Philosophy
“You have seen the puzzle of the Paper Ring?” Mein Herr said, addressing the Earl.
“Where you take a slip of paper, and join its ends together, first twisting one, so as to join the upper corner of one end to the lower corner of the other?”
“I saw one made, only yesterday,” the Earl replied.
“Muriel, my child, were you not making one, to amuse the children you had to tea?” “Yes, I know that Puzzle,” said Lady Muriel.
“The Ring has only one surface, and only one edge, It’s very mysterious!”
“The bag is just like that, isn’t it?” I suggested.
“Is not the outer surface of one side of it continuous with the inner surface of the other side?” “So it is!” she exclaimed.
“Only it isn’t a bag, just yet. How shall we fill up this opening, Mein Herr?”
“Thus!” said the old man impressively, taking the bag from her, and rising to his feet in the excitement of the explanation.
“The edge of the opening consists of four handkerchief edges, and you can trace it continuously, round and round the opening: down the right edge of one handkerchief, up the left edge of the other, and then down the left edge of the one, and up the right edge of the other!”
“So you can!” Lady Muriel murmured thoughtfully, leaning her head on her hand, and earnestly watching the old man.
“And that proves it to be only one opening!”
She looked so strangely like a child, puzzling over a difficult lesson, and Mein Herr had become, for the moment, so strangely like the old Professor, that I felt utterly bewildered: the “eerie” feeling was on me in its full force, and I felt almost impelled to say “Do you understand it, Sylvie?”
However I checked myself by a great effort, and let the dream (if indeed it was a dream) go on to its end.
“Now, this third handkerchief”, Mein Herr proceeded “has also four edges, which you can trace continuously round and round: all you need do is to join its four edges to the four edges of the opening. The Purse is then complete, and its outer surface--”
“I see!” Lady Muriel eagerly interrupted.
“Its outer surface will be continuous with its inner surface! But it will take time. I’ll sew it up after tea.” She laid aside the bag, and resumed her cup of tea. “But why do you call it Fortunatus’s Purse, Mein Herr?”
The dear old man beamed upon her, with a jolly smile, looking more exactly like the Professor than ever.
“Don’t you see, my child--I should say Miladi? Whatever is inside that Purse, is outside it; and whatever is outside it, is inside it. So you have all the wealth of the world in that leetle Purse!”
Klein Bottle
Möbius Strip
Lewis Carroll:
Sylvie and Bruno
Sylvie and Bruno Concluded
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Philosophy
Mr. Klein and Mr. Möbius
Sylvie and Bruno Concluded
1893
by
Lewis Carroll
Chapter VII
"Mein Herr"
1893
by
Lewis Carroll
Chapter VII
"Mein Herr"
“You have seen the puzzle of the Paper Ring?” Mein Herr said, addressing the Earl.
“Where you take a slip of paper, and join its ends together, first twisting one, so as to join the upper corner of one end to the lower corner of the other?”
“I saw one made, only yesterday,” the Earl replied.
“Muriel, my child, were you not making one, to amuse the children you had to tea?” “Yes, I know that Puzzle,” said Lady Muriel.
“The Ring has only one surface, and only one edge, It’s very mysterious!”
“The bag is just like that, isn’t it?” I suggested.
“Is not the outer surface of one side of it continuous with the inner surface of the other side?” “So it is!” she exclaimed.
“Only it isn’t a bag, just yet. How shall we fill up this opening, Mein Herr?”
“Thus!” said the old man impressively, taking the bag from her, and rising to his feet in the excitement of the explanation.
“The edge of the opening consists of four handkerchief edges, and you can trace it continuously, round and round the opening: down the right edge of one handkerchief, up the left edge of the other, and then down the left edge of the one, and up the right edge of the other!”
“So you can!” Lady Muriel murmured thoughtfully, leaning her head on her hand, and earnestly watching the old man.
“And that proves it to be only one opening!”
She looked so strangely like a child, puzzling over a difficult lesson, and Mein Herr had become, for the moment, so strangely like the old Professor, that I felt utterly bewildered: the “eerie” feeling was on me in its full force, and I felt almost impelled to say “Do you understand it, Sylvie?”
However I checked myself by a great effort, and let the dream (if indeed it was a dream) go on to its end.
“Now, this third handkerchief”, Mein Herr proceeded “has also four edges, which you can trace continuously round and round: all you need do is to join its four edges to the four edges of the opening. The Purse is then complete, and its outer surface--”
“I see!” Lady Muriel eagerly interrupted.
“Its outer surface will be continuous with its inner surface! But it will take time. I’ll sew it up after tea.” She laid aside the bag, and resumed her cup of tea. “But why do you call it Fortunatus’s Purse, Mein Herr?”
The dear old man beamed upon her, with a jolly smile, looking more exactly like the Professor than ever.
“Don’t you see, my child--I should say Miladi? Whatever is inside that Purse, is outside it; and whatever is outside it, is inside it. So you have all the wealth of the world in that leetle Purse!”
Klein Bottle
The above is the only literary reference I know describing one of two famous and curious topological oddities...the "Klein Bottle". The other item is the "Möbius Strip".
Möbius StripLewis Carroll:
Sylvie and Bruno
Sylvie and Bruno Concluded
- One's Private Reading Room Reveals A. Hitler's "mein Kampf" Is #1
Roll over Dickens and Asimov. What is next...quotations from Chairman Mao Tse-tung's Little Red Book or Karl Marx's Das Kapital? "Mein Kampf becomes an ebook bestseller" Digital editions of Adolf Hitler's fascist screed, in less public format,...
- "mein Kampf"...a Best Seller?
This is a curious news story. Book sellers will market what they think will sell. After all, the end product is revenue. This controversy is mute. Perhaps Muslims are horribly offended by lavish displayed bible marketing or by mass marketing techniques...
- Mimas--pac-man
A slow science day? "1980s Video Icon Glows On Saturn Moon" March 30th, 2010 SATURN DAILY The highest-resolution-yet temperature map and images of Saturn's icy moon Mimas obtained by NASA's Cassini spacecraft reveal surprising patterns on...
- Saturn Loses Rings On Christmas Morning--naw
A Christmas treat via compliments of Saturn. So get up before sunrise and with the aid of a telescope [which might be under the tree] view a Saturn with nearly no rings. And, at that early hour, you might meet "the man". "Saturn's Crazy Christmas...
- Newton's Rings
Long before sitting at the computer and manipulating images, the realm of the darkroom ruled and when making prints via contact of glass plate negative with sensitized paper using a contact print frame this issue may occur. The phenomenon will also occur...