Kandium Stars

Kandium Stars

Just a little drafting last night. I found a five-fold version of the six armed star of yesterday (a five pointed star in its center)...but it brings home the idea of when we view a series of numbers as if to divide them by ten (that is 89 and 109) this structure of numbers as if a varied but directed scale is a legitimate way to work with them throughout the wider patterns of numbers.



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I did not find an example of dividing the circle into golden proportions (like the Kandium Star) such that instead of the smaller stars reaching a limit on the arms, or for that matter the Penrose tiles so extended, that they in a sense concentrate toward a singularity or limit in the center of the structure. A unit and flat fivefold star itself can roughly be seen as the circle that describes the internal or external representations of the non-Euclidean geometries.

When we investigate these square root of n, +1, quadratics and their squares the golden section is flat unity (I would imagine these are vectors as linear in any general system of space) But the others differ apparently in multiples of 1/4. Thus at some dimensions these become binary multiples of unity again, and so on.

If we then imagine a lattice of indefinite but self contained scale we can imagine it containing some other geometric structures- say cubes that turned a certain way can fit thru certain holes in the space, that is to in a discrete manner to escape say from the internal or into it or external space at the unit star Unity or Flat Euclidean surface (even is this is a sphere or torus or plane that is abstractly flat. This seems to describe the linear binary points (as in Kea's braids of crossovers) in which a system of particles might have an average escape from some system as well as the mixing of its dimensional star densities. In a senses this is a sort of generalized and minimal percolation model which of course as with Turing's chemical equilibrium ideas may have bearing on organic states.

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In reading Kea's paper I would say she has the general landscape down for my use of quasic coordinates in relation to six space things as in the application to the gene codon of 64 things. Her use of the matrices is very clear and that these, in solving the problem perhaps of a more Machian-Dirac physicality approach where these models of topology and arithmetic apply if not directly then with mirrors of a sort when these matrices operate together in a more general space.

A paper today on her blog list discusses where magic squares fit into the scheme- an idea I posted yesterday but with the further concept that, because of at least the depth and span of internal considerations, that these matrices can be both a source of stability and unity in solutions to integrals as well as a source of instability.

We return again to the three and one ideas much as with the Sudoku cube structures.

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http://www.newscientist.com/article/dn20320-dark-matter-could-make-planets-habitable.html

Interesting as closer speculation on opaque (dark or creative objects) but is it that fixed and after all in relation to matter? My fist blush is the the idea of WIMPs is a consummate frivolity of the vague dreams of too concrete a reductionist longing.

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"These are operations on sets... and not necessarily vectors."

I had a stray thought on the logic of surreal numbers, "not greater than or equal to" and which nevertheless describes a system that has a grounding null so that from some view the overall space is in a sense a reality as if positive. So in a sense some of the views on my blog lately are a little more general than the idea of the surreal logic- trans-surreal's. The question is just where initial or final or general null and flat things are if such are creatively included in the models. I note, if I read the notation right, that a lot of this as some variation on interpretative theory goes, is what happens with algebraic expressions of absolute numbers- including when they equal other values that are not absolute. This is an area to be investigated and one that perhaps gives an overall system of how in a still plane individual points might move intelligibly between curves in the graphs- or perhaps we can show this as non-linear and ultimately random. The logic of transsurreal numbers would most likely fit our ideas of mirror symmetry and that of the creative flow or forces by the dense entities of the vacuum such as black holes.

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One of the early names for our candle companies (at first Candice Candle) was the motto Kandium- a coined word meaning radiant more or less. In this crude drawing above the stars should be tilted away from each other a bit and the rays were meant to suggest magnetic lines of force. Later stars were added in golden rectangle proportion, after the red and blue these generally were yellow. The Otto symbol in the red star as a golden area logo since 63, and in the blue star Morse code O T T O for the sense of radio signaling. In the battle ensign the four winged bird of time which is six if you count tail and head (but not an archangel) not spread eagle but perching on the M for Scorpio and the golden star arm theme. All filimbrated in gold.

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http://uduality.blogspot.com/2011/03/is-n8-supergravity-finite.html one of the blogs I follow links to a most interesting paper which seems to be saying things we have all discussed and suggested in these blogs. I welcome a more finite approach to the problem but think it is only the beginning to extending things abstractly to such ideas of vacua and higher dimensions. The E7 ideas are but a steppingstone and the idea of 28 (or 56) involved here especially in relation to E8 is but what is left over of the four dimensional natural case when we focus on the spatial 36 of that region of Conways matrix on the chess board (in quasic arrangement, indeed in the quadratic numbers the squares deviate from unity by .25 increments such that at the binary powers of dimensions we find whole numbers again- this leads to some interesting stars of which we inscribe in them (in reverse shell order from the circumference) This perhaps explains what to do with that part of this that has effects in depth that are only seen or assumed finite for energy.

I begin to think that even on a local positive range of such zero to other light cones including the complex areas- that, just as there are no star honeycombs as in general five fold things in life tend to set individuals away from the collective, that There are no fairy fields at all- perhaps the quantum idea is not quite enough to explain greater mass or momentum in itself- if there is no Higgs why should we not expect a pure theory of superspace even within nuclei and particles in general? This is not to say that the string theorists have not made a great intellectual achievement at least if not a close description to the physics.

Some say the God has determined (before or after the fact in the here or here after) all of our reality, even geometrizes the design potentially intervening from time to time. Others hold that that is an unnecessary hypothesis and the design of the geometry does it all.

Others insist that "God does not play dice with the cosmos." And a fourth direction would say "In the cosmos the dice does not play God, literally." (these folks tend to see things from a more extra-sensory interpretation).

It is good to see the usual notions and tools, a look at at least the types of finite shell structures, and the idea of symmetery and action -action is the dynamic drive that gets magically and squarely between all the competing theories of everything prevalent today- academia may sooner or later catch up with our constellation of bloggers here! Or at least the ideas involved, in difficult symbols but pushing the point a little further by this lady's most excellent paper.

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Flattened (zero-point?) Ratios of Dimensions

I did rather little last night other than explore this relationship between the golden ratio and the lines connecting the midpoints of an equilateral triangle then extending it to the surrounding circle. I found this interesting shape (anyone seen it before in art or architecture? As with such shapes there is an ambiguity of perceiving it- for it suggests motion on one hand- and to my eyes at least it tends to describe three space perception as if from the point view of a cube.

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Yuri sent me an interesting link where the author discusses certain things like zero point and quantum ideas and so on... there was no other comment in his e-mail.

http://bourabai.narod.ru/winter/publications.htm

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Now I am not sure what to make of this article in the news:

http://news.yahoo.com/s/yblog_thelookout/20110329/ts_yblog_thelookout/for-12-year-old-astrophysics-prodigy-the-skys-the-limit

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The sites I found googling phi yesterday gave me the feeling that it is a balance of notions as well as properties of space- On one hand we analyze it with no particular interpretations other than the nature of numbers (most interestingly the inverse of 109 has patterns of 24 of which it is still a little mysterious.) On the other hand there is just too much speculation as if sacred geometry that is stated as fact in which it is not clear even the artist, contrary to say Kepler, deliberately used the golden ratio. Now I have made many Cheops pyramid candles and for mathematical reasons made the face in that ratio- but I never read into it some clear and accurate relation to pi and so on or the golden ratio of the real one at all. Still, there are some properties of such shapes that really need a more scientific analysis (for example, structures made with toothpicks and marshmallows after three days of rain outside they slowly flow off the desk, save the smallest and strongest like the tetrahedron and the largest of the varied structures with spaghetti and toothpicks- that golden great pyramid. Or if allowed to cool too fast the wax cracks in the base in some interesting curves across the diagonal.)

From either over or underestimating this idea of ratio both sides of our stance to geometry as mystery suffer in reputation as to its taken seriously- but what is the golden structure but at once a spiral of ratios from one view of smaller and smaller stars and yet from another view all such stars from the same idea of a general scale and perspective are equal?

Too many sites are on the side of magic in the sacred geometry, seeing, even naming the symbol for the golden ratio for artist that supposedly used it in their work. I even came across a series of poems based on syllables of the Fibonacci series- a form I used (even thought I invented) a lot and even made it one of my best liked songs http://www.youtube.com/watch?v=3emG_OfQZCU&playnext=1&videos=BCJ6uddXpJg&feature=mfu_in_order - but this was a deliberate admiration for the properties of phi- the artist, concerned more with the content than the measure used certain ratios for squares (one site called the orthogons) like half the square root of three or five, which more or less guaranteed generally good proportions.

It is difficult, even when aware of our perceptive and creative processes, not to overestimate or underestimate the solidity or magic of our mathematical tools.

But this you can download as an .exe I find rather beautiful- sorry, I did not save the direct link.




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Sometimes I think that Nash, (a Beautiful Mind) in his later speculations where he turned everything into alphanumeric number relations- may have been on to something that the spirit of it could have some merit or relevance to how such minds relate to notions of reality (how would we others know the difference?) I have wondered of the geometric symbolism, say of state flags, or cutting little stars of David out of a tray of wax with cookie cutters how what was left looked like swastikas if you punch them out in a square array. Two powerful designs that have come to take on powerful symbolic meaning in our day. Oddly, today's star figure, especially when colored black, has ambiguous meaning- but is this not some way of viewing a cube where there is a central one of seven- the eight one in four-space in the center also and the flyflot to be viewed right or left handed from two sides of viewing the cube?

Three government officials walking thru the woods, a president, a governor, and a civil servant come across a large bag of gold coins. The divide it into three.

The governor says: "I will give 30% to the people for national security and jails and incentives for corporations to move into my state, and keep the rest."

The president says: "I will give 30% to health care, recycling, global warming and other environmental concerns, second hand smoke and the homeless disabled, and keep the rest."

The civil servant bureaucrat says, the people are sovereign, they are God."

"Hear, hear", the others shout to agree."

"I will toss mine into the air and let God take what He wants, and keep the rest."

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I had forgotten, a thin speculation perhaps, of the great distinction some have posted concerning the first two elements, H and He, and how it may relate to the overall picture of space and stars. I had a comment and reply to such a paper somewhere which seems right on in my world view (was it Yuri D?) The connection with the thought of some days ago of the stability of five objects being a sort of a limit, say of nucleons or quarks- if that possible at all. So we vaguely have the length as a count of two things plus five as a star for the idea of seven to which we from our maths of the eight or seven and a half. The pairs of primes perhaps.

I noticed on the phi page the 248 flat representation was shown with a series of links that overall made concentric circles in the golden proportion- but this I am not sure is an artifact of the geometry or the longing for a hopeful pattern with the usual uncertainties of perceptive or experimental fudge factors.

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Went to library where you get ten copies of anything free. I copied one of Kea's PDF of 8 pages but the machine made 8 copies of it- not my error so they did not charge me. Easier to study hard copy.

I found another phi lover site which suggested or hinted at the brain looks a lot like the surface of a structure derived from a four space sphere- an interesting idea considering the role for bilateral symmetry in my speculations. But to focus it into the brain which after all seems to map the body, a general brain at that as our brains have some variations especially in the frontal lobes, is an interesting idea in general. A sort of an old theory of cephalization.

After reading Kea's paper I found much in agreement- but it got me thinking about this idea of 109 in phi, you see it involves 24 digits that mirror over the extent coming from both ends of the decimal place. And it involves reductions to 9 (I think of how Kea used them in the matrices, that and 8's and 3's and all the braid stuff including the problem of crossings over (and a new view to what may be dark matter or no need for the idea of antimatter or super-symmetry as such. But in four space where phi is the signature the combination's of things is after all a little different from what we expect with three things so to permute as she does and points out for further investigation. But this phi stuff is too vague yet- I would ask Pitkanen about it as he mentioned the properties of 89. Hmmmm 109-89 is 20.

OK, nine or eleven abstract higher dimensions filling space or not, that seems to be the issue where we treat an integer, even a prime on, as if it contains the general information of the dimension. Of course the range of dimensions and what moves or affects each other, fields or matrices or what have you, is not simply linear steps but a little more general in which particular orthogonal motions and rests are embedded in or move thru different subspaces of any such dimensional orthogon. In this sense we are merely distinguishing the way we use natural and mixed or even Clifford type discrete dimensions. In many ways it does not help to use standard terminology if it is misleading or restricts us to the methods of that terminology so as to slow the theory down or find a bottleneck in its developmental path.

But in general I have long favored things involving E8, but the interpretations of how it fits 6 dimensional groups should be more generalized as dimensional spaces.

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In a sense of mirrors or palindromes of digits or decimal numbers I make a crude analogy with that which is ordinal from or to zero in relation to infinity- thus the view of this permutation of 24 is that it covers a quasi-finite effect of numbers. In general, at unity, of whatever roots complex or not, when it is unity it seems to involve, at least in fundamental scale of four space of five symmetry, normalization which indeed can resolve to some of our more classical ideas of physicality. Why would we not expect that in the final theories things are clearly simplified?

Imperial Physics

Imperial Physics

One of the links I explored yesterday:
http://www.spsu.edu/math/tile/aperiodic/penrose/penrose1.htm

Note: in Penrose's first set of aperiodic tiles there are six figures of which in the sense of making a candle mould that can when solidified have the pieces outward expanding or translating instead of impossible to pull out save in a flat unstacked vertical direction, that half of them are self-empires with this restriction.

The idea behind this post, although many theoretical physicists were drawn to study these patterns for something, perhaps coincidence not realized in their appeal- but then the symmetries of the Platonic solids have long been a source of science and mysticism- is that explicitly the vague idea of utilizing geometric structures to try to describe some physical phenomena, even if most abstract, can find a more solid grounding as a possibility and method. The theory is one of depth and is not necessarily a self contained empire stuck in the tessellation of what is asserted logically as a vague ground for a total theory of everything.

Such a purely topological mechanism, within the span of its natural dimensions, would go far to explain, as an alternative theory, how in creative objects like black holes or in the concept of dark or opaque matter, the momenta is transferred in relation to electromagnetic (or other) properties or not.

Recent posts in the blogs I follow raise questions about the top quark- I have long felt and felt this a mistake that somehow this five-ness of things would apply to quarks and that from a wider view the sixth is an implied or different creature- in my poetic mythology of the Olney godhead I did eventually expand these to 8.

This is probably a question of number theory for we can regard an edge as part of the structure, say a pentagon (or any such idea of density of its internal stars) plus the edge leads to a seven sided or pointed structure. Here the idea of primes and pairs of them may be important to consider.

If somehow, in the general representation of numbers on the same integer level as if they are partition numbers then clearly where the shapes are symmetrically square, especially if a magic square, this is a case where as empire these are not stable or are self-restricted matrices- contrary to matrices in general representing stable solutions to integral equations.

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Footnote to yesterday's post: I find it interesting historically that Einstein considered the Brownian motion in relation to gravity and how it showed up in different levels of a jar of liquid to the values.

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I find today a most interesting post from march 08, 2011 linked to Kea's blog and on Michael Rios pages: http://uduality.blogspot.com/ http://arxiv.org/abs/1103.1014

I find it of course intricate in the symbols and language but the conclusions of which this paper is talking about string and twistor theory and so on... seems to be along the same lines as I have here talked about.

At the coffee shop from time to time I talk a little biochemistry with someone raised near Princeton whose parents were part of the academic seen, indeed he has met many of the Nobel Laurette's of the era while young and brings these up if it fits the conversation- for example in this issue today of gastrointestinal bypass and diabetes and the laser mapping of insulin it came up that if subatomic phenomena were involved in the biochemistry it was probably related to the genetics- "Well, I was thinking a little about that yesterday and the spirit of it is right even when we go on to deeper laws that make the earlier prizes a little thin in retrospect- you thought is a good suggestion for breakthrough research."

He replied after asking me for an example of such ideas over time- certainly the first ideas on how the nucleus was held together, before quarks I told him. Then he made this point: "But these abstract ideas such as do parallel lines intersect, which should a carpenter believe if he has to make you a door?"

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Again, scientists, forgive my lapse of reductionism here but when I first came to the blogspots my selections were quite at random in some cases simple blogs to keep up a little with Spanish and Portugese, art and of course some of the science including cheese and turtles. One such interesting blog I found most interesting:

http://materialintangible.blogspot.com/2011/03/ufo-as-note-in-multi-dimensional.html

Part of creativity is trying to make sense of such worldviews- I see he too has posted the Pythagorean Snail and is excited about the sciencedaily new ideas on music article. The spike to so called collective psyche experience and the recent Japanese tsunami I find the usual intriguing claims- but what if there are such connections that are explained by the newer science? I do not mean this idea of UFO's and all, ghosts, what have you in the nature of theories of mind and perception or even those special people, prolific and with focused insights, savants.

So the news the other day shows lights in the sky spooking a small town in Arizona. The video made artistic inclusions from recent alien movies of which one could not tell if it were a spoof or a matter of entertainment.

It is not shown at all that certain things like the moon closer contributes to the earthquakes and so on... this is still an unpredictable gray area. But how can I not form an idea, fanciful, of three lights in the sky making triangles when I am deep into speculation on geometry of triangles. Perhaps these are some sort of singularities that fall our of some more general adjustments in a more and seemingly magical space- perhaps they are magical. The underlying application of such notions as metaphysics or geometry are still a mystery of sorts as to how we organize our perceptive realities. It is too easy to place a theme on the music of the sphere with a vague general concept like all is mind- or is it? I mean we still as scientists cannot dismiss meanings of a vague religious depth, if we are honest. Reality, in end full of neutral currents sometimes forces the triangulations of our minds.

I will say this, that sometimes I do feel we have collective dreams. Certainly in Jung's thermodynamic model of the psyche, perhaps from an industrial age mindset, such ideas at least in the short range seem to expand a bit into seeing the future and not from a mystical foundation. I think it was not since three mile island that I had a dream like last week of being caught in a dark rain of nuclear fallout. I had not paid too much attention the disaster in Japan far to large to truly get my head around but many more of the unstable around me seemed deeply concerned as if this was the greatest reality in their news and many more lately have asked me if they think the world was coming to an end in general.

Have we not noticed the animals act strangely before quakes? When I awoke I did not feel the dream was as intense as earlier ones and I found myself asking- Was the New Japan worth it? Have we not benefited from her achievements even if she is gone? But this question is true of any empire that lives and builds for its day when perhaps we should listen more to our intuitions as far as we can see into the future.
This seems too to be the general trends of our political parties, at what cost do we protect or use our environment for the individual or those to come? But you know this already (like so much of news is just an indifferent product that tends to say their view is the decisive one in a general mindset of history and certain laws). The question is, especially for our young, have you had any such dreams of the deeper terrors always unexpected but well known of the day?

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Poem: Astrophysics

Core Photo from Virginia Beach by Sebastian Otto

Astrophysics L. Edgar Otto


The street lights rise over the melting snowbank
leaving a long shadow on the sidewalk

I feel the music of it in the soft contours
here and there a bunny's paw prints, avalanche

Icy tells over the layers of snow and wind, sunlight
wasted this walk out of the way, countless crystals

But I would not change the song, deconstruct its
message, I like keys lost still there in the parallel universe

Perhaps I still cling to the myth of right and wrong
winter struggle not like the storms to be ruthless

Yet the windchill can be stimulating in the dunes
digging children on the beach, a puzzle of a dog's vertebrae

The scavenger gull eyes us, lovers skirt by the waves
arm in arm and bundled still in their innocence

The young lady screams stumbling over the man castle
we made just before the tide line, and the sitting sun

The old judge by his walks, the city streets and sea walls
picks up another marble, cat's-eyes and earths

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Nothing today. I worked toward a variable star mould of five points because I had a close idea of two layers a halving of the stellar arms- but it did not work out. I know it is a minor puzzle and obsession- but it brings home to me that with such ratios really to do with higher space partitions cause strange things like perhaps the broken symmetry, five things, particles, not to be some single constellation.

I keep finding gaps in my experience with these simple geometric things, but alas I doubt there is time to amass a formal study. At least I know what is lacking.

Knots and crossings? I take five coffee sticks and make a pentagram. Four of them one over the other at two points then they interlace. Now, add the five such that along the line one is alternately over and under. Lo, the fifth one at the last point was crossed as over has to be changed to that crossed as under.



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Some links- old and new:

http://www.sciencedaily.com/releases/2010/09/100927105029.htm

http://riofriospacetime.blogspot.com/2011/03/yet-another-top-50.html
what a find constellation of my fellow bloggers!

through xcthulhu on philosophychatforum.com What is Logic?
http://www.dcs.kcl.ac.uk/research/groups/gllc/philo/

This on that page and on my mind to visit or live there for next month:

http://www.philosophychatforum.com/viewtopic.php?f=65&p=176337#p176337



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Later that evening:

http://www.cs.washington.edu/homes/effinger/files/empire.pdf

I did some drafting with the empire problem of Penrose tiles and come to feel it would amount to my problem of such variable star moulds. Note in this article the connection to music and that other links recently posted describe star and convex areas for musical scales.

I also thought about one of my links above- which seems to me that in general the Brownian motion is that between the quantum and classical views of things- in that sense Einstein observed the square root of the time. And this we do to scale model things so that a tsunami or model railroad would look normal scale.

I also, if I recall it right, from a closed hot body an aperture of the square root of two would allow escape- a thermodynamic and space consideration here. Can we say that the extra mass comes from the dancing of quarks in that article and they imperically yet independently align the left and right ones- is this idea of mixing or of momenta as a quantum idea enough to describe say the translations in general space for such subatomic Brownian like motion?

The other thing I encountered in number theory, so wide it is hard to find some of its divisions- well Ullam divided the numbers as to the factors possible and found that the dark regions, divided by quadrants more or less, grow toward the center as having more factors. While it was said that it was not an understood but an intriguing pattern it certainly looks to me like a quasic region and principles- and perhaps the vibration that supposedly measures deeper areas of mass and energy beyond what may be the "neutral classical currents" tend to arrange into shells as if a nucleus or whatever creative dark region may jet out or decay from such geometry imperially forced locally or remotely from some region of space, and some such root of things, like perhaps our concept of the square root of clock time.

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Discrete Wormholes

Discrete Wormholes

Please read the comment to my post of yesterday from Matti Pitkanen as it synchronously addresses some issues which came to me on my morning walk to the coffee shop after a good night's and normal dreaming sleep. He has summarized the issues at hand in relation to quantum things- a good grounding as philosophy to which I can only say that is what my post today represents in hope the quality of it shows the need for creative philosophy as well as creative science if any of us can represent either.

*1 If I can imagine black holes within black hole structures in an intelligible manner (that is in the totality of such things (as creative) and touching on the ideas of centered shelled entities, then our ideas of wormholes may also have such deeper structure in relation to the geometry or reality of substance and vacuum.

*2 When we can find an equilateral triangle by extending any triangle by them externally or internally then finding there centers, once we have such a triangle the scale of it may expand (possibly contract) into larger equilateral triangles.
*2a We can extend this principle of a ray like object (a point or iota and its indefinitely extended "string") to other intelligible ratios such as triangles involving the golden proportion, this generalized to higher dimensions and other intelligible structures so found there.
*2b To such an iota point the ordinal number may approach from or begin then leave into infinity. But the two together may limit the relative invariant length of what can be realized and thus beyond issues of scale, so can be foundational deeper as a foundation for physics.

*3 These are issues of discreteness and continuity as if a quasinfinite view where we ask, as Newton so defined continuity, what is consecutive and what is (topologically) contiguous.
*3a A pipe (so as to carry water) can do the dimensional work of a hole yet direct the flow because it is at least in infinite series of consecutive and contiguous holes. Thus contiguity may be close to the idea to which so many struggle to see the geometry of this world only as continuous theory.
*3b We may as well use the word stargate for the idea of the mouth of such holes in relation to what sort of dimensional space or topological structures they describe or are "embedded" within. Thus we have a hierarchy so far of hyper-pipes and it is important to so consider where these have distinct physical effects. It is not clear at all that all such flat event horizons or singularities can be interconnected or even contiguous in some generalization of space geometry.
*3c A series of line segments, presumably of unity length, may be considered a contiguous pipe of one dimension and in some ways asserts a linear idea of clock time.

*4 Part of the concepts here are ancient philosophic issues along the lines of Zeno's paradoxes. These are in a sense solved by the calculus, but on a deeper level philosophy holds that the issue is not resolved at all. But along the way we can derive intelligible notions as regards the idea of division by zero.
*4a In particular the idea that in the physics we can have differentiations that are opaque to the system in which they apply, that is some particle may be thought to not respond to acceleration or velocity, one or the other a neutral zero background across the potential infinity.
*4b Ideas also on the macro-level of observation, the relativity's, in which a description of the constant velocity of light as variable or slowing down, where light is fundamental, is as good as a description of this general idea of dark matter in relation to centered things or things with singularity centers. (see Louise's blogspot for formal research and an example).
*4c The idea of light cones with such internal and external substance and shadow depths and spans- as Rowlands general metaphysical principle expanded wherever there is a local variation of what does not exist from something that is substance as if light cones (read the mouths or rims of these event horizons and singularities), if the light relative to the rest of the general universe slows down then the shadow cone may speed up. This would explain the acceleration of cosmic rays, indeed, that if there are deeper structures and even deeper ones, local or not of them, that we as we do can observe the varieties of such cosmic rays.
*4d The unity as a product of zero and infinity, one side of this inductive equation a sort of scaleless or indefinite invariant and the other side that leads to a wider dynamic of what may be changeable thus not fundamental in measure sense implies that: Division by zero on all topological structures and scales from an iota point to a ray is a dynamic motion overall, not just a static equation.

*5 We imagine then a discrete but contiguous structure to the stargate rims with the embedded flatness intrinsically and a level of ambiguous within or without-ness directions. At these stargates or portals a continuous brane idea of those which are spaces contiguous suggests at least binary decisions as to what bifurcations such tree like wormholes may divide into, and binary may be the default grounding. In as sense from a constellation of such stargates quantum and peculation like properties may be computed and observed as well the integral structures of shells.

*6 In relation to a cone extended to the minimum or invariant singularity-event horizon length we can reflect to the outside extent on the other side of the cone, a mirror light cone- but in the process we bifurcate the angles also such that within the same circumsphere of expansion there is a slight but meaningful difference in the linear expansion (by zero measure considerations) that have physical effects.

*7 In discrete wormholes where they branch even into twofold it is not clear that such branching is unique discretely with reference to higher topological spaces of freedom to do so. Yet, the totality, including internal steradian angle idempotence of multiple generations (colors and flavors) may default to the level of the dimensions of the topology in question.

*8 Knots and braids on some level intelligibly describe such connections as if the vague relation of fields around some material or structure of physicality.

*9 Clearly, the representation of particles which on either side of the mirror, as dust as well as energy, holds on at least the same topological level of what is expanded or compactified locally and generally (expansions and contractions) explain that similar particles even of the same generation and virtually as shadows or neutral particles also, may have vastly different values of mass to which when they become dust they seem to weigh more in less space than perhaps an atom itself- clearly such scales apply to the energy released in supernovas in a galaxy in relation to the total energy in all the stars. While we can imagine a difference in the quality of an emitted photon, even derived from different topological levels these appear the same structural entity despite what spectral differences are encountered.

*10 [As an after thought I can imagine a whole new area for research if I ask the question what happens if such discrete wormholes can intersect, somehow pass thru and ignore each other, or their grounding elements relate or are superimposed? In a sense all equations are descriptive on some level even when they seem concrete. In that sense some of these notions may already be in the literature somewhere in the form of logic or some view of physics or something. Perhaps at this level of things some ideas like tachyons (not part of Rowland's considerations)may find use. If creative forces are also in a sense dynamic, yet dark, could the dynamics of such philosophical topology not have its global mirror counterparts of fixed or movable reference frames? Could these not also have such a scope of intersections?]

* * *

So Angel comes into the coffee shop fresh out of the state mental institution in Mendota. She is full of metaphysics and street drugs and says she is an angel. She was actually paid to lecture her philosophy class with her view of things. But she gets way to loud and the owners would kick her out. I found one way to quieten her so she would not get kicked out (for after all when the local missionaries came and we have our own here already I challenged them prove she was not an angel- after a few times their pastor forbade them to visit and discuss things here- We told them we would pray for them and if they were not careful next time we would send them a prophet!) "Angel," I said, "you are not really in the coffee shop or going to the university. You are still in Mendota and Johnny who everyone thinks is slow is really our orderly who passes out the medications." She gets quiet for five minutes then bursts out laughing and settles down. "Indeed, Angel, we are just a shadow world of He-man and there they watch us on television and the kids even beg their parents for little Johnny action figures."

Words like symbols sort of intersect like discrete wormholes, meanings shift and they seem to be limited in their directions and numbers as all such fleeting notions and fads. The terrain gets crowded at times and no two things sharing the same space even without baggage tends to fade into the chaotic decoherence. Stargate, well the science fiction writers are a step ahead of the popular culture in theory beyond the space opera of aliens, violence, and the usual romance but there is a lag from the frontier of speculative theory- it evolves. Stargate sounds like an appeal to a nerdy sci-fi futuristic viewpoint. And as we walk on the sand of idea, if we find our footprints by triangulation, that place is where as in the zeroth law of thermodynamics that two things in equilibrium to a third are in equilibrium to each other-despite the fact that from some higher or lower view these things can be asymmetric or even cyclic. But the poet in me, inspired by the Eastgate shopping center mall in Chapel Hill, used the word much earlier very long ago- so too the general quasic structure at first called the Odo-cell, but try to find that among the links to the shape changer- Odo, rich, Otho, Otto... This meta-information can be lost in the wider publication, a sort of purloined letter. But who know how it will all come down in the end?

* * *

I find it rather interesting when people use the old worldview analogies. One in particular is "this will go the way epicycles went as an old theory." In a sense even with an invariant length or the idea of a centered objects (as if shells from outside perspective) we can imagine little spheres as if the idea of this model of a particle or electron can be in fact compared with an epicycle in this manner. This as I say true on the compressed linear model (even if as an atomic string it contains three objects one not clearly in the center and one relativistic. Obviously we need a more general view of these basic (well, for the classical physics I use the general symbol of a hedgehog and for quantum the beehive- the spines of the creature from this christian symbology like the perpendiculars from a center. Lubos has an interesting post today on futurism, the book Future Babble where the hedgehog and the fox are symbols of such grounding world views.) The quasic view, as I said, is the peacock with a thousand eyes. If somehow the general background of the cosmos eliminates this natural center of things as an evolved perception view (Pinker whom Lubos also mentioned today if that is the same Pinker) then it seems we would have to eliminate the thousand eyes in a thousand eyes and so on- that is if we have ultimately a more chaotic world view. But keep in mind if we can imagine such further generalizations, structured or not, these could be a possible physicality and all hint at things way beyond even these current speculations of such complexity. Here for now one might truly say we are still dealing with philosophy. Eliminating such epicyclic views, linearly or not, may not be as simple as our current view of the continuum- even those along the line of baby universe analogies from a more biological viewpoint.

* * *
Some relevant sci mag articles today (it has been awhile since in checked them):

http://www.sciencedaily.com/releases/2011/03/110324153753.htm

http://www.newscientist.com/blogs/shortsharpscience/2011/03/tychos-supernova-remnant-shows.html

http://www.newscientist.com/article/mg20928054.800-escherlike-impossible-shapes-confuse-newborn-chicks.html

What Mirror?

Comment to http://matpitka.blogspot.com/ today's post:

Matti,

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.

ThePeSla

* * *

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.

* * *

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.

* * *

Take a look at this. I found it on Science Daily while reading Matti's link:

http://www.sciencedaily.com/releases/2011/03/110325102008.htm

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.
http://www.principlesofnature.net/principles_of_the_new_art/index.htm ]

* * *

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.

* * *

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.

* * *

Ulla just sent me these most interesting PDF links:


http://vixra.org/pdf/1102.0052v1.pdf

http://arxiv.org/PS_cache/gr-qc/pdf/9406/9406044v1.pdf

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."

* * *

Through the Mirror (and PeSla's Cube)

Through the Mirror (and PeSla's Cube)

Yesterday, I considered some fundamental and general principles concerning the properties of the Golden Section to which I will post more today here. I found an interesting Rubik's Cube puzzle, probably as a consequence of trying to figure out the various steradidan crown and star point designs.

In my illustration of yesterday I posted an earlier photo I called Breakthrough in honor of Pitkanen's statement of one- but I cannot say I find enough in his links to truly understand his applications- and in honor of Kea for I think she too has made a breakthrough- I imagine these sorts of things, like my recreational mathematics cube before physics interpretations, is a matter of higher generalization or a wider world view. For me the exploration into such new realizations at the frontier can be a sort of vertigo while our intensity of concentration and free association in which case one might doubt or feel some solid achievement is made later- in effect we doubt our work and selves especially if circumstances is exhausting and we may not see errors or false paths in the moment. In a sense what is to be unified here when we understand each others abstractions and language is the generalization where it is real of the connections between us as we all are surprised as to on what level we have used but not been aware until the sense of breakthrough of subtle mathematical connections within the methods and notions of our own work. There is a lot here in this theme of mirrors to write- but on the way here I may have got a glimpe by dreaming of just what some of these braid twistor ideas mean as if we have to deal with each others theories in such subtle ways to learn them as we do our own internalization and creativity of the body of learning.

* * *

Synchronously I see that some of the considerations for sketching the Steradian crowns and stars from basic Geometry looks similar to Kea's link today:
http://en.wikipedia.org/wiki/Weierstrass_substitution. In it I am considering the square abstract quasic region, the boundaries for certain 8pt stars from four directions as if (on the mirror) these are actually straight and consequently the quarter edge seems to be divided into three while the quarter circle circumscribed around the square is 4 x pi. In many ways the irrational numbers seem intelligibly concrete and integral if we treat them as geometrical objects. And the tau or phi ratio cube above is certainly such a case.

But let us consider again what happens if we take a 5-cell (four space analog to the tetrahedron with 5 points determining that space) and explode (popcorn vector) it out such that we have one tetrahedron in the center and four on each face. After expanding out from four space into three space and since the center point has the coordinate of w x y z each equal tau, the four tetrahedra on the edges of the central tetrahedron all are Golden tetrahedra. This general concept applies to the analog of the octahedra (and stella octanga) also and recently is popular again as a fundamental object of foundational physics study. Recall that the tau relations as if linear are actually "on the mirror".

* * *

The Pesla cube can be arranged into octants each a Pesla cube and so on. Good luck on designing the mechanism for such a cube- my best guess is some hard shapes with that soft glue to hold them together while turning- a sense of coherency awhile anyway. This model is like the brick or integral idea of the mass of particles and the mortar of fine adjustments between them. This generalization suggests to me that there can be further structures to our concepts of black holes. Black Holes can have black holes within them, at least over a certain ascending or descending generational scale of things into generalized singularity dimensions. Clearly we might have a hierarchy of Planck like volumes to consider on and through the mirror.


* * *

Guess, I am backlogged on ideas so I will just make summary points as the recollections come back to me- forgive duplication if any.

*1 Generally I have regarded physics as a branch of biology- something that seems to go back and forth. With these newer ideas it comes back to physics again- but thinking about this there may be a place or time, or times when these are really the same question.
*1a. Looking at the trees just before the budding of spring I am reminded that the fractal trees are really but an approximation of real trees although these do express growth and energy by Fibonacci growth. I recall also that in the structures of chemistry that the world of Buckyballs is also but an approximation, the 108 or 109.54.54 angles are a little fuzzy, perhaps this difference accounts for some of the aromatic and superconductive properties we observed in such carbon structures which more or less are based on geodesic domes (92 the element limit in three space).

*1b. There seems to be a major distinction between plants and animals

*2 In a sense this is a question of art also. I was checking out the art store and for forms of clay for mould making and in looking at the spectrum of acrylic paints on a finer detail I realized that there is no good reason for buying materials only as good as the student grade. Essentially, without a thin under-painting or with latex gesso, or some pigments like zinc oxide white, in a century paint cracks. I did find the right sized prepared canvass to make paintings for my 1024 x 512 illustrations here so to paint them then photograph them for a series of subjects one vaguely the world of this idea of brading.
*2a This leaves me with a general idea- I wanted a modular and standard spectrum, one that moreover translates well into the ideal of internet color values. Yet it depends so much on the actual physical pigment- and that in turn is best with the human eye and artistic temperament of those who mix the colors. So we compromise with what we find in our reality on a less defined or precise scale. After all in the presence of strong gravitational fields the colors can change.
*2b So in a way our artistic vision of physics in relation to light is the idea of what is this variable and discrete spectrum. We use it to decide what is the stuff of stars for example. Color then is of a higher qualitative dimension than just light and dark, and that over what is substance and space in a quantized hierachy of things. In the other direction the more subjective and mental concepts on which we colorize the world with such human notions, even generalize the feeling to great systems of magic and metaphysics beyond the actual facts, perhaps, of our reality. In the matters of pixels of dark and light we gaze into the cosmic background to make reductionist conclusions about the general process and shape of the universe. And here we discuss the metaphysical fundamentals of something and nothingness. In the other direction it certainly seems that on some threshold of emergence that mind and life can be considered a foregone given and perhaps an ultimate creative foundation.

*3 Considering the abstract structure of the Pesla Cube, Rowland's took up formally the consideration of a Rubik's cube corner twists and related to plus and minus fractional charges. What then does this ability to break the cube into binary octants mean for this idea of fractional charges (and as a generational-creative thing)?
*3a This question of scale as the uncertainty of a constellation of particles when considered as finite is a source of unity as well as the more general diversity of paths of topological structures possible. We note the unit cube as we can see any constellation or class of subparticles as part of own substance or grounding unity of discrete measure.
*3b Clearly with such a hierarchy or fractal like series of such cubes while we may twist the whole we may not do so in the largest binary (quasic) division while it is in a constellation of such cubes (and perhaps the twists and turns of cells within them across the internal peslacube mirrors. In a sense there is no center to this constellation as part of the concrete substance of it all.
*3c We can use the F-of-n abstract quasic motion notation to list the possibilities of what happens if we start with such an octant then place it into a constellation in which its relations between its smallest and greatest tau cubes is relatively coherently fixed. In a sense a unit cube can be in a corner and the tau^6, which here I suggest along the lines of Clifford algebra we have the six dimensional compactified structures of which clearly in such a hierachy and constellation the complexity of such compactified structures is much more general then we have said is too vast yet to pin down as to which applies to the universe's physics. So in relation to the unity the tau^6 can be in three of the motion corners thru a face, three thru and edge, one thru the digonal (a point) and abstractly the tau^3 and unity cube may be superimposed on the same point unto the dimension in question and in a sense at rest.
3d. If we consider the unit cube as the continuum aleph we also then can consider the tau^6 cube as 2^n continuum which is a fundamental idea of the subsets of R somehow greater than itself. In this sense the unit cube is my iota particle.
3e. So at the abstract quasic motion function of zero and a change of four coordinates in four space we have n^3 + 3n which = 4, 14, 36, 76, 140 ... of which 14 reminds me of associahedra vaguely, but in any case these can be divided by two
3f. That tau is involved here shows the slowest irrational expansion in 4D and the idea is that octants are not trivial but are important to the more general coordinate system contrary to the usual of only considering one such octant.

4. In the expansion of the irrationals to a spiral where we erect a right angle length of unity for he series the square roots of the natural numbers which leads to 17 as the ancient Greek knew was a limit or it simply filled up the circle of 360 or so degrees- let us note that the unity to which we erect the two dimensional steradian base of the square root of two is also a root. It is that we exclude this radius unity and the origin in consideration of the 2pi jumps or an iota model of string like things (in my theory) as the beginning discontinuity and singularity.
4a. The jumps between octants if relevant may be useful to describe equally well our ideas of charge, gravity, mass, volume and so on as a generalization method.
4b. In the unit cube, within cubes with a center or not and with the self dual inversion of old structures like Kepler's stella octanga or Plato's metatron cube in consideration again we can envison candles of stacked stars in four space that have spherical symmetry in three space. In general the tau^n defines the natural notion of dimensions as the six colors of the rubiks faces for example are self fixed.
4c. Sometimes the popcorn vector or expansion of what is measurable within when it comes to the without is of a fixed angle in reference to linear tessellation grids so we can observe in say two space these same general principles of rotocenter symmetries and exhaustive lattice possibilities. In particular in the stacking of such hyper-stars we do not necessary just alternate them shifting a half angle as in three space.

5. In consideration of steradian crowns and stars (I may post an illustration along with the fano candle of seven hexes stacked in the 12 color diatonic notes). when we compress or expand angles we can imagine them as quasic polygon straight limits at infinity (not necessarily a fixed idea of hyperspheres that can compress to some point from some imagined maximum equator) such that an equator around a polytope may be a discrete loop of these abstract boundaries.
5a. Let us imagine a loop around a discrete or continuous spherical object; it may have one or several twists, when it is not twisted it is "on the mirror" but even with one twist in one direction or the other in the stacking as if stars, it will stand out in a sense (and in a way I am not sure I understand in depth for these things any more than when they twist hands somewhere between there and back again across some supposed intrinsically curved circumference of the universe- one that moreover these quasic notions justify when some ask if the universe is expanding where does it expand into or does the universe have some sort of a wall.)And that standing out seems to have the concept of charge, especially the idea of chirality and handedness as charge as subtle difference it is on either side of the mirror. [but this is from of what I could make out in the hard to forget dream of last night.] Certainly when these things cross in higher space they are subject to the same wider freedoms we experience in say permutations of axes woven in space.

On the Mirror (Phi-Tau and Concrete Space)

Art in this post-alphanumeric age may not endure as the best concrete ground of human experience and consciousness between it and science, philosophy, and religion.

For we are on the mirror of the dust and shadows of our perceiving. As the coffee shop was down for maintence a couple of days, and we had cold March weather, I went downtown to get ideas from the shops. I speant a few hours in many places and filled a few pages with candle and mould making ideas. Looking back to more innoscent times I find my studies of the last few years- on that virtual world of the internet whose ground is information beneath and finer than the social content and subject of physics in which we are concerned. We dwell in the art of it on some vague general level. We literally eat signs. We crave the imaginary. We are part of a more general nation where the new media is for all practical purposes the ground reality in which only in the face of time or disaster, or if the lights go out, do we confront reality again and the direct dealing with others.

I am amazed how expensive the candles are in the shops since I last tried to sell them in mass, and then charged the same as in 72. Of course a little bit of algebra tells us there are times when charging less for things maximizes the profits. In one case a small Buddah cost $3.00 but it was not as detailed as my own, really it takes a couple of hundred standardized cuts by trained people for the original. I conclude that these people used their small silicon moulds way beyond their lifespan.

I looked up metal cutting and am amazed at the precision of what can be cut- a precison in the world of flat tolerences I need to make things work. I see such percision, not perhaps as detailed as what nanotechonology promises, in the bracelets cut by abrasives and water out of hard wood. But it is the symbolic art of it that the people buy, the sense of reality of the object itself.

In the walks thru the sense of walking on sugar, its lumps and sounds, and up so early in the wind- I found so many new methods and ideas to the point at times I made some mistakes of which a model corrected later (I think, but in the back of my mind I still do not see why it is so hard to make a variable 5 pt. starmould. For all my sense of seeing space now there is something I am missing- perhaps this idea of things in fourspace itself. Where higher dimensions are possible we encounter whole new properties of the symmetry of what we mean by space.

When we add even one more dimension, say from 9 to 10, 10 to 11, from the physical viewpoint we vastly multiply the divisions of space and properties possible.

Rowlands metaphysical principle suggest that nothingness or the vacuum comes into existence with the muon, there is a muon and all that is not muon.

Let us then think of space as if a subtance. One that cannot exactly and abstractly to be said it is something or nothing- both descriptions suggest this idea of substance.

This idea of space moreover can be thought of as continuous and thus perhaps infinitely divisible. Where it is real as a sort of Euclidean geometry, and it is not clear exactly if as Non-Euclidean geometry despite we can say make hyperbolic tessaleations of say seven sided polygons is a complete generalization of space in terms of these familiar and seemingly concrete structures we build. HGere I assume so for now, and I imagine in this space we can have two notions that exist (independently) that of a point and that of a measureable length (a straight line segement or ray).

Recall, that with phi-tau (I use tau, the European symbol for the golden section) that we can have a line segment so as to make a right triangle without area- that is the 1 or tau part of the ratio if flat when tau + 1 and either end of the segment can find these two values as less than or greater than tau or 1. The connectivity in such a line segment triangle cannot exceed the first power of tau. In three space the shortest to the longest ratio of the edges of say a tetrahedron cannot exceed the third power of tau or in all such cases we lose a natural dimension.

Now let us consider a square of the side 1 + tau + tau^2, that squared. We find in fact there are 9 sections 1 + 2tau^2 + 3tau^2 + 2tau^3 + tau^4. But since tau+1= tau^2 we reconditely divide the square into 2 or 4 quadrants. This continues into higher space dividing things (quasically) ino 2, 4, 8, and so on. Furthermore we consider in some higher spaces that we have a sort of fractal like echo of these recondite 4n ratios. Interestingly if we take the first three quadrants only and count the number of squares in them beginning with prime 3, the rest of the values 12,48,192,768... are the rotation groups of orthogons. What this amounts to is the description, perhaps from a view of inversion on the other side of a mirror, of the circumsphere, intersphere, and insphere of the orthogonal subcells (in three space here and so on) for what I thought of as the fsubn functions of abstract motion.

Of course these have square root values as diagonals across the orthogon. In four space it is the square root of 4 or 2 which is the same as the one dimensional unit length. In fact from some center of such an object we encounter 1/2 in the real constructible part right away and all that implies for force laws and so on.

Newton made a major leap in extending Pascal's triangle to the negative values. The -1^n is a powerful notation for alternating values and oscillating values. And on the mirror we have our conventional ideas of -1 as filled space and have to determine in the complex space what exactly do we mean by -i in the scheme of such extended algebra of twistorian considerations.

Of course the general equations of polynomals, the variables and the powers are as far as deeper information goes equal in the effects. In fact we can use these square roots of the natural numbers as coefficients all in informational notation. In a sense that things exibit fields with right angles is also a property of numbers, integers in fact, in this concept of our familar dimensions of space. We recover them further when at a center (as a singularity of points or as a point) we imagine from this side of the mirro things can have discrete shell structures (and the corresponding nothing ground on the other side of the mirror).

Clearly, in these recondite constructible structures we see that in a space representation (tau^2+tau+1)^3 that the largest cube is the sum of the exponents which would be in a sense 6 space, ie 2x nDimensions.

I had some further thoughts that the 24 cell, which is its own dual is in a sense broken down into three beta4 or analogs to the octahedron in three space and these are composed of 8 abstract points. Thus from all directions we have point singularities which involve the division of subtantial space into the 8 octants and so on. I briefly glimped the possibility of a beautiful informational lattice composed of these objects- and perhaps other such resonances of such lattices and yet the fractal like embedding of such obejects tends to balance our idea of scales.
Here, of course we encounter 240, the eight dimensional packing of spheres, as one steridan star before it is broken down, presumably into spaces of ideal jets or points or stretches for observed but relative force values and lifetimes of said particles. Perhaps only abstractly can some such particles present themselves as eternal and irreducible, at least in the short run from all sides of these topological twists and mirrors.

I know these are perhaps very simple ideas of space, then again it could be we have not seen some of the seemingly trivial and too intimate to stand out as obvious that we have long overlooked what is concrete and what is abstract in the art of our notations and notions.

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This Side of the Mirror (Steradian Stars)

Here closer to the original Starbabies: In the process of looking for centered hexagons I came across this link which of course is an interesting abstract idea in the realm of some logic, concrete or not as the link wonders for its utility. But such logic also intelligibly connects with basic ideas of geometric modeling:

http://www.seop.leeds.ac.uk/archives/spr2010/entries/logic-deontic/

After all this is a creative philosophy blog too.



This Side of the Mirror (Steradian Stars)

In trying an idea for stacked star candles (there was not much else to do) I realized the principle could be useful and it lead to some general thoughts on space of higher dimension. This in a sense the Mystique of Multi-Dimensions part II. But the paper drawn star is only similar to the crude paint sketch above as it was difficult to draw and I do not have the time.

It is based on the idea that to a chord in a circle the angles on that circle drawn to the chord would be all the same. In fact this seems true infinitely close to one end of the chord. Naturally it occurred to me to ask if this principle might hold in three or four dimensions and in what sense.

In this simplest of diagrams, the triangle, it turns out that the angles mesh together as if in a lattice of say triangles and hexagons linear, discrete, and straight.

We observe this difference again in the symmetry of a circle or a polygon as a matter of space filling that compresses or expands around a polygon chord. In a sense, and in the colorful labels of the stars obeying four fold symmetry, What is up or down is more significant than the "starfish" of right or left symmetry. (This however may be an artifact of our evolving to so see as Pinker suggests). But by up and down I mean in and out directions- for higher space perception this can be thought of as contraction and expansion.

Imagine playing golf in three space. The holes would vaguely be spherical rims as if we might imagine the surface of a black hole. (I hesitate to use terms like N-sphere or N-ball as I feel them misleading so as to hide the generality.) Obviously the golf ball can fall into it in a sense into the forth dimension.

Another way to see things, by this common aid to visualization, is to imagine it like a potential well and volcano. If the ball is charged it may be repelled before it gets to the circular rim to fall in. If it is neutral but going fast it will overshoot the rim. At just the right speed it falls in. This analogy is used to describe what happens when we shoot neutrons into a nucleus. The spherical rim of it can have the neutron pass thru it and touch nothing- so we slow them down that they fall in.

1. From the viewpoint outside such a sphere or a polygon, such a centered object can be thought of as a chord on this side of some mirror of things opaque or hidden underneath. Thus, at some shell or wider, even expanding sphere around it we have all the steradian angles (cones) the same.

2. This depends on the diameter of the "hole" or chord. Thus no matter how far away from the center in expanding there is a constant or minimum value akin to the ideas behind Euler's constant where the constant angle really never vanishes in theory.

3. Nine dimensions are not the only dimensions where the orthogonal and transcendental spaces have the same volume. This is true of a chord of one dimension and possibly at zero dimension. (How is it then that we observe integral values in the shells of things this side of the mirror?) The Cyclic group of polygons stand out here as if structures of infinite number and complexity. On this the relation between the chords forming them define questions of star density.

4. I imagine that when we ask the general shape of the universe as if it a Sphere we are not asking for an abstract conception- we may say that if we travel in a straight line we come back again because of "intrinsic curvature", but some really mean it is literally curved concretely only the scale is too vast for ordinary measuring. In this model the density of things assumes a default to something of total compass and in a sense finite. It is not accident that among the current models that the dodecahedron one is the only finite universe in the running.

5. Yet we can have an abstraction many ways as to how something straight may intrinsically curve even in a flat space. In a sense the current debate as to unification of the physics is one that approaches from the idea of an invariant intrinsic curvature as if from such cyclic chords (or even strings) in dealing with higher dimensions and those who strive to see it more from a totality where we have to begin to unify the properties with at least nine natural dimensions. (How then do we decide if such dimensional ideas are physically abstract or physically concrete?)

6. It is of some interest that we explore things like quasiperiodic five fold tiling as the golden ratio is a key one in four space. We observe this ratio in nature say in the stacking of certain crystals. Many see the evidence of the Penrose tiles at work here in the idea of darts and kites. So let us not be surprised (despite the general fact that deviations from a recurrence formula for hyper-volumes is here a matter of default and this in a sense linearly intrinsic and invariant to the supposed differences and flows of things as or in the universe- that is beyond the questions of genus structure where these can be hidden on one side of a mirror intrinsically or even expanded in principle- the 24 cell the best structural example) that in three and four space of these steradian angles that the internal to such polyhedral chords (let us not forget how long it took to see that if we divide the angles of any triangle an equilateral triangle is defined inside it) We have analogs to such kites which in general, at least as Euclidean, show the natural doubling of such angles.

6. But these polyhedral, polytopal, spheres as chords describe but one internal angle as the steradian angle- we are not necessarily subdividing the internal ball as if it were composed of many normally defined steradians cones. In a sense we may find the stuctures on such compression principles stable or compactified with a multiple density of such cones superimposed intrinsically.

7. In the original steradian star we imagine also the hexagon with its 15 connections of its points and this is a good representation of triangle or simplex groups of things where everything is connected to everything else. Thus this five dimensional representation may contain four dimensional simplexes. If we exclude one point and those to which it is connected (this may determine if we are dealing with a flat or round space but here internally everything is already round) that we have one such simplex of five points. But in this structuring we have the representation as if a rectangle of the square root of three and on that a quarter of it such that the hatted pentagon appears as if in three space a pyramid of five faces. This particular shape can lead to some interesting lattices in two space. But let us not forget as in the rhombidodecahedron (of two varieties and from and internal dissection of a ten sided polygon Coxeter found both the flat and three space quasi-tilings.) is also as a four space shadow and "chord" hiding one of its points ideally aligned in the center, thus the two of the count of things in odd dimensions, and the 14 abstractly on the invariant chordal ground symmetrical to the outside of this rim or flanged compressed sphere.

8. With such considerations we clearly see why in the imagining of multi-dimensions we intuit what is mystery or what is trivially intelligible structures. So when we apply such intelligible notions to ideas of general physics and space we can have a wide variety of possibilities in determine what is the concrete and what the abstract.





I find he so called near miss polyhedron truncations most interesting in that in a sense these can be impossible structures- in particular the internal volumes in dividing them up may in some way be abstractly but not concretely regular from some view- and that where it is obvious one cannot say have a square, a hexagon, and two triangles meet at a point and the combination not be flat- but perhaps in a sense from some view this is abstractly intrinsically curved. These also come close in actual construction say of paper models where certain ones almost close like those concerning 11 points for an impossible 18 faced deltahedron. In building on such polyhedra as in my Triaconway game, it is possible to arrange holes down from some of the faces in which to embed the thirty cube puzzle.

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I think it would be worthwhile to look at particle decay from the old picture of they being composed of so many levels of bricks with small variations between them. I keep coming close over the years for haunting integer numbers much too soon to say they actually apply or how. Clearly the Pion can be counted a few more electron masses than the muons and so on. In a lose sense some more fundamental idea of a particle as integral yet for general reasons intelligibly diffuse could be what determines some of this discreteness. A lot of interesting things have come from experiments, angles of incidence of refraction for example, and these in a sense with a negative value.

I do not think a general concrete sounding description of say some change in our normal group invariants without a more general theory can prove anything. From the very start, way back to Descartes, we know a hyperbolic lens (say around the z axis) can focus light just as well as the more elliptical varieties. We know also that flat mirrors can concentrate the heat if slabs of them are arranged in a parabola that focuses on a smaller set of them also made of flat slabs mirrors in the opposite x y direction. Beyond that a mirror as the inside of a cone can focus light diffusely so as to in theory concentrate the light hotter than the surface of the sunlight going through it.

Part of the general geometry models then concerns this depth and span of distinguishable ideas of contraction and expansion of what is within or without some general idea of a membrane, be it a plane or a sphere or some difference such that we can take some models of geometry as concrete when we consider if the primary ground of a geometry is not a general mixing of what is hyperbolic verses elliptical. In general the multi-parallel but no-perpendicular geometry is that which is in the inside of such a boundary and although but a sketch to which some say we cannot have the total vision, from some perspective we can take these as a concrete representation of the space as if we view it outside some mirror. All the geometries like this stand and fall (logically) together and so apply. In a sense that we are on the outside of such objects guarantees that properties we observe of them seem to reduce to concentric spheres- so to the description of how nature realizes the phenomena of action in regards to real and abstract symmetries.

An iota particle may just do the accounting abstractly as things tend to fall to some center, or such may be as real as anything. But what are such abstract structures really save a vibration or duality between or analogous to such in say the polyhedra and their duals? This same general idea on some level of the steep climb to a more general physics may be said of any levels of particles- and some of the resonances or even jumps to higher shells as abstract become concrete or physical. But from a more limited view it is not clear that we understand how light can determine the space and space the path of light. I suppose this means that our logic of CPT, even if these are conserved only as the three-ness together, is not as fundamental as we hoped. But hen how many logical systems that treat notions as if in some sort of polygonal relation, if the assignment of the notions to the structures are exact enough, are logically possible even with all this abstract geometrical reduction. Surely, with the polyhedra as the ancient model there are whole new area of apply our (partial) differential equations in an intelligible manner in a more general and fundamental theory. Like many other such theories part of the problems are filling the steps on steppingstones to reach a clearer path to the more intuitive and general picture. Nothing actually forbids that we cannot have interconnections between the successive shell structures of objects- but nothing assures us that in the enumeration such it can give us a total picture of the topological terrain.

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Coffee shop closed tomorrow and day after for maintenance, a rare event like for some holidays. It is possible I hang out in the library- but for now, I again think I have nothing more to say. Still, the shut down for some train of thought is not always a radical break as the ghosts of ideas like old lovers linger in the streets of cobblestones and your dreams. Happy Spring!

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