PLato said,"Look to the perfection of the heavens for truth," while Aristotle said "look around you at what is, if you would know the truth" To Remember: Eskesthai
Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography. Quasicrystals had been investigated and observed earlier,[2] but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter.
Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. The first experimental observation of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1982 and it was reported in print two years later.[3] Shechtman received the Nobel Prize in Chemistry in 2011 for his findings.[4].
In 2009, following a decade long search, a group of scientists from University of Florence in Italy reported the existence of a natural quasicrystals in mineral samples from the Koryak mountains in Russia's far east, named icosahedrite.[5][6] It was further claimed by scientists from Princeton University that icosahedrite is extra-terrestrial in origin, possibly delivered to Earth by a CV3 carbonaceous chondrite asteroid.[7]
"The end he (the artist) strives for is something else than a perfectly executed print. His aim is to depict dreams, ideas, or problems in such a way that other people can observe and consider them." - M.C. Escher
I too have always been interested at the idea of what we can see deeper then what we observe on the surface. As if an abstraction in the geometry may be leading when considering Polytopes and allotrope s or even Penrose Tilings as to the Truth?:)
In quasicrystals, we find the fascinating mosaics of the Arabic world reproduced at the level of atoms: regular patterns that never repeat themselves. However, the configuration found in quasicrystals was considered impossible, and Dan Shechtman had to fight a fierce battle against established science. The Nobel Prize in Chemistry 2011 has fundamentally altered how chemists conceive of solid matter. See: The Nobel Prize in Chemistry 2011 Dan Shechtman
I do not think one can ever imagine what goes through my mind and I guess that's part of my artistic journey is to better learn how to describe what I am seeing. It goes back some time as to what I learn about myself and how some of these geometers see. I did not ever feel apart from them as I tried to look deeper into reality and see what the basis is and how we might describe that.
You must also know I now sport an interesting tattoo that I will share shortly. Maybe even consider it as a line break, and as a pointer. You'll see why when I upload picture. So, that has been my thing when I look at all this science and those espouse the teaching of, that I tried to find my place in it. I mean I could be so wrong in a long of things.....but isn't that part of the evolution of being? Learning about those mistakes and dealing with the responsibility of finding that truth within self?
My second tattoo will be as in the picture showing below on this blog site demonstrating and seen above is an ancient idea about "our heart" in relation to "the truth." How we weight that against one another and how the choices we make will have us asking whether we acted in accordance with that truth. That is "the final judgement" and if this is understood then we can access whether or not we have much more to learn. I know that setting right past mistakes is not an easy thing but if you at least start then that is part of the success of not of having to repeat them. Maybe repeat many times until you finally actually get it.
Well then,how does one simplify that picture of such Judgement in the Hall of Ma'at as to know that this message is alive and well in today's world and just as valid? How well will the tattooist portray this design? I'll have to give it to her so she has some time to look at it and decipher.:)
Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. Classical theory of crystals allows only 2, 3, 4, and 6-fold rotational symmetries, but quasicrystals display symmetry of other orders (folds). They can be said to be in a state intermediate between crystal and glass. Just like crystals, quasicrystals produce modifiedBragg diffraction, but where crystals have a simple repeating structure, quasicrystals are more complex.
Aperiodic tilings were discovered by mathematicians in the early 1960s, but some twenty years later they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography and solid state physics. Quasicrystals had been investigated and observed earlier[1] but until the 80s they were disregarded in favor of the prevailing views about the atomic structure of matter.
Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than 2, 3, 4, or 6. The first officially reported case of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1984.[2] The distinction between quasicrystals and their corresponding mathematical models (e.g. the three-dimensional version of the Penrose tiling) need not be emphasized.
Put briefly — and Schrodinger did not say so guessing his intuition is up to us — I think his intuition was that an aperiodic crystal breaks a lot of symmetries, therefore contains a lot of (micro) constraints that can enable an enormous diversity of real and organized processes to happen physically. This idea of organized processes seems to be hinted at in his statement that the aperiodic crystal would contain a microcode for (generating) the organism. I have inserted “generating”, and this is the set of specific processes aspect of information that I think we need to incorporate into our idea of what information IS. I think Schrodinger is telling us both a deeper meaning of what information “is”, and part of how the universe got complex — by repeatedly breaking symmetries that enabled organized processes to happen that both provided new sources of free energy and enabled the breaking of further symmetries.
