Saturday, May 5, 2012
Shadow Polytopes Grounded in Generalized Euclidean Planes
L. Edgar Otto May 05, 2012
If we think of dimensions naturally we can quite imagine that with strict separation if we can draw a higher dimensional object it would be for all practical purposes solid to our world as if a cartoon creature in flatland could not cross a boundary without breaking it. But in the more generalize Euclidean space of higher interacting dimensions this is not necessarily the case for such solidity (stereonometry and natural my use of these terms technically) is more of a shadowy world between the concrete and the abstract space as if a general cloud, perhaps a grounding for our thoughts on a distant quantum probability field also rigidly imagined. But as such I can imagine if we extend these ideas beyond the Euclidean spaces only that they in a sense justify and ground our ideas of things like mass more from the motion of a system than the sum of the parts, particles.
Also our key ideas of compactifiaction or "volume" in relation to the compression of space- and that can be asymmetrical or even a relative measure of which our complex plane ideas do correspond to some degree as the concrete of substance or the default apparent influence of the GR as if force context. The world in the context of these shadow sub-grids where these regions mix or meld or remain distinct in the existential point or in the general space as singularity should contain some rather interesting physics in the sense that we have by an alternative definition merged quasifinite phenomena.
I wonder or tend to feel this sort of logic is too simple in its explanations and depth of assumptions but this needs explanation as to our psychology and perceptions in the depth of the axioms and the span of the postulates as explanations. I wonder if there are such natural restrictions among all the possible designs of physics or for that matter thought experiments or surveys in depth or span of what we colloquially think in accumulating data in "experimental philosophy" and where it may required deeper physics and that that physics also may have innate design limits as to what we imagine we could do with the physics of space. (see a relevant article in the Dialogs of Eide along this theme that raises also our social question on how we do science.)
Also the comments were extended as I presented in the last post on the TGD Diary Blog with new interesting ideas and suggestions of new paradigms- and self doubts of which I wish not to duplicate here. Also Pitkanen has not weighed in on the dialog but the last thing I want is to divert his thinking for our dialog is in a virtual world and it is after all his project. So in that respect I apologize for the interruptions if I have offended or embarrassed anyone except maybe those who demean others and suppress the spirit of open enquiry when they have the authority and opportunity to contribute. Let no one feel that even there theoretical physics, as with a little more careful writing, is not hard work.
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Footnote: the * or wildcard suggests a center in the shadow diamond which is a natural dimension higher at a singularity. As I am grounding things here in a shadow of the five cell in four space of 9 + 1 circumference triangles within such a shadow face region and one less than the natural dimension we explain by a first pixel tract region in the quasic plane ordering which implies beneath unity the inverses or half value if these were in a depth of the general grid (see zeta function considerations so generalized in this space of multiplicity and indefinite span) the transparent idea of which we presume two of the microwave vibrational states of five items say like Methane are superimposed for the set of 15 things in of course the world of natural four dimensional space. In these simple theories we bring home the patterns of arithmetic to the simple patterns of geometry, hopefully to find further foundational connections or as in the comments mentioned in TGD recently, a new intuitive paradigm where the natural log base as pink noise measure may correspond in the remote depths of the infinitesimal to the remote heights of the potential infinity where they seem to ambiguously meet in the interpretations of our zero division like spin dynamics. But our concern here is shoring up our experience of space as we know it or now find experimental verification at the foundations at least as we speculate on higher spaces and decide to what extent these may actually be the reality.
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We can also consider the shadow square grid for the counts in which case it considers 20 x (16 or 12) and so on in the quasifinite numerology...