Epsilon-Delta Honeycombs (a math recreation)

Epsilon-Delta Honeycombs (a math recreation)
Without deeper projects and directions and that questioning of what we do and what we are looking at and what principles may be there to make better sense of life and make our world a better place, I fall back awhile with mathematical recreations. After all it seems such things can be the start of more formal principles. The philosopher and mystic in us are drawn to the Platonic solids, and in more modern times the Penrose tilings seem to attract many scientist and physicists- and always it seems that the power behind the scene calls for the intimate intuition of woman, Alicia Boyle, or the lady in Australia who worked out as recreation the five fold tessellations of tiles. And Dear Rosalyn- who brought a great deal of no nonsense common sense in the reading of her crystal data.

I do, but am not sure of what I am doing as seems the general case of our humanity allowed to play awhile, if we take thought on it. It is hard to tell if we are subject to those who would call such thinking fantasy, when it seems that fantasy can be true to its own inner laws.

I find it most interesting, as if following some collective trend of inquiry that I would casually post in my illustration the fano plane (and in color code question why the directions in it are what they are) and Kea posts it as part of her updates.
I suppose that synchronicity has to have some intrinsic property of surprise.

One recreation I attempted was to recall and count in a lattice of cubes how many it takes to form the trifoil knot in right angles. Somewhere in my papers this was part of a puzzle I called Lost Earth. A box where a blue marble, perhaps with a clue to sounds inside, had to negotiate the maze by twists of the outer cube. Clearly in more complicated knots it may take rather long before the marble exits the other side. Such toys inspire deep principles or methods sometimes, here perhaps some measure of lifespan or probability of that caught in such a lattice.

But, in this casual search for or stumbling on first principles I have to look back again at this idea of "wildcard" coordinates not making the chirality of such knots clearly right or left handed- that was an advantage for me and not a problem. Certainly, if we can regard things as three holes (as Kea pointed out) these can be used to abstractly orient the axes of roughly where one would find the path of such a threefold knot. Without considering the internal lattice grid one has to literally separate the paths so to tie such knots. With my straw model hanging in the window- certainly 9 or 12 straws the minimum but not enough, in the loose tying or untangling this knot into three space lobes the illusion of pentagons came up time and time again. These straws of just the right tension for such projects do bend at right angles, and do so in all the directions of natural space. In the illustration above in the upper left corner is an orgami octahedron of which as its faces are corners of cubes the person who made it for me called it the intersection of two tetrahedra.

It is an accident, but seems appropriate terminology, this idea of the epsilon honeycomb and delta honeycomb to mimic that principle of calculus- for after all in matters of locating as if by changes from the alpha and beta sides of the quasic or even the natural plane when we locate the finite from continuous functions- that sort of natural labeling at some presumed narrowing to an infinite grid becoming ever finer or for some ever more complex in space structure or vibrations on the small scale- my intent was to explore certain structures and question my own sense of principles of fundamental chirality. What I do then with the general right and left divisions of the cube of 3x3x3 suggests that in using these sorts of units and distances we have to consider them as if descriptions of basic series involving not only the ones and zeros but that part of the values chasing values in between.

I will now draw this cube project- pretty free really from preconceived ideas, even my own, so I will post it whatever the results. Shortly. I saw a young lady who had an art project where she tried to make a cube but wound up with a very odd path which I have always called after her last name: The Harper Cube. I met her long enough in the UWM student union to make a sketch of her art project. So the Harper cube or path is really the opposite of the internal three lobes of those cells not the corners of a cube- with the possible exception of the central cube special in the labeling to both lattices or honeycombs. So, indulge me if you will my recreations- it is not easy always to keep up such a pace of creativity.

Oh, to the right of the illustration walking to the coffee shop I spotted this interesting arrangement of snow on the black metal outside bench. It seems to suggest to me a background of what can be saved as concrete from the blowing snow and what is lost in the space or virtual of it all. And it has a symmetrical order like the picket fence (of which Wyle noted seemed to gain our interest and sense of beauty for after all we have a similar thing as the vertebrae of our spinal column).
There were no profound or deep dreams last night, only my swivel chair finally broke so I had to rearrange things with my pallet in the kitchen- and this question of sleeping in which direction- belly down or on one's back had come up- as to which is better for the pressures of one's body. In the shallow dream face down I realized one can sleep clinging to the earth facing it or to the empty sky...and, the old question of do we put an infant on his back or belly- all the advice over turned and the very opposite recommended at better for young developing humans...

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So Here is Math Recreation figure 1- Perhaps I leave this blog as for such recreations even if others are posted so check back.:

I was looking for another pattern I felt relevant to discussions of late- but for figure 2 I offer some older patterns to perhaps visit again. :





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In reply to Ulla's email on graphene and Higgs particle link:

at http://physicsworld.com/cws/article/news/44994

Ulla,

Thank you for the link via email and clarification. (Re: strings and ceiling wax and things) Yes, there is still much for us to learn and who knows, maybe we need older ideas to stand on in order to make sense of the new.

ahhh I see what you are thinking- there is nothing wrong really with the authors ideas in this link and there simple analogy on a simple grounding level.

But is just is not enough to describe the topology of things with deep understanding.

I find it most interesting as I did not check before hand that I am surrounded with blogs of such women of insight.

This hexagon stuff, lattices and honeycombs, idea of some sort of unifying energy from the idea of volume of space itself, of the idea of inverting the universe as if some sort of compact six dimensional (and that Riofrio's inverted) topology, looks a lot like Kea's researches.

Of course we can make a chain of pentagons of water now. We can make all kinds of new inorganic and organic combination's of life forms yet still do not know just what is happening even with the naturally evolved one.

Let us start with the incredible idea that in a molecule of six carbons we can have a seventh at the center. What would this mean for the graphene plane? Is the consideration of some real center here not a sort of moving or dancing point, some sort of consideration of seven dimensions implying an eighth- and the stances to twists and turns of octonions and such? Does this not look like Kea's area of enquiry?

A string is a one dimensional thing close to the smallest Planck length- so what is it made of ? Points? Now the finding of neutrinos and whatever in the greater unified model has to be worked out also- but why not more application to the real points in the crossing of paths of things as if they were string like? After all a cosmic string of 27 dimensions has its asymmetries and excitingly, superconductivity- as with such Fullerenes. The real can be creative in a more unified sense as well that idea of some flexible zero point in an atom or volume of space that makes real particles by pair production, so too protons perhaps as in the steady state models of the creation field.

Well, just stray thoughts for now. Pitkanen's on primes certainly fits into this in his recent thinking.

The PeSla (I will post this on the recreational page but will remove it if you object).

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