Is Alice in Wonderland really about drugs?

[Phillip Grayson]

That was cool, thanks!

On Thu, Aug 23, 2012 at 3:15 PM, Bekah <bekah0176 at sbcglobal.net> wrote:

> From Alice in Wonderland
>
> Number theory:
> Chapter 2    "Let me see: 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!"
>
> ME:  There are two ways to think about this.  First she quite simply won't
> get to 20 because generally the multiplication tables end at 12 x ?  - at
> least in elementary school!
>
> But second (and more interesting),  if 4x5 does in fact equal 12 then she
> has to be using a base 18 number system. And if 4x6 does in fact equal 13
> then that base  be 21.  Do we see a pattern?  If yes,  what is 4x7 going to
> be -  answer - 14 from a base of 24.  She'll never get to what we know as
> 20 because continuing that pattern,
> 4x8 = 15 (base 27)
> 4x9 = 16  (base 30)
> 4x10 = 17 (base 33)
> 4x11 = 18 (base 36)
> 4x12 = 19 (base 39)
> 4x13 = 20??? (base 42)     BIG OOPS!   Base 42 cannot have 20 at this
> point  - it has to be a 1(A = 1A)
>
> ************
> Chapter 7
>
> "The Hatter was the first to break the silence. `What day of the month is
> it?' he said, turning to Alice: he had taken his watch out of his pocket,
> and was looking at it uneasily, shaking it every now and then, and holding
> it to his ear.
>
> Alice considered a little, and then said `The fourth.'
>
> `Two days wrong!' sighed the Hatter. `I told you butter wouldn't suit the
> works!' he added looking angrily at the March Hare.
>
> ME:   They're at the center of the earth going on lunar (-tic) "time."
> But those missing hours will be needed later on when they get to the
> endlessly rotating chairs -  they're missing "time."
>
> ********
>
> Quaternions  (like that?)  (g)
>
> http://www.npr.org/templates/story/story.php?storyId=124632317
>
> "One of the big developments that was going on at that time ... was work
> by an Irish mathematician called William Hamilton," Devlin explains.
> Carroll wasn't a fan of Hamilton's work, a new arithmetic called
> quaternions. "Quaternions were numbers — not to deal with counting things,
> but to deal with understanding rotations.
>
> "Back in Victorian times, when Hamilton himself was doing this work, he
> tried to understand his new arithmetic in physical terms," Devlin says. "He
> said one of the four terms that was involved in these numbers had to be
> time. So time was inexplicably, inescapably bound up with these new
> numbers."
>
> Yet it's the Mad Hatter, the March Hare and the Dormouse at the tea party
> — the character Time is absent. (You can read the chapter here if your
> memory needs refreshing.
> http://www.npr.org/templates/story/story.php?storyId=124632317    )
>
> "What Hamilton said was if you take this time parameter out of these new
> numbers, then the numbers would just keep rotating around — they won't go
> anywhere," Devlin says. "It was just like the characters rotating round and
> round the tea party, round and round the table."
>
> "In fact, when the Hatter and the Hare try to squeeze the Dormouse into
> the teapot, they're trying to somehow get away from this complexity — throw
> away another of the parameters, if you like — so that life can resume as
> normal."
>
> Devlin says Carroll's message is that we "get rid of all of this
> complexity in the first place, and let's just go back to the familiar old
> geometry that we've had since Euclid for 2,000 years."
>
> ****
>
> Just as complex numbers work with two terms, quaternions belong to a
> number system based on four terms.   Hamilton spent years working with
> three terms - one for each dimension of space - but could only make them
> rotate in a plane. When he added the fourth, he got the three-dimensional
> rotation he was looking for, but he had trouble conceptualizing what this
> extra term meant. Like most Victorians, he assumed this term had to mean
> something, so in the preface to his Lectures on Quaternions of 1853 he
> added a footnote: "It seemed (and still seems) to me natural to connect
> this extra-spatial unit with the conception of time."
>
> As Bayley points out, the parallels between Hamilton's mathematics and the
> Mad Hatter's tea party are uncanny. Alice is now at a table with three
> strange characters: the Hatter, the March Hare and the Dormouse. The
> character Time, who has fallen out with the Hatter, is absent, and out of
> pique he won't let the Hatter move the clocks past six.
>
>  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.
>
>
> http://www.maa.org/devlin/devlin_03_10.html
>
> http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true
>
>
> That's enough for now -
>
> Bek
>
> On Aug 23, 2012, at 10:08 AM, Joe Allonby wrote:
>
> > First, we have to remind ourselves of what was going on in mathematics
> > in the latter half of the nineteenth century, when Dodgson wrote his
> > story. It was a turbulent period for mathematicians, with the subject
> > rapidly becoming more abstract. The discoveries of non-Euclidean
> > geometries, the development of abstract (symbolic) algebra that was
> > not tied to arithmetic or geometry, and the growing acceptance - or at
> > least use - of "imaginary numbers" were just some of the developments
> > that shook the discipline to its core. By all accounts, Dodgson held a
> > very traditionalist view of mathematics, rooted in the axiomatic
> > approach of Euclid's Elements. (He was not a research mathematician,
> > rather he tutored the subject.) Bayley describes him as a "stubbornly
> > conservative mathematician," who was dismayed by what he saw as the
> > declining standards of rigor. The new material Dodgson added to the
> > Alice story for publication, she says, was a wicked satire on those
> > new developments.
> >
> >
> > http://www.maa.org/devlin/devlin_03_10.html
> > On Tue, Aug 21, 2012 at 4:40 PM, David Morris <fqmorris at gmail.com>
> wrote:
> >> Contemporary social commentary, more likely.
> >>
> >>
> >> On Monday, August 20, 2012, Joe Allonby wrote:
> >>>
> >>> I thought it was about irrational numbers.
> >>>
> >>>
> >>> On Mon, Aug 20, 2012 at 5:08 PM, Dave Monroe <
> against.the.dave at gmail.com>
> >>> wrote:
> >>>> http://www.bbc.co.uk/news/magazine-19254839
>
>
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