Combinatorial Physics 101 and Particle Generation Foundations
L. Edgar Otto August 06, 2013
The idea of quasi-sufficiency asks (of the physical properties of Higgs as dynamic biological analogy) not only Turing like if a large but finite sequence will halt, terminate as well as initiate a structural phenomenon.
On the viXra blog Jonathan asked the fundamental question why are there particle generations to which a reply to him was rather standard from the valid but insufficient statistical view. For such a view that only sees the result of indefinite initiation we can assume life can be maintained on the pink goo made from stem cells and there are no qualitative consequences for extended human life in such everlasting stances of expansion. If we take the quantum view as a measure of ignorance should we not as just what or who it is that is ignorant?
Ben replies he thought the situation was part of the patterns of geometry, which also is a valid but insufficient view... both things need deeper foundations. Statistical views have the power of observation that in fact nature is how it is although we do not seem to explain why on a deep enough level. Surely it is abstract as in the string theory we have colors and flavors that are named that only as a metaphor we come close to understand as if there is say a literal idea of spin as quantum spin. One view leans too much to reduction and the other to what some vaguely object to as obsolete classical bias so constraining progress.
A. suggests the four color theorem applies to our debates on the blog and that certainly seems the case in the general application of combinatorial theory - An approach Marni and others had the deep intuition and insight to suggest we explore although there is something about such easy 101 geometry that escapes the comprehension of theorist otherwise fluent in their mathematical language and training to the point at times they have to defend that position as strongly as those who initiate a project of new general theories of everything or try objectively to teach the subject to others.
Perhaps the illustration above will be too abstract for readily grasping as it involves the algebra, or it involves the geometry, or it is not in the language of those who have gone before us with household or obscure names pinned to refer to the principles involved. Yet one should at least be familiar with the spirit of it for in such visualization we come closer to that which in depth awakens to us as different or obvious.
I would answer Jonathan that the three or four generation view is intrinsic to nature, that it is at least the properties not clearly defined or discovered of the projective plane (as a quasic plane, as the distinction that can be made among the landscape of what is the central reality of all such models, why there is "Brane Cancer" as a mixture of the states that go beyond the simple pair production, the dimers that divide a plane intelligibly. It is in the stable mixtures that statistics seems to apply in the algebra as well the certainty of structure between the absolute of unity or zero as existence or not.
In the shadows what from one view seems necessity at a certain level of complexity (I mean when we consider where three generations are projectively possible in an 8 x 8 collection of points or singularities the number is much larger than the 4 x 4 case yet is relatively small in general.) we find the roles of what we consider as sufficient or as necessity reversed or existing as phenomena mixed in between these stable views that in principle may absolutely exclude each other. Duality, and the obvious algebraic extension in the computation and application of groups as some space a product of the Cyclic group and so on simply cannot be applied with good results from a rigid concept of the totality that results. Group theory in this sense should be generalized so as to tell us more than the mere tautology of what we already know uncertainly.
Now, ponder the intuition counting diagrams as these are actually notations... we see moreover the ordering between the elements of such matrices may indeed be in different ordering paths so as say to apply where it is first defined as a unique sequence say the Klein group between four objects as part of the picture or some point of departure for other free systems. Note that if we imagine the 16 x 16 case which should be a rather large number some my prefer to generate by polar methods and angles and such, we can have surprising results more than the simple three generation case can picture or possess... and so on.
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