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If one wants to summarise our knowledge of physics in the briefest possible terms, there three really fundamental observations:
If one wants to summarise our knowledge of physics in the briefest possible terms, there three really fundamental observations:


# Space-time is a pseudo-Riemannian manifold M, endowed with a metric tensor and governed by geometrical laws.
# [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] M, endowed with a [https://en.wikipedia.org/wiki/Metric_tensor metric tensor] and governed by geometrical laws.
# Over M is a principle bundle $$P_{G}$$ with a non-abelian structure group G.
# Over M is a principle bundle $$P_{G}$$ with a non-abelian structure group G.
# Fermions are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ are not isomorphic; their failure to be isomorphic explains why the light fermions are light.
# Fermions are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ are not isomorphic; their failure to be isomorphic explains why the light fermions are light.