Twenty First Century Top Spinners
Here is the encoding idea, although just a suggestion and arbitrary coloring and choices of paths in a much wider world of possibilities for the 8 tetracubes.
I find it interesting also (while exploring some of this issue of triality) that Kea posted the idea of turning pentagons into prisms- I mean if we count the struts I added for stability to the Stasheff associahedron since the triangles are arranged as a prism and not antiprism ( here an octahedron ) we could add three more to the 64. but in this prism I have then 8 triangles and by doing so with three less the general symmetry as a twist feels right in this abstract higher space- one that is perhaps a stepping stone to further understanding of the symmetries of this structure. In any case on the surface of a cube with the diagonal struts the analog
of the shadow is that of 4 space octahedron. The triangle prism with 6 struts is one of the strongest structures once suggested for space station assembly do to its light weight.
I recall in the small booklet with the SOMA cube by Piet Hein he mentioned he thought of this puzzle while doodling in a quantum physics lecture. Hmmmm, maybe it came from such study after all. This seems to involve electron structures much in the same way these geometrical recreational mathematics involve Rubik's cube as QCD explanations or haunting similarity to rotation as 1/3 or 2/3 charge (yet we can do things with which fractions are the starting place for this says Rowlands).
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I am beginning to receive generous comments so feel a little pressure to present my work more clearly and more dignified in this otherwise remote project where I do not really have to censor myself- at least not as a poet, but maybe so as if a scientist.
I hope some of the ideas are worthy of such high praise.
In any case I have enjoyed being a tutor for many people, in basic algebra or geometry when otherwise they would fail and have to retake the course. I find it gratifying that some of my students not only outdid me but come back to show me a few things like the calculus, or when on to make money with certain geometric shapes.
Some of my reasons for starting a candle company was the study of space structures with the hopes to understand higher space structures. The envisioning of a 3x3x3 cube too some initial effort but can be done in one's head. I have tried to make many variable molds and for our stacked star models I have found dozens of ways to make variable 8 pointed stars but never a variable five pointed one even when I felt it could be done but was not sure why- after all the metrics involved here are the square root of two and phi. This of course shows us something of topological restrictions in nature. I also feel nature herself has a little trouble reversing things that are on the inside or outside when this is confused in the discrete world and is an issue I address in the above illustrations as to the handedness of the sequence of tetrahedral face and point colors. But this idea I posted first as a comment asked for by Yuri Danoyan at http://vixra.org/abs/0907.0008
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The PeSla Yuri:
I really liked the article and the terminology and notions behind them. The symmetry of the discrete has some interesting properties in that in structures it is not clear what is the inside or the outside and nature too has to sort this out. In fact to some other force or particle passing thru such a structure it can be transparent or invisible. Yes, we have to count the discrete as if points and resolve that view with continuous methods of numerical analysis. This ratio has more to do with things like 3+1 dimensional formalism. I am sympathetic to your ideas on H and He and find that a most brilliant insight and hint of fresh views on physics. I feel there are other ways to ground in the concept of three-one ratios from a geometric view around structures involving 24 but I do not know how this might apply to high energy physics, certainly your notions are part of the bigger picture we seek.
Today, 9:22:34 AM
The PeSla
Sorry, it has more to do with physical descriptions "than" just our debate as to 3+1 dimensional formalism. Note, the group of the tetrahedron is 24.
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Dionysus, who studied Plato's solids and spun tops- a further commenter to his article had interesting things to say about chirality and the tetrahedron where Yuri and I can see a "metasymmetry" breaking (his terms). But did not Fuller explain such ideas which after all is not meta is the heart of the Rubiks cube mechanism?
But, so the comment was not too long I wished to tell Yuri that Fuller sees 92 as a limit of his touch geometry of structure for atoms- his world appeals to 4D while our current interest in structures seems to be a dimension more or so.
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I just came back to google Jim Stasheff.
It is a small world. I keep thinking of Nietzsche's saying- I paraphrase: "History is a process to arrive at a few geniuses, and yes to get around them."
Every so often as time goes on I find I have spoken with a few people, not seen profound at the time but became so in truth and legend. The musician struggling in the run down apartment near me who later becomes a god in his field.
Oddly enough I spent a good deal of my life in Chapel Hill, NC and met a lot of the UNC students. I briefly attended a couple of clock hours without ever seeing a book and constantly was entangled with admissions due to ill treatment from the Veterans Administration more than once. Few understand the constitution, even state statues. But between the times of eternal musical admissions chairs I felt I should continue my work and interests. At times I have talked personally over some issue to students or professors who became much more influential later.
Stasheff, the name rang a bell today and I was delighted to find him on the internet but I could not see the java 3D version of the associahedra on these computers. I called him once after seeing his article in Scientific American as he was near by. He teaches topology. I tried to explain my sort of space at the time. He said that the string theorists had just asked him to consult about topological theories. We talked introductory topology (hey, with kids my keeping up with the ideas were falling behind) He asked me about an initial point where one cannot be said to know topology unless early on one saw the split in types of spaces. Yet, after some discussion we agreed that in a sense there is not good concept of a "hole". What I best recall of the conversation was how nice of a man he was, even to non-students, and that trait I have found in others who take their time for dialog. (now I vaguely recall the question had something to do with the 92? stellations of the icosahedron).
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I am not sure in the final accounting if my thoughts have relevance or significance more that what can be done in a free academic setting- sometimes I feel that if I had gone down certain paths of training, or say had stayed in the Tidewater area, or concentrated more on analytic geometry rather than constructing polytopes, that I would not have been fortunate to discover the few things I see, uniquely. But the human equation in all this, our true creative peers and model heros, both in the past and those I feel strongly will stand out in the generation to come, is perhaps a great strength and source, reward for the effort that keeps our core strong in bad days. As people age or not in our vision of them in our dreams, so too in the background our dreams and science evolve in our comprehension, and with this thirst in the desert that seems to give us the urge to write- it is said, the only difference between a poet and one who is not is that they take the time to write some of it from life's highs and trials, and intervals boring desperation.
We may not be of one body but we are not alone. There is still much to be done and worlds to explore, maybe more than we have those who dare to dream or sacrifice for this probably absurd gift and consuming challenge as passionate creativity. We, like Nietzsche may speak of it but it is no more consolidation than trying to cheer someone who experienced deep loss with an arsenal of cliches they do not hear any better than most things said when the mind is not open, this drama of its unfolding, and perhaps we are closer to some idea of consciousness as a science- in our age a rung up on the ladder to see things as say the higher dimensional M-theory, and other notions of pure topology.
Of course there seems always a paradox and crap shoot at the frontiers and we think about sayings from many angles- Riddle me: Take thought on the logic of it all, what is mapped or not in our multidimensional universe of brain- He who doubts the indifference of the universe doubts his (Personal) self.
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yes, back to science mags: the chromosome links and cancer I find especially interesting from general biology and my own more consciousness organizing chromosomal view. Did humans have more cancer after descending from apes? These magazines are said not of journal quality so-
http://www.sciencedaily.com/releases/2011/01/110106144735.htm
http://www.sciencedaily.com/releases/2009/12/091207123107.htm
The new genome explosions caused 239 rearrangements on a single chromosome in one case of colorectal cancer. would the number (topological near 8D packing, soma solutions, tesseract unfoldings, and so on Numerologically be significant here- there is another link I could not see on new scientist as it asks for subscriptions to read where the quantum imprints for reconstruction of a chromosome and yes it can and it seems to cause these mutations by errors rapidly- but perhaps there is something in the twists and turns of things here in the far reaches of topology.
http://www.sciencedaily.com/releases/2011/01/110110090425.htm
http://www.sciencedaily.com/releases/2011/01/110111132721.htm
Do we not see a link here with storm antimatter production on surfaces and a possible recurring quasar activity as if its surface creativity- then again there can be a sort of structural patterning numerology too as a first guess as to when something from some imagined action at a distance, non-locality but not as simple as quantum theory initially a crap shoot where nature imposes its own but averaged out confusions of the chirality?
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