Analogical Anomalies
L. Edgar Otto Saturday, 24 November, 2012
"Fallacy
is neither originally nor primarily a term in logic."
"Parents also
console themselves by the American fallacy that one can only be young
once." Elizabeth Bowen, Punch, 9 Aug.1953
Merriam-Webster
Dictionary of English Usage (1989)
But where it is a
logical term we can realize these fallacies instinctively rather than as an
affectation of education usually of the newly educated young people who should
know better if they are worthy experts to state in fallacy the value of expertise outside their own field, for example.
Scientists with claims of knowledge concerning metaphysics in a gray
area where perhaps they use core philosophy of which they usually say
philosophy is no longer relevant. This
of course the evolving concerns also from the Greeks and Latins as to the
nature of language itself. Much of my
time in trying to communicate some ideas on the internet has been taken up with
debate on who may or may not be using fallacies this way but the issue has more
foundational basis.
On the frontiers of
at least poetic creativity the use and coining of words is one of its
functions, perhaps with the same aim of science to condense meaning with
concision.
English or any
language in a general state within an individual and between individuals is
like a living thing. I continue to try
to learn my native language and the usual fallacy is to question if it is my
native tongue as if there are no other tongues as true to or advanced as one's
own in its divisions and traditions, the attack on character as proof against a
concept or theory offered.
If in the making
sense of some states of mind, finding and streamlining a pattern with choices and
exclusions we are successful as minds in filling in gaps in the missing data
not to find erroneous connections, that is to find the trick or trip up needed
to explore a pattern and intuitively know when we have done that, artful or in
problem solving or even in the art of deceit which gives us the term
fallacy. Magicians entertain us as we
desire to open up to a balance of thoughts with this illusion and hallucinogenic
suspension of disbelief.
I have apologized
much for those within my native speech for items of confusion who seem to have
some degree of fluency and thinking on their own beyond that aspect of language
as dominating the logical view. This is
perhaps no longer a good use of time or needed in a failing educational system
with cultural agendas or with greed that amounts to social theory as
marketing. A world safe for enquiry and
transcendence will not stand only on what the market will bear at the auction
block as some escape too far from the game and the group therapy of the
political arms fall apart because of the lack of those who make the rally and
meetings.
I still apologize to
my foreign readers for terms, known as standard or coined anew, present
difficulties in the translation. But
this is not because they are foreign but because in a given individual in the
same language those with less than a unified spirit insist on a clear division
of multiplicity or unity, that is what is plural or singular- yet in the
incorporation of a foreign term the usual usage only recognizes the singular
form. It is perhaps a measure of the
fluency or expertise in a language at the frontier, where in my case one does
become young again and there are choices that follow from some previous state
we imagine as a cause for that reason (the situation analogously and thus
considered true analogies by virtue of those being geometrical) is the idea
these possibilities are non linear and may not be contained in a unity of a
higher pattern. Thus we
allow some freedom or
exceptions to which we only see the face or surface of what can be similar
linguistic structures or viable ones in the depth and communication between us.
Sometimes it makes
sense to mix our metaphors or to enlighten beyond initial confusion hidden
parallels in the matching of ideas and the concordance of word species as
perhaps a level of thinking about language which only on the lowest level of
the perceived error most people cannot see or care. Yet as a general mechanism this too guides
the evolution of our particular states of language. At ground we in the resonance and
recognition, receptivity to natural laws we have innately a high sense of
beauty in the idea of symmetry.
* * * * *
This brings me back
to what I originally intended to discuss concerning the matching of color cubes
in the Otto-Conway Matrix and what my terse notes hint at in methods and
generalizations (as usual independently) which surprise me having thought
nothing much to post today (an ongoing state I suppose, after all, the curse
and joy of working with both the foundations and the frontier). I find it embarrassing to myself what it takes
to finally solve what proved to be a simply stated but most difficult problem,
what such a pattern would look like in higher spaces.
The counting looks
intelligible, my recent extension of the dihedron domino idea as fault shift
intuitively suggested that this could be a combinatorial aid to generate and
classify the Soma cubes from a single formula rather than a rather irregular
interconnection of exchanging the pieces on Conway's Somap. This among may approaches to explore (Conway
considers the rules of things from the surface colors and from the perspective
of say an upward gravity direction) which are more of a qualitative nature.
In the casual drawing
of the ideas as shown in the illustration above it dawned on me that the
arrangement of the color faces for the thirty cubes matching in all three space
directions would be a torus mapping over the matrix. The knight move shift a way to align those
color elements that are successors of each other. We can have a line of the thirty cubes where
each color is present once from the center of all the cubes as if superimposed. All such ideas I first felt intuitively and
so used them as principles to move on to others and then to edit or refine the
ideas in standard methods such as graph theory.
Now, we know the
simple cube, its structure as if spinning, is not a simple at it appears. But what I find intuitively astounding and
maybe original, is that the icosahedron symmetry rather than a centered program
for colors can be seen as not that simple either but is rather an abstract
torus really of which part of the divisions of the thirty-six bicolors cancel
out. We in fact derive the 248 of the
ten fold space.
Moreover, we can ask
then of the case in super space beyond the 24 dimensions as to what sort of
structure torus like may exist if we assume the great grand stellated
hypersolids are not as simple as our theories assert now.
* * * * * *
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