Basically I considered in the quasic grid a count of the contents as if a series of Conway matrices in a sort of hyper relation to each other and their dimensionality, that is the more general idea of mixed, covariance, and so on from the symmetry in the grid. The numbers come out intelligible.
The relate specifically to the Triaconway puzzle of the 30 cubes- but the diagonal of the Conway matrix as with any matrix has special meanings and uses including the wild-card primitive initial cell of all quasic matrices at the grounding finite or infinite region or pixel. This as with Eddington's insight helps to explain what the value seems to require +1 to some accuracy (other than Eddington's more relaxed philosophic explanation).
In a sense these "quasi-scale constants" can be found from a general counting of group numbers and symmetries in much higher topological spaces than from the Pascal triangle considerations in the very low dimensions. These are then able to act with the usual mathematical operations. We might regard for example of the 6! six color cubes hypersets of 6 of them (12 with inverses) describing the 60 group of the dodecahedron (in ten binary coordinate quasic space =1024). That is of the six colors one is the center (or outside shell) of the singularity status of the other.
Thus we have the six pairs of inversion axes through the dodecahedral faces as a way to interpret some of the properties of numbers and higher crossing spaces and topologies- in any case the fixed space of these six cubes even when expressed as all possibilities does not cover the non-dimensionality- but it is a vague mistake only justified by a quantum interpretation that such effects are necessarily active on structures because they are "non-linear" - rather, it is a cop-out to which like with all faith that one might find the shamans sometimes use tricks and magic and part truths as lies to lead the student into either an understanding or the priesthood.
But, with the snow and all and still not access to my old work in storage, I do not have the time nor inclination to recompute the symmetries of Triaconway today.
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A Footnote on Mirrors and Non-mirrors in the Standard Physics from the traditions of Maxwell and symmetry unto particle and field theory descriptions as strings:
I still do not think many have grasped the wider generalization and complexity of the idea of chirality in the twists and mirrors for a foundation of physics.
Although many have stated the problem- for example that of the question of where are the monopoles. A few have understood this problem by the postulating of say a discrete system of some sort of particles, asymmetric or neutral or otherwise.
It seems intimate to our current speculations on dark matter-energy and the behavior of anti-particles. But we have taken an unsolved problem in the realm of physics as general relativity, frames involving space and matter and so on, and applied it as still an unsolved problem at the subatomic level and at what may be happening on the string level to which some things are still outside our experimental observations and may forever be so. It is really this tradition and agenda of physics that is to be defended or adjusted to what we say we mean by physics as concrete and not say its extensions into things like string theory. That theory only keeps its seriousness as science in that it supports the old applications of the old physics- even if in a sense the quantum theory trumps that of the relativity's, at least to the point we ask relativistic questions, like Dirac brilliantly did so on the scale of electrons and so on... The cost of defending such science as faith to to leave its progress to a great extent in formulations that remain mystery and faith. It also undermines from a slightly greater generalization or unification if that is possible, where clear applications of quantum and GR (Qlassical) notions do and will always apply if it maps to the functions and phenomena of reality.
The question brought up on the blogs lately is that of matter and antimatter being an attractive force- they certainly can annihilate and we can compute the resultant energy which may be the greatest method possible short of perhaps creative states of vacua like the black holes. Is this not a logic question? Someone had said, in some book I forget among the popularizations of the time soon obsolete and growing dusty in used book stores today, and in little diagrams, that antimatter and antimatter in a sense gravitationally repel. Why could matter and antimatter not in a sense attract or repel, but only from one of the poles of such a direction? At what level may we say that an atomic string might break into isolated quarks? Is the universe expanding as such its space or in a sense is it pushing away to distant structures or places and times what is after all the rare antimatter in the universe?
Or again is this a matter of the logic of possibilities where that logic is intelligible?
Surely there are already theories that question or eliminate the need for theories of dark energy, if not opaque matter virtual, continuous or discrete or not. One would be the universe as a whole spinning. Sooner or later, in the tradition of the last century's physics we might tweak the values as reductionists in style- even prove and not hold off the question to remote times and distances, if for example some particle such as the proton are our everlasting grounding of the real. That many have this faith already, one day we may show the material cause, one day we may understand the brain for example by the nerve connections. One day we may but it may also only reach a level where there are still mirrors of doubt and mystery of what is understood but remains hidden. One day something entirely new, and as physics, could arise for there is no reason to assume we now the pinnacle of science and philosophy and not but here in the beginning of a longer life of such if our world survives natural and man-made disasters.
In a sense if a path can return but in the process become its opposite, or objects in return and facing each other in direct seeing in effect look away- if after infinite time and speed some idea of acceleration becomes rest- how might we really distinguish what is the matter and what is the antimatter in an ultimate theory?
What does it matter from the omnic view or prove if in saying some state, discrete or continuous is but a unity of some measure of dimension if ultimately any such unity of scale or not are known to be composed or break down into the still vague but inductive confusions of the zero and potential infinite? In this sense the speculations on ideas of dark matter, even as just a notion, is good for physics.
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Yesterday, Lubos had a youtube video of one of the founders of string theory lecturing at Stanford. To that I make a comment, not his post today as political concept on "feminazis" (yet his posts state from the start a right wing bias.) Perhaps that level of bias between philosophies of gender colors our ideas on what is matter and anti-matter, handedness and so on. The old French saying goes, "a man without a woman is half a man, but a woman without a man is nothing at all." Surely we may claim some benefit to a woman from an evolutionary stance that even if pregnant sperm stimulates her immune system, or we can say socially that the closeness or intimacy of sex during pregnancy helps socially bond the family.
But I have to admit that the part of the lecture I saw, up to where he describes the difference of strings on the nuclear level then to the Planck level- that the ideas in a way game me things to think about the reading here and there did not clearly convey. But thru my eyes and now a long history of speculations, if you could see the lecture thru my eyes perhaps some of you would not fall asleep. Not to be unkind to the effort and awakening of that part of physics- even if once something is achieved early on the old guys (and some gals in the same field, a married couple in particular as biochemists who dismissed my more topological ideas on the gene code and who said it was just a matter of electromagnetic induction) seem to sit on their early laurels forever. Some of course, like Stasheff, continue in a fire of discoveries.
Well, some parts of the lecture - and I really do not know what they teach in schools- and by no means do I not respect the noble profession of teaching as opposed to research- struck me as historic developments with commentary- like the discovers of the resonances being linear were lucky in the guess- two points determine a line the professor said they discovered, jokingly. Now, I suppose humor is a good way to teach, at least entertaining as if the professor had read deeply from the Holy Book of Seinfeld. But it is a way to educate, lead to an idea rather than educat to lead what may be thoughts from within the student innately. This seems to me done by glossing over certain ideas or at least questioning their case logically. But I must say the quality of the questions the students asked him and the disruption in the flow of the presentation seemed to me to be of a very low level, perhaps embarrassing for them to ask. He seemed wise and old- but the result of this as ancient as I am I felt much younger.
I think, as in the simplification by Feymann's diagrams as to say turning them at right angles, that such simplification, loosing some field information I suspect, is only possible because of an underlying new physics. The intelligibility of quasic and topological fields- in fact the linear resonances are a direct result of this as well the significance of diagonals. But some lost information is really that which was not there- perhaps there are no gluons or gravons or Higgs and so on, not even in the artificial grounding of physics could we make a world more than one of notions only based on it. It is clear that in the reading of some matrices as some of our new physics theorists here in papers point out, there is the up and down, sometimes asymmetric result when we reach the two space in which these reactions occur- this is most evident in the new theories as to how the physical structures of the gene code evolves, is expressed, and is read. These theories have not envisioned the quasic space save perhaps the first inclination of it as a disembodied M theory. Nor have they yet to explicitly apply the arithmetic ideas and topological ideas assumed vaguely in the background of theories that after all must progress in the expediency of publication and discovery.
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