Monday, August 29, 2011
Dihedral Entropy L. Edgar Otto Aug 29, 2011
*1 Part of the general idea of containment by a sphere or surface as if a polyhedron is the "last face"... Thus the sixth mirror is not needed to describe some of the infinite reflections... but as always the last face may only appear to reverse itself chirally in respect to the other faces.
*2 Where near miss polyhedra exist in actuallity and locally these can revert to the idea of a Euclidean space.
*3 Other lattices are possible to which the counting of cells is intelligible. We can imagine for example isolated dodecahedra of 60 triangles (after all the full group if made notes on dodecahedral dice with inversion also must interchange the pentagonal order with the pentagram order of five objects and these in the same global sense of the rigid rotations.
*4 These dodecahedra determined by 14 sided figures (ten pentagons and 2 hexagons) of which there are 72 triangles. In this sense of the dynamic dihedron entropy the axis between the hexagons can in a sense be emitters of rays or half rays from an emitting stellar object or particle.
*5 The 20 possible tri-onimoes of six labels can be stacked into twenty triangles on an icosahedron. But again, on an octahedron only four such triangles will make a valid group of them. ABF is valid but AGF is not.
*6 One curiosity of last night was the using of pentacubes to describe the skeleton of a 3 x 3 cube (the skeleton involved in ten fold symmetries considered too) These in a sense make a puzzle of 20 things or so determined only by the axes-one corner cube could be rrryyo for example- these worth exploring (recreation-ally).
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State of the Vison:
We crave the light and for some reason want to speak out our vision to others, that or hold a conference where we all seem to agree at some interpretation of reality. Lubos has an interesting article today on a string theory conference (of course I do not quite think it is enough to consider compactification and weak theory alone- nor that cosmological constants and in general dimensionless constants can be ignored or dismissed and true grounding for physics found- but it is worth a try I guess- some versions of string theory are trivial and will not be but an equivalent version of one true unification of such theories. What is the point really of making a whole new particle zoo that cannot in principle be that clear as to masses?)
Still, the monkey tinkerer within us- for example, Leo has an interesting idea about lattices and photons- and today there is a lively discussion in the comments on Kea's updates. Ulla sent a link I could not access but from what I can tell it involves a catalyst of elements for a form of local (tinkered) cold fusion involving the cold transformation from nickel to copper with a gain in energy- while this is not forbidden by quantum ideas there is no general theory these tinkerers operate on but the old fashion way of invention- we monkeys and holy men messing with and exploring our environment.
But whatever the vision, the overcoming of the way of doing things as the playful monkey stands beside me in recreations- and believe me one has only to surf the internet to see how elaborate such visions can become even when they strive to be scientific (and not an outright delusion or scam) as well those who work in the field who only suspect some higher vision but intuit enough to call it a mystery that they assert or hope can be solved later. So in a deep sense, and who but us care for these difficult things for now? - we really should realize what is actually the way of doing science as some responsible higher being beside the struggling monkey evolving (hopefully) within to undertake new work and explorations.
It is not enough to be competent and even poetic in our visions, the work cannot be divorced and sanitized, laundried, and that makes it scientific and far from the human considerations that in the end are essential for life and science- that we can call an elaborate work a deep and sane science or philosophy. We can be competent scientists and still not do competent science, we can be great tinkerers and stumble on some great instance of useful vision and still remain blind to the bigger picture no matter how much a so called theory of everything our dawning, dimming light fills the vacuum of what we think we can see.
Only those with creative vision and a sense of being a part of the abstraction of space and time, can see in others such potential and state of the vision that unto its day we may say- behold, this is a scientist. Some science may be foundational because such an awakening for the sake of we sentient and social beings and the spending of the mysterious touch and light to find this- is the essential and fundamental and proper object of enquiry.
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Note: my use of the word "dihedral" does not necessarily refer to say "dihedral angles" but more so the polyhedron with two sides and no volume, the Dihedron of which it is a legitimate but less obvious form of the possible Platonic polyhedra and I suspect that even in the more continuous group theories that such duality and dynamics of surface interactions and dipoles and chirality and so on- that this for some is treated as a group principle as if it does make a function that organizes other groups and phenomena. How is it that there can be some sort of intermediate entropy as if a surface phenomena much like the stacking of cubes- say those with the edge of the Planck length?
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I had some thoughts casually last night for those cases where I encoded the dice faces with the international signal flags- just like with the applications logos can we make a meaningful international artificial visual language? A fan of interglossa now glossa- while these symbols could easily supply the articles of a language tenfold- the logic under it as that draft as on auxiliary in the face of more modern physics would have to be radically revised for some of our simplest notions of space and motion- yet, some notions such as the counting number system with multiplication by say tens as in the Greek alphanumeric system or the resistor code tolerances would be valuable. But this is mostly fun, like the shadow code that fascinated a generation using their imaginations listening to the radio. Still, there is something here about structure of patterns that draws me, along with the sense of color. Of course this system, basically unfolded tetrahedra, are perhaps not good for the case of tricolor flags. A new flag principle for me has been also a new principle of the underlying logic - including what only works if the field is limited.
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