Editing Space (section)

=== Gauss and Poincaré ===
[[Image:Carl Friedrich Gauss.jpg|upright|thumb|[[Carl Friedrich Gauss]]]]
[[Image:Young Poincare.jpg|left|upright|thumb|[[Henri Poincaré]]]]

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. [[Carl Friedrich Gauss]], a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by [[triangulation|triangulating]] mountain tops in Germany.<ref>Carnap, R. ''An Introduction to the Philosophy of Science''. pp. 134–136.</ref>

[[Henri Poincaré]], a French mathematician and physicist of the late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.<ref>Jammer, Max (1954). ''Concepts of Space. The History of Theories of Space in Physics''. Cambridge: Harvard University Press, p. 165.</ref> He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a [[sphere-world]]. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface.<ref>A medium with a variable [[index of refraction]] could also be used to bend the path of light and again deceive the scientists if they attempt to use light to map out their geometry.</ref> In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of [[Conventionalism|convention]].<ref>Carnap, R. ''An Introduction to the Philosophy of Science''. p. 148.</ref> Since [[Euclidean geometry]] is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.<ref>Sklar, L. ''Philosophy of Physics''. p. 57.</ref>