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?
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