Thursday, May 5, 2011
Information Dimensions and Higher Abstract Motions
Information Dimensions and Higher Abstract Motions
L. Edgar Otto 05-05-11 Eau Claire, WI
The power of art and science does not consist of the cult of one over the other, nor that in understanding one we have to diminish the influence of the other, but in the transition between them, at the core of our dreams and in our awakened breakthroughs and epiphanies. For at this transition close to the mysteries of time and entropy, meaning and information, we can choose to interpret things in terms of one stance or the other, keeping the other out of sight, a distant inspiration. Or we can without clear choice descend into chaos in the transition. At this place we have the interplay of concrete metaphor into intelligible information wherein the deepest of philosophy tries to deal with the possibilities of time, things in change but somehow fixed as one fundamental law such that we expand in complexity what on any higher level stays grounded so as to intelligibly use there numbers and space of many dimensions that such hidden knowledge may emerge into oneself and the world where our notions of time philosophic and scientific are in a unified system of conscious accentuation as art and awareness, simpler or more complex is justified.
Some of us can take the hints of the chord or of the melody. Some of us can play the music like careful engineers without the emotions or sense of beauty of it all. Then again some of us can just bask in the ambiance that even the simple thing so encountered is a cloud of dreams that also does not need justification other than the risks and fact of our being, so to the lesser poets of physics theories initiate worlds in the beginnings and ends in isolation but part of all things of the speculation that may or may not end.
*From the perspective of a power N of a Clifford algebra, N is the natural dimension, and the number so raised to that power can be seen as the root of the space. Or such a dimension N can be mirrored in the notation such that it is a root, a unity to which the value can be squared or a number can be embedded in some idea of an intelligible dimension of space.
*Unity itself can be thought to have these higher and lower relations, each of which can be imagined infinitely distant in depth and span of space and time, to one place or countless many. In the abstract model of motion where ultimately what are products or sums and values absolute the same, still in a binary system of coordinates as if these have a qualitative property of color, we can have spaces that are powers of other numbers for other continua than two, such as 3^N
*This is a subtle but intelligible concept. The simple (3+1)^N of analogs to Pascal's triangle (considerations of which extended to the negative integers inspried Newton's calculus) would suggest a richer view of space than we now have with properties that seem confusing to us now should we exclude the artistic view, the human spectrum of the equally exceptional philosopher, Goethe. While it is not saying much to insist on a 3+1 formalism information wise we can say that this grounding thought, and not the only such thought, contains higher meaning- such that in four space a line may intersect a point without being a part of the three space (that is one could ideally remove someone's appendix without cutting the skin). Or in the 3^N space, which is the hierarchy of powers and their differences ultimately, we can read into the structure a deep principle that applies to stars and atoms, as Yuri does, of this formalism, or as Ulla does in her intuitive reaches of the structure of carbon atoms as the medium of expression in living organism just as we might suspect in such abstract plane vectors in motion not yet seen in a unified theory where the organic molecules and structures are aromatic as squares and hexagons, and so on...
*In the 3+1 expansion of Pascal's triangle the sum of the rows are of course the squares of multiples of 4.
1 6 9
1 12 54 108 81
1 15 90 270 245 243
1 18 135 540 1215 1458 729
1 24 + ... = 256^2 that is 2^16th Clifford like dimensions.
*In this formulation (not the power of 2+2 to the nth) we note that the numbers of subcells can be read two ways- the orthogonal analog directions and the antiorthogon analog directions. This suggest fundamental systems of differences in what precipitates out in mass decays of say atoms and shows we should keep in mind such higher dualistic fields of spaces, composite ones.
*Now, here I talk about the geometrical structure rather than the higher abstract quasic motions but these can have a notation of their own to keep clear what level (here Yurion space, the Tricontinuum) things are relevant of position and moving within. Perhaps a prime value and for the f function always use the sub script as say 3^n. Of course this sort of ways at looking at the topology as vectors can be confused with the normal form of calculus. With even a fanciful Goethean calculus, so the calculus prime idea may be confusing. But in any case we clearly see this is an alternative calculus to be developed and is after all a "pre-surrealistic calculus" as perhaps all these issues of intrinsic weights and values over limits and invariants, and uncertainties as in the relativistic and quantum conceptions.
*The idea for this post comes from my dream this morning, and some of the images referring to a discussion with a young lady poet asking for ideas for a class- we talk poetry sometimes as she did with my son- I went with her own suggestion on her seeing a small chocolate Buddha downtown and I remarking on the small Buddha candle by the coffee shop which after too many uses of the silicon mould looses its definition. In which case the insight she developed (after telling her of course I did not want to influence the directions of an artist, as with learning the students have learn to think on their own, even for the engineers awake and problem solving.)
*So, in my dream I see a large ball of chocolate on a panel like I post here usually 2:1. And beside it are the letters LHC (which of course I already know the meaning referring to my color labels, my old home base of CHapeL hill, and the discussion these days on the collider.) And under that some abstract notations not familiar nor recalled but understood in the dream as I awakened - with a sense of embarrassment that I did not think of these before.
But as I awakened I asked what the ball of chocolate had to do with the abstract letters and numbers and the visual focus shifted from the ball to the letters and I understood!
*Imagine then soft chocolate and hard chocolate bits, the bits also winding strings like a hair ball. In the dream I could taste and crunch it too noticing the texture. But it was not just one system of chocolate delight- all its diverse features where composed of interlocking light and "Dark" chocolate. In some ways this just a metaphor, or perhaps a metaphor for dark matter like things in the minds resolving of things then to put them aside for survival in the real concrete world or sometimes the need to look at the foundations and observe our transitions between the poetry of scientific beauty and the touch and taste of our grounding for the science of our dreams.
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I just read an interesting discussion on
Of which the combinotorics issues seem related somewhat to the wider ideas some of us have been dealing with in the blogs.
Found thru facebook http://www.facebook.com/pages/Science-Chat-Forum/104787332929459
but no comments to be made on facebook, one can for the related
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As far as this recent discussion and science news events go:
I have stated my position a long time now- that in theory we are not going to disprove or challenge this view of physics- yet it is only part of what we may think of as total separate pictures. A surprise would have been if observations said otherwise. Still, we need to look deeper at the physics that involves the depth of these considerations of spinning things and mass and fluid concepts and so on, if we want to get a wider picture of the dynamics of what is going on- this is not just some statement saying we may need something like a string view and so on or some sort of particle that gives the mass aspects. Like with quantum theory physics this view, if we desire, it needs to be transcended- but it will not become obsolete anytime soon if ever.
Clearly, if one gets the gist of this post that reaches into a wider concept of dimensions, they may find analogs to such ideas of the relativity assumed higher in our ideas of space- as as structures and processes in Six dimensions- as not as simple as assumed by our clinging to what we think is the absolute and simple ground of foundational systems for physics and our systems of mathematics.
Now, if in the simple demonstration I have made on this post for such an alternative concept in the depth and span of structures- a hint really of a more comprehensive concept to come (most likely involving our concepts of time) then any theoretical system extended and developed will be like the GR theory and in retrospect will seem a part of the bigger picture even if the logic shows it as complete. Is this not the case in the growth of science, physics, that we reach a point where like Hawking once that "we almost know everything, including ideas of dark matter as all there is even if we do not quite know what it is." paraphrase more or less or "the wideness of the string landscape appears to me as evidence that there is no God."
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Here is a related article on dreams and memory I just found (other than of course the changes in chemistry upon awakening.) It is relevant to my post above where it is creative philosophy and this suggest creative science also.
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Those who see the hint of fresh ideas in all the physics on the nature of time will know my position on this: Such things may intrinsically not show up in our conventional replication of such experiments- (as if perhaps, and in detail, there may be more fundamental physics than the three I envision- that or as a forth one - Phoenix Physics, and so on... it is intelligible in the way that four things of the three are in some sort of psychological analog to these higher dimensional spaces- of which one can extend beyond my diagrams obviously, and maybe beyond that in a more subtle generalization. After all, some lower numbers and dimensions in the quasi-continuous aspects of the perceptible universe to mix groups and systems so as to limit them close to the flat grounding or local grounding of such extended beyond our earthbound simple view of systems.
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It should be clear to many that our theoretical models are at least as powerful as our trust in physical experiments. Emotions perhaps are what we accentuate artistically or care about in order to mix higher systems of fact and metaphor. That is to say, given the right theory in a sense its intelligibility matches that of what we should not be surprised at when the research confirms what we have predicted. Yet, considering the emotions and deceptions of the paranormal researchers in the controversy- what if there is a sort of physics theory that has to resolve things that is intrinsically something that raises these deep questions of coincidence, discovery, and the nature of physical and philosophic time- certainly this is a concept we should keep in mind- an separate to a point from our usual theories of observation while the technical study of any of the three physics.
Do we invent the world in our discoveries? Is the quasic physics the only tangible and local idea of scale for mental observations of the three physics- or in some deep way at infinity beyond the greatest and lowest dimensions, scales, is there another shadow place to which we somehow orient ourselves as if particles somehow twist toward and sense an irreducible and simple concept of gravity?
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I reread one of Pitkanens recent post (and btw if somewhere the half life may vary then why not this sort of aether effect for opaque or dark matter like ideas?) So I made this post comment at
I am not so sure we can say that a deep idea of dark matter is what the issue is here. But I get a grasp of just how the TGD framework can shed light on some of these issues. That is in reading some of your core ideas as foundational it may be but a small step to a wider view of things if you yourself can apply them or interpret them.
Of course I am lost in how we may compute the energies as you and Kea do- but in my last post I again came to her 256/81 value but I believe in a different level of the structures of such spaces.
We touch base on so many levels. But one thing I thought of as a major intuitive mistake on my part was my assertion there were only five quarks- and they announced the discovery of the top soon after. Yet in reading your post I begin to think that in some sense was not a mistake after all- just the descent into enshrining the limitations of current theories which of course would put your ideas out of their mainstream.
Nevertheless, after a couple of decades there appears something very strange about this top quark. It does seem somewhat unobservable in the Higgs-like sense as if it did live in a wider physics- and it could indeed be this idea of yours even if it is not the grounding of our ideas on dark matter- especially if we insist on these being in a sense a reductionist dust.
I have some general disagreements with some of your stuff but on philosophic grounds, again in how we interpret the hard issue of the finite and the infinite in equations.
I note here you have suggested ideas as to what is to be done in the development of the mathematics and theory. But otherwise you have stuck to the intuition and from my view your notions are much less speculative than the current state of our particle and cosmic physics.
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Later that Evening:
I looked at the next case, it would be labeled 5D in the above illustration- and I found very interesting numbers... all around 27 and 36n, it make me think of an analog to the Conway matrix one step higher Cw' prime. Of course there are interesting things to consider and a three dimensional representation is better for it, and the numbers intelligible carry over with more connections of the five fold to consider- and the enumeration of dice with 8 color faces... and so on.
1 8 16
1 12 48 64
1 16 96 256 256
1 20 160 640 1280 1024 ...
Of course along Eddington's lines there would be a whole new relation of the coordinates as a little more general vectors and such- that is where we can connect the ideas as not a uranoid of 64 with 4 items but one of 80 with 10 items. It is clearer than ever we should specify exactly what we mean by these sorts of dimensions. A lot of interesting numbers show up as they would in other structures like 480 and so on... but, it is clear this extends to more than our current ideas on six space- to 8 and beyond. I do not know if we can compress them building on such sets to make more general sets than the binomial value, yet in a way we can say that (2 +2)^n or (3 +2)^n may have no direct intelligibly visible representation in such partition space. Other symmetries do exist as if on a super symmetry, or super conway order- and some are to be distinguished in normal spaces as pairs or duplications and thus even breaking of the conway weights and symmetries... quadrants, octants and so on...
double pairs for example, that is for the same orthogonal entity under consideration. And this can be drawn in normal space as if the cube symmetries were beyond the 48 of its group in some cases.
Perhaps, also the idea of a slice, perhaps in but one of the 6 ways, say of 20 things is like a diagonal in a matrix wherein what is left is 120 or four sets of analogs to the 30 cubes- this is a most interesting space to travel in.
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Next Morning: I forgot to mention that when you take the half value of the rows you can have a 1/2 for the generator- a hint perhaps of how such structures may physically appear if we treat the symmetries as if complex space- but this is just a general passing speculation leading to principles today called: Natural Symmetry.