuangzi, however, Yukawa writes that he had read Taoist books Zhuangzi and Laozi in his middle school days, but was forgetting philosophical thoughts in them for many years after that. This means: When he was thinking about meson theory, Yukawa was forgetting Zhuangzi. Thus, the words of Zhuangzi Kimura mentioned had not been a direct hint, at least, on the idea of the meson.

It was reported [6] that the meson theory had been motivated by the occasion of the childbirth of Yukawa's wife. Namely, the judo expert Sachio Ashida remembered to have been told in a commuting tramcar by Yukawa, "A baby can exert an attractive force between the parents. There may be a similar existence in the nucleus." I suppose that this was Yukawa's jocular explanation of his idea for the layperson. Yukawa should have gotten the idea of the meson from the study of earlier papers by Werner Heisenberg and Enrico Fermi together with the analogy of the electromagnetic field mediated by the photon. Note here that he used a good analogy.

In his essay mentioned above [5], Yukawa writes that he reminded himself of an allegory in Zhuangzi when he was thinking about something at a deeper level than "elementary particles," which amounted to more than 30 kinds those days. The allegory was about the king who lacked all the seven holes in the face, i.e., ears, eyes, nostrils and a mouth, and was named Chaos ("Konton" in Japanese). The underdeveloped state of the king was appropriate for Yukawa to express his idea of something at a deeper level.

Yukawa also liked the following words from Zhuangzi: "On the basis of the beauty of Heaven and Earth, we arrive at the reason of everything." He made these words in Chinese characters use as a watermark of the invitation letter for "International Meeting on Elementary Particles: The Thirtieth Anniversary of the Meson Theory" [7].

To develop a new theory in the field of particle physics, it is necessary to have good mathematical skill of formulating equations to express a physical model, as well as strong imaginative power to think of a new model. One of the important device with which Yukawa cultivated the latter ability should have been Chinese classic literature, which includes a lot of allegories and helps one to develop thinking by the use of an analogy. Thus his reading of Chinese classic literatures in his young days was useful not only directly for the idea of elementary domains, but, quite possibly, also indirectly for the idea of the meson.

(This article owes much to the discussion we have had at Osaka Science Museum among the members of "Citizens' Study Group on Hideki Yukawa.")

References

1. Y. Katayama and H. Yukawa, "Field Theory of Elementary Domains and Particles. I" Progress of Theoretical Physics Supplement No. 41, p. 1 (1968).
2. Y. Katayama, I. Umemura and H. Yukawa, "Field Theory of Elementary Domains and Particles. II" ibid. p. 22 (1968).
3. H. Yukawa, Auto-selection of Hideki Yukawa's Essays Vol. 5 (Asahi-shimbun, Tokyo, 1971) [in Japanese].
4. H. Yukawa, Unified Theories of Particles, in Iwanami Lectures: Foundations of Modern Physics, Vol. 11, H. Yukawa and Y. Katayama, ed., p. 563 (Iwanami, Tokyo, 1974) [in Japanese].
5. H. Yukawa, Zhuangzi, in Auto-selection of Hideki Yukawa's Essays Vol. 3, p. 363 (Asahi-shimbun, Tokyo, 1971) [in Japanese].
6. Personal connections in Japan: The spirit of Judo (8), Asahi-shimbun, Evening issue (May 25, 2006) [in Japanese].
7. The 30th anniversary of Meson theory (1), Asahi-shimbun (September 20, 1965) [in Japanese].

Relationships between Arts and Science

These days we often find the topics on the relation between arts and science in newspapers. (Here I mean arts and humanities by "arts," and natural sciences by "science.") An example is the news that the Faculty of Culture and Information Science was opened in April 2005 at Kyotanabe Campus of Doshisha University, Kyoto, Japan [1].

At the Web site of the Doshisha University [2] they write the characteristics of this faculty as follows: "The educational programs are designed for students to understand the significance of cultures by analyzing them with the concept of data science. The curriculum promotes the interdisciplinary methods which connect the traditional studies in the field of humanities with information science."

This is a trend to be welcomed in education and research at universities. However, the analysis of the products of humanities by the method of science is only one of many possible aspects of interaction between arts and science. I write here a few examples of other aspects I have learned from the book-review pages of the science journal "Nature" (It is to be noted that the book review pages in this journal have been entitled "Books & Arts" since 2003, and includes introductions to exhibitions and stage arts related to science or the "Science in Culture" column.)

In the book "Madam Bovary's Ovaries" [3], David Barash and Nanelle Barash attempted to interpret fiction in terms of biology. The reviewer of the book, Michel Raymond writes [4] that the classical boundaries between biology and the social sciences are fading away and that the above authors explore various aspects of human mating strategies, rooting human behaviors within the animal repertoire and using novels instead of scholarly publications. Raymond also gives a useful suggestion that an evolutionary book could provide some welcome insights on the historical origin of the novel in various human cultures and its relationship with other kinds of literature such as myths or fairly tales.

The neuroscientist Steven Rose published the book "The 21st-Century Brain" [5]. The reviewer John Marshall of this book writes as follows [6]: Rose stresses the observation that individual life stories are shaped by culture, society and technology and is even prepared to believe that science is perhaps intrinsically incomplete and must be complemented by the kind of knowledge we gain from arts. Marshall warns that Rose's observation, however true, does little to bridge the gap between brain and mind. At this point it does not seem that Marshall looks at the future.

The above examples are related to the usefulness of arts to complement research in science. The next example shows an aspect different from these.

Paul Davies reviewed [7] the book "Warped Passages" written by Lisa Randall [8]. This is a book for general readers on hidden dimensions being studied at the frontier of theoretical physics. Davis writes, "Perhaps readers don't really intend to follow [popular-science books] studiously, but wade through the expositions as a cultural experience, rather like reflecting on a Jackson Pollock painting -- you know it's very clever and you assume it means something profound to the creator." [Pollock (1912-1956) is an American painter famous for drip painting.] Davies's words may be a little extreme, but suggest that artists and scientists can learn each other about their methods of expressions.

1. Asahi-Shimbun (April 8, 2005).
2. Web site, Doshisha University.
3. D. P. Barash and N. R. Barash, "Madam Bovary's Ovaries: A Darwinian Look at Literature" (Delacorte Press, 2005).
4. M. Raymond, Nature Vol. 435, p. 28 (2005).
5. S. Rose, "The 21st-Century Brain: Explaining, Mending and Manipulating the Mind" (Jonathan Cape, 2005); Published in the US as "The Future of the Brain" (Oxford University Press, 2005).
6. J. C. Marshall, Nature Vol. 435, p. 27 (2005).
7. P. Davies, Nature Vol. 435, p. 1161 (2005).
8. L. Randall, "Warped Passages: Unravelling the Universe's Hidden Dimensions" (Allen Lane, 2005); To be published in the US in September by Ecco (HarperCollins).