Monday, January 27, 2003

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.

Thursday, January 09, 2003

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).