Relay Composition

In my childhood I played a word play, "Someone did something with some other one . . ." It needs a plural number of participants. Each participant writes "Someone," "did something," "with some other one," "at some place," and "at some time" on separate sheets of paper by putting concrete expressions for "some . . ." as he or she likes.

Then all the sheets of "Someone" are mixed, all the sheets of "did something" are mixed, and so on. Each participant randomly choose a sheet of "Someone," a sheet of "did something," and so on, and reads them aloud. A set of sheets thus chosen often gives a wild story.

An extended version of the above play is "relay composition." I also played it in student days. In this play, each of several participants reads only one paragraph written just before and adds one paragraph. The story completed can be quite funny.

When I played relay composition during a New Year vacation, a friend of mine with the nickname of Sam wrote a good final paragraph. I still remember its plot after more than 40 years. I do not remember earlier five paragraphs written by participants other than Sam (including my own), but in essence those must have been something like this:

Jack and Betty lived in K City and were good friends. After graduating from a university, Jack got a job at another city. It was far from K City, and Jack had to move there. Betty was going to be lonely.

What do you write after this, if you are requested to conclude the above story? Sam's final paragraph was as follows:

On the day of his removal, Jack got a card from Betty. It read, "I'm going to move, too. My new address is 1-2 S Street, T City." Jack wanted to take a walk to relax from the work of removal. Outside the gate of his new house, he looked back to see the nameplate. It read, "1-2 S Street . . ."

This is so witty a plot just made for a game, isn't it? Regrettably Sam died several years ago.

The Logic of Love

Assume that the statement

A is B.

is true. Then the statement

"Not A" is "not B."

is called the obverse of the original statement. The obverse is not always true. Interchanging the subject and the predicate of the obverse, we get another statement

"Not B" is "not A."

This statement is called the contraposition of the original statement. The contraposition is always true.

I learned the above logic from a young lady teacher of mathematics in the first year of senior high school. So I remember it well. However, you can understand it easily by drawing a small circle enclosed in a large circle and supposing that the inside of the small circle is A and that the inside of the large circle is B.

In the previous story A Mathematician's Desire, I mentioned about a comical essay written by the mathematician Masahiko Fujiwara. I found another short essay [1] of his that treated the obverse to be quite funny. The essay is entitled: Is ' "Not A" is "not B" ' true?

Without using jargons, Professor Fujiwara teaches the reader that the obverse is false in many cases, but can be true in some cases. He does this by the use of interesting examples. Examples of the false obverse are given by the original statements of daily observation, “The tulip is beautiful," "Snow is white," and "What bothers others is what you must not do." An example of the true obverse is given by the mathematical original statement, "If the polygon is the triangle, then the sum of its inner angles is equal to 180 degrees."

Finally the mathematician gives an example of the obverse that can be decided neither true nor false. The original statement of this example is "If the woman is your wife, then you may love her." He writes:

As for the statement, "If the woman is not your wife, then you must not love her," my wife's opinion and mine are different.

I guess that Professor Fujiwara is actually a good husband as well as a good teacher.

1. M. Fujiwara, Asahi-Shimbun, Evening Edition (17 Dec. 2002).

Young Ladies' Conversation

One day in early autumn about 20 years ago, I was on a bus. Then a conversation between two young ladies was heard. One of them said, "I went camping this summer with our group." The other said, "So, you were seen naked by lads, weren't you?" The first lady replied, "Maybe. In the morning a lad pointed his front side and said to me, 'Look at this. This is the proof of my vigor.'" And both of them chuckled.

Having no experience of camping, I do not know why lads can see ladies naked in camping. Anyway, I thought that this was not the kind of talk to be made in the public vehicle. The ladies' voices were however so fresh and innocent that I liked their conversation after all. When autumn comes, I often remind myself of that private talk between the nymphets.

A Mathematician's Desire

In the 15-Aug evening issue of Asahi-shimbun, the mathematician and essayist Masahiko Fujiwara writes a comical essay entitled "Odoriko Motomu (A dancer wanted)". When his mathematical work comes to a difficulty, he goes on a trip as he pleases. During those trips he wishes to meet such a lady as the heroine dancer in the Nobel-Prize winning writer Kawabata Yasunari's novel, "Izu-no-odoriko (The dancer of Izu)". The hero of the novel, a high school student, found the dancer crying without being able to say him "Good-bye".

Prof. Fujiwara writes that the lady whom he wishes to encounter is not necessarily be a dancer but that it is important for her to cry without being able to say "Good-bye." His desire was intensified because his wife got love letters from an English gentleman. However, the desire has never come true, and thus he has lost hope for its realization a little.

Everyman possibly has a similar desire of having a romantic adventure on a trip, but no one can write about it with an excellent sense of humor like Prof. Fujiwara. I am only afraid that as a result of that essay he might get so many letters from ladies who want to be a dancer for him.

I have memories of some young ladies with whom I talked on the train during my trips in younger days. A physics student going to get an exam for the grauate course, an office lady of Hiroshima, a mysterious lady who majored in English literature, . . . I do not think that they remember me. Each one of them and I enjoyed our conversation to some extent, but said simply "Good-bye" to each other when we took off the train.

The Spinning Egg Rises

Scientists theoretically explained the paradoxical behavior of a hard-boiled egg: if it is spun with its axis of symmetry horizontal, this axis will rise from the horizontal to the vertical, raising the center of gravity. -- This is not a joke. See the reference [1]. -- They traced the essential mechanism to the action of the frictional force between the spinning object and the table. Their paper was referred to in a column of a Japanese newspaper [2]. A non-scientist friend of mine read the column, and told me that she wished to experiment. I noticed the original paper before, but did not think to experiment by myself. She had more of a scientist's mind than me.

Being stimulated by her words, I tried to rotate a boiled egg on the floor. It seemed difficult to make the egg rotate fast enough around its axis of symmetry put horizontally to cause rising. Starting from rotation around the axis a little off the vertical, however, I could see the axis rising and becoming just vertical. This is wonderful enough. I heard that the friend had also succeeded in observing the odd motion of the egg. She added that she had been quite thrilled when the axis became vertical.

The scientists also write why a raw egg does not show the same behavior. It is because the angular velocity imparted to the shell diffuses into the fluid interior; this process dissipates most of the initial kinetic energy imparted to the egg, making the remaining energy insufficient for the condition of gyroscopic balance to be established. This is a type of research Torahiko Terada (Japanese physicist, astronomer and essayist. Professor of Tokyo University. 1878 - 1935; see a portrait) would have liked.

1. H. K. Moffatt and Y. Shimomura, "Spinning eggs -- a paradox resolved," Nature Vol. 416, pp. 385-386 (2002).
2. Y. Uchiyama, "Self-rising boiled eggs," Asahi-Shimbun, 22 Apr., p. 23, (2002).