A proper understanding of possible kinematical groups helps us to understand why spacetime symmetry groups are possible.
Suppose that somebody had been bold enough in 1908 to take [the kinematical groups] seriously. He would have correctly predicted the expansion of the universe twenty years before it was discovered observationally by Hubble. More importantly, he would have been led to postulate the curvature of space-time, and so he would have considerably eased the path which led to general relativity. Missed opportunities by Freeman J. Dyson