Extending General Number Systems (N Q O M
...)
Beyond the Complimentarity of the Quantum and General Relativistic Systems, Nature solves our notions full of contradictions. L. Edgar Otto Eau Claire, WI
http://arxiv.org/PS_cache/hep-th/pdf/0702/0702177v1.pdf
Some of the ideas in this paper I found from anna as a comment in Motl's blog today comes at a time when reaching the limits of the mathematical operations involved in notions and thinking, the loss of them in more generalized number systems left me with little to post or write. Consequently, my notes of last night were rather sparse. Yet, I am not now surprised at this for I begin to see we, when of all the changes of systems happen, find ourselves, our awareness in at least one circle or pehaps fixed point as a reference to our reality in existence.
What I noticed was the idea of quadraples, that is in the number theory formula (2^n x (2^n)! / n!2^n) = (4n -2)! , that this is also (2(2n-1)) ! which recalls the magic numbers of electron shell configuration, ideally. thus we have the sequence 1 2 6 10 14 18 22 ... and so on (with of course a view or actual limitation of the number sequence for general number system reasons intrinsic to the algebra and numbers themselves. This multiplied out results in the sequence 1 2 12 120 1680 30240 665280... any successive two divided together gives the magic sequence.
This would seem trivial but I was trying to count some combinatorial relations in higher space and coming up with some interesting integers such as 5040 in the counting from other considerations of what sort of matrix we have that applies a group rotation if the diagonals are 1 to 9 and we simply add the elements together- being the sum of 25 x 20 or 500. This is 168 x 120 which are both important numbers in such theories of some background of general space.
As with all things at the limit of our comprehension so limited by say mathematical operations we are in an area of speculation which seems rather wild to me then and this morning which after all is about our concepts of Higgs-like, gravity-like, mass-like analogs, monopolel-like entities which is the professional and crackpot propaganda of the day in the SUSY or dark matter war. I may put the down at the end of this post as background to my more concrete philosophic considerations.
The simplicity of all this, as well the complexity when we explore, develop, or ignore some path or view to an idea of a more unified system - how this differs when committed to a method or system is the issue and is one about the foundations of mathematics and physics. To start with we note that these issues are stated as theorems which exclude the zero vectors. This is the origin when we try to extend our number systems (of the imaginary variety) of concepts like zero-point energy, or like the differences between phase and position space. It asks or explains also the unanswered question concerning neutrinos if they are Majorana- this itself a question of information that can be transferred non-locally for finite values or any number in the entire Riemann sphere- including of course the zero and the infinity poles themselves involving rotations at this last property of octonions and beyond that into an inferred or hidden system without complementarity at all- that of course only thought existing if at all as a structural background. We can claim from some view many physical properties as illusions or for some objects that they only exist- despite the same information there, from an alternative reference.
For such general systems which metaphorically I designate KLMN OPQR as a token to the 120 elements from my view possible in three space for an atom, N the natural system, Q for the quaternions, O for the octonions and M and R depending on how we approach the macro or micro scales and what is within or without some structure in the depth and span of our methods and systems... M-onians for our vague conception of M theory, and R for the Ramanujan background or phaneron of space and perception. KL held in reserved for existence thus metaphysical. It would be useful to describe simpler states or transcendent sates of the physics of a World if any.
This leaves us with N Q O M the P the topology background and the order of the general number systems seemingly out of order as a reminder that some things can be mapped as braid space.
Some generalizations may exist mathematically of which we are not sure have physicality, at least for some theories in the present- of which in our time octonions may still be in that position as some papers in our blogs suggest should get into the mix of the debate. I further suggest, for theories that move the background based on arithmetic and those for topology R and P, that M is also a structure to extend into that is at least the 16 dimensional case of neutral or null effects.
Yet, even here we can have a looping back of sorts to a more unified theory of things in the level of the context background in question. This, when we in effect find a three space number system as if it a complex space by simple labeling, begins to explain the ideas of the generations of physics and analogous concepts of triality like our notions of color and flavor of particles- those a generalization of numbers in some sort of different representations in the same number if we so order them- and apply, like partitions, with rules that factor them akin to factoring spaces and numbers.
Yet, even here we can have a looping back of sorts to a more unified theory of things in the level of the context background in question. This, when we in effect find a three space number system as if it a complex space by simple labeling, begins to explain the ideas of the generations of physics and analogous concepts of triality like our notions of color and flavor of particles- those a generalization of numbers in some sort of different representations in the same number if we so order them- and apply, like partitions, with rules that factor them akin to factoring spaces and numbers.
I still do not see the magic values in nuclear shell numbers as a beautiful ideal system say as if the dual of some hyper space solid like 120 to 600 cells in 4 space for example. A great grand theory of things. But again with zero vectors and time in motion linearly in the microcosm view this side of singularities we expect in the three space variations if we insist three space as a dimension is fixed and independent of other dimensional effects and not at least a triplification. Of course the internal protons are complimentary to the electrons so octonions may suffice.
When we consider 8 dimensional objects it is as clear as pascal's triangle that when we add two from the last row we get numbers in the next and thus extend the binary value a dimension. In this sense the claim the world is 9 or ten dimensional, or 11 or 12 and so on is a matter also of specific structural computations, the row in such a 2^n in the triangle can be extended to 16 or 18 in some cases fairly close to our standard maths and so on. Here my intuitive grasp of the spaces of games and cubes finds the reason the 4 space chess was 1024, that is 2^10. I note also that if we consider 2^X as subsets intrinsically not 1 to 1 greater than X this has a compliment in the sense it is also that much smaller intrinsically in some background representation. But there is nothing to say that beyond some general number system values these cannot materialize again into some real space of our natural dimensions nor vanish to some ordered evolving existence.
The promised speculations: Some particles may exist only as exclusions or illusions where they are in other dimensional or opaque spaces and have no intrinsic existence there- in that space we may claim they are constrained in their measured value by something like quantum mixing or combinatorial considerations of the topology- these two not necessarily the same thing outside of some sort of complementarity and duality or quadrality...
So the terms Higgs-like, monopole-like, gravon like as a position of exclusion, from the view of only so many special subsets of primes, and from the extension say into p-adic lattices as primes all of which ultimately can be explicitly expressed as factorials... an idea perhaps there is no ultimate chirality for black holes where there are no such X-like objects singular or multiple, singularity or singularity complex, for the exclusion, the vacuum implies the notion as real of the unified concept of what is mass that is gravity virtually. The Higgs-like may not exist as it is one with its anti-self, similar to monopole-like entities and just like the imaginary gluons as if a particle we can expect in such proofs of valid infinite descent, probability considerations and a hierarchy of such mirrored real or illusionary illusive objects. The general idea of H and anti-H like objects is simply that in the 4ness of them the implied space and its solutions are in five natural dimensions.
And the pseudohedrons are such a description of any unification of Fermion or Bosons systems.
* * *
Thus the elegance of super symmetric matrices determines if neutrinos (momenta and angular momenta conservers for accounting) and the relation to our notions of energy and entropy is that from some view and in some thus basis in some statistics is if it is Majorana or not. If there is a confusion speculation on the ultimate nature of some particles discovered, or even imagined it is evidence of these elegant and mathematical considerations of disembodied symmetries which in the reality of the objective experiment is the result physically of our general number systems in our existing and perception of the cosmic and atomic backgrounds.
Strings on some fundamental and measurable scale of levels and application, and an analog even if only in the form of things for life "force" or mind, also tend to divide into notions of phase and position- the over all limits to our three space as a dynamic one between its adjacent dimensions where there are asymmetries of complimentary as we know by the application of group theoretic ideas that not all of some things can be delineated in both directions of a theory- the prime example of this is as in the article in the link above, what is real and what is complex in the solutions of general numbers, vectors themselves a generalization for some physics applications. And of course what we can or cannot find as we explore matrices from one direction of an equation or another as we intuit some wider planes and landscapes.
* * * *
John Baez had this most interesting link up about fundamental constants: (Through Kea's blog, not sure why I checked this today but find it rather relevant).
http://math.ucr.edu/home/baez/constants.html
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http://www.sciencedaily.com/releases/2011/04/110421122327.htm
From an evolutionary point of view, this article points toward the G to C quadrants of quasic space 8x8 at least, as a matter of topology or chemistry and the extension in my view to deeper binary powers of elegant matrices. From the Omnic view it is suggested in the article that in a sense there is a "setting back the clock" with the ALT structures in tumors.
* * * There is an interesting article I could not access on newscientist without a subscription. I was going to quote the last paragraph and supply the original paper by the most interesting author there. But when I went back to find the spelling of his name a note at the header said please do not cite this as it is a work in progress. Its content is social as well as about numbers and counting. That is, I have begin to search google lately for more original sources for some articles.
Well, not since Gammow inspired a generation of young scientist with his book 1 2 3 Infinity have I seen much on this issue- our generation seems to have its savage numbers or limits to counting... can we not see beyond three space? Can we see beyond aleph 2 if that? Can we not insist like the prehistory sheep herder to divide transactions of trade into 2 if we reach the confusing number 4? In our time this reflects an attitude to more primitive man in the still to be colonized world and the literature of the time seems so politically incorrect. But there is a science issue here, well, maybe a social one, for in a sense are we not still primitive in a sort of prehistory of counting? History repeats itself in a way for not since childhood reading of the first world war has the world come back to things like a state of Serbia, or the old flag of Russia and so on... what numbers would the Hindu god count with a thousand hands? If SUSY is a noble green mansion of innocence or just a savage, either way she is not without her warts and beauty. It may not be about race really, but it is certainly in our genes.
I would like to see what he said about Cauchy and Euclid... but so many things seemed tied up and hard to access, when you try to download from the university repository it says : you do not have the right to download this document. well, what do we savage number counters know anyway?
* * *
The Rose Between the Ages of
Poetry and Prose
L. Edgar Otto 01-24-11
Here falling up or down into the aether
its shadows a firmer ground than light
I recall my explorations through the
petals of a rose, its scent and velvet feel and taste
Oh that was another time, no noble savage place
to explore before the age of steam, then Witches of Endor
When poetry was empire and progress, that or gyres
were one cannot see the sun save its dark side fires
If this is what we take with us, shorn of thorn
life was no waste, no rose spiders for butterflies
'Tis said the hourglass figure is a sign of intelligence
I must say you were very smart
Back when Time's river flowed four fold in its floods
as did the budding stars within my heart...
* * *
Footnotes of a sort:
The issue of Hardy's poetry
R Langbaum - Victorian poetry, 1992 - JSTOR
http://www.jstor.org/pss/40003067
As we slowly emerge from the shadowing power of the age of modernism, Hardy's poems can
be felt as more durable . . . than those of, say, TS Eliot Reading Eliot (or even Yeats) one may
say, "ah, here in fulfillment is the sensibility that formed us." Reading Hardy one may say, " ...
Thomas Hardy: The Tragedy of a Life Without Christ
by AWR an Agnostic - 1997 - Related articles
Thomas Hardy had considerable biblical background. His life-dream as a child was to ... I have read 9 of his 14 novels and all of his 947 poems. ... The Return of the Native (chap 6) mentions "the witch of Endor [who] called up Samuel. ...
www.faithalone.org/journal/1997i/Townsend.html
The Spell Of The Rose by Thomas Hardy
The Spell Of The Rose - by Thomas Hardy .. 'I mean to build a hall anon, And shape two turrets there, And a broad newelled stair, And a cool well for ...
www0.poemhunter.com/poem/the-spell-of-the-rose/comments.asp
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