Thursday, December 27, 2012
Generalized Vector Algebra beyond the Monster Group
L. Edgar Otto 23 December, 2012
The very large but finite group of 196883 dimensions concerning rotations can be thought of as Godel metalanguage unique using the notation of prime numbers.
The ground for vector properties as jot products expands the usual laws into those of a wider non-necessity wherein our intuitive inspiration involves geometry that goes beyond our notions of linearity into the natural dimensions.
The reduced large number of dimensions should be seen as derived from its component parts foundationally and not yet a group number that we understand if it can be used in a strait forward operations as in the study of subgroups which in any case we do not necessarily bias the power numbers from the number powered as the fundamental grounding as in the case where primacy related to only part of such parallel cases of what is or is not in sequences definite relations of generating certain numbers as prime such as this question involving Fibonacci numbers.
There are 15 primes involved in the numbers to be powered that define the Monster group.
The numbers in the powering, including 1, sum to 95. Such distinctions of the numbers suggest a simple relation of expanding basic orthogonal models for these rotations as if starting from reduced geometric structures to understand the complexity as if the elements of them undergo expansion dimension wise. We also analyze the addition as a property of clear integers as to the inclusion of the 15 into the general 16 cells in the 4D matrix such that where it applies we consider the nonnecessity of the null origin or addition.
Let us observe, informally, the following additions and subtractions of these levels of powers of natural integers as defining sets (still we need to find the rational in the expansion choices of which, evidently low primes, are used and which are repeated to multiple powers, these distinctly unique and functional sets obeying what in arithmetic seems sound and consistent in general number properties.):
95 +1 = 96 of which different sets of subgroups of the monster if made as distinctions act as a measure of proximity to some aspect of rotational subsets of lesser but included dimension groups, here four times 24.
90 + 5 = 45 where the bicolor (hypercolor) is related to the possibilities of combing 15 colors as abstract color vectors in these group interactive dimensions.
95 - 81 = 14 which recalls the spaces of the associahedron, and ideas of the count of elements in a holographic surface as well the internal center as null or two, or as gender unified and confused in four space.
95 - 89 = 6
Nine of the primes are taken to the first power 1 and 6 to some multiple power of which 11 is significantly the square 2.
95 - 35 ( the 1 2 or 4 possible subgroups, here for 4) is the reduction to the number 60 where it occurs as 5 fold symmetry.
121 - 95 is 26, and all that number means
if we add to the 81 elements of the hypercube 2, then 83 may be thought to exist as null shadow elements for a triality of creative objects in a centering. This number can be successively found by loose additions and divisions.
Lastly, 95 is not that special save it is 5 x 19.
We can privilege one element of a group to generate a subgroup.
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Would any group of symmetries that did not distinguish its members as some hierarchy of measure no matter what the complexity of paths and dimensions be intelligible if it were only an abstract set at singularity?
Once this structure is more concretely obtained then the missing numbers in a natural order unto the maximum symmetry of the physical field in question, may in a sense contribute as null (Rowlands metaphysical) values that influence the constrains and evolving structure of a physical system.
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Such abstract thoughts may apply concretely to the expression and development of subjective or the physical for organic organisms. For such problems in that mathematics relates to our psychology, science claiming it has no definite answers at this time for certain human behaviors, this alternative theory may show a new direction to solve the problem and the possibility that foundationally that science but a hopeful monster generating hopeful monsters that science at its ground may not find the problem without some future solution.
I have the utmost respect for artists or even scientist that might be said to be held back or broken in their mental development as if in fact what we consider a disease element may be helpful for the breakthroughs for the mainstream not otherwise found by irrational intuitive passion that seems to be part of so much creativity. But in that I may be considered by others a scientist or artist, we all crave role models for some level of obtainment thru admiration including the open minded possibilities of our own achievements even if these models are myths, I tend to judge the work for its beauty and for the product or result of it as a work of quality. In my neighborhood I have known a few artists of higher genius and yet it was among one of them who was a real threat to his co-workers, it can happen anywhere.
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