Wednesday, December 29, 2010
Motlampion 1 (Poron Brain Puzzle)
[sorry if the changes in the relaxed values of angles I made on this last illustration were confusing. Basically, we have here a triangle without area. One can get a little sloppy when thinking from higher space to the lower cases.]
Motlampion 1 (Poron Brain Puzzle)
I did not do much of anything last night- I discoverd the straws with a flexible tip were useful for constructing some geometry projects.
I recall when I first joined the philosophychatforum that our founder mtbturtle when I showed her my first notebook of metaphysics (and she and no_reason sent me a book on philosophical paradoxes and a surprise xmas $100 when I had nothing) that her eyes glazed over when I talked mathematics on the chat channel. (This was of course before the zit faced scientists thought they had a monopoly on metaphysics with the intent to hold all philosophy as obsolete.)
So I had read and commented in general on Lubos Motl's apparently most popular posting on the Brain Puzzle book and some of his solutions. But I did not recall much of it in the pattern having the straw triangles and squares- so I thought of some general things- Oh, as geometry seems so mysterious to those deep into algebra and vice verse I admit my eyes glazed over with all the equations Motl offered (anyway I have had doubts that programs like mathematica can do some of this work if we do not know how to program it maybe) Clearly our pattern recognition makes the computer's "eyes" glaze over just as we are lost in brute force rapid calculations.
Poron is a word that I saw on television for materials, Dr. Oz I believe to balance the weight of women while they walk on high heels- it sounds like a particle or something but in general I mean it an abstract or Zeno fixed interval or distance of which the edges of this puzzle is assumed such a unit. The question is how does such an interval relate to the rotations in a general (flatened) space.
I like Lubos's appeal to the Pythagorean Triangle in looking for solutions but these after all are unit or interger like solutions. I chose then the golden section as the first and slowest irrational quadratic number to get an idea of what is over the field constructible or reduced to rigidity over space.
Clearly, playing with such squares and triangle the question comes up as to how these may be generalized to natural n-dimensions. Clearly in my view of quasic space (and I assume other ideas of space of compressed or superimposed latices into a plane or membrane of any dimension) is approached by overlapping of the polygon elements as a possibility and the physics question of what is frictionless or not in the idea of real and abstract vectors. (In fact I now wonder if the idea of 8 instead of 9 gluons is but an artifact of how we set up and deal with space in say the calculus. Three space itself should have this general idea thru unglazed eyes.
So (and here we find the square root of 5 times phi^2 = 13.0901685...) a refined look at the continuity here of things in the rotocenter coordinates of such space rather than the just 3 4 5 Pythagorean triangle- that is the square root of the golden and fractal like effects rather than just 13.
Obviously, the sum of edges of a triangle involves a journey in the equation into four space and back again. Obviously, the five foldness and importance of the golden section in four space suggests higher space resolutions of say the idea of some sort of string relationship or some sort of topology involving 5 space- as so many intuit. More than that the diahedral angles between rigid rotations in such a five space would involve the square root of the all important number 11 for the fibbonacci series and not just the square root of 5 whatever the polynomial in the quadradic roots and their signs.
Our instinct, a radial centered pattern as a solution to such problems (I note this tried by Lubos too) is that such rings of them will stablize multiple squares- but of course the rings in ring edges may shift as with all counter rotations and gears and so on.
Here is a puzzle: Can we make a variable 5pt star candle mould?
Lastly, one can read Fermat's remark on the analog to 2 space Pythagorean law in the margins of that book- where he speaks of cubes in general he means a picture of literally cubes and not just a glazed over equation with hidden roots and proofs.
(ps...I hope I did not make typos with the numbers... a little under the weather yesteday)
One futher remark : The Zeno length thus encodes information which does relate as if the holographic princple to the depth of the greater space (thus in my illustration photo I place these things on a window surrounded by other figures of depth- by the way the cube there shows variations on what we consider friction or frictionless points.) And some of that (quasic or dimensional) information can be encoded back into the assumed linear zeno interval or element. Such thoughts on information should be the concern of both the string guys and the general topology guys.
* * *
This article seems relevant to me: a brittle liquid (glass) and a solid (dust). Now it is suggested on sciencedaily.com
That the fracture patterns and scale calculations have reasonable correspondences. This in relation to climate change. However, a scientific as this approach to global warming seems to me (take note young Lubos) it is not clear that we have such mathematics for such folding and breaking in a space, crumpling and so on. Yet I recall another article this month somewhere that had a new take on such changes in structures- most likely Lubos will comment on this article (I hope).
We know dust can travel far and wide- influences in North America from the Sahara for example- there is wide room for such global effects to research.
I have always thought it significant that on the beach the grains of sand tend toward a certain minimum size.