What we call geometry is nothing but the study of formal properties of a certain continuous group [...]. The notion of this continuous group exists i… - Henri Poincaré

" "

What we call geometry is nothing but the study of formal properties of a certain continuous group [...]. The notion of this continuous group exists in our mind prior to all experience; but the assertion is no less true of the notion of many other continuous groups; for example, that which corresponds to the geometry of Lobachevsky. There are, accordingly, several geometries possible, and it remains to be seen how a choice is made between them. Among the continuous mathematical groups which our mind can construct, we choose that which deviates the least from that rough group, analogous to the physical continuum, which experience has brought to our knowledge as the group of displacements. Our choice is therefore not imposed by experience. It is simply guided by experience. But it remains free; we choose this geometry, not because it is more true, but because it is the more convenient.