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Author Topic: The (complex) Math behind Alice In Wonderland  (Read 3084 times)
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cKleinhuis
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« on: April 02, 2010, 04:49:14 AM »

have you ever thought of the rabitt as "k" from ( quaternion (r,i,j,k)?

http://www.maa.org/devlin/devlin_03_10.html
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jehovajah
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« Reply #1 on: April 02, 2010, 10:14:38 AM »

Thanks for the link Trifox,an interesting article on the emotional effect of these mathematical ideas we take for granted nowadays and the increasing abstraction. In this light i think cyclops could not find a better advocate of his complaint against mathematicians, nor a wittier one. However it is clear that the significance of what a mathematician playfully finds of interest is determined by the cultural needs  s/he is immersed in. Hamilton's quaternions by all accounts are crucial to modern avionics and space flight, a proposition Dodgson could not have envisaged even from the ballistics available to him then. We also would not have  such compact and speedy 3d fractal generators either, and dare i say no einsteinian spacetime metric?
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cKleinhuis
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« Reply #2 on: April 02, 2010, 05:32:46 PM »

this is my favorite part for fractalians:
Quote
Reading this scene with Hamilton's ideas in mind, the members of the Hatter's tea party represent three terms of a quaternion, in which the all-important fourth term, time, is missing. Without Time, we are told, the characters are stuck at the tea table, constantly moving round to find clean cups and saucers.

Their movement around the table is reminiscent of Hamilton's early attempts to calculate motion, which was limited to rotatations in a plane before he added time to the mix. Even when Alice joins the party, she can't stop the Hatter, the Hare and the Dormouse shuffling round the table, because she's not an extra-spatial unit like Time.

The Hatter's nonsensical riddle in this scene - "Why is a raven like a writing desk?" - may more specifically target the theory of pure time. In the realm of pure time, Hamilton claimed, cause and effect are no longer linked, and the madness of the Hatter's unanswerable question may reflect this.

Alice's ensuing attempt to solve the riddle pokes fun at another aspect of quaternions that Dodgson would have found absurd: their multiplication is non-commutative. Alice's answers are equally non-commutative. When the Hare tells her to "say what she means", she replies that she does, "at least I mean what I say - that's the same thing". "Not the same thing a bit!" says the Hatter. "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"

When the scene ends, the Hatter and the Hare are trying to put the Dormouse into the teapot. This could be their route to freedom. If they could only lose him, they could exist independently, as a complex number with two terms. Still mad, according to Dodgson, but free from an endless rotation around the table.

and the complex numbers lived there ever hapilly after cheesy

how would alice be with triplex numbers? funny axis games come to my mind
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Timeroot
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« Reply #3 on: April 02, 2010, 09:13:57 PM »

She trips, and falls into a ditch in the ground. And, oh dear, her head lands at the pole! Now, not only has hey body been disproportionate in several different ways, she also has had non-conformal, non-smooth mappings applies! Oh, poor Alice...
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kram1032
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« Reply #4 on: April 02, 2010, 11:46:33 PM »

nice story, lol. Interesting ideas smiley
So this story actually was created by a desperate mathematician who didn't like the new discoveries? xD
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cKleinhuis
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« Reply #5 on: April 03, 2010, 12:17:35 AM »

i see it more as a good "visualisation" of the theories ... and could even be used in math lessons cheesy
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