The Resolution of Singularities

The Resolution of Singularities

The above illustration reflects two explorations of last night. One is taking a new look at the color matching with hypercubes and because of the greater possibilities in the combination of four things that two of what would be one 3x3x3 color matrix arises with more symmetries (say we interpret these as if particles).

Along the way I tried various labels, alphabets, diagrams, to begin a list of these, this symmetries and seeming asymmetries in matrix. This lead me to read again the book on Nash on his later thoughts on such states of thinking even when that of which he scribbled sometimes made vast sense in say a space of seven dimensions. So this will be a psychology theory post too (and goes at the heart of what is the nature of consciousness if we apply the new physics topology to biochemistry as a consequence of our pretensions or certainties of scientific discovery or invention.

It is of interest that Nash used a 26 base (alphabet) in his numberology. I have had to encounter (hopefully rationally) the 24, 26, and 28 bases for my notations in terms of the colloquial alphanumerics. In the bosonic numbers how do we know we are not just imagining the voices of the end times where the Arabs vie with the Asians to play the world's end board game, like Nash, rational but not demented- and not an intelligible and non-schizophrenic experiencing of the cosmic code?

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Arising from philosophy more that science, and although I do not feel very old, and what a cute young lady thru Kea's link I just read of her walking and running composite particles and so on- I put off by all the co-authors and the wonder if someone so young can come up with the deepest of ideas- I have taken a general stance of remaining at a distance from the fray, a philosophic overview of this birth of further new science- an old man with the myth perhaps of sage wisdom of the East quite outside the details and the hard work of the debates. I record then but may not be as good a teacher as some on these blogs.


Tommaso Dorigo in particular today has such an inspiring yet instructive blog concerning the fact or rumors of the new particles in his introduction as an overview to the theoretical process and possible methods and consequences if there is to be something beyond the standard theory.
http://www.science20.com/quantum_diaries_survivor/new_massive_particle_some_kind_higgs-77857

Lubos too has had detailed posts with the idea of presenting the physics so as to encourage interest in science. Yet, existentially and politically even with his background he is definitely committed to what is complex but limited views for most as if his potential cannot quite join in the fray of our new discoveries.

I have already said Kea if she were not needed so much for research would make, at least for me, the finest of teachers and a no nonsense over viewer of even a hive of researches all full of their pride.

Pitkanen, well, this is to be a psychological posting too about crackpots and I do regard those sorts of mere word statements and more blog ranting than professional- so some walk the fine line, probably from their own moods, between passive and overt aggression as if the battles alone determine the agenda and evolution of things. I remains to be seen how emotions ultimately fix the mix, even in computation as to how well they fit into the objectivity of scientific enquiry.

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* Incompletely comprehensive self-perpendicularity, the cold machine, seeing in its way a little further down a path of external, natural, or self programming, finds base composites the rational mathematician may only have struggled with or suspected. But it insists its rationally that as self-programmer researches are independent of human mood states.

* The poet toys with symbol, (see Yeats prose work), metaphors of gyres, and builds a myth that if the inner clockwork drives the symbols and not the symbols that clockwork, then historically the myth is expressed in its own right that what is poetry, as if to be read by others and written carefully and formally, the poetry in it does not become unintelligible to those who would translate, solve the singularities, as though a unifying and unique truth was at hand - unquestionably right even if grandiose to follow in trust as it inspires and satisfies the human craving for curiosity and belonging, being, so to follow with their own intentions.

* In this atmosphere of thought, the artistic ambiance is everything- at the creation, at singularity, it is as hard to distinguish a work as mathematics or poetry for the core vision as numbers or language. When this dialectic struggles, the within and without caged by the expediency of battle. there were eccentric forerunners, crackpots not demented by time save perhaps their own times, before our at a distance computational abacus culture and a society of chemically imbalanced theories of healing by drugs full of artificial insulin's and sugars.

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The crystallographers in general seem to want to touch a model as well as imagine one on the screen or in the algebra. Desk weights now, relics from a past when the little wooden unit cells, not worn, someone used to perfect the angles.

I tried to find a physical set of say cubes to express such models as to what was happening on the next level of spaces. It is fairly straightforward in the coloring of such cubes with 8 colors some way- or say with 8 of them and 24 runes that match another set of such colors (that is I did make a notation of the base 24 of the squares in a hypercube, standardize them, use the pairs of them and excluding the signal flags A and B as they are distinct and only 3/4's the other flags which in the hidden background of our influential real or hoped for models express what for Nash was the appeal to a computer, a pure counting, to factor the A and B of it into a composite number.) One must wonder if the intuition of such algebraic topological models at least in what we may suggest is a whole person who perhaps has the ability to count as well as see in balance, once seen or felt in the mind's background, that it would cause the structure of said mind to become unhealthy- or perhaps even the partial vision of it if we are lucky enough to confront it salvages what little sanity is left- this question too came up with the ideas of Cantor.

In any case I am not satisfied with any of these hand held models that involve a sort of colour matching or contiguous (potentially, hidden, or physically) mirrors. I did find a variation on the quasic notation in black and white for the points of the 8 cubes which expressed this natural idea of half being translation and half being rotation in such unfolding of the cubes- but it is different than my piano dice to the extent I now call them zebra dice- but these are still rather abstract for the problem. I imagine I just have to enumerate the possibilities. In any case the poetry of such higher combinotorics may be there so to learn to aid me in the complexity of the mathematics let alone we who would do physics interpretations.

Part of the problem is the simple choice of arranging things as alphanumerics based on the 24 as 3 x 8 instead of 4 x 6 in two space, but things have to already be thought of in the higher generations and hierarchy spaces as doubled, even doubly doubled.

With four axes and these odo256 level cubes as "felix cat-whisker matrices" we expect a set of four of them two of which share one color of two on each axis- so in a way the diagonals involved certainly have to do with half diagonals in the quatrants and octants (I wonder if this is also a TGD theorem?) I wonder also that in the two 4x4 matrices of the first illustration above where we have *UX becoming *XU does this sort of directionality correspond in some way to Kea's observations of that which is expressed as asymmetric?

Again, I found many multicolored cubes in my designing of them based on various symmetries or notions- now with a little less innocence, a little isolation and less struggle for basics, I find those fancy doodles useful in more formal theories where I can finally begin to arrange them without knowing when some label is arbitrary. So for the advanced out there help me connect the 42 8 color hypercubes that they match contiguously in all axes in a hyperconway array, if possible.

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As I have posted, Nash on my mind because of a friend in the coffee shop who as a kid in Princeton with shrink relatives and administrators (who by the way has trouble with face recognition) says he saw Nash a lot usually yelling at people passing by. Oddly, some of his alphabet based equations seem to read as if the last equations of Einstein on his death bead about density of combination's and stars which seemed so arbitrary among the sea of solvable equations and like Nash asks us to solve the singularity, the =0. Would that it applied to today's economics better.

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I return also to the clear and beautiful blogspot of Michael Rios with two quotes
with the thought that as far as the unification of physics goes, quantum and geometric physics aside to be so unified, that the best of string theories needs unification with the best of our algebraic topologists. Where after all does 3+1 and 2+2 formalism meet but in these issues of dimensions and vector solving of singularities? To what extent is the 4n splitting of such compositions not relevant to the geometry and extremal counting of things?



http://uduality.blogspot.com/2011/04/qm-over-split-composition-algebras.html

"When one attempts to give a similar normed space construction for Jordan algebras over the split composition algebras, it turns out the story isn't so nice. The first property that goes out the window is positive definiteness. So in quantum mechanics over split composition algebras there are a bunch of rank one projectors that have zero length. To this, one may say, "so what?" Well, for one, one can't assign a probabilistic interpretation to pure states described by these vectors. Now one may reply, "so just mod these out and define your projective space accordingly" Sure, we can try to do this but what if the physics actually requires the use of these pathological rank one operators?"

http://www.superstringtheory.com/blackh/blackh5.html

"The entropy of a black hole is one fourth of the area of the event horizon, so the entropy gets smaller and smaller as the black hole decays and the event horizon area becomes smaller and smaller.
But until string theory there was not a clear relation between quantum microstates of a quantum theory and this supposed black hole entropy."



Perhaps, evolved and individual evolving split personalities (as well of composite conceptions or even multiple views as of the dynamic replication of chromosomes- that difference between the mirror of the doubling and the expression in a bee hive) describe more closely the links between cosmic codes and the biochemical codes of thought and life. But can we be satisfied with new methods of useful probabilities when there may after all be a little deeper theory of these things?


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http://www.sciencedaily.com/releases/2011/04/110407171718.htm

"Geometry is defined as touch and sight." Singh

Semi-transparent Mirrors L. Edgar Otto 08-08-11


You who crave my touch
cocooned in your sticky webs
Compensate by sight
present to me obtuse angles
Around corners with perfection
Brighter head on your explosion

Thus I drink of your rays of light
that darkness fades it not
My crystal radio my mind amplifies
finds the sweet spots, sparking cat whiskers
As whispering stars in motion I hear
the snow belt city, double pleasure mint gum

Our glass windows seen not heard
we reach beyond the light and whips of strands
Your stinging hair in a pick up truck on the way
to the Springfield Fair I so cradle you
How else in our entangled synchronicity
we both awake or give in to sleep?

We both in our ground of sensations
see the other dimly, less intense, or wise
In this world, in this life, in time less than frozen
half again beyond light our event horizon
Glues us to each others half fulfilled dreams
all there is we will not leave our shared warmth

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