Tuesday, November 2, 2010
From my block game I called Butter, a geometric language theory in general with a fluid view of what we mean by dimension. Like the Horus eye there is always something left over by division by two- and yet the sum remains one. What is the analog to butter in four space I asked myself last night.
Here I use the analogs to pascals triangle and the butter block can be arranged into a large block or stick of butter and so on. Now, what did Matti mean by four space is fatter than three space? In the triangle of these golden powers we see the stacking of three of these forms in three stacks (thus three of the nine dimensions) and in four space there are six of these stacks on a tetrahedron that breaks down into two sets of three stacks.
As the representation is in the form of a simplex (triangle...) the higher dimensional structure reads all but one of any structure on an edge thus we can say tcubed tsquaredk tksquared and null or null and tsquaredk tksquared and kcubed.
The significant dimensions in four space along these lines (is the square of d) or 16 dimensions. But this can be seen as the add one or three plus one idea for in the irrational golden number we add one (be it a block of geometry, a number, or maybe some dark force concept of a constant.)
Now, this line of thinking came last night in thinking about language, linguistics, in general. The division into subunits can proceed subconsciously in the collective history of man or in an individual if he designs a language from scratch. His first attempt, like Sequoia by himself, was a symbol for each word and then as 2000 yrs ago a syllabary. The cvcvc form can be seen as one style of language of the several forms and moreover as the hidden variables on a deeper scale that determine the cycle or evolution of the phenemes and phonemes as those values shift- they may also shift because the general intellect of energy or frequency changes value over time- the will or shall (mayest) of purpose- sphere and plane of some symmetry such that intelligence and emotions evolve or increase in mammals over the millions of years. Symmetryai - that which has a center but mutterbutterly such a center could be as if a level or balance and not a circle or sphere although these are the same sorts of symmetry. (muddersmilk also a related concept as the quality of our intellect depends on "milk" and "milt".)
The center of such abstract dimensional simplexes (triangles) goes a long way to explaining nucleation in the world in a quasic manner (as well as for the totally of the division of such shell space and partons.
Not long ago many thought equations could not all be put into geometric pictures. In these times in the study of physics it seems to have become essential to do so.
Splitting the Infinitive is a matter of the rhythm of the flow of a language and not technically a sin of grammar- such is this geometric splitting of a nucleus.
Quasi-paradox in this malleable or plastic idea of dimensions is thus an "interpretivist" view of physics including quasi-probability and quasi-discreteness. To understand a theory we have an analog to the evolving of language and organisms where one must evolve in order to understand- including the developmental aspects his is native language and cultural resources.
Will or rest in the plus one idea is after all Newtonian inertia( where Eddington as old Plus One for his 137 in a sense is vindicated for this refinement because of the central left over piece in the above diagram just as we added the Lambda of Einstein, or mass added ad hoc to equations- for not all powers as square may reduce to a number plus one and remain a solid structure not reduced in natural dimensions or coherence between a structures elements.) This is somewhat a fractal or quasi fractal idea and yet in a higher space a dual triangle or tree space may not connect in the abstract space of the dimension yet does on the higher abstract dimension. The twin towers of three high rises each are a fluid tension and compression that may move in the various directions of symmetry and symmetryai (from Blake).
Not only do our perceptions and interpretation of space have to evolve first but we have to learn or evolve abstractly to do it.
Because of the inversion of the golden number the volume of the cuboid is equal to one. Beginning in four space we say that the golden number plus one as a fourth coordinate or vector is equal to the various planes that are squared- be they complex or Cartesian or quasic or even Euclidean and indefinite.
A little later after coffee: Note: Explain has Plane in it and part of what we do in physics and philosophy is to try to make sense of the infinite plane as well the spheres and ideas of will or purpose seemingly in it, and the breaking down and permutation of things in it. This I used from metaphors to our familiar metaphysics of religions. (and I have several chats concerning linguistics with Sultan Ratrout in which I explain a lot of the theories as I post them day to day which may help highlight some of the more esoteric passages in these ideas (they are really rather simple once mastered). In our discussions from a philosophy-linguistics-religious view and poetically we in things like fate and time great ideas come up on that acid test of philosophy- free will vs determinism. Oddly, some shared links in the physics and linguistics I have the uncanny ability to question there assertions as if they are a little lagging behind my private contemplations- and I do not mean just any posting on the net but some of what is accepted by the more highly regarded journals. Not that I have lost my humility, maybe for me that goes way to far- but that I expected so much more of those in the schools. The university hare has an on-line degree now- one can major for a "professional degree", well what is the point at my age? I mean they did not say if I could have an honorary degree based on my life as a "professional student" without the benefits of bus passes and binge drinking and football at homecoming!
One thing for sure I realize now I should have explored this arithmetic and geometry deeper and followed down certain paths of reason- but thinking of language developmentally helped- and the philosophy learned since I last made butter (wish I had access to my old puzzles I would post a pic) made me realize its value I could not see before- or as seems the case with most of us when we get an idea in the theoretical realm it can be so fundamental and striking we overestimate its value so do not go a little further to find the deeper jewels that we could have. This must be part of the process of thought, human thought anyway, and the quality of our research after all can go either way in the drama depending on not just how much we are aware of our emotions and the universe's actions and motivations- but that what works for some in some frame of culture, language, faith, stance to a philosophy of science, and so on may or may not be beneficial to this or that individual or group while is so for others.
This is at the heart of what we think are the quantum models of things, time and entropy in the moment, the question of infinite descent not terminating to some infinitesimal vanishing point in parts of physical and mental space...From my standpoint how that theory applies is intuitively a part of us even if it is not the final solution- There is nothing mysterious about the quantum theory other than that our experience of being in the universe, familiar or not to us, explained or not, remains a miracle.
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I just posted this comment to Lubos"
"But if you invent e.g. a theory that will be able to revive Kepler's ideas that the planetary orbital radii are linked to the sides of Platonic polyhedra, good for you. If your hypothesis will be compatible with the other - directly or indirectly - observed facts about gravity and the birth of the Solar System, you will surely become very famous."
"But if you invent e.g. a theory that will be able to revive Kepler's ideas that the planetary orbital radii are linked to the sides of Platonic polyhedra, good for you. If your hypothesis will be compatible with the other - directly or indirectly - observed facts about gravity and the birth of the Solar System, you will surely become very famous." by Lubos
Kepler's was the first scientific cosmology in the sense it was falsifiable. Some of his ideas are used by NASA for satellite decay nodes and so on. I did not see him as mystical and are we to ignore the historical contributions of his laws on which Newton relied?
Kepler is not so much to be revived, and it has little to do with fame or brilliant rhetoric of which your posts are quite impressive! But it is the case (if we can not confuse super in supernatural or super-string theory) that he just did not know the four and more dimensional solids or that all three ways to view the extraordinary apply- and that your way of seeing our grounding in-determinism in probabilities applies as well like what may one day be a falsifiable theory. Are the moons of mars caught stray asteroids or some form of science intimate to the creation of the planet? We study abstract things and for me quantum theory is not counter intuitive (as in your next excellent post) but easier to understand as we come closer to understanding ourselves and the world.
If course we can see dark matter Neutrilinos or what ever as natural for if they are real, like God may be real (says Fred Hoyle) then He would be a (natural) part of Reality. But the idea of deep nothingness absolute or of a layer of reality of lawlessness can be an interesting part of any total picture of things.
We explore and test the "hypothesis" before a theory 101, and I agree Anthropocentric anything is not an adequate explanation as science. But in exPlain is the world Plane and that is precisely where our equations break down. In one of my models the idea of a zero approximation makes not sense because there is a fractal like descent that never reaches it and is quite normalized naturally.
I find it far better to explore the unknown and consider inputs than to expend too much energy in the ranting against what is suggested as if our agenda is a response only in reaction to another's agenda.
Deep down, if the lawlessness of nature is what you say and not ultimately as deterministic as relativity or some forms of quantum theory, it may just turn out that God may be a necessary hypothesis after all- which of course may come as quite a surprise.
One point I forgot to mention. Consider the Lick Observatory. The donor of the land and money for the project of the world's largest telescope of the time did not live to see it completed. The making of the glass from various firms in Europe took a long time with many broken. Now the trustees continued the project but they had no say so in who would be the astronomers to work and run the place. They tested the site for its stable view. Insisted the mechanisms had practical and simple buildings with the best clockwork mechanics. The result of this plan was that any particular astronomer and his project would have to make do with what was given to him in the machines and designs. Such is science, and such is the luck of it where the optical lens came soon because someone wanted to trade it for a photo lens.
Perhaps we can suggest that in some big projects into the unknown such as the LHC, we make do with what we are given risking some dream. Looking back we have to judge for ourselves if such projects were worth it for the benefit of science and mankind.