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Carroll's Paradox

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April 09, 2003, 19:59
Morgan
Carroll's Paradox
A friend brought this to my attention. It appears to be a very interesting article about Lewis Carroll. I can't remember who was the Carroll fan, so I thought I would post it here for all to enjoy.
April 09, 2003, 20:08
Kalleh
Morgan, that was great! Big Grin BTW, our Carrollian is Bob.
April 09, 2003, 22:33
<Asa Lovejoy>
The site reminded me of one of the passages from the book, Boners, which is as follows: The Stoics were followers of Zero, and believed in nothing.
April 10, 2003, 01:47
BobHale
If you enjoyed that you should try Alice In Puzzle-Land by Raymond Smullyan. This is a book of logic puzzles written in the form of an Alice sequel.

I read the book but I have to confess that by the end the puzzles were getting so convoluted that I stopped trying to work them out and skipped to the answers.

It's fun all the same though by now it may well be out of print.

Vescere bracis meis.

Read all about my travels around the world here.
Read even more of my travel writing and poems on my weblog.
April 10, 2003, 07:54
Duncan Howell
Thanks, Morgan, for bringing that Carroll link to our attention. I can't say I followed the reasoning....which illustrates why Carroll was a mathematician and I'm not. However, I think I can add a note of interest..

Early on in the dialogue between Achilles and Tortoise, the two seem to have been engaged in a foot race. They speak, vaguely, of diminishing distances. Carroll, here, was alluding to an old, old, mathematical conundrum:

Tortoise challenged Achilles to a foot race, on the condition that Tortoise be allowed a short headstart.

Achilles agreed, and let Tortoise go ahead.

When Achilles started to run, he quickly got to the place where Tortoise had been when he (Achilles) started.

However, Tortoise, not having stopped, had in the meanwhile gone on another short distance.

No matter. Achilles, not having stopped either, quickly arrived at that spot, only to find that Tortoise had moved on again.

...You can see where this is going. Achilles never caught up with Tortoise, who was always ahead, no matter by how infinitesimal a distance. (This explains the "diminishing distances" Carroll referred to.) Ancient logic could not solve this puzzle. It hung around until Newton came up with Calculus. Carroll allowed that Achilles eventually caught Tortoise, in keeping with the mixed-up timelines he interspersed through the whole story. Smile Cool
April 22, 2003, 11:10
Kalleh
Perhaps this post belongs elsewhere, but since it's about Carroll, I am putting it here.

I was reading a fabulous word book today, "Predicting New Words (~Allan Metcalf, 2002), where he writes that according to OED "pretend" used to only mean "making a false claim." It wasn't until "Through the Looking Glass" with the discussion of "Kitty Dear, Let's pretend...." that it was first used to mean "make believe" or "feign in play."
April 22, 2003, 19:30
wordnerd
That "Achilles and the Tortoise" paradox is called Zeno's Paradox, after the ancient Greek philospher who first posed the stumper. I assume it's not the same Zeno who Asa mentioned in connection with the Stoics, but I'm too lazy to check that at the moment.
April 27, 2003, 14:34
Duncan Howell
quote:
Originally posted by Kalleh:
I was reading a fabulous word book today, "Predicting New Words (~Allan Metcalf, 2002), where he writes that according to OED "pretend" used to only mean "making a false claim."


It's so easy to pick up new ideas or to clarify old misconceptions on this board! Now I understand what the "Young Pretender" (Bonnie Prince Charlie) and the "Old Pretender" (his Dad) were about. They were pretending, or making false claims to the British throne. Of course, "false", as used here, is purely subjective, is it not?
May 08, 2003, 08:55
Kalleh
Hmm, interesting perspective, Duncan. I am interested in the opinion of our Brits on this one.
May 12, 2003, 10:20
pauld
Duncan is correct in every respect. Smile
May 12, 2003, 10:21
pauld
And I expect you know that the name Wendy did not exist until J M Barrie invented it in Peter Pan?
May 12, 2003, 11:39
Kalleh
No, I didn't. How interesting! I love Peter Pan. When I used to read it to my kids, while they liked the central story, I used to appreciate a lot of the humor. For example, here is one of my favorite parts:

"Peter flung my arm," he said, wincing, "to a crocodile that happened to be passing by."

"I have often," said Smee, "noticed your strange dread of crocodiles."

"Not of crocodiles," Hook corrected him, "but of that one crocodile." He lowered his voice. "It liked my arm so much, Smee, that it has followed me ever since, from sea to sea and from land to land, licking its lips for the rest of me."

"In a way," said Smee, "it's sort of a compliment."

"I want no such compliments," Hook barked petulantly. "I want Peter Pan, who first gave the brute its taste for me."
May 14, 2003, 03:04
pauld
Tick-tock, tick-tock!