 We can summarise his argument this way. Our knowledge of the geometry of the external world is founded on our basic physical experiences, which lead to our mental ability to deal with a group of rigid body motions. There is a very limited store of these groups, but no experiment can decide between them. All we can do is make a choice, and we shall choose the simplest one. As it happens, that was the Euclidean group, because, said Poincaré, we had found that one of its properties not shared with the non-Euclidean group (corresponding to the parallel postulate), was particularly simple. But the human species had, as it were, made a choice, and that choice was now innate in the human mind. Because of the way knowledge is acquired and the fact that there is more than one appropriate group, one can never know whether space is Euclidean or non-Euclidean, only that we construct it as Euclidean.