Wednesday, July 6, 2011
Phase Space as the Arquasic Plane Squared
Phase Space as the Arquasic Plane Squared L. Edgar Otto July 6, 2011
Here I jump a few posts, hopefully to include the essential ideas and not forget what the purpose was of some note in the writing. I want to review or emphasize the general principles I have used to arrive at these parallel ideas of our theoreticians.
Basically, the complex jumps of Riemann, and the multi-reentry describing faces of a polytope, are to be viewed in quasic and other standard ideas of space. The Arcadian Quasic idea seems to be concerned with phase space (forgive me I forget what name was assigned and refered to for say certain angles- that can be found in the use of the names and terms in posts my my fellow bloggers).
Quasic General Principle 1 - The phase space can be conceived in a self contained region of the quasic plane as its extent is indefinite and not clearly a simple manifold as in Pre-string physics.
Quasic General Principle 2 - We may string these together in a square or a line, the jump order being a question of which sub-planes (branes) are at right angles or linear or not and to how many structural steps or partition configurations. This is possible in the general quasic space especially between dimensions.
QGP3 - We can accept some cell in the quasic plane as unity. It can be the initial cell of which (in the span and not depth of the quasic plane in this case) we may say it can or cannot be subdivided. The Arquasic Plane is brane-like in conception but it is an infinite or n-brane of n-dimensions and more. Or from this unity cell we can descend toward the upper main diagonal corner by the halving of binary powers.
...1/64, 1/32, 1/16, 1/8, 1/4, 1/2, 1, 2, 4, 8, 16, 32, 64... [in this sense it is interesting to imagine what either side of unity sums up to say in increments of 1/3 by Eulers early intuitions, in which case the Triality + 1 concept that distinguished Arqs from Qs does relate to the main diagonal of these planes as some variation of matrices.]
QGP4 - Crack Sand - we advance along the main diagonal as far as size of the contained internal grids by multiplication of the 4th power. If we take the square root of the plane (or alternatively the general square root of 2pi in the polar coordinate view) We find the edge sequence at the unit cell to be 7/2 or 3.5. The next squared object along the diagonal would be 4n this to get this sequence of numbers which are really parallel sums of binary powers doing what just one sum would in quasic space and causing an open sequence as an abstract^2 motion or rest (much like the quesion of monopoles on one hand as 0 magnetic or j as a current in the symmetry considerations of Maxwell. Thus we find these numbers: 3.5, 14, 56 ... recognizable from the braid work and particle ideas of Kea et al. This of course continues to higher dimension 2^2n, 224, 896, 3584 (at 16 dimensions I find especially interesting as the addition or substraction from the rotation group number of the orthogons of these parallel binary powers result in these powers in the sense of something between 4096 and 256 in the all important space involving the numerology of 32 and 12 and so on- in fact this intuitively suggests why the string theorists tend to imagine such a limitation into 6 space and 11 or 12 dimensions.)
QGP5 - I add here that in the general idea of extending from the square x^2 the larger square of 2xy and y^2 up to a range of 1/16 to 2^10 cell grid values, that we find the main diagonal of 6 units and the side 2xy areas composed of 10 units for the 16 of abstract rest or motion as with the idea of ten rest values in Einsteins presentation. It is moreover at the summation over an infinite but bounded case that this constitutes certain phase angles of interest.
QGP7 - Let me also remind the readers of this idea of a more general condition of boundaries than the fundamental theorems involved- for a flow as a line or sting may not exactly determine what is inside or outside some boundary composed of finite points. Thus where the jumps are separate, or in phase space which might describe a multiverse of the usual pre-string manifolds- that is the three contending theories of space, steady state, big bang, oscillating - are conceived as only that which is related to a region, spherical or imaginary or hyperbolic and so on, and not a totality as an infinite space physically at all. But this is the problem of what is measurable and not a question of thermodynamic symmetry of the entropy where we in fact information ally have to make the numbers and coordinates intrinsically and more fundamentally descriptive of the physics rather than just adding on scalar values and interpreting them as a style of physics locally or in general space.
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On the Illustration of the Franklin Magic Square (For those who appreciate the information aspect of the I Ching as did Leibniz Some have said this order applies and to the seasons- but I am not sure in these issues of time measure that other than the notions of matching the calendar to the seasons, or that we try to make commensurate lunar or solar divisions is not a good thing when we are asking if after all there can be some numbers that in the universe are not intrinsically commensurable even when taken ultimately as we imagine the primes so are.
It seems there is offered justification for the duplication of complex and real systems so as to so justify the doubling of real system dimensions. Abstractly the imaginary sphere is a mirror of a real sphere so much of these QGP apply.
In the Franklin grid we raise again this issue: (and one from the Arq-i-ology page not yet posted) Can we imagine the tetracubes of which there are 32 in a cube of 64 with i32 more of them? Solve the possibilities. Note the 1 x 4 tetracube may cross over both the imaginary and real space and in a sense all is independent of color and chirality of the unfolding of such cubes and of the general symmetry of the grid or higher space forms of it (I prefer a different ordering where in the division of the above grid the difference (as +32 or -32) of the alpha crack and beta crack quadrants (as in the genome encoding) the two top quadrants not here the left to right.
We note further the blending of the concepts of even and odd- yet as if we are describing a six dimensional structure (presumably to involve the possibility of a weaving of planes and crossovers and so on) that nevertheless makes a difference in the summing to 260/2 of sets of two of them that differ by 2 where even or odd. Moreover, the symmetry of these alternate with the quadrants, and in the top down direction we note the difference of 3 an 5 alternately.
The sequence, as if one of the fractal patterns that is a closed loop, in this magic square is such that like those patterns it divides things into two mirror groups of 32. (let me not forget here that if we have a crack sand formula 2^6 + 2^0 that we have a skeleton of sorts of one dimension to integrate as current or flux, j, and that these generate the wider expansions of the phase numbers above as more a function than an algebraic set- with the idea leading to say compactification.) So with the purely quasic sequence itself we do not have a closed pattern +1 which as a mirror view is the main emphasis of Arqs. So in effect this matrix idea above is in fact a rather general unity of the purely Quasic and Arcadian Quasic (just Quasic or perhaps Quasonic) properties of space and numbers. Each continuum universe has its fundamental boundaries and conservations to consider, but the boundaries are fuzzy and not fundamentally conserved as to what enters or leaves that general separatrix between the polar continua in a more general (but not clearly the ultimate) ultranscontinuum. Ideas of gravity as such leaking needs to be revised for these more intermediate stages of cosmic theory- it is not clear for example if there is a totally separate universe, in space or in time, these influence each other like the general conception of the pre-string universe models may or may not allow.
Apparently, what we mean by solving an equation- especially involving singularities, is at least the solving of a system. In the Pre-string world where a sort of absolute principle as if only a (Otto-Motil OM) statistical foundation for science (a tenable position actually) precluded clear pictures and a theory of everything (then the idea of a unitary field theory- which of course Einstein pictured as a simple algebra but we now suspect at least a simple picture of arithmetic. It is not clear that (well after all Einstein's world only had our galaxy to contend with and some models suggest that could actually happen one day again in actuality.)
The DeSitter and Hoylean hyperbolic models are a sort of limitation on systems as we now imagine them (after all Einstein stated he did not believe the moon was not there if it was not seen despite the hints of that truth from some quantum views). So we have really an OMNIUM General Principle (OmGP) level of abstraction wherein it is beyond the difference of the holographic and fractal division principles - which is to say that boundaries are fuzzy even if in the unity of Western and Eastern ideas of grids, and some higher ideas of topology including string theory restrictions and freedoms, that the idea of symmetry and the holographic principle is rather fuzzy a concept- especially if we imagine a travel across space to return to the same place and the changes in chirality and so on.
Yet, we can state a more general idea of conservation after all if we see the universe globally on the average where something enters or leaves all boundaries which of course quasically are more or less the same boundary and higher phase like space "separatrix" (standard, not my term). While we solve for the general case and ground certain ideas like renormalization, in the ultimate case it seems to me still an open paradox to suggest that somehow we can go beyond the idea of but one and not a sort of Multi-omnium universe.
The simple ideas of this complexity of space and its configurations and uncertainties that involve with the magic squares (physical and stable and so on thereby) or not as far as nature code (Rowlands) applied to genetics seems to open up a better understanding of how to read and decode this new vision of a wider dynamic complexity of where it applies to organisms. This could lead to a vast whole new world of what we mean by medicine and gene related experiments. We at once find a simpler and yet a more complex universe than some have imagined heretofore.
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