This is just a random thought, may be totally wrong. Euclidean geometry was originally described as a constructive theory in which the axioms state the existence (and implied uniqueness) of certain geometrical figures. These constructions are the ones that can be done with two concrete tools: a compass and straightedge. In a more modern presentation, we might describe (plane) Euclidean geometry as the geometry implied by the metric ##ds^2=dx^2+dy^2##. Now SR (in 1+1 dimensions for simplicity) can be described as the geometry implied by the metric ##ds^2=dt^2-dx^2##. Could we describe this in terms of concrete tools, and if so, what would the be? Light beams and a clock? If we were to write axioms for SR in the Euclidean style ("Given a ..., to construct a ..."), how would they look?