Tuesday, January 25, 2011
We find a quasic or z-code order in the reading of dimensions- dimensions are then the same description as quasicity. These moreover are the same description as that of the fractal triangles. All of this arithmetic and algebra of the finite and the infinite. The quasicity as powers of 4 is evident from the right or left of these graphs- also the easy visualization of the orthogonal structures.
The supercolor, that is the expansion of information in the quasic dimensions is binary base representations and not just mere, but ordered duality. To reach the colors involved in 16 dimensions we have to imagine a grid of 32 x 32 which contains in each pixel 8x8 sub-pixels. 32x32 is of course the ten dimensional case.
The need to add further dimensions for that case assumes that we cannot distinguish in itself in graph theory that a line for example separates a plane into two regions and thus its existence as a grid element cannot be self contained. Upon this and with the division of the powers of 3 and 4 we have to generalize the idea of holographic and matrix algebra into some line as to what is the outside boundaries and to what extent we interpret or decipher information contained in them and the space(s) they contain.
Lampion: 01-24-11 To Kea's observation that a value is close to pi which I suggested was 256/81 I note this ratio can be the squares of each also...
Using these orthogonal representations it is an easy effort compute the combination's of some things like color visually. The Dihedral group in a sense is an overgroup fractal like to the others where they are treated factorially.
Thus in the diagram above we note on the 15 + 15 color level that all the spectrum is is represented linearly at the 8 corners of a cube or one side of the quasic grid, while the diagonals of those 6 spectral colors (6!) break into BKD or the other side from the center of the cub GIN or half the colors.
Interestingly, 9 +28 +27 = 64, which is to say something about the 36 inner squares of the 6D grid and 28 which with the nine in a reversal of global signs is the left over squares after the color fills; and of course 28+28 = 56 as all of this does relate algebraically and topologically and arithmetically to these triangular numbers.
Sometimes, as in the classification of the Soma cubes, the concept of abstract quasic motions as the power sums of two is the topological combination's of groups.
* * *
An Overview of Fourier Methods in the Description of Physical Phenomena
It is clear that we can construct physical things (our sense of the solidity of things or force of things) by taking literally our intuitionist notations. Is this the fundamental question we are asking and seeking for a unified theory?
In effect we imagine exploration into concepts of space where in general there is no central singularity (multiple or not) or there can be seen one by the notation.
To start with the idea of transformation of assumed prime and simple solidity of three space is what happens when we transform with linear matrices into coordinates using the trig functions. This reductionist view works but does not really tell us about deeper theories of space from a more general and real grounding. We can then only assert a connection between quaternion like numbers and natural vectors when we can already examine or observe the duplication of spaces so to define these as a doubling of the grounding dimensions. This is a powerful tool but can leave us blind to the deeper reasons for measurement as the complexity of our theories fall down the rabbit hole- alternatively we can assert deviation from the methods is merely an Alice in Wonderland hope or dream.
We can divide space into so many regions over a region, say to the approximation of 64 subcells in a division to compute the Fourier transform so to find an approximation on the quasic level to things like matter distribution or any other key concept so far to describe what we see in the cosmic background.
I have to question things there at the creation of these method which is not wrong but not as a profound and historical all in all breakthrough in our methods. I want to keep in mind in the ideas of heat transfer explained it may not be the best or only thing to separate the values which are real from the imaginary so as to compute these separately.
If, as in Kea's excellent link today on braids, we utilize the 12 of things [actually we see only 6 of them with the 9 empty squares make 15 from one view rather than my vague sense of the 21] and what is within them- I imagine in the triangular orthogonal notation if we exclude the outer boundaries we have twelve things on the inside- as if a triangular geo-matrix cited yesterday on new scientist. But I only feel this for now vaguely and intuitively. Part of the game is getting ahead of our notation to see it from a more complex or even from a simpler (as if consciousness but objective view) as well as our search for a unified theory. Color then may be a composite thing or it may be that the spectrum of Newton does indeed reduce to single frequencies as per his experiments with prisms- or in some sense Goethe's color theory still has some points- especially those of asymmetric complements of subjective proportional areas.
Of course for the 3D elements of which 12 are the center the missing elements of 4D added make 21 in the three quadrants. [Note: when we go up to much higher pixel spaces into sixteen dimensions ( a sort of Fourier transform on things here divided as each pixel into 64 of 32x32... eventually in the complexity the number seven can become a divisor where it is not if the ratio of values in a lower conception of the dimensions is not that between squares. ) In this sense we may have to generalize a little bit that region from small groups to very large simple ones for some physical properties in between in this long plateau of measures. These things we should visualize after all we are indeed asking questions that eventually relate our ideas of mass and gravity to what we think about the symmetries of thermodynamics. Still, even if some of these laws are abstract they can have real consequences. The idea of a center singularity or not is essential to explain certain differences of the photon count to further explain as space properties in directions away or toward it so as to realize a difference in the stored energies. Perhaps the iota behaves like this as a theoretical subparticle not quite a string as if a general quantum like analogy to these leptons.
Interestingly too, the threefold structure's can make thee dimensional puzzle games in their own right and may have been discovered first. We can slice through the Soma cube and the slices do form so many structures based on the combination of hexagons and triangles which from that view make intelligible puzzles.
Sometimes, if we make an error in counting it is instructive to know why, a sort of doubt in the cross checking. In playing with these numbers when the calculator works- that is the factorial button now gives me error message- I have the distinct feeling there are things like quasi-rational numbers which sort of divides things intelligibly as if integers - that is certain repeating decimals of which it is not clear to me where and how they may ultimately approach the value of pi. Unless the products of pi itself makes more complex the totality and expression of its contained information in binary description. In this sense also we might find some unity somewhere in our concerns with the ideas of fractional charges although I do feel they will prove, at least on the lower dimensional levels, integer values if not binary (of which some authors like Rowlands already hints).
* * *
Some years ago the mall had a puzzle store which sold such cubes and I had grown tired of finding one again on paper so I memorized one. Ever once in awhile I would go into the store ask what this was and accidentally knock it apart. It's OK the clerk said to me, we can put it back again like we did this morning. I'll fix it I said and rapidly put it back on the shelf.
One kid exchanged two corner tapped colors of a Rubik's cube and asked me to solve it- I cannot I said, for it is impossible you must have rearranged the colors.
I was helping another child read for my boss as he had failed the 4th grade and would do so again. He was very good putting these cubes together so I knew he was not slow. But he did not want to read so I said what the hell and played hide and seek in the college green- I thought he was tricking me when he should have seen me finding him- turns out he needed glasses and when he got them and moved up to the front of the class he had no trouble at all. I sometimes feel that the study of geometry is one of the few things that can or seems to raise our intelligence.
* * *
Clearly, it is worth stating again, that in the 3+1 or 2+2 formalism we need to consider both options that apply and one not preferred to the other. TGD as I understand it is the latter only, and for Lubos I imagine the former. So it amounts to sorting out what we mean in the dimensions of things by orthogons and simplexes when we try to calculate the global view if by any one view we may resolve things to the vague idea of 5 or ten space intuitively- but at the higher and better idea of the complexities involved in defining what we mean by such dimensions. It is not enough to divide a fivefold polyhedron into vectors that are confined only to our familiar ideas of three space for it misses more refined and general topology. Let us not forget that at whatever level of complexity the simplexes (as if a continuum in itself- the Celestic continuum in my conceptions) and orthgons(antiorthogons) have analogs on the familiar intelligible level into n-dimensions. Of course in the application of this to the genetic models this complexity has to be dealt with there too. It is not enough either to ignore exceptions like the C groups in which we conclude there are infinite numbers in the duality (viriality) applied of polyhedra. This combination of vector and octonian like spaces leave far behind the most general descriptions of space we now have- like configuration or phase space and even those purely a matter of complex space- all of which have their place in the bigger picture.
* * *
Note: Duh, I have just read Kea's (MDS) various papers and find them clear reading with several conclusions I agree with or speculations on concerns I have thought about. It will take a little longer to digest all of it but what a beautiful person behind this paper, what a clear and intense mind with no nonsense objectivity- and what a good time for her to be here in this golden age of cosmology. Note, nothing I wrote above was intended to challenge or critique her presentation.
With the Shepherd Moons and their braids, the discovery at the time suggested to a few people that we had to go back to the drawing board of our foundations of physics.
* * *
Well, so much more is on line since 95 or so and so many have investigated things like the soma cube puzzles and other geometrical structures. So I spent the afternoon googling a lot of things. In a lot of this I feel so obsolete, that is compared to who was on line doing certain things when I was there alone or almost alone- some of the original people have sights now (some whom I corresponded with or did an email) that have vastly grown. I especially liked the C++ generation of the soma cube and the debate as to if there were 240 or 480. Note: the inversion of such a cube will invert the handedness of those two pieces but not the color! I note that Conway seemed especially active or creative long about 95.