ONT Re: Zeroth Order Theories (ZOT's)
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Let's now pause and reflect on the mix of abstract and concrete material
that we have cobbled together in spectacle of this "World Of Zero" (WOZ),
since I believe that we may have seen enough, if we look at it right, to
illustrate a few of the more salient phenomena that would normally begin
to weigh in as a major force only on a much larger scale. Now, it's not
exactly like this impoverished sample, all by itself, could determine us
to draw just the right generalizations, or force us to see the shape and
flow of its immanent law -- it is much too sparse a scattering of points
to tease out the lines of its up and coming generations quite so clearly --
but it can be seen to exemplify many of the more significant themes that
we know evolve in more substantial environments, that is, On Beyond Zero,
since we have already seen them, "tho' obscur'd", in these higher realms.
One the the themes that I want to to keep an eye on as this discussion
develops is the subject that might be called "computation as semiosis".
In this light, any calculus worth its salt must be capable of helping
us do two things, calculation, of course, but also analysis. This is
probably one of the reasons why the ordinary sort of differential and
integral calculus over quantitative domains is frequently referred to
as "real analysis", or even just "analysis". It seems quite clear to
me that any adequate logical calculus, in many ways expected to serve
as a qualitative analogue of analytic geometry in the way that it can
be used to describe configurations in logically circumscribed domains,
ought to qualify in both dimensions, namely, analysis and computation.
With all of these various features of the situation in mind, then, we come
to the point of viewing analysis and computation as just so many different
kinds of "sign transformations in respect of pragmata" (STIROP's). Taking
this insight to heart, let us next work to assemble a comprehension of our
concrete examples, set in the medium of the abstract calculi that allow us
to express their qualitative patterns, that may hope to be an increment or
two less inchoate than we have seen so far, and that may even permit us to
catch the action of these fading fleeting sign transformations on the wing.
Here is how I picture our latest round of examples
as filling out the framework of this investigation:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| s_1 = Logue(o) | |
| / | |
| / | |
| @ | |
| · \ | |
| · \ | |
| · i_1 = Model(o) v |
| · s_2 = Model(o) | |
| · / | |
| · / | |
| Object = o · · · · · · @ | |
| · \ | |
| · \ | |
| · i_2 = Tenor(o) v |
| · s_3 = Tenor(o) | |
| · / | |
| · / | |
| @ | |
| \ | |
| \ | |
| i_3 = Sense(o) v |
| |
o-----------------------------------------------------------o
Figure. Computation As Semiotic Transformation
The Figure shows three distinct sign triples of the form <o, s, i>, where
o = ostensible objective = the observed, indicated, or intended situation.
| A. <o, Logue(o), Model(o)>
|
| B. <o, Model(o), Tenor(o)>
|
| C. <o, Tenor(o), Sense(o)>
Let us bring these several signs together in one place,
to compare and contrast their common and their diverse
characters, and to think about why we make such a fuss
about passing from one to the other in the first place.
1. Logue(o) = Consat.Log
o-----------------------------------------------------------------------o
| |
| (( pete_plays_guitar ),( pete_plays_sax ),( pete_plays_drums )) |
| (( paul_plays_guitar ),( paul_plays_sax ),( paul_plays_drums )) |
| (( jane_plays_guitar ),( jane_plays_sax ),( jane_plays_drums )) |
| |
| (( pete_plays_guitar ),( paul_plays_guitar ),( jane_plays_guitar )) |
| (( pete_plays_sax ),( paul_plays_sax ),( jane_plays_sax )) |
| (( pete_plays_drums ),( paul_plays_drums ),( jane_plays_drums )) |
| |
| (( pete_fears_13 ),( pete_fears_cats ),( pete_fears_height )) |
| (( paul_fears_13 ),( paul_fears_cats ),( paul_fears_height )) |
| (( jane_fears_13 ),( jane_fears_cats ),( jane_fears_height )) |
| |
| (( pete_fears_13 ),( paul_fears_13 ),( jane_fears_13 )) |
| (( pete_fears_cats ),( paul_fears_cats ),( jane_fears_cats )) |
| (( pete_fears_height ),( paul_fears_height ),( jane_fears_height )) |
| |
| (( |
| |
| ( pete_plays_guitar ) |
| ( pete_fears_height ) |
| |
| ( pete_plays_guitar pete_fears_height ) |
| ( paul_plays_guitar paul_fears_height ) |
| ( jane_plays_guitar jane_fears_height ) |
| |
| ( paul_fears_cats ) |
| ( paul_plays_sax ) |
| |
| ( pete_plays_sax pete_fears_cats ) |
| ( paul_plays_sax paul_fears_cats ) |
| ( jane_plays_sax jane_fears_cats ) |
| |
| ( pete_plays_drums pete_fears_13 ) |
| ( paul_plays_drums paul_fears_13 ) |
| ( jane_plays_drums jane_fears_13 ) |
| |
| ( pete_plays_drums pete_fears_height ) |
| ( paul_plays_drums paul_fears_height ) |
| ( jane_plays_drums jane_fears_height ) |
| |
| )) |
| |
o-----------------------------------------------------------------------o
2. Model(o) = Consat.Mod ><> http://suo.ieee.org/ontology/msg03718.html
3. Tenor(o) = Consat.Ten (Just The Gist Of It)
o-------------------------------------------------o
| (pete_plays_guitar ) | <01> -
| (pete_plays_sax ) | <02> -
| pete_plays_drums | <03> +
| (paul_plays_drums ) | <04> -
| (jane_plays_drums ) | <05> -
| paul_plays_guitar | <06> +
| (paul_plays_sax ) | <07> -
| (jane_plays_guitar ) | <08> -
| jane_plays_sax | <09> +
| (pete_fears_13 ) | <10> -
| pete_fears_cats | <11> +
| (pete_fears_height ) | <12> -
| (paul_fears_cats ) | <13> -
| (jane_fears_cats ) | <14> -
| paul_fears_13 | <15> +
| (paul_fears_height ) | <16> -
| (jane_fears_13 ) | <17> -
| jane_fears_height * | <18> +
o-------------------------------------------------o
4. Sense Outline: Consat.Sen
o-------------------------------------------------o
| pete_plays_drums | <03>
| paul_plays_guitar | <06>
| jane_plays_sax | <09>
| pete_fears_cats | <11>
| paul_fears_13 | <15>
| jane_fears_height | <18>
o-------------------------------------------------o
As one proceeds through the subsessions of the Theme One Study session,
the computation transforms its larger "signs", in this case text files,
from one to the next, in the sequence: Logue, Model, Tenor, and Sense.
Let us see if we can pin down, on sign-theoretic grounds,
why this very sort of exercise is so routinely necessary.
But first, a trip to the training table ...
Jon Awbrey
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