The Large-Scale Spatial Geometry Of The Universe Viewed Through Systemic Functional Linguistics

Penrose (2004: 46, 48):

What about our actual universe on cosmological scales? Do we expect that its spatial geometry is Euclidean, or might it accord more closely with some other geometry, such as the remarkable hyperbolic geometry (but in three dimensions). This is indeed a serious question. We know from Einstein’s general relativity that Euclid’s geometry is only an (extraordinarily accurate) approximation to the actual geometry of physical space. This physical geometry is not even exactly uniform, having small ripples of irregularity owing to the presence of matter density. Yet, strikingly, according to the best observational evidence available to cosmologists today, these ripples appear to average out, on cosmological scales, to a remarkably exact degree, and the spatial geometry of the actual universe seems to accord with a uniform (homogeneous and isotropic) geometry extraordinarily closely. Euclid’s first four postulates, at least, would seem to have stood the test of time impressively well. …

What, then, is the observational status of the large-scale spatial geometry of the universe? It is only fair to say that we do not yet know, although there have been recent widely publicised claims that Euclid was right all along, and his fifth postulate holds true also, so the averaged spatial geometry is indeed what we call ‘Euclidean’. On the other hand, there is also evidence (some of it coming from the same experiments) that seems to point fairly firmly to a hyperbolic overall geometry for the spatial universe. Moreover, some theoreticians have long argued for the elliptic case, and this is certainly not ruled out by that same evidence that is argued to support the Euclidean case.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is an important distinction between space (location and extent) and the processes that unfold in space. From this it follows that there is an important distinction between the geometry of space and the geometry of processes that unfold in space. As a consequence, while the geometry of space may be Euclidean, the geometry of motion through space may be otherwise.

This confusion of the geometry of motion through space with the geometry of space leads to the misunderstanding of General Relativity in which curved trajectories (geodesics) are misunderstood as curved space(time).