Saturday, November 24, 2012

Analogical Anomalies

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.

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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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