The Japanese Mathematician Shigekiyo Muramatsu

Yesterday, Arjen Dijksman, a Twitter friend of mine, told me on twitter that the Twitter user by the name of OnThisDayInMath was looking for pictures of Matsumura's tomb, Sengakuji, and the inscription on the path, in relation to a blog article (Ref. 1). This article quotes the following description from a March 1908 article in the American Mathematical Monthly:

[O]ne of [the 47 ronin], Shigekiyo Matsumura, was the greatest Asiatic mathematician of his age, who in his work Sanso, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 215 sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimalsone of them, Shigekiyo Matsumura, was the greatest Asiatic mathematician of his age, who in his work Sanso, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 215 sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimals ...

I made the search of "Shigekiyo Matsumura" and "Sanso" on the Internet to find that the correct name of the author of Sanso was "Shigekiyo Muramatsu" and that he himself was not the member of the forty-seven ronin (赤穂四十七士). The most useful source of my finding was Ref. 2, my translation from which is given below (the original Japanese text is given in Appendix):

Shigekiyo Muramatsu (村松 茂清, 1608–1695) published Sanso (算俎) in 1663. Muramatsu served Asano (浅野) family and possibly had a math institute in Edo [present Tokyo]. Muramatsu had only a daughter, and took Hidenao (秀直) into his family as a son-in-law [the daughter's husband]. Hidenao and his son Takanao (高直) joined the forty-seven ronin to cause the Akō incident. In Sanso, Muramatsu arranged idai [problems published in earlier Japanese mathematics books written without answers] by classifying them into different levels with consideration for ease of learning. In this book, he also showed the calculation of pi from the regular inscribed polygon of 32768 sides to correctly obtain the value 3.1415926. Thus, this book was the first in the mathematical calculation of pi in Japan. Sanso was republished in 1684 by the title of Sanposanso (算法算俎). This item [possessed by Kyoto University Library and presented in the exhibition] is the copy of this republication, but it is not clear if this is the one published in 1684. Inside the back cover, it is written that this was bought in September 8, 1857, in Asakusa-kuramae.

We can see the names of all the forty-seven ronin in a list of a Wikipedia page (Ref. 3). The list shows Hidenao and Takanao with their middle names included as 村松 喜兵衛 秀直 and 村松 三太夫 高直, but not Shigekiyo. It is natural because the Akō incident was in 1703 (Refs. 3, 4), and Shigekiyo had died in 1695 as written in Ref. 2. Thus, I am not sure if Shigekiyo's tomb is in Sengakuji Temple together with those of the forty-seven ronin.

References

1. "Pi and the 47 Ronin." Pat's Blog (September 5, 2009).
2. The Catalog of the Exhibition "Wasan no Jidai (和算の時代, The Age of Japanese Mathematics),"edited by Kenji Ueno, Chapter 3, p 28, item 66 (Kyoto University Library, 2003) (In Japanese).
3. "赤穂浪士 (Akō-rōshi)," Wikipedia, The Free Encyclopedia, Japanese edition (March 19, 2011, 10:23).
4. "Forty-seven Ronin," Wikipedia, The Free Encyclopedia (23 April 2011, 05:32).

Appendix. The Original of Ref. 2

　村松茂清（むらまつ　しげきよ、1608－1695）は寛文３年（1663）に算俎を出版しました。村松は浅野家に仕えていましたが、江戸に数学塾を持っていたようです。村松には娘しかなく、婿養子秀直を迎えましたが、秀直と秀直の子高直は赤穂四十七士の討ち入りに参加しました。村松は「算俎」のなかで、遺題の問題を内容別にレベル分けして配列し、学習しやすいように配慮しました。「算俎」では円に内接する正32768角形の周の長さを計算して円周率を3.1415926まで正しく計算しました。円周率を数学的に計算した我が国初の書物です。「算俎」は天和４年（1684、同年貞享に改元）に「算法算俎」と題して再版されました。本書はこの再版本ですが、天和４年に出版されたものかどうかは不明です。裏表紙の裏に「安政四丁巳九月八日浅草蔵前求之」と記されています。

Notes added later

• The revised version of Ref. 1 with an addendum appeared: "More on Pi and the 47 Ronin," Pat's Blog (May 3, 2011).
• According to the Japanese Wikipedia page on Hidenao Muramatsu, Shigekiyo Matsumura had the middle name Kyūtaifu (九太夫) (the "middle name" was used as the daily nickname in those days of Japan), and he had a son. However, the son disappeared from home and was lost, so that Shigekiyo took Hidenao as a son-in-law.

The Disaster Report from Tohoku University

Coming back from a bus trip to Okayama Prefecture late last evening, I found an email massage from a former colleague of mine, Naoki Toyota, who is now Professor at Department of Physics, Tohoku University. He writes as follows:

Find the file attached, "The March-11 disaster report from Sendai." I have sent this nonofficial, rather personal document to my overseas friends and asked them for distributing it to their colleagues. I would appreciate it if you could upload this email on your home page or provide a link to the URL of the report (a link to the home page of our Low-Dimensional Quantum Physics Group is also okay).
By the way, all my family including my mother-in-law and her family, living in the devastated coastal region, are safe.

Naoki's report consists of four pages of a PDF file and describes the damage caused by Tohoku earthquake and tsunami, as well as the status of recovery from it, at Tohoku University. Especially, detailed descriptions are given of those at Department of Physics and related facilities.

Just after the March-11 disaster, I thought of sending Naoki an email message of sympathy. However, I supposed that he might be busy responding to many similar messages (even I, living quite far from Tohoku, received some such messages from abroad). Thus, I refrained from sending a message. On the return path of yesterday's trip, I was thinking about sending him a note during this week. What an interesting phenomenon of synchronicity it is to find his message after returning home!

The Mirror Puzzle: Reversal Is Attributed to the Direction Defined Last

Yesterday, a friend of mine invited me to join the Internet site "Quora." This site consists of a continually improving collection of questions and answers created, edited, and organized by everyone who uses it. I thought that one of the topics I was able to give the best answer was the "mirror puzzle." Searching the topic of "Mirrors," I found it in the subcategory of "Optics" in the category of "Physics." It included a question, "Why does a mirror reverse things horizontally but not vertically?" This is what I call the mirror puzzle stated in a little different manner.

The question seems to have been posted on July 14, 2010, and there are three answers. The first answer is as follows:

A mirror actually reverses front and back. The image of your right hand remains directly in front of your right hand. But because you think of the image as a rotation of yourself, you're led to think that left and right are reversed.

Richard Feynman explains this with his usual wit and smiles here.

The next answer is similar to this, and is the quotation from Martin Gardner's book, Aha! Gotcha. The third answer explains that things seem to be flipped horizontally or vertically depending on your point of view. This does not explain the left–right reversal that appears as the difference in shape between the object and its mirror image. Only the last paragraph of the third answer explaining that mirroring is mathematically "orientation reversing" is meaningful.

In the first and the second explanations, the essential reason why you compare your image with yourself rotated along the vertical axis is not made clear. Noticing this point, we reach the following explanation I gave there as the fourth answer:

The "mirror puzzle" is commonly stated: Why does a plane mirror reverse left and right, but not top and bottom? This question refers to the left–right reversal in the shape of the mirror image of an object as compared with the original object, i.e., the reversal of the left–right asymmetry viewed from two different coordinate systems, each of which is intrinsic to the object or its mirror image. The left–right reversal in this sense always happens in mirroring the object for which left and right can be defined, irrespective of the relative configuration of the object to the mirror. The reason can be explained as follows:

Mirroring reverses the direction perpendicular to the mirror surface. Thus, the mirror image of an asymmetric object becomes its enantiomorph (an example of enantiomorphic pairs is a pair of left and right hands). An enantiomorph is, or can be considered to have been, obtained by reversal in any single direction of an object ("orientation reversing" mentioned in the third answer; also equivalent to "space inversion" or "parity operation" in physics, in which all the three directions are reversed).

However, we can define the left–right direction of an object (or the mirror image) only after defining the top–bottom and front–back directions from the external view* of the object (or the mirror image). Thus, the top and front of the enantiomorph is always regarded as the same sides, in the external view, of the top and front of the original object, so that the direction reversed in the enantiomorph has to be attributed to the direction defined last, i.e., the left–right direction.

The key point lies in the nature of the definition of left and right. Explanations by Richard Feynman, Martin Gardner and many others missed this point. The method of Feynman and Gardner to make a comparison between you and your mirror image is nothing but the precedent determination of the top–bottom and front–back directions of the mirror image.

More detailed explanations can be found in the following references:

1. M. C. Corballis, "Much ado about mirrors." Psychonomic Bulletin & Review, Vol. 7, pp. 163-169 (2000).
2. T. Tabata and S. Okuda, "Mirror reversal simply explained without recourse to psychological processes." ibid. pp. 170–173 (2000).
3. H. Yoshimura and T. Tabata, "Relationship between frames of reference and mirror-image reversals." Perception Vol. 36, pp. 1049–1056 (2007).

* The external view is mostly the shape. However, for a street car with a front–back symmetric shape, for example, motion defines the front–back direction.

Fumiko Yonezawa Reviews the Japanese Edition of The Strangest Man

The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (Basic Books/Perseus Book Group), written by Graham Farmelo, was the winner of the Costa Book Award for Biography and the Los Angeles Times Book Prize for Science and Technology, in the year 2009 of its publication. This book was also selected as one of the best books of 2009 by The Economist, The New York Times Book Review and Amazon.com. The Japanese edition of the book was published by Hayakawa Shobo, Tokyo, in September 2010. The translator was Michiyo Yoshida. The Japanese title is not the literal translation of the original but means, "The Sea of Quantum, Dirac's Abyss: The Highly Gifted Physicist's Glorious Achievements and Reticent Life."

Fumiko Yonezawa's review of the Japanese edition has appeared in The Akahata. This is the first review of it I have seen in the mass media. Fumiko Yonezawa is Professor Emeritus of Keio University, the first woman President of the Physical Society of Japan and one of the laureates of L'ORÉAL-UNESCO for Women in Science Award 2005, for her pioneering theory and computer simulations of amorphous semiconductors and liquid metals.

The Akahata or Shimbun Akahata (literal translation, Newspaper Red Flag) is the daily organ of the Japanese Communist Party in the form of a national newspaper. Started in 1928, Akahata has a 16-page daily edition and a 36-page Sunday edition, and the total circulation is 1.68 million (quoted from "Shimbun Akahata," Wikipedia, 7 December 2010 at 20:41). I subscribe to two newspapers in order to get deep and balanced view of politics in Japan; one is the "national newspaper," The Asahi, and the other is this Akahata. The latter often carries more excellent articles not only in politics but also in science and culture than "national newspapers." The review by Yonezawa has been printed on one of two-page "Books" column of the issue of Sunday, December 26, 2010, of the daily edition.

The title of the review in literal translation is "The group of scientists depicted elaborately," though the treatment of the book is centered on Paul Dirac. First, she introduces Dirac as a British theoretical physicist and one of the contributors to the establishment of quantum mechanics. Then, she praises his mathematical method of describing quantum mechanics as the most beautiful and his book Quantum Mechanics as the most outstanding among similar books. Especially, she notes that Dirac's book does not have any diagrams, includes a minimum necessary number of equations and many explanations by words like a book of philosophy. She even devotes a paragraph to describe how she enjoyed Dirac's book in her student days, being enchanted by and intoxicated with the beauty of the system he developed.

Next comes a brief introduction of Dirac again (namely, "he got successful results in young days and received Nobel Prize at the age of 31"), and the book being reviewed is mentioned as the biography of Dirac, consisting of more than 600 pages in the Japanese edition. Yonezawa writes that she liked the detailed depictions of the group of scientists in the ages of the formation of quantum mechanics and succeeding to it (the title of the review comes from her words here). She mentions about Dirac's extreme reticence and infers that only the truth of nature and equations would have been swirling in his brain. She quotes the following episode as contrary to this character of Dirac: When Peter Kapitza, a scientist friend of his from Russia, was forbidden to depart from the Stalinist Soviet Union, Dirac was busy trying to collect signatures from physicists for the request of release.

Finally, Yonezawa refers to Dirac's belief, "Physical laws must mathematically be beautiful," and concludes that everything of the physicist Dirac is described in this book. This is a relatively short review but invokes the readers' interest in the person of Dirac quite well so as to make them want to read this book.

About a quote from Marie Curie

Madame Marie Curie: Science is essentially international, and it is only through lack of the historical sense that national qualities have been attributed to it. (iWise Wisdom Web page)

With regard to the purposes, efforts and benefits of science, these words of Marie Curie are valid. Thus, I do not think it appropriate, for example, to count numbers of Nobel-prize winners in science by nationality. However, the quote does not necessarily mean that science is a-cultural. Scientific activity is part of human culture, so that regional flavors are sometimes observed in the methods of doing science. Such flavors should be valued. (Adapted from my post on the above iWise Wisdom page.)

Note added later: By the way, I found the book, Radioactive: Marie & Pierre Curie: A Tale of Love and Fallout" by Lauren Redniss, among Amazon.com editors' picks for the best books of December 2010. I like Richard Rhodes's words of review, "Absolutely dazzling. Lauren Redniss has created a book that is both vibrant history and a work of art. Like radium itself, Radioactive glows with energy."