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The primary aim of this paper is to provide a simple and concreteinterpretation of Cartan geometry in terms of the mathematics of idealizedwaywisers. Waywisers, also called hodometers, are instruments traditionallyused to measure distances. The mathematical representation of an idealizedwaywiser consists of a choice of symmetric space called a {\em model space} andrepresents the `wheel' of the idealized waywiser. The geometry of a manifold isthen completely characterized by a pair of variables $\{V^A(x),A^{AB}(x)\}$,each of which admit simple interpretations: $V^A$ is the point of contactbetween the waywiser's idealized wheel and the manifold whose geometry onewishes to characterize, and $A^{AB}=A_\mu^{\phantom{\mu} AB}dx^\mu$ is aconnection one-form dictating how much the idealized wheel of the waywiser hasrotated when rolled along the manifold. The familiar objects from differentialgeometry (e.g. metric $g_{\mu\nu}$, affine connection $\Gamma^\rho_{\mu\nu}$,co-tetrad $e^I$, torsion $T^I$, spin-connection $\omega^{IJ}$, Riemanniancurvature $R^{IJ}$) can be seen as compound objects made out of the waywiservariables $\{V^A,A^{AB}\}$. We then generalize this waywiser approach torelativistic spacetimes and exhibit action principles for General Relativity interms of the waywiser variables for two choices of model spacetimes: De Sitterand anti-De Sitter spacetimes.

Gravity, Cartan geometry, and idealized waywisers