**For a flat spatial geometry, the scale of any properties of the topology is arbitrary and may or may not be directly detectable. For spherical and hyperbolic spatial geometries, the curvature gives a scale (either by using the radius of curvature or its ****inverse****), a fact noted by ****Carl Friedrich Gauss**** in an 1824 letter to ****Franz Taurinus****.**^{[2]}

**The probability of detection of the topology by direct observation depends on the spatial curvature: a small curvature of the local geometry, with a corresponding radius of curvature greater than the observable horizon, makes the topology difficult or impossible to detect if the curvature is hyperbolic. A spherical geometry with a small curvature (large radius of curvature) does not make detection difficult.**