## Wednesday, August 3, 2011

### Hexaplexus Hexanexus Hexacube Fields

In this illlustration a 8x8x8 hexacube (and a field with an intelligibility as a count if not an order axiom also) such that = 512 of which the hexanex leaves 480 in the hexaplex which differs from 512 by 32. In a sense the hexanex centered diagonal can be mapped on one cube of the octant if we so desire a more compact representation. Now, consider the vague concept of half of some infinite diagonal across a cube- this is the origin of the notion of on one hand the doubling of the speed of light which becomes the speed of light when the old initial paradoxes are resolved to that which is under acceleration so to speak- that is even in the quantum theory we observe this privileging of some value that the deeper field reasons assumes or explains a certain direction or surplus over the positive (after all the negations are a matter of simpler formulas and not necessarily the reason for something physical in itself and that includes complex number concepts.) Thus at a certain level of primitive or assumed primitive origins in a world where it seems matter is preferred over antimatter, the nucleon and anti-nucleon as the same mass- and this is more fundamental than showing by the sub-parts that the field ratio of remarkable coincidental parameters (that say life exists and in relation to the big bang idea) shows the apparent immortality and by reason of some incomplete part of a general theory makes that an advantage as if a proof the proton is not possible to decay under all but maybe extraordinary circumstances. That the world is symmetric and not so is an issue to work out deeper than quantum gravity notions.

Hexaplexus Hexanexus Hexacube Fields L. Edgar Otto August 1, 2011

As I come here with my thoughts of yesterday (which I did not get to post and had some more time to think about them) I find this blogger I follow with an interesting graph along the same lines of this fundamental thinking on the principles and axioms of fields. http://hoggresearch.blogspot.com/2011/08/velocity-space.html

Part the revelation of these concepts was the attempt to plot Peter Rowlands ideas on the nature of fundamental particles, the Dirac formulation to the quasic field. But what came out of it was that his map speculating on said particles was already field equivalent as complex numbers to parts of the quasic field where they share some various concepts of symmetry- such as my Conway representation. Yet the realization is that these are not quite the same thing - otherwise would we still have a problem describing these particles and such super-symmetries (of which in general Rowlands does suggest the concept can go multidimensional despite his insistence on the chirality of weak forces as the fundamental difference that measure mass or for that matter the string theories as if a form of quantum gravity.)

Basically he presents charts for the 25 or so particles. Now if things are quasical in my sense the idea of a need for four mediators in the weak world makes sense to me at last, as well the possible further inclusions. It is at this stage that we really should not assume physics is derived only from the mathematical formalism- for in a sense the trivialities reduce to what of more general systems we do not imagine or see, even often experimentally. From my understanding then the properties (which I feel based on rather vague and questionable theories that cling to old field formalisms of the quantum and relativistic tradition as the only views of which their lack of resolving can be shown on the level of existing theory and of which to suggest neutrinos have small mass is to fudge on our technical ability now) He puts the so called gluon in the upper matrix (or quasic plane) left hand corner and the Higgs or Higgs-like complex in the lower right- symmetry across the diagonal which does not in the same structural plan necessarily represent eigenvector diagonals.

I would only add, what I metaphorically call half of infinity, a sort of singularity complex- is the case where in the general quasic plane we can expand the resolution of the total system. We can of course imagine particles beyond this doubling and halving of things represented as the core three (and also possibly 4) dimensions, the viriality point made by Rowlands.

So the halve diagonal in a sense can contain any integral or binary function of the gluonic like things (hmmm where is the gravon in this, I must continue my reading him). It is here we may show the utility of applying something like Pitkanen's arithmetical theories for one thing.

So as a matter of counting pixels or unit cells, and the complexes of complexes of the quasic objects stacked or centered, that is the field assumption of order so included in the mix (hence arrows and asymmetry) we understand the ideas of braiding and so on and where the topology is in a certain sense unique as if a dimension.

I call these Hexa- for the preoccupation so many have with the representation they consider the "compactifications" of six dimensions- and that there are six faces to the three space orthogon (well 3n actually). The abstract diagonals are the nexus and that left over the plexus- these can be zeros and the diagonal of various signs. It is Rowlands concept of two three spaces each described by complex quaternions and thus more of the more fruitful string theory involving E8 that describes his table of particles. I note however it involves ten and ten things in the Conway like interpretation of the matrix (as if my first puzzle of "sea dice" A through J for ten number symbols and ten anti-symbols)... The next step is also a Pascal number of 15 which is more the first Conway like matrix and more like four space vectors.

Let us consider then the "Quasex" as a quasi-vector... for somewhere or from some fundamental view what we consider a vector or a scalar is the same thing and our theories are only so successful in making them distinct in a quasic or omnic field.

It would not be enough for example to find a theory that purely reduces things to scalars to describe particle behavior. For all we know that not observed may in fact totally vanish to creatively and probabilistically return, or that where the field is residual as creative we imagine it a mysterious, even dark force.

Still, in the quasic axiom one might ask if all surfaces are in theory connected somewhere then what does establish the sense of them as a separation and difference, I mean ultimately? Part of this is apparent logically as a dissection of abstract spheres (that is the spin is also abstract in Riemann's sense of his Plane mapping)

again the utility but inadequacy of complex planes and projective geometry only, in the division of one into five or six parts with vague detail of the cuts in the boundaries (See Tarski) so as to define the quasic apparent distance between created and creative object fields. (note also that this may involve super-transfinite numbers_

Part of the new complex of things traditionally conceived as knowledge and methods may limit newer and more accurate enquiry to the extent of their similarity of its underlying field concept. One such spatious concept evidently exclude is the idea of a fourth value or fundamental unit as mass, and perhaps the idea of gravity where these are not simply a matter of what is say some form of "inertia" continuous or discrete. That these are in a sense quasically recursive we would expect the structure if not the ultimate gain of structure in the world including mass-energy and say as Rowlands suggests the use of the "classical radius of an electron" to be intimately related to such shifts that are derived from the vibrations at the infinitesimal to which in the apparent space without need for amplification the quantum like field idea allows creation from considerations of complex number branes.

So the diagonals may be counted and treated as if coherent light or centered or focused light- that is we can define and distinguish thus the directionality and magnitude of what we mean by vectors and scalars. After all rotation and translation are also somewhere in theory indistinguishable. But this sort of finding was one of the things hoped found by our current atom smashers.

There may be developed across they abstract motions of abstract dimensions a sort of "taffy out" of the paths of mass decay minimum quasication and quantization, where also these states are free to mix while keeping their general identities.

I leave to the readers the remarkable whole numbers in considering complexes of these various hexacube tallying.

Let me return to a poetic metaphor- to see the universe in a shell and eternity in a moment- such a metaphor seems more a concrete reality when we consider what on different scales may apply when infinity is defined as subsets of itself and can relate to that which is discrete actively and creatively. But what is half or double eternity? Is this not a biological question par excellent also? I mean the idea that we encode things in a quasic field as if boxes in boxes and in that the varieties of linear encoding like DNA itself doubled and halved? What then a part of an n-dimensional quasicity of cells and that of their differentiation as a form of separation (which also may be considered a property or difference of handedness of the totality with small differnces- thus a theory hiding a deeper one again.)

So the simple idea that we could take something say 400 feet or so long and lay it across the diagonal of a 1.x or so foot unit cube which is a shadow of or the part of a face of say a 32 dimensional space. Or we can double this to include the centers of things at half-the-potential-infinity. In this sense we can imagine we can apply a measure of sorts to the flat and limitless and continuously elusively immeasurable.

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Footnote: perhaps I should call things like this ensembles or constellations- that is my use of the term sheaf after reading Kea's post I found it in relation to Higgs bundles. Hard to find terms, not like fiber bundles and so on, pencils etc... But my use of those terms is not necessarily the standard use. Most likely less than the standard term. In any case the generalizations I propose do take some of the narrowness out of our standard views, terms and methods without really giving up our intuitive tenable stances. But if in some way a reduction to and integrated plural and biology like metaphor says something about how we use existing mathematics over the physics of reality, given or created, invented or discovered, inter-subjective or unique and individual, and these be in a wider sense a unification- the result can be that our social projects as well as our big science projects are at the whim of a narrow ideology of one sort of the other, for what in the face of what is rather than why it is not as a default somewhere is greater than a particular philosophy that in effect is life and death at its minimum complexity and maximum boundaries of what in this world is then the assumed purpose and view?

A better picture of the universe, as a totality and absolute limit or not, will go a long way towards clearing up the false and the small but significant percent of anomaly in our reasoning so as to allow an honest and more human approach to various now without compromise political issues that as a matter of survival and not false claims may make hard decisions that transcend the issues of the day.

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A comment to Pitkanen at TGD diary today 2:33 pm CDT :

Note also an assessment of the situation by Rio Frio on the future of science on her blogspot.

Matti,

Of course if we throw a dart at the number line the chances are zero for all practical purposes that we do not find a transcendental number.

In my post today I think I found an area where your theories may apply to distance measure as the diagonal of matrices and of cubic structures.

See Hexacubes.

Of course from my view limiting the numbers to ten or eleven things is not good enough to transcend standard motion spaces. Clearly, (2^6 - 1)x 2^5 in the count of + or - 32 could be interpreted as 11D - 5D representations of continuous algebras of such vaguely defined dimension of the Clifford type.

In my hexaplex and hexanex count differences some binary representations occur on many scales where the count of each is equivalent. I am open to a better term for this. Note that Kea's relation to the zeta function considerations at 1/2 is very relevant. But how this can be a good future and of shown importance in society for the careers of those involved may take some time- the next century maybe as we are in a sort of dark ages awhile.

ThePeSla

* * *

I wish to state that physics may not just be about particles (Dear Lubos) as much as the general idea behind the geometric structures- otherwise, what is the ultimate use of the string theories and so on that still has to add mass ad hoc and can only speculate should experiment find the need for more refined levels?

* * *

Personal Note to Coffee Shop student friend:

Hi, from here check the sited I follow. Kea has an interesting page for Europe funding independent research... check it out as a new astrophysicist and what the future may hold for the ladies- and check out Rio Frio's concepts. See you in he coffee shop. Hope you can find these places. Here the blogs I mentioned:

http://riofriospacetime.blogspot.com/2011/07/higgs-to-be-confirmed-or-not.html

http://pseudomonad.blogspot.com/2011/08/same-old-same-old-ii.html

http://hoggresearch.blogspot.com/2011/08/velocity-space.html

* * *

Sci Mags today:

http://www.sciencedaily.com/releases/2011/08/110801094715.htm

Look for nature to utilize physics and mathematics in free possibilities! I would have predicted as much having never seen a body cell- but the symmetry of plants with cuboctahedral rigid walls in general would access the structure method here given- then again it develops flowers and is intimate to the light.

* * *

The sciencechatforum has an entry which is called pure crackpot and can be found at

http://vixra.org/abs/1107.0052

Now there are reasons to criticize this theory as will be apparent from my general discussion on whatever problems we have with the negative- and yes from some observations on the so called dark matter. But let us not so criticize this idea on its own terms for it also strives to take a first blush as fundamental notions. In any case the same unresolved problems and a shown dead end is the poster who said that of the theory, who is deep into the idea of the Minkowski models. To me both are now alternative theories that begs for a breakthrough in understanding.

I add the bubble question also posted there as new news for I did not include that link from science daily today as it too is not quite up to the more general case of what such sort of space actually may be or appear from the quasic view.

The theory has the germ of many truths to come and if they are saying in the forum it is an alternative theory we are still waiting for one that has shown there are no alternatives they present for a more complete or even a final answer. But let us not in these breakthrough or crackpot papers build up our hopes too high as the authors when we use notions of the old science and its methods- other than of course the author here shows great potential for abstract enquiry which to me is less metaphysical than those employed by the so called defenders and propagators of the science that may be- especially in an atmosphere where enquiry seems to be retarded. Perhaps the author will consider things like tachyons as one might surmise from some of the notions of his theory. The symmetry breaking concept of the Higgs looks remarkably like his graph does it not?

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