NABOKV-L post 0005895, Fri, 6 Apr 2001 10:49:16 -0700

Subject
Query: Ada and pangeometry
Date
Body
EDITOR's NOTE. Read the following exchange from the bottom up. Some of
Chimene's ideas might be worth pursuing.

-------- Original Message --------
Subject: FW: Query: Ada and pangeometry
Date: Thu, 5 Apr 2001 10:37:07 -0700
From: Jeff.Chimene@etest.com

-

Thank-you for the encouragement. The post was not intended for the list
as I
feel it's incomplete. However, if you believe it will provoke other
research, please post it.

I've always enjoyed Mr. Gardner's writing, even if I didn't understand
all
he was trying to convey. That he knew VN is a charming coincidence in a
bookish life. I look forward to the Gardner and other references you've
been
kind enough to provide.

FWIW, Tom Lehrer wrote a song "about" Lobachevsky, whose lyrics may be
found
at the following
URL:http://wiw.org/~drz/tom.lehrer/revisited-frames.html

Regards,
Jeff Chimene
-----Original Message-----
From: D. Barton Johnson [mailto:chtodel@gte.net]
Sent: Wednesday, March 28, 2001 13:05
To: Jeff.Chimene@etest.com
Subject: Re: Query: Ada and pangeometry


Dear Jeff Chimene,
You have some interesting thoughts on a non-Euclidean ADA. Alas, I
am
woefully ignorant about geometry. BTW, you might want to
take a look at J. W. Dunne's _An EXPERMENT WITH TIME_ that VN was
reading
during the composition of ADA. Also, Martin Gardner's _AMBIDEXTROUS
UNIVERSE_ (last edition). I have written about the Gardner/VN nexus and
also, at length, about the Scrabble game which is based upon
multilingual variations of "clitoris." Both the Gardner & Scrabble stuff
may be found in my book _Worlds in Regression_.

Best, Don Johnson


Jeff.Chimene@etest.com wrote:

> Hello:
>

> This is my first reading of Ada; it has taken me years to prepare for it,
> and I'm in no hurry to finish.
>
> I don't have the book in front of me, so some of these points may be
spelled or referenced incorrectly.
>
> The question was prompted by a few observations:
>
> Euclid's fifth postulate (from www.aleph0.com):
> "That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight
lines, if produced indefinitely, meet on that side on which are the
angles less than the two right angles"
>
> The Euclidian game "Flavita/Alfavit/Scrabble" is an example of this
> postulate in Ada.
>
> >From http://www2.ispa.fsu.edu/~lcrosswe/paper/paper.html The diagram
> referenced below can be found on that page. Observe the name of the "main
> line" of the diagram.
>
> "Lobachevsky presented the more complete account of this new geometry in
his book. He prefaced his work with the conclusion that "in geometry I
find
certain imperfections which I hold to be the reason why this science,
apart from tradition into analytics, can as yet make no advance from
that state
in which it has come to us from Euclid" (Lobachevski 1914). He first
said
that "all straight lines which in a plane go out from a point can, with
reference to a given straight line in the same plane, be divided into
two classes - into cutting and non-cutting. The boundary lines of the
one and the other class of those lines will be called parallel to the
given line"
(Lobachevsky 1914). The diagram above is from Lobachevsky' work. This
diagram helps to explain the classes that Lobachevsky sorted his
figures into. However, it may not quite yet be clear what these
assumptions have to do with the
development of a new geometric system. This issue will be addressed
shortly.
>
> Lobachevsky showed that if the angle of intersection between AE and AH
(boundary line) was 0° , then Euclidean geometry holds. However, if the
angle of intersection is less that a right angle, but greater then 0,
then
a new geometry is found to exist. Lobachevsky, in his memoir On the
principles of geometry, writes, "This (angle) sum is = p or < p . Both
can be assumed without any subsequent contradiction, and this gives
rise to two
Geometries: one, in common use to this day owing to its simplicity,
actually agrees with all measurements; the other, an imaginary one,
more general and therefore more difficult in its calculations, admits
the possibility of dependence of lines on angles" (Rosenfeld 1988)."
>
I think this is an interesting viewpoint for the Terra/Anti-Terra
relationship. Eric Veen's imaginary train trip (a parody of the Scrabble
game) is an example of a non-Euclidean diagram made possible by
Lobachevsky.
I think it's important that the Lobachevsky theme doesn't emerge until
Part Two; One is Euclidean, Two is non-Euclidean.

I don't fully understand the Terra/Anti-Terra relationship, but I'm
enjoying the theme's gradual unfolding.
>
> -----Original Message-----
> From: D. Barton Johnson [mailto:chtodel@gte.net]
> Sent: Thursday, March 22, 2001 17:43
> To: vn; Jeff.Chimene@etest.com
> Subject: Query: Ada and pangeometry
>
> SEE EDITOR's NOTE below.
>
> From: "Chimene, Jeff" <Jeff.Chimene@etest.com>
> To: "'Vladimir Nabokov Forum'" <NABOKV-L@LISTSERV.UCSB.EDU>
>
> ----------------- Message requiring your approval (11 lines)
> ------------------
> Hi:
>
> I don't have ready access to the Nabokovian, so perhaps Boyd has already
> explored this topic:

> Has anyone explored the theme of Euclidean vs. non-Euclidean geometries
> in Ada? I think there are interesting references to Lobacevskii and Euclid,
> but I'm having some trouble teasing them from the text.
>
> Regards,
> Jeff Chiimene
> ------------------------
>
> EDITOR's NOTE. I don't recall any specific references to Euclid in VN
> criticism although the non-Euclidean Lobachevsky does seem faintly
> familiar from the novels. The idea of Euclidean /Non-Euclidean worlds
> would seem to be analogic to Terra/Anti-Terra. Certainly worth
> exploring. Several scholars, including Vladimir Alexandrov and myself
> have toyed with VN's familiarity with various turn of the century
> thought systems such as Blavatsky's and others. I discuss some of this
> in _Worlds in Regression: Some Novels of Vladimir Nabokov_ in one of the
> chapters on LATH. My comments were triggered by the exchanges between
> Nabokov and Martin Gardner and his _Ambidextrous Universe_.