Quasic Motion in Pascal Analogs
The abstract motion numbers (between orthogons and anti-orthogons that use the same motion numbers thru cells and same null states to connect consecutive motions and structures) can be represented as well by the absolute change in the information coordinate numbers.
This assigns a meaning to structures such as (3+1)^n which can be 9 6 1 = 16. These then the multiples of 3. Now the question of what happens at 0D (that is 3^0) as if in a sense this is an even integer suggests to me fractional charges that at the very low dimensions may not otherwise deal with triality.
We note also that (similar to the pattern of Conway's nimbers in squared space) the quadrature of the grid such that (in internal or fractional "holes") at a given quasic dimension the motion in that dimension with no change in coordinates is a rest or linear concept of motion (the sidewinder infinite in and out of a gravitational region imagined as a non-linear motion or acceleration of these vague differential orders of the continuous). The question the as to how we interpret the signs of such geometries in four space + - - - or - + + + and so on. But in the fractal like lower informational dimensions we can have an observed motion which in this superlinear model of "recondite systems theory, 4n+1 of Fermat" is the ration 3 to 1.
Philosophically, we exchange the Zeno invariant distance or invert it with the non-linear explanation of his paradox as solved by the calculus. This, if we view it as an unsolved problem can be seen as a dynamical situation between the natural and quasic (or internal and symmetrical orthogonal) types of space. This goes far in generalizing what may happen as we do not notice the passing into even horizons or what actually happens if there is an inside to say, a black hole. In four space we note there are six f4 motions thru a 2D face for the 1 3 6 3 1 slicing of the hypercube.
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A Word about The Metaphysical Assumptions Regarding Higher Space Structures:
I have from time to time been surprised by things I have read, even titles of books, where the authors argue there is no Fourth Dimension, or they remark that we do not yet understand what happens in 6 dimensions- that even more philosophical.
As six dimensions, (evidently the power set exponent the algebra of dimensions in question here) I do not mean to simply assign any particular place in the order of reading the Z code- that is the invariant Zeno relations of these abstract motions and there intelligible interacting occur wherever there is a local motion between any two coordinates whose absolute change of the 0's and 1's describe such motion. It seems to me of deep current concern that in the 64 case all of this begins to describe the interaction of DNA, genes, protein conformalities and so on.
In a sense I vaguely perceive that the "compactification" into six dimensions of some spaces, and the topologies, knots etc... is the matter of current research- abstract or not. Nor do I understand why octonians are regarded beyond current applications to concrete physis relations. So, for me the "flanging or shadow polytope is the higher issue of such compression of dimensions (as nature also sees it and we in our limits try to imagine it). So of the hypercube 4D I now mention these general observations:
If we assign the tesseract points their quasic coordinates we can analyze what these are for its subcells, that is the 8 cubes that make up the structure. Thus, whatever we interpret such a structure of space, whatever sense of its uniqueness and centeredness as inversion, wherever we make the distinction between even and odd dimensions where needed for our equations such that the sum of subcells add to 0 or 2 in these simple equations (for informationally we need not make that distinction) we find:
Of the 8 cubes of the tesseract the appearing outer one in 3D is inverted or negative to the internal seven others. This we can expect from the experience of the connecting of the last face of say a hack-n-sack ball or glues of polygons into a polyhedral structure. Such laws of nature in the sense of touch seem scaleless.
So, the metaphysics (as in Rowlands and he Muon- or for that matter any "creative" structure- that there is the muon and everything else to define a filled vacuum- I see that the filled everything else may only be so as the boundary of the muon. So this concept of filled vacua and even such brane like concepts as gravity or magnetic leakage between such dimensions may not be as metaphysically fundamental as we have seemed to have limited in our imaginations.
As far as the above illustration is concerned with fn quasic abstract motions for he tesseract, we note the sum of the corners of each of the 8 cubes breaks into two sets oriented to three space. 3 x 27, and 6 x 27, the old doubling of that seen outside and that inside the cube. Moreover the outer cube and inner cube of the 8 also have this summation of doubling for a total of 12 x 27 of the sum of coordinates but the w axis into fourspace might be seen only as a zero point or relagted to an idea of time or imagination. Here we may also ask in the doubling and halving of things if the inner cube is in a sense a half value, the zeta idea, as far at least of concrete and observable structures. Again, the muon is a closed quasic systems with regard to the "rest of the multiverse". Thus we begin to see even higher concepts of complex zeta like functions possible, and restrictions on the proofs as ambiguous, and these questions of unitary, halved, or doubled spins.
But in the reading of this grid for say 5 dimensions of orthogons of 32 points we cannot simply use the same fractal like quasic numbering as we can with binary systems reading off the conversions of bases in the notations. We need 32 cells on this slightly higher level language notation.
Interestingly, we could have a representation of 1 2 4 8 16... such hypercubes arranged in Z order with Z ordering so as to make a flanged drawing in 3 space of what is going on if we take things into higher dimensions such as 8 as 16 such smashed hypercubes. This in the raw geometry is a physical board of 1024 cells for my 4 space chess game.
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A Stray Thought I Forgot to Include (which may be of some use for those who are actually trying to do calculations)-
We can regard the orthogons as having diagonal distances which are of course the square roots of the equal unit sides- that is the square roots of 1, 2, 3, 4, 5 ... much as the spiral starting with the square of 2 and on that length erecting a perpendicular of unit length to find the next (dimension) root length. Interestingly there is debate rather than the messiness of that construction beyond he square root of seventeen by that ancient Greek geometer. But 17 is after all a quasic number, that is 4^4 + 1 , so maybe he had some forgotten form of insight (and that word seems especially useful to describe dawning of topological analogs.) All these generalizations with their unique styles seem hauntingly close to each other and to a possible higher theory. But to regard the square root of two as a rational number then all the further ones is rather Conwayesque in this sort of surreal calculus.
I recall Conway's statement- "calculus is a way to torture wave after wave of uncomprehending freshmen..."
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I am One with the Weather L. Edgar Otto 01-19-11
I am one with the weather
Seeking not avoiding the sun
as I walk on the melting below zero snow
Rare the wind chill's intermittent reminder
its the humility not the temperature
Homeless or at home brief recollections
being one with life and my freedom
Not caught in a sweating box, layers
one with my winter coat and scarf
Trapped in a cave or sooty fire place
as if that my one, soul far from equilibrium
Darkness above the dipping midnight sun
surprised at the quenching of light that
I can still see, no need for torches
when the stars are once again so close to us.
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Kea has an interesting post today on qubits and qutrits ? where 3^2 does not equal 2^3 but I made similar statements seeing dimensions as simply adding integers many time, most likely somewhere in philosophychatforum or the dalnet-philosphy chats if any of that survives. If two planes can intersect in a point then 2-2=0 but clearly 3-1=2 can be interpreted that a line might intersect a volume in three space only at an internal point... Now, these pascal analogs show when to mix the square pegs with the round holes on what level of dimensions.
I also sees her links to someone discussing how the Riemann mathematicians might feel defensive about physicists making statements about it- these simple concepts synchronously seem to be related to my posts lately- but I am not clear how- nor do I understand why the number 57 dimensions is important or how- yet it has come up a few times in the middle of these analogs of threesomeness and twosomeness. I note also her "anomalies growing" post that neutrino idea seems to add my extra twist of k and w neutrinos- all of this is hauntingly vague with similarities.
Anyway the poem after a dry spell of that mood was inspired by Sultan_Ratrout's facebook status and my recent closer understanding of the pointlessness of the anthropocentric idea in the most general creative space- so that issue also applies to ideas like Motl's where this concept might for good or ill apply to global warming.
I remark also that my friend Chris figured out why all the bird fell out of the sky, because Green Bay killed the sea hawks and The Steelers killed the ravens and so on- not a good season of football for the birds. Next Sunday Chicago and Green Bay- now I rarely follow sports but when I do it seems magical- three of my favorite teams- as long as in this reality of the Favre dimensions I watch... To repeat myself posting here and there...
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Vive la différence? :
http://www.sciencedaily.com/releases/2011/01/110118200813.htm
http://www.sciencedaily.com/releases/2011/01/110118101342.htm
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