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Observerse: Difference between revisions
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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 \(Y\), | 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. | ||
== Exogenous == | == 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. | |||
$$ X^4 \hookrightarrow Y $$ | |||
== Bundle-Theoretic == | == Bundle-Theoretic == | ||
In the observerse's bundle-theoretic construction, the manifold \(Y\) sits over \(X^4\) as a fiber bundle. | |||
== Endogenous == | == Endogenous == | ||
In the observerse's endogenous construction, \(Y\) is the space of metrics on the manifold \(X^4\). | |||
== Tautological == | == Tautological == | ||
In the observerse's tautological construction, the manifold \(X^4\) equals \(Y\). | |||
$$ X^4 = Y $$ | |||
[[Category:Geometric Unity]] | [[Category:Geometric Unity]] | ||
[[Category:Ericisms]] | |||