 Poincaré’s argument in favor of the necessary transmission of the conventional character of geometry to physics is based on an analogy, which shows another important relationship between geometry and physics. The methodological function of transformation groups with respect to the representative space corresponds to the function of geometry with respect to physics. The analogy runs as follows: Just as the law of displacements may correspond only approximately to the law of groups and is consequently considered to be the result of two component changes, the first being a displacement, and the second a qualitative alteration, so Poincaré regards the physical “complex” relation between two bodies \(A\) and \(B\) as the result of two components. The first is regarded as a “simple” geometrical principle, while the second is itself composed of two “epistemological laws.” The bodies \(A\) and \(B\) are related to figures \(A'\); and \(B'\) of the geometrical space so that