Femto-Column: Short Essays
on Science and Humanity
Tatsuo Tabata

"Femto" is "a combining form used in the names of units of measure that are one quadrillionth (10 to minus 15) the size of the unit denoted by the base word" (Random House Webster's College Dictionary). Femto-meter, fm, is a unit suitable to express the size of atomic nuclei. Thus, "femto" is used here for the name of a very short column.
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Copyright © 2000 by Tatsuo Tabata

Contents of This Page

21. What Happened to the Garden of Eden?
22. The Reform of Education
23. A Hard Nut to Crack Even for Tomonaga and Feynman
24. The Japanese Concept of Education
25. Dreadful Crimes by Boys in the Technological Age
26. An Example of the Effect of Bad Education
27. The Crisis of Basic Sciences
28. The Fortunes of the Woman in a Pi Mnemonic
29. Readers Don't Be Fooled! Again on Mirror Images
30. Mathematics and Nature

To All the Contents of Femto-Column

21. What Happened to the Garden of Eden?

A good friend of mine, Kazu, began to study the Bible from religious mind. Last year he asked me a question about the Garden of Eden. His question can be summarized as follows:

God closed the way to the Garden of Eden after he had driven out Adam from it. What did happen to the Garden when the flood of Noah covered all that were under the whole heaven? There is no description about it. However, we find in Chapter 21 of Revelation that the holy city comes down from God out of heaven and that the city consists of almost the same materials as the Garden of Eden. So I think: The Garden of Eden had once left the earth and came back again, and to behave this way, it should be a super-three-dimensional entity. What do you think about this observation of mine from the viewpoint of a physicist?

He studied the Bible well, and it is true that the Bible includes such profound stories that allow one to make various interpretations. However, I did not find it meaningful to analyze the descriptions of the Bible from the physical point of view. Then what could be my polite answer to Kazu? I thought that reading books on the relation between science and religion might help me. So I read a few of such books.1-3 In the book written by John Polkinghorne,2 I found the following passage:

Jürgen Moltmann has evinced a desire to take modern science into account, . . . In relation to a discussion of the "Space of Creation," he acknowledges only a future willingness: "I hope to be able to develop this subject further elsewhere in the light of new scientific conceptions about the space-time continuum."

The space-time continuum is just the concept of the super-three-dimensional world view. I do not think that Moltmann would get any fruitful interpretation of the Space of Creation by applying this concept of the theory of relativity to the Bible. However, I told Kazu about Moltmann's idea to please the former with the thought that his question was an advanced one.

Finally, the principle of NOMA discussed in Steven Jay Gould's book3 (see the previous section of this column for details) was decisively useful as the reason for writing my answer not from the earnest viewpoint of physics but from the standpoint of enjoying an intellectual play.

  1. B. Russell, Religion and Science (Oxford University Press, London, 1961, first published 1935).
  2. J. C. Polkinghorne, Belief in God in an Age of Science (Yale University Press, New Haven, 1998).
  3. S. J. Gould, Rocks of Ages (The Ballantine Publishing Group, New York, 1999).

15 Jan 2000

22. The Reform of Education

On 28 Jan 2000 Japan's Prime Minister Keizo Obuchi delivered the annual policy speech at the Diet under the boycott of nongovernment parties. It was the first time that the opposition refused to attend the speech. This happened because Obuchi's coalition pushed through a controversial bill to reduce the number of seats in Japan's lower house the day before (the Associated Press).

Obuchi's speech included the setting of two specific goals. One of the goals, "the reform of education," is to foster children so as to have a good command of English and the Internet and thus be international. The other is to make this country play a major international role in science and technology (Asahi Shimbun).

Setting goals is not bad, but the Prime Minister's speech seems to have lacked the proposal of concrete and persuasive plans.

In 1947, two years after Japan's defeat in the 2nd World War, I was in the 6th year class of a primary school. The teacher of our class, Mr. Arama, was a young and enthusiastic person filled with the passion to try out new methods of education. What he did first in our class was to write the following words (in Japanese) on the blackboard:

I wonder!
What is this?
Why does it so happen?
Let's think about it.
Is this a valid solution?
Let's think it over again.

He made us recite these words every morning for some days or weeks, and ordered us to write them on the cover of every notebook we had.

I have seldom reminded myself of these words after finishing the primary school, but I still remember them well. They might have rooted deeply in my mind to affect my style of life. This was only one of many effective things Mr. Arama did in his reformative teaching.

One of the factors that brought about Mr. Arama's passion is considered to have been Japan's situation in those days, when everyone was eager to work for the reconstruction of the country. It would be necessary for the present politicians to induce good and strong passion in teachers by pursuing sound and rational politics and showing themselves to be a good model of persons working for people and the peace of the world.

30 Jan 2000

23. A Hard Nut to Crack Even for Tomonaga and Feynman

There is a moderately famous teaser, "Why does a mirror invert left and right but not top and bottom?" The Nobel-Prize physicist Sin-Itiro Tomonaga discussed this problem with his colleagues in his young days. They reached a thought that the top-bottom and front-back axes had absoluteness in a psychological space, but were unable to find a completely satisfactory answer.1

Richard Feynman, who shared the Nobel Prize with Tomonaga and Julian Schwinger, also puzzled over this problem in his MIT fraternity days. One of his biographer, James Gleick wrote that Feynman's explanation was a model of clarity, and cited it in detail.2 However, Richard Gregory criticized Feynman's following words: "We cannot image ourselves 'squashed' back to front, so we imagine ourselves turned left and right, as if we had walked around a pane of glass to face the other way. It is in this psychological turnabout that left and right are switched." Gregory added that psychological turnabout might not be entirely clear.3

What is a clear explanation of this problem then? Is it related to psychology? Early 1998 Yohtaro Takano published "a hypothesis of multiple processes" in a journal of psychology to explain this problem.4 I thought it too complicated like Ptolemaic epicycles theory of planet motions to explain their observed peculiarity on the basis of the earth-centered cosmological view.

In the summer of 1998, I discussed this problem with my former colleague Shuichi Okuda over beer, and we decided to submit a paper to the same journal, in spite of a little reluctance of publishing the definitive solution to the good teaser. After some fighting with one of the reviewers and the editor and rewriting twice for improved clarity, we got our paper finally published (it is entitled "Mirror reversal simply explained without recourse to psychology,"5) together with Michael Corballis' similar paper.6 I heard from Takano that he was not persuaded by Corballis' and our papers and was going to publish another paper on the same problem.

  1. S. Tomonaga, "Kagaminonaka no Sekai (The World in the Mirror)" (Misuzu-Shobo, Tokyo, 1965) (in Japanese).
  2. J. Gleick, "Genius: The Life and Science of Richard Feynman" (Little Brown, London, 1992).
  3. R. Gregory, "Mirrors in Mind" (W. H. Freeman, New York, 1996).
  4. Y. Takano, Psychonomic Bulletin & Review, Vol. 5 , No. 1, 37 (1998).
  5. T. Tabata and S. Okuda, Psychonomic Bulletin & Review, Vol. 7, No. 1, pp. 170-173 (2000). Read Abstract
  6. M. C. Corballis, ibid., pp. 163-169 (2000).

14 Mar 2000

Related reading added later

Go to “What Do I Care What Mr. Feynman Thinks?”

24. The Japanese Concept of Education

Some months ago the journal "Tosho," published by Iwanami-shoten, started to carry a column for questions and answers about the Japanese language. Answers are provided by the researcher of the Japanese language Susumu Ono, who recently wrote a best-selling book, "Nihongo-renshu-cho (An Exercise Book of Japanese)."

The above column in the May issue treats the origin of the words "manabi" and "gakushu," both of which mean studying. Ono analyzes the construction of the two Chinese characters that in combination express "gakushu," and infers that the original meaning of this word is "repeated interactions of a teacher and children." Thus he finds that the Chinese concept of study includes the activeness on the side of those being taught.

Ono next analyzes the Chinese characters for "kyoiku (education)," and again finds the meaning of "interactions with children" in the character "kyo." However, he does not see a similar meaning in the proper Japanese word "oshihe" that corresponds to the Chinese character "kyo." He writes that the dictionary of the Heian Period (around the 9th century) "Ruiju-myogisho" includes 37 Chinese characters that can be read "oshihu (the verb form of oshihe)" and that most of them mean one-sided action to the other party. He insists that this is an evidence of the old origin of the meaning of "striking into the head," which is included in the present Japanese word "oshieru (teach)."

Ono concludes that the method of education in the style of striking into the head cannot make the most of individual characters and that Japan would fall behind other countries if the Japanese do not aware of this. I completely agree with him.

4 May 2000

25. Dreadful Crimes by Boys in the Technological Age

In the beginning of May 2000 two dreadful crimes by 17-year-old boys happened in Japan. One boy in Aichi Prefecture killed a woman with a kitchen knife in the evening of May 1. The other boy from Saga City hijacked a highway bus destined to Fukuoka to drive it to Hiroshima on May 3 and injured a woman among about 20 passengers to death. Is there any common cause in the cruel deed by young people of these days? Is "environmental hormones" or the deterioration of education responsible to these crimes?

I happened to read the following remark by Rupert Sheldrake, a leading thinker of New Age movement1:

Our societies are evolving with the dissolution of the old social structures, hurtling into the future in directions that nobody can foresee. The dissolution of traditional morality and traditional social and family patterns is happening far faster than I think anyone imagined in the past, and in the future will lead to a kind of society that no one can really envisage.

The remark was made in reply to Wim Kayzer's question about the importance of the cultural evolution that had been caused by the awakening of human consciousness about ten thousand years ago. However, the dissolution of traditional things seems quite rapid during these ten years or so. Is the acceleration of such dissolution not related to the too speedy spread of the application of various technologies into our life?

  1. W. Kayzer, "'A Glorious Accident': Understanding Our Place in the Cosmic Puzzle" (W. H. Freeman, New York, 1997).

11 May 2000


26. An Example of the Effect of Bad Education

The following news was recently reported by media world over:

On 15 May 2000, Japanese Prime Minister Yoshiro Mori said that Japan is a divine land with the Emperor at its center and that the indigenous Shinto religion should help society flourish. These remarks were made in a talk at a meeting of lawmakers and Shinto religious leaders in Tokyo to mark the 30th anniversary of the Shinto Political Federation. The comments risked stirring controversy in Asia, where many people have bitter memories of Japan's World War II military aggression carried out in the name of the Emperor (adapted from an article in "Asia Now" of CNN).

The thought that Japan is a divine nation centering on the Emperor was taught at school to all the Japanese children until the end of World War II. Under Japan's constitution, however, most of the Japanese have learned that such a thought was quite wrong. Thus, commenting on this news, Peter McKillop writes correctly,1 "Most Japanese do not believe the Emperor is God. Most do not practice Shinto. Most are genuinely remorseful about Japan's wartime past -- that is, if they can remember it." Then, why the idea of divine land did remain in the Prime Minister's mind?

McKillop points out: The problem is that a small group of well-organized, well-funded conservative pro-Shinto organizations have had a disproportionate influence on Japanese politics for too long.

Then what did make this disproportionate influence spread? It would be that many Japanese people were not keen enough to notice this influence hidden behind LDP politicians in voting for them. And what did make such pro-Shinto organizations survive after the war? Isn't it the effect of long-lasted bad education? Prime Minister Mori, now at the age of 62, must have been in the second year class of primary school when Japan was defeated. Therefore, he must have learned the divine-land idea for nearly one and a half years at the ages when his emotion was most sensitive, never to become able to get out from the anachronistic principle. A poor fellow!

  1. P. McKillop, "Letter from Japan: Hail Emperor -- We're sorry, we really are," Time Magazine Online, Asia Now Page, 19 May 2000

20 May 2000

Related reading added later
"Japan's Two Nationalisms," Washington Post, June 4, p. B06 (2000).

27. The Crisis of Basic Sciences

A graduate student of a technological university in India, who happened to become an e-mail friend of mine, recently wrote me the following: He and his colleagues were suddenly obliged to live outside the campus. The reason is that the Vice Chancellor of the university decided not to provide the research scientists with the hostel facility but to encourage only engineers. The aim and merit of this decision are incomprehensible. Even in a technological university, the co-operation of scientists with engineers would be important for the development and education of new technologies.

A similar and more serious crisis of basic sciences is anticipated in our country. The Japanese Government is preparing for the transformation of all the national universities into independently managed agencies. This would drive them to give priority to economic efficiency and marketable research, thus causing the deterioration of basic research.

Further, such a plan of the Japanese Government is dramatically opposed to the declaration of the recent UNESCO's documents, "Recommendation on the status of teachers in higher education" and "World declaration on higher education for the 21st century." These documents state that education is the base for achieving human rights, democracy, sustainable development and peace and that all the governments are basically responsible for it. 1

In the above two cases related to the possible crisis of basic sciences, the planners seem to lack long-range insight, which is indispensable for the real development of technologies. This reminds me of Robert Wilson's excellent words. Being asked by a Senator about the role of the Fermilab accelerator for the security of the country, Wilson said, "Only from a long-range point of view, of a developing technology.  . . . it has nothing to do with defending our country, except to make it worth defending."2

  1. S. Yuasa, "We Reject the Plan of Transforming National University into Independently Managed Agency," The Bulletin of JSA, No. 73 (1999).
  2. B. McDaniel and A. Silverman, "Robert Rathbun Wilson," Physics Today Vol. 53, No. 4, pp. 82-83 (2000) (An obituary); Correction, ibid. No. 5, p.83 (2000).

12 Jun 2000

28. The Fortunes of the Woman in a Pi Mnemonic

David Blatner's little book1 tells you cheerfully about the history and snippets of the number pi, the ratio of a circle's circumference to its diameter. In the section "Memorizing Pi" the author gives mnemonic devices in different languages. One in Japanese is: "3.14 strawberry country . . ." Strawberry country is "ichigo kuni" in Japanese and can be associated with the numbers 1-5-9-2, which are just pronounced in Japanese as ichi-go-ku-ni.

In my primary school days I learned from a children's magazine a better mnemonic: "San-ishi (314) ikokuni (1592) muko (65). Sango (35) yakunaku (8979) sampu (32) . . ." These Japanese words mean: "An obstetrician goes to a foreign country. After childbirth, medicine was unavailable and a woman in childbed . . ." I had not memorized the rest of the mnemonic. So I did not know what happened to the poor woman.

The numbers that follow the last digit given above are: 38462643383279. Aside from "46264," these numbers made me guess the following: "The woman, at the night of childbirth,  . . . heavily cries in the darkness." A sad story.

I wished to know the continuation of the above mnemonic, and tried a search on the Internet to find an excellent site.2 The site gives different mnemonics in Japanese along with much information on pi. A version of "San-ishi . . ." treats the digits down to 1000th!

I learned that my memory about "yakunaku" was wrong or of a different version not given there. In addition to medicine, "yaku" also has the meaning of "misfortune" in the old usage of the word. Thus the story continues as follows: "After childbirth, without misfortune a woman in the state of maternity (rests) in a shrine. At the time when insects chirp hotly in the darkness . . ." The woman was well and did not cry. I was relieved to know this.

  1. D. Blatner, "The Joy of Pi" (Viking, Canada, 1997). The web site of the same name as the book is available.
  2. The Page of Pi (in Japanese).

18 Jun 2000

(A modified version of this essay is posted as tttabata's review of "The Joy of Pi" on the bying-info page of this book at

29. Readers Don't Be Fooled! Again on Mirror Images

The distinguished theoretical physicist at Rutherford Appleton Laboratory and science writer Frank Close recently published a book.1 Reading the earliest pages of the book, I was quite worried about his statements concerning the question "Why do mirrors reverse left and right but not top and bottom?" The author first refers to the above question on page 16 as "an old canard" and writes: "This question is actually a fraud, inviting an answer under the implicit, and illegal, assumption that the question refers to a real event."

Surely, the world in the mirror is not the real world, but comparing your mirror image with yourself to find left-right reversal is a real event to be explained more educationally. Especially this would be necessary because the author talks about mirror asymmetric left-handed and right-handed molecules in a later chapter. Both L-tartaric and D-tartaric acids that are mirror images of one another are the real things that have the relation similar to the one between you and your image in a mirror. He also writes, "Our DNA is right-handed. In a mirror, all the component parts would be reversed and the mirror DNA be left-handed." Does't he here refer to the mirror reversal of left and right? He might reply, "Handedness and the left-right direction are different things." However, the reversal of the asymmetric property in the left-right direction just leads to the change of the handedness.

Under the section title "Why do mirrors reverse left and right but not top and bottom?" that appears on page 51, Close writes, "The short answer is: they don't!" He adds on the next page, "So what do mirrors do? The answer is that they interchange front and back: the axis perpendicular to the mirror reverses." This answer is correct so far as one speaks only from the viewpoint of the frame fixed to the person facing a mirror. The author is overlooking the following fact. The asymmetric feature in the left-right direction are always reversed in the mirror image's frame as compared with that in the real object's frame, namely the left-right reversal occurs in the object-centered view with "object" implying both the real object and its mirror image.

He gives an example of a fancy dress party. "The condition for admission will be that every one comes as a harlequin where the right half of their costume is red and the left, lilac. Everyone in the room will be an RR (red right), LL (left lilac). Now you look in the mirror. What you will see is a gatecrasher, someone who does not existed at the party: an LR, RL (lilac right, red left) harlequin. The mirror no longer reflects left and right!" What he wants to explain by this is not clear. Does the author wish to make the reader think that the left-right reversal of RR-LL should be LL-RR (in fact it is the same thing as RR-LL), by the poor magic of using the colors whose names just begin with R and L? Contrary to the author's wish, the conclusion the reader thinks of is: "The mirror no longer respects the condition for admission: left and right are reversed in the mirror world!" Close should study the peer-reviewed papers on this problem published recently.2,3

  1. F. Close, "Lucifer's Legacy: The Meaning of Asymmetry" (Oxford University Press, Oxford, 2000).
  2. M. C. Corballis, Psychonomic Bulletin & Review Vol. 7, No. 1, pp. 163-169 (2000).
  3. T. Tabata and S. Okuda, ibid., pp. 170-173 (2000). Read Abstract

12 Jul 2000, modified 26, Aug 00

(A modified version of this essay is posted as tttabata's review of "Lucifer's Legacy" on the bying-info page of this book at

30. Mathematics and Nature

We read in a number of books that the physicist Eugene Wigner puzzled over why mathematics was so effective to describe the natural world.1 In an essay entitled "Why is the universe mathematical?" John Barrow, Professor of Astronomy and Director of the Astronomy Center at the University of Sussex, discusses about this problem.2 He first mentions that the sorts of answers depend upon what we think mathematics, giving four options: formalism, inventionism, constructivism and realism. Then he puts a puzzle for the future to decide which is more fundamental in the laws of Nature, symmetry or computation; in other words, a pattern or a program.

In the final paragraphs, Barrow states that the science is the search for algorithmic compressions of the world of experience, and comes to the conclusion that mathematics is useful in the description of the physical world because the world is algorithmically compressible. I have difficulty in finding how the earlier paragraphs are related to the last ones. However, the conclusion seems to be very simple, and would be paraphrased as follows: Mathematics is useful in the description of Nature because she has the characters of orderly complexity. Is Wigner in heaven satisfied with this answer?

Note added later:

The following passage by Gordon Kane3 is also relevant to the above problem.

Indeed, it is often remarked that it is "amazing" that our world is comprehensible scientifically. But is that really surprising? Our world must behave according to mathematical regularities if it is to exist for some time. Given that these regularities exist, we can learn what they are.

Here Kane does not directly refer to the effectiveness of mathematics for describing the world. However, if the world has mathematical regularities as he mentions, then the effectiveness of mathematics follows naturally.

  1. For example: G. Johnson, "Strange Beauty: Murray Gell-Mann and the Revolution in Twentieth-Century Physics" (Alfred A. Knopf, New York, 1999). Wigner's original essay is: "The Unreasonable Effectiveness of Mathematics in the Natural sciences," Communications in Pure and Applied Mathematics, Vol. 13, No. 1 (1960).
  2. J. D. Barrow, Scienza e Technica Italia, 1990 Yearbook, pp. 10-15; reprinted in "Between Inner Space and Outer Space" pp. 85-98 (Oxford University Press, Oxford, 1999).
  3. G. Kane, "Supersymmetry: Squarks, Photinos, and the Unvailing of the Ultimate Laws of Nature" (Perseus Publishing, Cambridge, Massachusetts, 2000).

26 Jul 2000; note, 19 Sep 2000

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