Tuesday, April 26, 2011
Geometric Analogy in Super and Sub-standard Space
Geometric Analogy in Super and Sub-standard Space
After sleeping in, with normal dreams, the two lectures I viewed sink in a bit to the point where I can question some of the ideas, or see through some of the things that intend to lead the viewers toward a certain conclusion or deflect them from what is a competitive view or something the lecturer does not know, if indeed aware he does not.
There is obviously a lot of energy, and a few sink holes too, around what at first seems a glitch and of course I, being not tied to some state or institution with a career to risk, chose to ride with the assumptions of new things found in the experiments. I do not know enough to bravely deny the existence of some things but I can support those who claim they do when I so suspect it myself.
I did some rather foundational thoughts on math awhile last night, the symbols of things fluid as the range and value of the ideas- it has been awhile I took this childish approach to physics- but it is a fresh breath in the less polluted frontiers in the sense that we work somewhat for the near future beyond the current fray and heat of this golden age of particle physics and cosmology.
Hmmm, the one lecturer- through Kea's blog, used the term "teleology" which he said he had learned recently. Such an application to perhaps the term "leading singularity." So there are some things of which I am impressed and some not so impressed- for one my conception of space is much wider- and for another what I saw in this and the other lecture through Lubos blog- is after all traditional mathematics and physics- more a math and geometry than its applications, more a context of things.
For example, if we are looking for some sort of brane like entity or plane in which things occur beyond our familiar way- it is a quasic plane but it is not just a quadratic plane- That is as we understand quadratics we can solve them by the matrix of the eigenvalue diagonal.
The rather fanciful symbols and equations I scribbled down all seemed to involve our deeper conceptions of mathematics than the physics. In the world of the multiplicative inverse of Cayley number systems we can find the super-space and sub-spaces to which we are now on a tightrope with the experiment and standard particle theory.
I will try to put some of these ideas down here today, ideas or just questions rather. Some of it involves the ways Matti Pitkanen sees things as as with such theoreticians both lecturers converge to at least some of the things seen in his vision.
Basically though, the unification of physics on some level as some not seek it, a third physics of sorts or a new physics, may not be what we expect or should call quantum-gravity, after all.
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The theme of this post then is that in all the more creative theories on the frontier, especially the growing influence of the blogs and internet for a more challenging and open discussion in the midst of chance and chaos, that in the diverse theories we can find parallels in them to signposts on the way to more general or unified theories (if those in a sense exist as such.)
In particular, and it is hard to show exactly where the difference may be as to the claims to at least published priority, is not a subtle change that embellishes, illuminated, or enhances notions as originality or borrows from an others theory.
But as in the lecture thru Kea from that institute of a theoretical group, should we not use the insight and assertion that what is required between the quantum field and string concept is the need for unitary and locality in the physics? And beyond this the great question of integrability? These reflect the background of the known methods of mathematics, its number theory that in itself has abstract limitation implied and sometimes proved so. Taking the surface of things, the solutions to squares into the diagonals and diagonalizations, is perhaps a cherished tradition now which in the more infinite and continuous cases can be physically interpreted as explaining things like the emergence of time or gravity otherwise an illusion and as the lecturer said from a more general view of the evolving of physics while these sorts of questions are unsolved on the level we can not ask them they may not be relevant to the solution and actually limit any breakthroughs to a more unified understanding. Yet, some among us, even vaguely in the doing so, continue to follow down the paths of such questions, bravely or in error of misconceptions, with courage.
When it comes to the foundations of mathematics and its relationship to logic it seems to me the theoretical physicists as well as the mathematicians are rather relaxed on the interpretations of their counting.
Is the recent confusion on what may or may not be there as discoveries of the atom smashers an implication of a new physics, support for some old direction and method, a compromise as to the idea there is a sub-standard theory where the resonances of particles are there in a sort of super-standard hierarchy as non-linear and of a different level of measures to evaluate?
I would have asked of he lecturer (thru Kea's blog) So, we have established that two planes are involved here with the usual idea of quadratic solutions by eigenvalues and these are inferred or shown as perpendicular and of course are four dimensional at least Euclidean, intersecting at a point. But in the scheme of things I would ask at what grounding do these two space vector entities dwell in, say in a greater Grassman scheme of things? Or if there is more complexity in such spaces would not this reflect, as a matter of integration, as a matter of applying a stacking of dimensions along a matrix as at least quadratic in the diagonals (a V matrix) and then the global mixing of the group of all such matrices reduced to ideas of two space--- of the notation little lamba and lamba tilde- apply the Dihedral or other groups for a general dimensionless universe of discourse and then not expect that if we so limit our vision of dimensions that enhancements and proofs to our standard theory can only be verified as sub-standard, or from the multiplicative inverse and complementarity of such mirrors, even as particles, that the range of these numbers on the Cayley level goes outward in the depth rather than be a theory that is contained within the subspaces or compatified spaces of particles.
By leading singularities I give you the iota particle concept but with a wider dynamics of dimensions, and the iota complexes. The quasic field, as we have gleaned from phase angles and so on, is after all at least potentially a matrix of infinite values rather than finite ones into which we expect the summations and reasonably expect the limits can be zero or some sort of potential or final infinity.
These questions are also about the nature of transfinite numbers, and even a way in which such numbers are also their own identity and multiplicative inverses that we may say the continuum can be seen to have a relatively real mirror continuum. And as a continuum the 2^n and that inverse apply also in a four way view with all the limitations and patterns of such numbers (can we not see that Pitkanen's probing into the Mersene primes may have deep value and relevance? and that still in the game yet beyond the physics of our time? Has he also not been limited by the traditional methods when we take the square root space for solutions of our matrices and singularities?) As far as these issues of transcendental numbers go, and the crude approximation even nature seems to have to make concerning factorial expressions of binary numbers, aleph 0 as finite is subject to these same restrictions and higher degrees of freedom that we may expect from higher alephs or other continua- as if they exist perhaps between them by default or exclusion to their not non-cantorian view in such local analogies of geometric laws to which things are certainly messy but unitary and local to some extent of physicality.
Such is a view of numbers as constrained but boundless singularities (iota complexes) that is a view defining the freedoms and uniqueness in complexity.
The looping that seems to constrain these singularities is already a property or an assumption of the quasic field (Qcm the Quasicontinuum) that does not seem to go on indefinitely or will make geometric structures to which these may emerge to make other structures of wider physicality (including perhaps the focusing of mass in its densities and the general expansion of the universe or dark energy "acceleration") is then the idea of hierarchical values not without some justification as notions?
The absolute quasic dimension (Cyrillic letter D sub n) is not the same, or is not necessarily the same as the nD of familiar or vector space, nor of some idea of a more fixed and less relative notion rR dimensions as representations.
But it helps to show the steps and details. I would suggest that for those of us with aspirations to more unified theories we point out just where some of our notions do match that of others and the mathematics established in the literature.
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