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Adam I. Gerard
ISU
NIU
CS MS TBD

Half Dimensions #3

Exploratory thoughts.

Prima facie - none of these appear to entail each other but the first set of topics appears to lend additional credibility to my original idea here.

  1. Fuzzy Spacetimes - treatments of Space Time Points as Operators and resultant Manifolds become Fuzzy.
  2. Fuzzy Topological Spaces - concerns the degree of Set Theoretic Membership within the context of a Topological Space.
  3. Mereological Gunk - that Spatio-Temporal Regions don't have boundaries (Mereological Fusion) or that Wholes have no bottom-most Primitive Parts (Atoms).

Centric Theses

  1. The Totality of Presence vs. Holographic Shadowing - a Point in a Space is represented with Scalars of all Coordinates (or quantity relationships with another Point that's respectively represented with Scalars of all Coordinates - Vector).

First Construction - a geometric object is Fully Present in some Spatial Dimensions but not in others.

i. Let X be a geometric object.

ii. Let S be a Space having N Dimensions.

iii. X doesn't exist in S.

iv. Let S* be a Space having N+1 Dimensions.

v. X is Shadowed in S* if X exists in S* but not S.

Second Construction - a geometric object is not Fully Present in some Space.

i. X is Fully Present in an N-Space S if X has exactly N-Many Scalar Coordinates.

  1. Dimensional "Unity".

    • That a Dimension can, or should, be completely represented by a single Number Line (whether the Reals or Naturals, etc.).
    • Regards the representation of a Dimension.
    • Consider a Discontinous Line - when we plot a Function it might be Discontinuous, but the background Spatial Dimension over which the Line is superimposed never is. Models of a Spatial Dimension in which the background Dimension can itself be Discontinuous.

  2. Non-Integered Space Time Metrics - not the representation of a Dimension but the quantity of Dimensions.

    • Where the quantity of Dimensions is not an Integer.
    • This was the original idea described here.

  3. Seperable, Sharply Bounded Space Time Dimensions vs Overlapment - that Dimensions are distinct and not overlapping. Consider if they weren't.

    • Suppose the same Scalar Coordinate for one Dimension was simultaneously a Scalar Coordinate for another.
    • Consider if a Dimension where treated as a Spacetime itself (or a multitude of converging Lines).

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