 Poincaré’s arguments also met with objections from the Italian mathematician Federigo Enriques. Poincaré had argued that one way to see the validity of the geometrical conventionalist argument was to consider a disc in which everything was made of the same material, which expanded as it heated, and in which the temperature was a particular function of the distance of the centre of the disc. This function, which Poincaré specified, ensured that the metric in the disc, as measured by rods made of the same material as the disc, was that of non-Euclidean geometry. Creatures living in the disc would report that their space was non-Euclidean; we would reply that their space was Euclidean but subject to the distorting effect of a temperature field. Plainly each side can maintain their position free of self-contradiction.