 in his 1898 paper, [Poincaré] put forward a (mathematical) explanation of the three dimensions of space. He observed that the Euclidean group, selected after many conventions, can be seen as acting on a space of three, four or five dimensions. The choice of a three-dimensional space is justified by considerations of commodity. Unfortunately, Poincaré’s argument is viciously circular because the choice of the Euclidean group was grounded on Lie’s classification of transformation-groups operating on \(\mathrm{R}^3\) (Heinzmann and Nabonnand 2008: 171).