Sunday, May 8, 2011
Canonical Identification and Hyperquasics
Canonical Identification and Hyperquasics L. Edgar Otto 05-09-11
Canonical Identification - A term for a notion or concept by Matti Pitkanen in the sort of higher space covered by his "sheets", a continuous plane or otherwise.
Hyperquasic - My informal term (also) for that beyond the quasic grid or sheet that is more than just the possible moves between it regions or elements in the array.
Conway Array (Cw') The fractal like repeating of patterns of depth as binary powers that encode as if a color space the Conway Matrix. In higher spaces the diagonals as if a super-matrix are not as simple to find as say some relation of elements in a matrix to its main diagonal and things like eigenvalues.
*Observation 1 - Pitkanen has a great reply to me in the comments. It seems to have confirmed my thought or intuition, synchronously today, that in a sense TGD and Quasic theory are orthogonal to each other at least conceptually, and both systems are in a sense above the mainstream as part of a bigger picture with new questions and interpretations to which they compliment rather than conflict but to the current thrust of theory such a possible conflict is far from the fray below of theoretical chaos.
Rectori or Rectangletori - a Canonical Series of fractal patterns based on rectangular numbers that embed within each other, the elements of the containing grid of the orthogons the skeleton which themselves are designated or made of sub-pixel quasic regions of the epsilon honeycombs. This is instructive for a notion of pair production. It asserts for example of an orthogon of so many sides two of them may be viewed as concrete or invariant and the rest toroidal and virtual.
Can the epsilon honeycombs vanish- this seems an issue of something like fractal dust or that property of holograms as to a limit of a pixels contained information yet paradoxically such fractal models have no such limit or loss of intrinsic information. Rectori also suggest that two orthogons as if particles may merge (or alternatively the "mouth of wormholes" in ways that explain particle decay in the specific examples. In short this grounds the idea that we observe in quantum and relativistic physics.
But in reality, observe the illustration above, the concepts we use and apply for the idea of
Virality - a term from Peter Rowlands that suggests the inverse square law is the foundation of our laws of space and its three dimensional structure. His Diracian system also is a sheet similar to Quasics and TGD.
holograms and taking the square roots for some functions over such brane-like sheets of many dimensions is that is how we have treated the question of boundaries and the holographic principle. But in the depths of these immanent forms are whole new ideas of what is symmetry as half or double (or any such numbers and processes) that utilize viriality principles, this includes virtual mirrors in the hierarchy of our models of complex number systems.
Observation 2 - The alpha and beta factors (and we introduce the more general idea here of quasi-factoring) is straightforward in the labeling of the sides of the quasic grid in the illustration above in binary numbers 00000-11111.
But this factoring (and the issue of what it contains as far as information relative to the information and meaning in the grid itself) is not just an ordered sequence from one view (the top of a system of trees, a canopy) but contains in itself a sort of quasic hierarchy as if the trees branch to it. This is a difficult linear way to try to sort patterns out if we do not make the distinction then to try to get around or unify them again without the benefit of these sheet like theories, this is a fundamental philosophic issue of methods which I have called Teleoscoping in the actual sequence, continuous or otherwise, directed or not, over discrete steps.
Observation 3 - This factoring is suggestive, from a finite view, of a wave and particle duality in that what is linear in the alpha and beta axes becomes circular in the sheet itself- and this property extends throughout the quasic grid and when we try to map abstract motion functions between various concrete representations. One can, as in programming, put in each cell of a quasic grid a linear set of bits- but this pattern does not show the depth and span or dynamics in terms of what is happening with such binary coordinates. It has its uses. I do not generally use the common way to make such multiplication tables nor have felt that comfortable with the decimal system for counting. Now, this core problem in how and why we favor some counting over others in this five fold case at last makes it clear that the decimal system has some great- if hard to see it so prevalent- benefits.
Observation 4 -It is clear also that within the quasic grid, here a Conway Super-array, that some properties of the position of things carry over (even if it is not clear to me how one may actually make a set of hypercubes with colors) For, and this is a key point for interpretation of the genome of biology as well as of the existence of the lifespan of virtual particles (thus the question of just how "everlasting" or "eternal" may be the half life of a proton) That the center of triangle grids, the H in my color system a neutral point on the center of the top right bottom down other or quasic diagonal describes where in a system something is initiated or terminated in the reading of the gene (or cosmic and particle) codes. Part of the location or coordinates for such pixels are such that in the quasic or circular order in groups of four (and here 5 as per partitions) these are symmetric with variations locally in the actual chemistry and its evolution, across the quasic quadrants (0124) the 2 and 3. This again is the order of things used to solve the quadradic equations involved in deriving some relativistic group transformations. It also amounts to halving or doubling things even in complex space.
Observation 5 - In the Rectori of my previous post we observe a ten and a six system of multiples of 5 that looks a lot like the first description of particle organization. I note that the 25th and 35th, initiator and terminator codon in this sea of multiples of 20 are symmetrically broken and not materially balanced between these triangles. 35 is not in sequence in them. The sum of the ten grouped triangle set to 5n is 240. It is also surprising where 5! falls out of these number theory considerations- as well 27 and so on... there was in the margins of the illustration above many such number observations.
Observation 6 - What then is inside as a lesser dimension in the illustration of the Conway array is not all of the (dots in the picture) cells involved but it too is a 6x6 array where 216 comes up often as part of the picture and this is not to be considered an artifact of number intelligibility of say factors of 8 x 27 which in itself would be a way to represent and divide associatively a 6 x 6 set of cubes. But of these, and I label the pixels or cells of the quasic grid (of 1024 elements although 512 as derived by TGD is an equivalent description of which we in effect have a hyperviriality concept for 3D symmteries carried thru the dimenions- see his comment for such concepts also had me explore what I now call the Icosatopes, but it would have been nice just to find 20 of them in the quasic grid and not 100 which of course if 5 or 10 fold of that 20.
Now the abstract motions listed in the illustration are in reference to 00000 for the hundred and 19 are outside the 6x6 inner elements (btw we can make some interesting grids of numbers of the dots and these summed up or down by 4's) or if we make the moves from 11111 the same case comes up again. It became a simple problem of intrinsic binary order and which of them contained 2 or 3 0's or 1's.
To compare the 25 initiator with the 35 range of terminators compares their information as an abstract motion to each other.
Observation 7 - As a matter of philosophy (I am not posting some deep speculations today outside this area of discussion that clearly are speculations) we may say that the 0's are non-existence and 1's as existent's, say mass- thus we can imagine structure and mass of the +1 (that is fuzzy pixel or wildcard* after all we have to shift sometimes to count from such a pixel as zero or one at the singularity.) and of course the symmetry of the mass and its mirror or shadow is there because at a wildcard the reality may be * = 1 v 0. But in the considerations of some god's-eye view property of the grid which is a sheet or brane self contained possibly or at least reaches out to contain all things, such a pervasive space is more likely to describe as an alternative interpretation our idea of gravity in its ultimate and bare form and thus its relation to space, and to matter so contained.
Of course we understand that 20 points determine the dodecahedron of 12 faces or 12 the icosahedron of 20 faces.
On this level of topological and numeric structures it is also clear that within this level we can have measurable differences in mass or weights of things that obey an intelligible number of things- as such these may change or oscillate in a system akin to particle exchange mediators- or between the duality of polyhedra- and this makes a whole new idea of a local or once only symmetry breaking where it applies as in if something (like a quark or black hole) may be considered isolated or in a system how it may radiate decoherence over existence of its inputs = to its outputs as real or virtual mass- this may lead to a concrete representation of what Hoyle understood as the processes of his creation field really just an interpretation of the usual hyperbolic groups applied to theories of space. It is not clear that the property if dark energy is one more associated with mass, or with gravity, or with ideas of the non-necessary density of general space.
In the 1 or 0 idea we have what we might consider, structures ultimately aside, a key difference between a center singularity or singularity complex or not, an that in some ways we might develop a symmetric relation by virtue of the simple act of multiplying or squaring things between these styles of singularity in some region of space where we desire to know if it is simply connected as an entity may metaphysically vanish into and arise from itself as to its entropy and complexity as a structured and evidently a directed entity at some point of its self-symmetry extent of its being.
(Perhaps I did include some of the further clearly speculative parts- but these did flow naturally from the discussion above as where they came up in the writing without those ideas in mind. Only the fifth idea of such speculation, and still in progress or on pause, is this question of representing particles in oscillations and decay in terms of this sort of array and colors (not to be confused with color as a term in the standard models or string models)- so I hold a working term, not one of the natural ones or of some symbol we use not sure of its clear meaning, Quasicolor.
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Well, in this thought on TGD I thought I should alert Pitkanen to my post today:
Thanks for the informative replies on comments in your last few posts.
Today I found similarities in our general approaches in which I have mentioned TGD so you might want to correct me where I may misunderstand it. Look under:
Canonical Identification and Hyperquasics.
Oddly enough 10D is involved here and it could possibly be seen as black holes- in the coordinate notation. But even this would be but a start to this new hyperphysics. I feel like Klein in relation to Sopheus Lie to you in founding a new level of theory.
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A stray thought again: I only touched on the much more difficult ideas in this question of information and meaning- those poles of what is consciousness as related to a more physical a biological formulation- that is how thoughts are conveyed and organized between us and in what poetic or earthly representation among all the noise. Of course we can measure the noise and take it for an advantage. We can paint the plane with quantum variations, look for tendencies and patterns in the Cosmic background, or chase down with our methods of statistics and improving power not so much some particles as to the theories themselves with hopeful goals toward some path that is sustained- or of course our outliers like the data fades away with finer analysis - the hysteria of those decays Lubos wrote about today as if we all sit around showing how to build the barn but not coming together to raise one- build unto nature its dikes only to break them down again when she goes beyond the expected- without a true deeper explanation than some always controversial theory of how we should all live together with the environment- ah it is so easy to play both sides against a shrinking middle in global weather, weather control and climate... nature should not rule when she gets her cycles, apparently, too powerful her hysteria and too isolated her premature menopause and averaging of hot flashes after hysterectomy- an operation percieved or needed to hedge the bets on what we my prevent of behavior that might be and expected from some pattern to hold so many guilty of free will, give a name we do not exactly understand but conveys a lot of meaning like pre-cancer.
What is a mother really but she who provides the seed and she who provides the breasts- while each has a life to live our relation to each other can be that of needing surrogates in order to do so? How many unhappy people expected much and claim the victory while the war continues many times over as long? We desire then the roles of Renaissance Man and Super-Mom, only in time shift the life styles or press it a bit by some human contract written into law, with our without covenants.
Yet, in this gazing at the earth while in the earth with wonder, in the forming of words and thoughts within oneself or between us- like the virtual particles that blink in and out of existence or stay around awhile consuming, emitting heat and light, on this human level that has finally touched the cosmos that what we thought was junk genes in some higher state of awareness and abundance, had deeper symmetries- ones that might be the mimetic inheritance of culture we thought at first when but a decade or so earlier this made sense at the frontier and fringe if we long for those simpler times. We are closer then to that question of where thoughts come from and how original they are or unique in the bigger picture of Nature. I suppose the philosopher wonders about the origins of his thoughts- and yet the poet, interrupted by the capturing of some of them, lives his poetry in the metaphor and the writing. We do not lose our childhood wonder as the theory progresses into adult and fading life where so much of everything over our breath of an infinite and natural space of a lifetime comes again to symmetries where we recall, as does the body, our early stumbling and scabs not healed as if some imagined bleeding from sacred wounds, that in such symmetry we feel them balanced at the end too late to take precautions with our own children, at least we tried a little better than those before us, words uttered not to be taken back, words not clear or misspelled to remain in that part of information and meaning not given a chance to find what in it is as much needed forgetfulness as our own real or virtual permanence and uniqueness. I wonder if our thoughts come from the fires of some first beginning and we in the same wavelength and timezone, that for all the slightly different perspectives- not to preach the parable of the blind men and the elephant that for some who want unity of things we make of strings the theory "M",
that for some of us so different yet unique, such fresh ideas come from the same place. And as we learn a few souls respond like new born stars, until all souls have the sense of awakening rhyme while the information falls into its quantum dusts.
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Is the Illusion of Perceptible Motion the Case in Physics, a Discrete Case as in the Theater Film and Marquis Lights? Where does the Magnetism Go in Superconductivity?
I suppose to have something god-fer-sure original I will have to at least go to the next case or level- if for no other reason to show there may be no cases beyond a certain point after all- that in a way the Higgs mechanism idea does not proliferate as a condensate (see links to Ulla's blog) if all of this is really about some sort of degrees of freedom- the next case may just solve the internal symmetries as analogs to he electric ones as the elegance of my grids are still not quite reaching the bigger picture. But such concerns apparently are but my own in these methods.
Is there a Cw" array? stay tuned folks, I am still looking for a fundamental breakthrough here past the things that some seem to say about groups and such- and this relation to the idea of curves and so on.
How odd that only a few people will be able to understand my posts. But that was said in the popular world for relativity (only 6 people understood Einstein's theory) I recall the time he passed away, that year mars was near, and my father explaining the fourth dimension as best he could for a radio engineer. Well, that and how long someone would live if we lived on Neptune - we pick up some strange myths from our parents quietly trying to interpret them... I think maybe he did respect my work, caught him admiring my science model of a hypercube he was showing his boss for RCA which to me he would say was fantasy- and he was right- I would be a little less employable if I were just a poet- damn, I am. But guess that is what days for our imperfect mothers and fathers are all about, search for a better life and theory and so on, worry if your children fit in as much as know their place. Hey, one day while helping pack some items he said to me "Hey Einstein, don't you know better than to put a damp sponge on top of the masking tape?"
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