Thursday, February 24, 2011
Global Symmetry of Dust and Shadows
Well, it is not as intricate but here is the picture- one can imagine with better consideration of the orientations involved a certain sense of braiding between the faces as if a finite and positive treatment of the particle-vacuum and topological field.
[Sorry, my first intricate illustration was lost in the saving to paint and at the last moment, this is the replacement but not as careful in order and details]
Global Symmetry of Dust and Shadows
(and On Linear Fractal Archetypes)
Two principles have occurred to me of which I am not sure such things do not exist in the literature. Some have said we are but dust and shadows (pulverius et umbra- or some such Latin would sound more learned if I could recall the correct words) What can I say save that we are looking into the heart of dust and are all really working in the shadows? What matters is that something works, and works for each of us in our perception and contemplation on the world.
In a sense we look into and question the obvious, at least intuitively have a sense of the intelligible for what system feel right thus obvious. We thus have a high level internal conversation and at the same time this conversation is influenced by and engages the external between us. The hint of such intelligibility and the exploration that something new on the frontiers may be worth enquiry- perhaps rumors that turn out to be a useful fact, one that on some level defends and promotes our survival. Even under the influence of the mystical traditions some notions are as archetypal and universal as our conventions of counting.
In a comment Ulla asked a question of which I was not familiar and had no way to gauge what she was asking. The mentioned the all important number 8 as a quantum number. I thought this most likely to do with chemistry, the magic numbers of electron shell configuration as she mentions such things in her speculations and one commenter posted a formal paper about such a way to see atoms. She also discussed some of the new number theory and asked a question about the octal bases to which I tried to answer clearly with what was generally known. It was these comments that led me to think of the obvious general principle I present today about the less obvious idea of linear fractals- a simple line in quasic space is after all fractal- and what does this mean for ideas of renormalization in comprehending some general region of space as dust, matter or as a topological shadow (evidently the idea of light or energy is archetypal here also as with all opposites in the West that can become each other even when we accept strict separation of our Good and Evil angels). This duality, as all things perfect come in threes goes the saying, also is an issue in Kea's work on triality where in the tetraktys we come to hints of new global counting wherein the shadow or the dust may be the ground of calculations.
In particular today Kea post things on the number 24 of which I was intending to post on that number and orthogons- and of which it applies to the new number theories as more general formulas. I do not know if we are talking about similar things. I am not sure these two principles I post are related other than synchronicity (this bedevils things really and covers all levels of mental activity and social activity- I mean, I actually used my Allegorical Physics post yesterday to have a musician friend read as he was discussing a friend, a Scorpio in the sense of the Knight of Cups- and of course his usual chi gung applies to music in the chords he asked about for a song he was writing. Despite his formal training I had to use these systems to have him understand the significance of the circle of fifths as a way to transpose his chords and base notes.)
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Linear Fractals In the Quasic Plane:
This is based on a ridiculously simple concept of counting independent tiles in an indefinite plane. It is finite in conception and exists only when we insist on an origin or minimum of scale, a zero.
This zero is a wildcard singularity, meaning the first tile can be subdivided into the whole plane itself and so on. We in regarding it as the origin or zero see this tile as unity, that is a normalization of what is a hidden depth or finite object or shadow. In a sense it goes beyond ordinality, a closure of sorts of distant rays into a ring. The idea of a ray or a line then while a good distinction may not be clearly made so as we imagine. While in theory the line can go to infinite smallness into the depth of the singularity- it nevertheless acts as if a finite value, zero, one half, 2, 4 and especially if we desire to so count that way, as 1 object with successors.
Thus the question as to how we can map something into a sub-part of itself or even between zero and one, or minus pi to pi, has to be asked with this in mind as to how trivial the grounding concept of what seems a line, what seems an explosion from singularity, inflation ideas and so on, applies to the actual physics of reality. On the quasic plane such hidden fractals (I am not necessarily speaking of some fractal ideas in the new number theory here) as lines or curves are differentiable and not simply a matter of say slopes. Whatever trivial properties of mapping in the idea of recursive fractals is a trivial and not obvious property of such lines and ray themselves. It is hard to not dismiss the counting of a grid of independent units as just trivial counting.
But there are several lines that can come from the wildcard origin and these are based on what choices of base as binary we use. One is the diagonal which is the progressive powers of 4. An important one is the octal base which gives us an endless and growing sequence of what we call the magic numbers of electron configuration (The nuclear count is in there somewhere but the electron count is more fundamental.) Of course in our space with consideration of global structures and mirrors we do not reach a sub-shell of 50 electrons. But the progression after 2 for the octals differs after the initial counting because of the normalization of the wildcard singularity as origin.
8 then is not just our ability to divide space into octants. In fact we see readily that this is too rigid a conception of dimension- or that we can generalize the ideas of dimension and then if we desire to impose a standard ordering on some structure. There is a deep connection between the 24 ways of rotating a square (the D group) of four colors and the same structure of 24 squares in the hypercuble. Such a small plane, be it a shadow or emptiness, or a place where it is a particle of dust subject to twists and turns, does not know what metaphysics or preferred dimension or philosophy it is in. (Typing this it occurs to me that some like galatomic may say otherwise that on this level consciousness is at work- but let us leave it to just the topology. It is alright to have an idea as vague as life force and feel excited about the conception (see a post called elegant universe on the philosophychatforum com and how it was discussed and the excited poster treated.- I presume not the same thing as that book title.)
I will discuss these ideas of the 24-ness, the all important dimension that Conway was supposed to see- Conway, who has covered so much area and new area future theoreticians have a lot of archeology to do, in the more easier to digest diagrams forthcoming.
I add, as to the linear fractal theory reduced to counting quasic grid square areas (actually we can get some unusual measures of using the Pythagorean theorem between these fractal lines as to what is left in the square between them as if to integrate over the area. In a sense this involves the very heart of the discovery of irrational numbers for example where they apply to that left under a matrix diagonal.) That upon this we can decide what partition numbers are involved... in a sense we take so many squares and put them in a square along the diagonal or a line along the alpha or x direction. Then we can see that in between.
There is an interesting picture today on Kea's update and links where there are pictures discussing the global SUSY data and one was posted in a different direction as we can explore these lines global over the D group- but the mapping does seem to organize the data on a quasic grid but only because of the use I suspect of half value compared to whole values.
* * *
To lose work at the moment of its completion- well, it has not happened for awhile. But it gets me to think about our costly large science project of the LHC.
It occurs to me, beyond the benefits of experiments that are undertaken to show that some notion is not the physical case that:
Lampion 02-24-11 - The apparatus of the LHC project may not need to be reconfigured to interpret the data but it is possible that the data itself can be used to support the new theories of topology as applies to particle and cosmic physics. In this sense I am optimistic that a new and positive thing is discovered that justifies and vindicates this human undertaking and those who are part of it. Surely those who have explored some of these topological paths should be consulted in the reinterpretation of the data.
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The lost illustration did this:
Take one Plane of a cube or hypercube as the wildcard dihedron, the D group that orientates the totality of the whole, the complex twists and braids on one plane that can be considered as a material (dust) or empty (shadow) singularity. This gives the 1/2 or alternate group of the rigid rotations 24 then 192 which is 24 x 8.
In the cube the faces are labeled as four colors and can be colored such that of the 6 possibilities and 4 orientations of a face the 24 group multiplication applies as if a so labeled cube itself can be used for calculation with a standard cube to compute the permutations to some identity.
In the hypercube case the six directions are labled as a line thru the hypercube or a circle around four of them, the same thing, as CDEF GHIJ KLMN OPQR STUV WXYZ The A and B for the alpha and beta directions of the quasic plane or alternatively as the rotation and reflections of the D group. We are counting changes in the sub-cells here as intelligible counting to orient the rest. These I have often labeled with the international signal flags. But in the cube case (of which the inversion results in the same color shapes possible of the four colors per face) I labeled them abcd and efgh to show the schematic of local inversion.
In this sense the color matching of cubes is also the consideration of the complex rotation and the braiding of them. I have not considered if say of the 6 faces of a cube what happens if we allow more than one face to have a different from standard orientation- of if that difference has physical or topological effects although it would be an interesting algebra in its own right.
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I do not think I have made one thing clear. I see this as a dynamic process more than fixed geometry no matter how complex. That is I vaguely imagine these application of groups and the distinguishing where something is dust or shadow or where it seems to have a fixed origin or not, as a physical process where we may ask for example what happens when grains of dust encounter a vacuum shadow. A description of particle physics perhaps? With innate and symmetry breaking of these things like fano planes and the alternative tiling representations on the familiar level if not in the remote scales- can we not imagine the D group operation as a dynamic description of some such topological object encounters another for decay and so on- and as a much better yet wildcard abstract candidate for our dark matter or opaque matter considerations. Even if some such dust were the explanation it would still have to be intelligible within the context of the arithmetic and topological ideas. Interestingly the 24 cell with a group 1152 is most instructive too for general ideas for consideration.
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At first I was going to call this post Archetypal Physics. One example would be the inclusion historically of the number thirteen. In the logic of Vexillogy (flag logic) the question is- other than the constellation Lyra as likely, what was the arrangement of stars in the first US flag?
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One Last Related Idea from Explorations Last Night: