Saturday, March 26, 2011
Comment to http://matpitka.blogspot.com/ today's post:
I do not think percolation is that profound a theory- but it is interesting. I agree it will make little difference for you concepts as it seems to me a matter of the right words for the right notion.
I am not sure I understand yet your breakthrough- as I said, certainly it must be a greater generalization. I do not think declaring something a new state of matter- although superconductivity is a great phenomenon to study, is more that a vague generalization to which certainly something deeper like how all the braids and twists work between dimensions would make things more definite.
If you get this comment I put it on my blog also in case. I do not have much deep to say today there, but it is probably an occupational hazard that those on the frontier like you and Kea, creatively and fundamentally, have come to expect breakthroughs.
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On the other hand on my walk to the coffee shop this morning after what were obvious things concerning the golden ratio extending the PeSla Cube I felt a little breakthrough in understanding things and that synchronously seems to relate to this issue you have raised today. Sometimes the smallest notion (and I was thinking of a new descriptive personal notation) leads to significant consequences.
If I postulate a deeper structure for black holes one could also say there seems to be a hierarchy of matter- or certainly some ideas of not only evaporation as if peculations thus a deeper understanding of thermodynamics (which you mentioned part of your new found wisdom) certainly there could be what seems different dimensionally related states of matter. The case is not necessarily one of some general minimum constant or invariant yet it is not necessarily a problem of infinite regress and inelegant recursion- these things come from our apparent inability to hold ideas of continuity and finite systems easily in our heads at once.
It is clear that we do not see or those entering an event threshold know they are going into a black hole. This is a sort of relative thing in geometric perspective and some have said it shows some things may literally be alive and dead at the same time. But at the quantum level I might ask when exactly does some particle decay or for that matter from the shell of an atom when exactly does the photon leave an electron. This is after all and intelligible question usually addressed by statistical methods. But from a more finite treatment I regard this as evidence of the paradox that in a constellation of finite objects we cannot be sure what is on the inside or outside of the system.
While we know the continuous and finite groups seem to correspond, this general principle of initial uncertainty of what is particle and field for me is evidence that some of the theories of deeper symmetries and intelligible extent has physical reality from what after all is a geometric viewpoint.
In particular I notice in a link from Kea's update that we can represent two dimensional sphere into three space and it looks a little like a Turks-head knot or some forms of loops or braids. My quasics has something similar where we can represent the game of chess in two space 2^6 in three space 4^3 and make it a playable game that seems to lose information in the possible moves or perhaps superimposes some of them and in general compresses some shapes involving the golden ratio defaulting them to some other irrational symmetry such as the square root of 2. It turn out to be very much harder to play than four space chess itself.
So I did the trivially obvious last night, extend the PeSla cube to the powers of tau in the usual Fibonacci manner. It makes a vast world of such cubes and the binary divisions of its properties. I suspect, from wiki links from Kea, that I am describing such vast spaces perhaps in a way much wider than the sight tries to portray- as if this notion were not hard enough to have the vastness dawn on us.
Actually, I was using the powers which amount to tau^n-1 + tau^n-2 = tau^n (I think I recall that right) so to make various parts or rectangles of metal so as to make these various holes for candle moulds involving squares of them and rectangles of them so as to have a full set of things to interchange the parts and colors. Again a trivial exploration not meant to raise the issues of fundamental physics.
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So, this question of what is a power as log addition for the multiplication- that is in the Products and Sums of series in a "quasic" sense this can be the same thing or we can make some distinction for them. My joint descriptive symmbol then would be the sigma to the pi power or pi to the sigma power but this is not clear for the very purpose of the notation. So I thought digamma, F, but this is too confusing and overused as a symbol. So I thought write it as a little capital gamma attatched to a larger capital gamma sort of the vertical of the double negation sign I use for non-necessity. But then, let me just introduce a new symbol (after all to put one or the other of sigma or pi smaller inside would be difficult to print and where these are juxtaposed it is not quite clear if they convey the idea of quantum like asymmetries) So just introduce a new symbol, a little vague perhaps, which is a large eight point asterisk in my square two cross shape- that is combines + and x.
Yet clearly there are opaque or concrete phenomena to say- it is the inside from which we see the particle has escaped. Or it is a higher symmetrical space to which the particle is adsorbed (or perhaps with due consideration for the probability chains and paths and even history) the particle exhibits a lifespan before its relative decay intelligibly if any.
After all, given sufficient dimensions when something is adsorbed into a shadow of them as a cube of say one inch on the side we could lay across its diagonal the length of the empire state building. Consider the ideas of time and duration involved here. It is a matter of the null or wildcard notation also in that in such sets most anything may be assumed as a grounding proof to generate an intelligibly designed system of proofs (which may just prove the logic designed itself).
Interestingly, we could have a hierarchy of such relativistic effects of motion much as your generalization of Planck s constants suggesting deeper vacuum structures and symmetries in the real or abstract topologies.
I gave some more thought to the Penrose kite and dart tiles seeing how simply they were made and based on the two shapes of triangles I was trying to force into some sort of variable molds- continuously or partially so, so as to do more things with the same material. Interestingly it is know that when we fill a plane with them- and it is proven they will so fill a plane, that the general ratio of the kite to the dart (I think) is tau. Where these come up in normal three space as in the z axis stacking ratios of some quasicrystals to me it speaks of what we are seeing as a dimension down from a more general four space in the geometry of unfolding structures.
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Take a look at this. I found it on Science Daily while reading Matti's link:
Of course the classification of melody as well the classification of knots have been a recurrent interest of mine- see my posts on music, especially in relation to the quasic concepts of dimension- and of course others have tried to see music from the viewpoint of group theory and so on much as is dawning on the authors of this article. But what is music anyway, but a sort of color and perception?
I once made some chimes based on tau with aluminum discs- I must say it had an interesting sound maybe a little sleep disturbing out my window. So there is the link to general thoughts related to my posts today- all is not necessarily in our normal dimensional space the twelfth root of two.
[or for that matter the 24th root of two music- anyway in goggling semi-regular tessellations I found this interesting site with things to say about erecting equilateral triangles and differences of squares which I immediately saw as a complement to Pythagoras reading before this link page which of course has a theme of our relation to art in all this- and of course, music. It would be nice to collect various people together so we can hypertext these trends and speculations.
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Kea is so right in her comments on the post of Lee Smolin. ( http://pirsa.org/11020116 ) It is presented as if a new and discovered concept. Yes, he has some creative ideas and has his share of followers and detractors. But I come again to such thoughts of a rather local relativity of centered things today from quite another direction although I posted the notions related to this before reading any posts today, synchronicity again, and like Kea I could reference many posts discussing such an idea from a few years ago now.
My thoughts near this were from a more sociology question on the nature of time, in particular the local relativity perception of one's own lifespan. I have not ultimately determined if it has a certain duration that leads to final vanishing or that the notion things may go beyond this somehow, here or hereafter, has some sort of intelligible basis. Is our lifetimes limited by such topologies that often loop back on themselves in parallels while what we are as centered has a certain invariance? I mean, it is not the institutions so much that is the reference for the lifespan greater than the individual as much as who is a little further along compared with others, especially children from their own somewhat predictable experiences, nor that a leader of a nation is there for so long- but that such a leader is relatively ahead of the new deal arising of lifespans of the young. A rigid time is of the essence, or that is the absolute important reference for those who struggle with their circumstances is but an agenda and philosophy that binds the idea of time in a way that the fleeting powers or institutions in question benefit best from the coherence and point of departure for control of evolution over the constellation of individuals with lifestyles and time concerns of their own at the time.
So, what seems in memory at least of my self as the same constant person and what I am now decades later suggests that in the relative lifespan I have lived from one perspective a relatively long time. Maybe it seems long or short subjectively in the sense that our awareness on some level depends on the rate of creativity or decay, that is, our intellect depends somewhat on our relations of time- even an opaque and neutral time, to all that is not us or our center, the rest of the world.
I go to the drive in as a small child and there is a horsey and Liz Taylor. Que Sera Sera the grade schools sing now and then in honor of miss wholesome lady who sings it whom Liz made the love in a season pairing with her husband for a scandal of our icons on the silver screen.
The flag is at half mast today in Wisconsin- no one knew what for but it turns out that it was for policemen killed in a domestic situation and the governor ordered the flags down. Some said it was for Japan, and I jokingly told them for Liz Taylor.
Japan, I recalled old television as a child- Ronald Reagan hosting "Death Valley Days" and the mystery of California everywhere from there to Disneyland. Reagan on "General Electric Theater" ending the show with that logo and his statement: "Better living thru chemistry..." So, I think of the aircraft carrier Ronald Reagan that had to be hosed down again for another raising of fallout from the reactors in Japan built by General Electric. Things like this make me feel that not only I have somehow survived a fleeting lifetime relative to the universe, but have lived a long time.
As far as who may have genuine concerns and understand my own perspectives, especially while the living and survival of my desire to add to human knowledge, time also for me seems to forever be fashionably late.
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It probably was not much of an insight but in the illustration where I regard the "on the mirror" as golden structure values (and ultimately we can describe wider spaces contrary to the two links below or at least show where the notions interrelate on some level or principles of level- we really need to get beyond these concepts of the most general spaces like that of configuration, Hilbert, even phase) that in the tau superscript at what level as if a power is the sum of dimensions equal to the natural dimensions in question and that relates to a general structure such as tau^36 as a triangular structure? This link to arithmos and topos should be better worked out.
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Ulla just sent me these most interesting PDF links:
The first is rather clear to me and those who understand where I am coming from in the post today can see the terrain of the discussion- only I would rather show correspondences in the actual dualities grounding this idea of constructions as if geometric principles of duality as oscillations of structures.
In the second link of course most of the symbols are over my head - not to say I do not understand a lot of it- obviously someone is making progress and there are a lot of suggestions concluded from this, some of a general nature. I agree moreover with the gist of the articles conclusion of possible observation of this other level of space. Both articles tend to support the idea of some relative hierarchies of values involving the Planck assertions- especially when the problems of deriving classical values still haunt the unification of the terrain. I am wondering if the term minispace is my general working term superspace... In any case I get the feeling of saying "Welcome to the local multiverse..."
In general it is not enough to suggest an axiom then go on to generalize it as a theory but the notions and the theoretician are important too in finding systems that go a little deeper and think about the foundations from which the axioms have fallen out from some wider theory.
"Happy Breakthroughs, Pitkanen et al... may the philosophers catch up with you."
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