Geodesics Viewed Through Systemic Functional Linguistics

Penrose (2004: 303, 295):

Geodesics are important to us for other reasons. They are the analogues of the straight lines of Euclidean geometry. In our example of the sphere S2, considered above (Figs. 14.2–14.4), the geodesics are great circles on the sphere. More generally, for a curved surface in Euclidean space, the curves of minimum length (as would be taken up by a string stretched taut along the surface) are geodesics. We shall be seeing later (§17.9) that geodesics have a fundamental significance for Einstein’s general relativity, representing the paths in spacetime that describe freely falling bodies.

Blogger Comments:

Systemic Functional Linguistic Theory makes an important distinction between things, processes and circumstances. From this perspective, a geodesic on the surface of a sphere is the curvature of a thing, and a geodesic path in spacetime is the curvature of a process. Neither of these is the curvature of space, since space is a circumstance, not a thing or process. It is from this fundamental confusion that the mistaken notion of curved spacetime in General Relativity derives.