We have many different ways to talk about the things in the physical universe. Some of those ways we think of as more fundamental, and some as “emergent” or “effective”. But what does it mean to be more or less “fundamental”? Are fundamental things smaller, simpler, more elegant, more economical? Are less-fundamental things always made from more-fundamental? How do less-fundamental descriptions relate to more-fundamental ones? FQXi Administrator Brendan Foster
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240 E₈ polytope vertices using 5D orthographic_projection to 2D using 5-cube (Penteract) Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.
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This is an interesting question for me. Because in a sense it is closely related to what is foundational. Let me explain. The foundational attribute of any perspective has to have a fundamental basis for an understanding of what comes next. The immediacy is recognition of the fundamental, is its beauty.
The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for his experimental breakthrough that changed our thinking about possible forms of matter. More recently, colleagues and I have found evidence that quasicrystals may have been among the first minerals to have formed in the solar system. Paul Steinhardt 2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?
So this leads me backwards to the idea expressed as the, "smaller, simpler, more elegant and more economical." Everyone wants to know when matter begins, and if such an expression is to realize matter is emergent, then it would require an explanation for what that matter may be as being fundamental. That all matter then, is a measure of the now "as a parameter of existence" of our current reality.
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| "From future structural and kinematical studies of known quasicrystals, such as AlNiCo, these principles may be established providing a new understanding of and new control over the formation and structure of quasicrystals. See: A New Paradigm for the Structure of Quasicrystals |
After working though the years gathering information and learning from many who I had come across in the pursuit of science and its understanding, I have been lead to believe that an answer to this question is like going back in time to the beginning of our cosmos. How the universe has been clocked according to the discoveries that have been made. It has been a leading insight to push further back to realize that such an idea of geometry at the basis of the existence is an old attribute given toward as the idea Plato had according to his solids.
"...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)
* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"
One should neither be fooled that I focus on the matter as being fundamental then, and as a substance,it is less then a desired result of any measure when I speak of that geometry. So how is it possible then to say that something is fundamental here if I say the geometry? The space-time emergence, is as from a liquid that the collision process extols the lighthouse affect and I am blinded by it.? This is given as an expression of the new ways in which we measure particulates outwardly expressed from the beginnings of that "collision process" only of in a configured in space, but within the LHC too?
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