Monday, October 10, 2011
The Inelegant Matrix Theorem
Alright, Ulla, referring to a comment I made to you a few posts back, that I would look again at your general question of matrices. I guess, if I let you into my head on some issue it most likely has some synchronous value- yet I saw the answer vaguely before I read deeply your posted comment.
The Inelegant Matrix Theorem-
The influences of things squared is all important for our theories of physics- and of those the square matrix stands out as that of stability or instability. We can of course work within a matrix and so apply the concepts of prime numbers. We can strive to place on such arrays some general expression as an elegant directionality or asymmetry to describe some physical situation.
Or we can see that in trying to impose a balance or a general elegance on the spaces and processes the matrices describe that it is the very inelegance that hints we can impose general theories of groups and symmetry. One might say it is the origin of where these symmetries tend in the search for elegance in multi-dimensional theories.
In a way then, the question as to randomness, is one of how in such matrix spaces we can regard them as unique and prime or as predictable so containing prime laws and interactions. As such we find what arithmetical and topological laws there are as intelligible as relevant to our experience and theory of the universe.
In a sense this justifies the general methods I understand as TGD or p-adic grounding of numbers (where even if a number is but a symbol that represents a class of things containing much information and little specific meaning, a theory tends to have an intelligible unity on some level, a reference to changes or deviations from such unity.
To start with the change from 25 to 37 if numbers are arranged inelegantly into a square array is one that for me kicks in the initiator and terminators of that level of symmetry laws that applies to DNA as we know it. But this depends on what seems a lack of finding ways to understand the primes as if their pattern were totally random or of independent units when they apply at some certain threshold. There are other ideas involved such as Pitkanen's use of such numbers (that too not clearly relating to what may be the differences in 4 or 5 space formulations or where on the linear level these are limited by some elegant idea- certainly the lack of combining the arithmetical and the topological inhibit our balancing of theoretical elegance.
Yet nothing ultimately shows the universe and not on some level forever inelegant, so far. So we have long standing unsolved questions on what are the primes that strives to solve things by long standing limits to what we know of groups and dimensions. In my notation above ::: could be a ratio where we are obsessed with six space as an emphasis. But how many ways must we enfold the idea of 6n + or - 1 and try to fit it into such a hint of a pattern? Not to say these ideas are not part of the general picture as good as any if the preferred one- albeit one of insufficient generalization.
Perhaps the reason I suspect this as a correct reply to you and an answer is that I have considered in quasic graphs the ratios and labels across the diagonal, more of a logic concept, perpendicular to the main diagonal as also theoretically significant for the physical world. But can the reflections across all limited groups that apply completely describe an elegant theory or would certain numbers be left in a symmetrical pattern, perhaps holes of the composite variety?
In which case the idea of entropy as randomness, or as part of some irrational number convergence or divergences may be grounded in such a general concept of primes as things balance and evolve and certainly can be interpreted as wave probabilities which is one of the essential philosophic views anyway. But can such views, especially if we have dark spectra of uncertain continuity of which no one seems to try to reconcile in the measure reconcile the wave description and the matrix description of traditional quantum theory shown equivalent, that is elegantly?
Sorry, my thoughts on this by the river were not as complex in the wording but it is the best I can do now to simplify it a little. I know 89 is important but it is not directly inelegant- so can it apply to a higher form of space or knots?
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Oct. 10, 2011 Dimensionless Structural Topology and Perceptions
I gaze into the river from the veteran's memorial bridge. The sunlight makes the spiraling eddies and the vortexes stand out above and below the water level. It is hard to tell at first which swirls are above or below the mirror of the river's surface. The muddy tornadoes spin as well those above the water level for the most part clockwise. A few seem to spin the other way. I pick one and try to make it spin the other way- and I did this a few times. Yet, who knows if it were just my imagination or some trick of perception.
There are dimensionless constants as numbers- and there are dimensionless constants as well topological spaces of the visible and invisible ratios. Pinker says we have evolved to see in two and a half dimensions, and can mentally orient things in three. In imagining higher ones I think we can orient them mentally to very high dimensions. Yet, what then of the viriality, the halving and doubling of things. For, in the inversions where mirrors complete the symmetries we only see half the next and forward dimension and part of the next particle generation. Thus if we imagine (and these simple concepts being on some frontier of cognition, Matti P. does make one feel the explanation is too simple or pat- as I too said once of some earlier insights- too good to be true.) So, we have the inversion of 2/9 which will express the 4.5 of nine dimensions. Thus we find these unities, scaleless, and projected and recursive pure numbers as part of a seemingly neutral picture that gives us the other whole values if we seek them in the measure of the particles on the other side of mirrors and statistical natures. This is too not weird not to be true and very simple awaiting the relations to pi and so on as part of the coordinates added or multiplied across mirrors. But that is all I have for now- some seen by other as for example the falling out of the number 163 (actually 162) in the mix. Note also the raw numerology of those spaces left in the 3+1 (that is 192) formalism as values of 28 across the 4 quadrants- or as values of 9. And in some ways we exclude the 36 of the real representations in three space of the Conway Matrix of Mahloon color cubes.
But to compute these things on this side of the mirror and change them physically (see the Kea post today on orbitals), to turn the spirals around anti-clockwise in the flesh- that is as hard as to have the insight to see into the depths of the river and keep clear what is real and what is illusion.
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Beyond Thirst in Scripts of Blood Sung in the Wilderness L. Edgar Otto Oct.10,2011
When, after a long climb to the highest mountain and
descent into the lowest valley- the same place, some Beatrice,
Some cosmology in the crawling or moments of
your pony express outrunning the masked outlaws
No matter how mundane the message you deliver,
that your found yourself whole again?
Or wondered if the mollusk shelled creature with
one life and no other was really you and not delusion?
Gods and parasites perhaps to blame for your confusion
wounded slave not at fault you remained so and
Forever the fool your fancy to transcend ruthlessness
in courage to walk away as much to stand and fight.
The universe as well the hungry know not what they do
Seemed so indifferent before we knew better...
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Lubos on the Higgs particles (4 becomes 3!) an interesting theory:
Where do the X and Y particles fit in to this?
Yesterday, 3:01:20 PM
Dear Pesla, if you mean X and Y bosons from grand unified theories,
then they are totally analogous to the W and Z bosons, including the spin. They are just associated with a larger symmetry - one that also transforms quarks to leptons and vice versa. But they have the same spin, they're massive (much more massive than W,Z bosons, if they exist at all), and their being massive means that they have eaten a component of the Higgs field (although it is often - but not always - a non-elementary field in the grand unified theories, or a stringy one).
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