Spin behaves as if it is one dimensional, along any axis you select. This behavior would be just what one expected from a vector which, owing to spontaneous dimensional reduction, lived in a one-dimensional world. But according to several approaches to QG, very small "things" or degrees of freedom DO in fact live in a world which is spatially one-dimensional. Steve Carlip recently posted on Arxiv a paper about the curious agreement among several quite different QG approaches that spatial dimensionality (which is not limited to whole number values) gradually goes down from 3D to 1D as one approaches planck scale. There is also a video of his talk about this last summer. If anyone wants links on this, please ask.