SUO: Re: Transformations Of Discourse
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Foreshadowing Transformations: Extensions & Projections of Discourse
| And, despite the care which she took to look behind her at every moment,
| she failed to see a shadow which followed her like her own shadow, which
| stopped when she stopped, which started again when she did and which made
| no more noise than a well-conducted shadow should.
|
| Gaston Leroux, 'The Phantom of the Opera', [Ler, 126]
Many times in our discussion we have occasion to place one universe of discourse
in the context of a larger universe of discourse. An embedding of the general
type [$X$] -> [$Y$] is implied any time we make use of one alphabet $X$ which
happens to be included in another alphabet $Y$. But when we are discussing
differential issues we usually have in mind that the extended alphabet $Y$
has a special construction or lexical relation with respect to the initial
alphabet $X$, one which is often marked by characteristic types of accents,
indices, or inflected forms.
Extension from 1 to 2 Dimensions
Figure 18-a lays out the "angular form" of venn diagram for universes
of 1 and 2 dimensions, indicating the embedding map of type B^1 -> B^2,
and detailing the coordinates associated with individual cells. Because
all points, cells, or logical interpretations are represented as coherent
geometric areas, we can say that these pictures give an "areal view" of
each universe.
o o
/ \ / \
/ \ / \
o o o o
/ \ / \
/ \ / \
o o o 1 1 o
/ / \ / \ / \
/ / \ / \ / \
o 1 o o o o o o
/ / \ / \ / \
/ / \ / \ / \
o o o >>>--->>> o 1 0 o 0 1 o
|\ / / |\ / \ /|
| \ / / | \ / \ / |
| o o 0 o | o o o / |
| \ / / | \ / \ / |
| u \ / / | u \ / \ / v |
o-----o o o-----o 0 0 o-----o
\ / \ /
\ / \ /
o o o o
\ / \ /
\ / \ /
o o
Figure 18-a. Extension from 1 to 2 Dimensions
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[ "Differential Logic & Dynamic Systems"
|
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Created: Dec 16, 1993
| Revised: Oct 31, 1994
| Revised: Mar 15, 2000
| Project: Engineering 690
| Advisor: M.A. Zohdy
| Setting: Oakland University
| Excerpt: Pages 28-29.
]
I am having to rethink how many of the different styles
of diagrams that I used in this paper I will be able to
render in this plaintext medium. But the decision will
keep until another day.
Until Then,
Jon Awbrey
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