Observed Spacetime Dimensionality from Fundamental Principles

It is shown by very simple arguments that the observed 3+1 dimensionality of spacetime may be understood on the basis of four fundamental principles of physics namely, Causality, General Covariance, Gauge Invariance and Renormalizability. This approach not therefore only fixes the spacetime dimensionality at 3+1, but also imposes the compactification of extra dimensions in higher dimensional theories based on these principles such as string theory as an internal consistency requirement rather than an external imposition.