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I love Maths, but this one got me. I admit publicly it is beyond me. When I was small my grand mother used to tell me this story: One night as the priest was l

by yannis 17y ago

I love Maths, but this one got me. I admit publicly it is beyond me. When I was small my grand mother used to tell me this story: One night as the priest was lying with his wife, he said, ‘Wife, if you love me, get up and light a candle, that I may write down a verse which has come into my head.’ His wife, getting up, lighted the candle, and brought him pen and inkstand. The priest wrote, and his wife said, ‘O Master of my soul, won’t you read to me what you have written?’ Whereupon he read, ‘Amongst the green leaves methinks I see a black hen go with a red bill’. To this day I have not grasped what she meant with this story. Please can you remove the Layman from the title?

acangiano 17y ago
> To this day I have not grasped what she meant with this story. The story is from a 19th century Turkish book: "The Turkish Jester: Or The Pleasantries Of Cogia Nasr Eddin Effendi" (http://www.gutenberg.org/etext/16244 http://www.gutenberg.org/etext/16244).
- swombat 17y ago
  For many more (and rather better written) Nasredin stories (all of which are highly interesting, entertaining, illuminating, or all three at the same time), see my father's story-blog: http://nasredin.blogspot.com/ http://nasredin.blogspot.com/ Start from the first one: http://nasredin.blogspot.com/2007/10/yes-there-is-nothing-new-in-world-but.html http://nasredin.blogspot.com/2007/10/yes-there-is-nothing-ne...
- pageman 17y ago
  here: http://www.gutenberg.org/files/16244/16244.txt http://www.gutenberg.org/files/16244/16244.txt "One day the Cogia walking along the plain met a heifer, and forthwith laying thievish hands upon it, led it straight to his house, where he slaughtered it and stripped off the skin. The proprietor soon appeared before the Cogia's house, making a loud cry and lamentation. 'Who would have thought,' said the Cogia to his people and his wife, 'that my flaying the heifer would have made that fellow's face look so black?'"
sorbus 17y ago
The entire thing hinges upon the fact that the set is defined to be infinitely dense, and that if you divide infinity by two (or, really, more), you will still have infinity - thus, if it is possible to subdivide a sphere into two sets with the same radius, and the original sphere was infinitely dense, the two resulting spheres will have the same radius, and be infinitely dense - and thus pretty much identicle to the original. The rest is just discussing various other aspects of it, so that their structure is also the same. As for your grand-mother's story, I don't have a clue either - my best guess is that it's something about love not caring about how little sense something makes, but that doesn't entirely make sense.
jerf 17y ago
If you don't get it because you know nothing about set theory, unfortunately, the answer is to learn some about set theory or the notation will just go over your head. If you don't get it because you are trying to visualize what the five pieces would look like, you can stop trying. It's not possible to visualize. Nobody knows what they "look" like, because there is no known algorithm to construct the five pieces. There is merely a proof that they exist, and that they are infinitely complicated little pieces. If you get everything before that, and you get everything after that, you actually get everything. The Axiom of Choice is basically the official mathematician version of "And magic happens here...". (I'm being glib, it's better characterized than that, but there's a large kernel of truth there.) (I'm not "against" the Axiom of Choice, but I think it should always be clear when it is necessary, as I think the division between "proofs that might mean something in the real world" and "not" is a division worth keeping track of, even if mathematicians aren't supposed to care about such mundane matters.)

by yannis 17y ago

acangiano 17y ago

> To this day I have not grasped what she meant with this story. The story is from a 19th century Turkish book: "The Turkish Jester: Or The Pleasantries Of Cogia Nasr Eddin Effendi" (http://www.gutenberg.org/etext/16244 http://www.gutenberg.org/etext/16244).

swombat 17y ago
For many more (and rather better written) Nasredin stories (all of which are highly interesting, entertaining, illuminating, or all three at the same time), see my father's story-blog: http://nasredin.blogspot.com/ http://nasredin.blogspot.com/ Start from the first one: http://nasredin.blogspot.com/2007/10/yes-there-is-nothing-new-in-world-but.html http://nasredin.blogspot.com/2007/10/yes-there-is-nothing-ne...
pageman 17y ago
here: http://www.gutenberg.org/files/16244/16244.txt http://www.gutenberg.org/files/16244/16244.txt "One day the Cogia walking along the plain met a heifer, and forthwith laying thievish hands upon it, led it straight to his house, where he slaughtered it and stripped off the skin. The proprietor soon appeared before the Cogia's house, making a loud cry and lamentation. 'Who would have thought,' said the Cogia to his people and his wife, 'that my flaying the heifer would have made that fellow's face look so black?'"

sorbus 17y ago

The entire thing hinges upon the fact that the set is defined to be infinitely dense, and that if you divide infinity by two (or, really, more), you will still have infinity - thus, if it is possible to subdivide a sphere into two sets with the same radius, and the original sphere was infinitely dense, the two resulting spheres will have the same radius, and be infinitely dense - and thus pretty much identicle to the original. The rest is just discussing various other aspects of it, so that their structure is also the same. As for your grand-mother's story, I don't have a clue either - my best guess is that it's something about love not caring about how little sense something makes, but that doesn't entirely make sense.

jerf 17y ago

If you don't get it because you know nothing about set theory, unfortunately, the answer is to learn some about set theory or the notation will just go over your head. If you don't get it because you are trying to visualize what the five pieces would look like, you can stop trying. It's not possible to visualize. Nobody knows what they "look" like, because there is no known algorithm to construct the five pieces. There is merely a proof that they exist, and that they are infinitely complicated little pieces. If you get everything before that, and you get everything after that, you actually get everything. The Axiom of Choice is basically the official mathematician version of "And magic happens here...". (I'm being glib, it's better characterized than that, but there's a large kernel of truth there.) (I'm not "against" the Axiom of Choice, but I think it should always be clear when it is necessary, as I think the division between "proofs that might mean something in the real world" and "not" is a division worth keeping track of, even if mathematicians aren't supposed to care about such mundane matters.)