0148400001395404836 the dwarf by Unknown

Author:Unknown
Language: eng
Format: mobi
Published: 2014-03-21T12:27:04.247000+00:00

The Klein Bottle 175

ered her eyes with the vice-steward’s handkerchief as well. “I thought of God’s grace.” Yo˘ng-i relayed these whispered words of Yo˘ng-hu˘i to me. I hoped that Yo˘ng-hu˘i’s god was the warmest possible god for her.

The greatest gift that Yo˘ng-hu˘i received from her god was that very benevolence. The day Chi-so˘p left, though, Yo˘ng-hu˘i was working her shift and unable to see him off. It was the same with Yo˘ng-ho and me.

Mother had prepared to leave for the lumberyard, and she stood in the dirty alley waving in response to Chi-so˘p’s farewell. Yo˘ng-i and the union’s general-affairs director saw him off at the station. The minister, the man of science, and the stewards of several other union locals turned out, Yo˘ng-i told me. I wondered what influence Chi-so˘p’s abrupt visit might have on me in the future. We had wasted too much time trying to figure out what was right, he said.

After

Chi-so˘p had come and gone, the first person to read the next

change in me was the man of science. “If you think about it, the minister and I are not in line,” he said. “I’m not standing at the head of the line, either,” I said. “I’m not worthy of it.” “But it’s your line. How can I stand outside the line and shout for you?” In his room at the workshop he showed me a bottle I could not make sense of at first. I call it a bottle, but it was not the usual type of bottle with an inside and a closed-in space. It was a peculiar bottle formed by making a hole in the wall of a tube and passing one end of the tube through that hole. The man of science called it a Klein bottle. Figure 3 is that very bottle. The man of science had made such a bottle from a glass tube like the one in Figure 1. After flaring one end of the cylinder and tapering the other end, as in Figure 2, he made a hole in the wall and finished up as in Figure 3.

02 Cho text ppF 92-220.indd 175

02 Cho text ppF 92 220 indd 175

7/5/06 6:04:46 PM

7/5/06 6:04:46 PM

176 Cho Se-hu

˘ i

Paper has two surfaces, inner and outer, but scholars have done re-

search on “one-surface paper,” “closed space,” and other things without insides and outsides—queer things that common sense would not

lead you to think of. And according to the man of science, this peculiar bottle was described in a research paper by a German mathematician, Felix Klein, that was based on purely abstract theoretical research. The man of science had me wondering. “This is the Klein bottle. No inside or outside, and it has a closed space,” he said. I looked intently at the bottle shown in Figure 3. It was simple in appearance and simple to explain, but I had no idea what he was talking about. I believed that since I hadn’t received a normal school education, I couldn’t understand a problem that was based on the most fundamental ideas.

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