Thursday, July 29, 2010
Lithon Fields, Peak Dot, Rock-n-Roll...
Lithon Fields, Peak Dot, Rock-n-Roll... (Number Theory, Geometry, and Quasi-singularity)
Lithos- stone, [from "Peter" rock and Row lands] and Peak Dot the cattle brand from Zane Grey's novel, The Raiders of Spanish Peak.
It seems a paradox to ask how the world or life began if the negative vacuum was completely filled. Perhaps it can be partly filled, that given the intelligibility and unity of geometry and number theory applied to dimensions to the extent it can be for all is not known and I suspect few are generally aware of and taught this simple foundational unity.
I googled the queen problem and knight tours yesterday (instead of googling my mind first) and could find very little that treated things from the view of this post- yet some issues were already explored. I find it interesting that in Rowlands in three space what might not be symmetric in three space is so in six. But I have a hard time with the simple idea of symmetry breaking as defined by the Fibonacci numbers (still, it may explain why the five or 8 nucleons are a sort of limit to a nucleus which obviously is not a limit so there should be further geometrical mechanisms.
Most of all I find along these lines begin with Coxeter who leaves long shadows in many different dimensions of his intellectual descendants.
Now, in the and-or of it, we have five planes of 11 x 11 or 121 and we take the central peak dot away and so recover the duality of 5 x 120 or 600 tetrahedra of the five fold polytopes. It is simple arithmetic.
It is especially significant that tau (phi) with its 0's and 1's notation does include the recursion ideas (mentioned in Rowland's book first time outside of my own contemplations I saw the notion) that the 11 Fibonacci number seems to be a limit or sum like a dimensionless constant at the number 89. 11 is in a sense 2, and 121 is 4 in notation of which 4n+1 is Fermat's recondite property of numbers that seems to apply to these ideas of queen problem structures especially when one is the center or peak dot of the finite cones.
I imagine a lesser quadratic the square root of 11 + or - 1 / 2 or eta in Coxeter is involved in the coordinates of peak dots in five space as to dihedral angles.
In a crude intuitive sense I suspect there are analogs to the icosahedron in five space and beyond but I am not sure if these in a sense are complete or regular nor if nature somewhere can express them in intelligible physicality. I do know that between dimensions say of the 17 lithons of 8 dimensions the idea of a center of some structure may be a quasi or multiple singularity. A classical black hole may have no, one, or some partial value of singularity. It remains to be seen if these 8 dimensional structures and their dualities have much to do with isotope numbers with intelligible calculations.
The 2 to the nth Clifford algebras in defining dimension comes close to my view, maybe the closest similarity or cultural precedent I have encountered. Again, the foundational ideas and their interpretation even as to the translated language of physics may be hauntingly close and yet not primary in the idiom and notions of such philosophies.
Five tetrahedra in the tetrahelix determines the chirality but it takes ten over all- which was Fullers explanation akin or isomorphic to the stacking of the ten faced deltahedron mentioned in Rowlands. One of these as a color cube like game I call the Lithon and there are variations of course with this labeled directionality (for example the complexity can grow enormous for all symmetric possibilities yet with this natural ordering we may consider mirror images of natural subsystems relavant- that is in the alpha beta gamma delta epsilon planes we can have these treated as if a form of dimensions which of course have two sequences (as does the two space of five things)as geometric density of the permutations.
We also note from a purely algebraic geometry note where this 10-deltahedron may be isomorphic to the null case of a dihedron, the Pentagon solid without volume. I would like to further understand if these have Moebius analogs and how they are constructed and how they relate to the general peak dot theory.
* * *
One Way Mirror
L. Edgar Otto July 29, 2010
My sky is clear as I touch Antares
my pinhole eyes compass dividers
that sees the lesser and longer motion
of the moon, feels earth in spin
My mood and poem interrupted
by the jet dark haired girl in the distant
surrounded by her cloud of smoke
I must check out her velvet sheen of darkness
She sees through and past me
her sky the grayness of the moors
her moral law within, her eyes disguised
doubtful of love yet churns the dew points
We know the hour's past for forgiving blemishes
we draw the blinds save for a last star at night
* * *
I knowing you once close in dreams
but you cannot know that, I but a stranger
in fantasy our soul's encounter breaks
doubts can only rob us of our healthful sleep
You of the apple when its ripe tease me
give me only shadows knowing I see them
as you lift your thin arms to wash your breasts
I cannot bite so green and bitter to my belly
I am the sun and source of clarity and light
you in your spin give sparks, store the songs
of meadow larks and shun the cacophony of crows
our bedbugs of time grow past our wars of pestilence
How could you know I was the one when our shared love
in each one way its melting fun house mirror?
* * *
This is where we were before, where we were expelled or
came in to some point, cycle in the play
when the world has changed, not renewed our love
as our bodies betray us, empty your hourglass form
I do not know if you got the message yet you stood there
so long by the screen and soft light as I
opened and closed frantically against the line wind storm,
you before the screen hearing the sirens
The I heart you cut out from a cereal box that only
the brightness stands out, sheet lightning but it was
not thunder to give you but your blue glow silvered glass
as I cannot just leave in anger, you alone
I passed this way who loved you or said he did
All you would let me give you in your naked singularity
* * *