Observerse: Difference between revisions

Revision as of 16:43, 19 February 2023

The observerse is the central mathematical object in the Theory of Geometric Unity. It is a mapping from a four-dimensional manifold [math]\displaystyle{ X^4\lt \math\gt to a manifold \lt math\gt Y }[/math], which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory.

Exogenous

In the observerse's exogenous construction, the manifold [math]\displaystyle{ X^4 }[/math] includes into any manifold [math]\displaystyle{ Y }[/math] of four dimensions or higher which can admit it as an immersion.

[math]\displaystyle{ X^4 \hookrightarrow Y }[/math]

Bundle-Theoretic

In the observerse's bundle-theoretic construction, the manifold [math]\displaystyle{ Y }[/math] sits over [math]\displaystyle{ X^4 }[/math] as a fiber bundle.

Endogenous

In the observerse's endogenous construction, [math]\displaystyle{ Y }[/math] is the space of metrics on the manifold [math]\displaystyle{ X^4 }[/math].

Tautological

In the observerse's tautological construction, the manifold [math]\displaystyle{ X^4 }[/math] equals [math]\displaystyle{ Y }[/math].

[math]\displaystyle{ X^4 = Y }[/math]

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-The '''observerse''' is the central mathematical object in the [[Theory of Geometric Unity]]. It is a mapping from a four-dimensional manifold \(X^4\) to a manifold \(Y\), which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory.
+The '''observerse''' is the central mathematical object in the [[Theory of Geometric Unity]]. It is a mapping from a four-dimensional manifold <math>X^4<\math> to a manifold <math>Y</math>, which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory.
 == Exogenous ==
-In the observerse's exogenous construction, the manifold \(X^4\) includes into any manifold \(Y\) of four dimensions or higher which can admit it as an immersion.
+In the observerse's exogenous construction, the manifold <math>X^4</math> includes into any manifold <math>Y</math> of four dimensions or higher which can admit it as an immersion.
-$$ X^4 \hookrightarrow Y $$
+<math> X^4 \hookrightarrow Y </math>
 == Bundle-Theoretic ==
-In the observerse's bundle-theoretic construction, the manifold \(Y\) sits over \(X^4\) as a fiber bundle.
+In the observerse's bundle-theoretic construction, the manifold <math>Y</math> sits over <math>X^4</math> as a fiber bundle.
 [[File:Observerse-Bundle-Theoretic.jpg]]
 == Endogenous ==
-In the observerse's endogenous construction, \(Y\) is the space of metrics on the manifold \(X^4\).
+In the observerse's endogenous construction, <math>Y</math> is the space of metrics on the manifold <math>X^4</math>.
 [[File:Observerse-Endogenous.jpg]]
 == Tautological ==
-In the observerse's tautological construction, the manifold \(X^4\) equals \(Y\).
+In the observerse's tautological construction, the manifold <math>X^4</math> equals <math>Y</math>.
-$$ X^4 = Y $$
+<math> X^4 = Y </math>
 [[Category:Geometric Unity]]
 [[Category:Ericisms]]