29 August 2008
Deviousness and No. 42
A kind reader of this blog has located a copy of Disney's Jabberwocky for me to buy. It costs 1 cent in USA and over ?17 in the UK - about $34. So what's the moral of that?
I wanted to write a bit more about secret jokes and mathematical curiosities in Carroll. There's a bit where Alice does some crazy multiplying: "four times five is twelve and four times six is thirteen and four times seven is - oh dear! I shall never get to twenty at that rate!"
Carroll's counting each calculation on a different base here (and mischievously using different bases on each side of each equation). So 4 x 5 equals 12 on base 18, 4 x 6 = 13 on base 21, and so on. It goes all the way up to 4 x 12 = 19 (on base 39). And sure enough, Alice never CAN get to twenty by continuing this way. Because 4 x 13 = 20 does not work on base 42.
....which leads onto the mysterious number of 42. The number 42 seemed to have a special significance for Carroll. It appears throughout his works, often in heavy disguise. Some people who are mathematically inclined like to track down the 42's. Carroll's puzzles and acrostics show the same devious intellect at work. Here's one of his Puzzles from Wonderland - very easy and aimed at children, apparently. The answer will be on my Links page (see menu) although it may not appear immediately.
"A stick I found that weighed two pound
I sawed it up one day
In pieces eight of equal weight
How much did each piece weigh?
(Everybody says "A quarter of a pound" which is wrong)
I wanted to write a bit more about secret jokes and mathematical curiosities in Carroll. There's a bit where Alice does some crazy multiplying: "four times five is twelve and four times six is thirteen and four times seven is - oh dear! I shall never get to twenty at that rate!"
Carroll's counting each calculation on a different base here (and mischievously using different bases on each side of each equation). So 4 x 5 equals 12 on base 18, 4 x 6 = 13 on base 21, and so on. It goes all the way up to 4 x 12 = 19 (on base 39). And sure enough, Alice never CAN get to twenty by continuing this way. Because 4 x 13 = 20 does not work on base 42.
....which leads onto the mysterious number of 42. The number 42 seemed to have a special significance for Carroll. It appears throughout his works, often in heavy disguise. Some people who are mathematically inclined like to track down the 42's. Carroll's puzzles and acrostics show the same devious intellect at work. Here's one of his Puzzles from Wonderland - very easy and aimed at children, apparently. The answer will be on my Links page (see menu) although it may not appear immediately.
"A stick I found that weighed two pound
I sawed it up one day
In pieces eight of equal weight
How much did each piece weigh?
(Everybody says "A quarter of a pound" which is wrong)
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that line in particular is one of my faves along with the funny yet clever line of the "lessons" that "lessens from day to day" by Mock turtle and Gryphon.
yah very true what you said about the multiplication... also a more simple explanation is cause the multiplication table traditionally ends with 12, so if you follow the secuence she will never get to 20... 4x12=19 the highest she can go.
and regarding the Mock turtle line, LC might be refering to negative numbers. when Alice said "How did you manage on the twelve" the gryphon interrupted by not answering the question cause he was "lost" by the introduction of negative numbers, that in this case falls when it reach 12. i mean... the "ten hours the first day", "nine the next" and so on, then the # 12 is a negative...
early mathematicians have problems with this numbers... so maybe LC point this out.
some other math curiosities, but more advanced, that i have read and found is the reference to the concept of Limit in chapter 1 "Down the Rabbit-Hole" when Alice ponder what size she will end up, as "going out altogether, like a candle." the substitution of variables in ch.5 when the Pigeon said that little girls are some kind of serpent, for both little girls and serpents eat eggs.
also inverse relation can be found in the mad tea party... "Why, you might just as well say that I see what I eat is the same thing as I eat what I see".
in TTLG logic and semantics can be found in the song " a sitting on a gate" by the White knight.
42. this # is very recurrent in L.C. works... one aspect that i remembered is that this # in the Kabbalah, mystical tradition of Judaism, refers to the Name of God which unites the conflicting aspects of the Divinity which preoccupied L.C.
In TTLG Alice was 7 years 6 month old... so 7 x 6 = 42.
other interesting views of this can be found here http://groups.yahoo.com/gro...
All this are controversial since we don't know in fact what he had on mind when writing the stories... but he been a mathematician/logician/intelectual then possibilities are high.