ONT Re: Differential Analytic Turing Automata

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DATA.  Note 9

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By virtue of Zipf's law -- yes, there is a dynamics to its economics --
I have found myself forced, when it comes to matters that I've been
thinking about for "years and years" (YAY) to make a heavy, if not
to say an overbearing use of acronyms, both for their utility as
mnemonic devices and as a "regime of code compression" (ROCC).
I'm well aware that this can be annoying at times, so please
forgive what I hope will be a transient nuisance and I will
do my level best to unpack these lexical quanta as we go.

A "moral of the episode" (MOTE) on the wing here:
A "transformation of textual elements" (TOTE) is
a "formal or mathematical abstraction" (FOMA) of
a very high order, to wit, a "formal object" (FO).

As an object example, let us consider the TOTE in progress:

<x, y>   =   F<u, v>   =   <((u)(v)), ((u, v))>

Taken as a transformation from the universe U% = [u, v]
to the universe X% = [x, y], this is a particular type
of formal object, and it can be studied at that level
of abstraction until the chickens come home to roost,
as they say, but when the time comes to count those
chickens, if you will, the terms of artifice that
we use to talk about abstract objects, almost as
if we actually knew what we were talking about,
need to be fully fledged or fleshed out with
extra "bits of interpretive data" (BOID's).

And so, to decompress the story, the TOTE
that we use to convey the FOMA has to be
interpreted before it can be applied to
anything that actually puts supper on
the table, so to speak.

What are some of the ways that an abstract logical transformation
like F gets interpreted in the setting of a concrete application?

Mathematical parlance comes part way to the rescue here and
tosses us the line that a transformation of syntactic signs
can be interpreted in either one of two ways, as an "alias"
or as an "alibi".

When we consider a transformation in the alias interpretation,
we are merely changing the terms that we use to describe what
may very well be, to some approximation, the very same things.

For example, in some applications the discursive universes
U% = [u, v] and X% = [x, y] are best understood as diverse
frames, instruments, reticules, scopes, or templates, that
we adopt for the sake of viewing from variant perspectives
what we conceive to be roughly the same underlying objects.

When we consider a transformation in the alibi interpretation,
we are thinking of the objective things as objectively moving
around in space or changing their qualitative characteristics.
There are times when we think of this alibi transformation as
taking place in a dimension of time, and then there are times
when time is not an object.

For example, in some applications the discursive universes
U% = [u, v] and X% = [x, y] are actually the same universe,
and what we have is a frame where x is the next state of u
and y is the next state of v, notated as x = u' and y = v'.
This permits us to rewrite the transformation F as follows:

<u', v'>   =   F<u, v>   =   <((u)(v)), ((u, v))>

All in all, then, we have three different ways in general
of applying or interpreting a transformation of discourse,
that we might sum up as one brand of alias and two brands
of alibi, all together, the Elseword, Elsewhere, Elsewhen.

No more angels on pinheads,
the brass tacks next time.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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