Notes
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See: Math
Investigation
Įsivaizduoti centrą (žvilgsnį iš viršaus) ir apskaičiuoti centro daugiaprasmiškumą (naudojant q?) Understand the generator point and mirror construction here https://en.m.wikipedia.org/wiki/Coxeter–Dynkin_diagram and the ringed nodes
http://math.ucr.edu/home/baez/week186.html dynkin diagram and q polynomial Coxeter group Dn and hemicubes Hemicubeoctahedron is halfcube (on the inside) and halforthogon (on the outside). It is thus without a center (?) and without a volume (?) Note that it wants to choose half of the orthogon. But which half? this would depend on the coordinates. But we are working coordinatefree. Thus the natural answer is ambiguity, as in a mixed quantum state. It is the same ambiguity that is in the internal tension of the original center, "those things are which show themselves to be"  "to be or not to be?" So it is modeling that ambiguity. And that ambiguity is modeled locally at all points. And that is how the simplex is adorned by local growth. Dn demihypercube construction
The polytopes are irregular because the Dynkin diagram is not a path but has a branch. Thus there should be not one center or volume but rather the "generation" of the polytope should derive from two perspectives. These two perspectives may relate to the bipartition of the demicube which itself is a bipartition of the cube. The two perspectives are related by double edges. There should be two different, complementary, flags of faces. And they should relate to the cross polytopes  one flag should be like the cross polytopes and the other flag should be the opposite  and together they should form a cube. The pascal triangle can be explained by noting that we have the fusion of two paths in the Dynkin diagram, one of length 3 and one that grows without bound. The first nontrivial example is the 16 cell. The purpose is to split the perspective. The human perspective is given by the short path. The Higher Dimensional Hemicubeoctahedron Daniel Pellicer, in: Symmetries of Graphs, Maps and Polytopes. 2014. http://www.sciencedirect.com/science/article/pii/S0001870809001017 Homology representations arising from the half cube http://math.ucr.edu/home/baez/week187.html The Coxeter group for Dn is the subgroup of the symmetries of the ndimensional cube generated by permutations of the coordinate axes and reflections along pairs of coordinate axes. http://link.springer.com/chapter/10.1007/9783642042959_1 geometry of cuts and metrics http://arxiv.org/abs/1506.06702 paper about 16 cube nim and sierpinski demihypercube http://link.springer.com/chapter/10.1007/9783642215902_15 nth roots of pitch class inversion Coxeter groups and polytopes
Symmetry groups
Exceptional groups Also this suggests that the exceptional groups are modeling interactions of limited human perspectives. Generative center Centras: apibendrinimas. Išrašus jį atsiranda matas. Projective space. All lines that go through the origin. Natural origin = "center" of simplex. Natural infinity = fold out the next point = so vertices are halfway between Center and Infinity. center is what gives 3 rather than 2. center is what links involutions in the dynkin diagram. the linked involutions, the edges, are numbered and are added as the normal form which is preserved. An add the center along with edges from the center to the other vertices. Then you can revision in a higher dimension. Qanalogue qcharacteristic 0=q=infinity jų požiūriu Visa šeima įvairių q  iš esmės panašūs  bet mes esame keisti q=1 0=1=infinity mes esame keisti. All of the nodes chip in a weight "q" to allow the new weight to be distinguished from the rest "q^k". They all go down by one (temporarily?) to stay distinguished, to meet their previous obligations. Young diagrams  qanalogue Chu qanalogue of a simplex is a projective space over a finite field homology Theological interpretation Would like to believe that God is good. Eternal life, eternal learning is driven by the building up that God inspires. And all learning is dependent. But at any height there is the dual: we can unlearn (or tear down) whatever we learn (or build up). Unlearning is independent like the cube. But in between is the space of eternal life. It is based on the idea that God doesn't have to be good, life doesn't have to be fair. We can unlearn in order to learn. And ultimately we hope that truly God is good, that truly we can learn without unlearning. That is what we are demonstrating. So it is related to John Harland's quest about learning. Field with one element David Corfield's post https://golem.ph.utexas.edu/category/2007/04/the_field_with_one_element.html about Nikolai Durov's book http://arxiv.org/abs/0704.2030 John Baez: This fits nicely with my own intuitions about linear algebra over the field with one element. A pointed set acts like a ‘vector space over the field with one element’; a set acts like a projective space over the field with one element.
Coxeter groups Lecture notes by Federico Ardila Videos
https://ecommons.cornell.edu/handle/1813/3206 catalan and coxeter https://ecommons.cornell.edu/handle/1813/17339 coxeter dynkin interview https://en.wikipedia.org/wiki/Conway_polyhedron_notation polyhedron operators https://en.wikipedia.org/wiki/Alternation_(geometry) 
SimplexNaujausi pakeitimai 
Puslapis paskutinį kartą pakeistas 2016 birželio 19 d., 12:35
