Is space infinite?

Georg Cantor

According to Georg Cantor, one of the first to study the concept of infinity in depth, there is not just one concept of infinity, but three different ones. Let's see how he expresses it:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number, or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Georg Cantor, Gesammelte Abhandlungen, Springer, 1980. Translation taken from Rudy Rucker, Infinity and the Mind, Princeton University Press, 2004).

Did Dante anticipate Einstein?

A recent article has stated that Dante Alighieri's Divine Comedy offers a cosmology that closely resembles what Einstein expressed in his general theory of Relativity. Is there any truth in this?

In another post in this blog I summarized the history of cosmology, from the geocentric Greek version formalized by Ptolemy, to the modern version by Copernicus, Kepler and Newton. It is evident that Dante, who wrote the Divine Comedy at the beginning of the fourteenth century, could not know about modern cosmology, but he did know the Ptolemaic system, which he adopted in its entirety, with an important addition.

The relationship between the systems of Dante and Einstein was pointed out in an article published in Scientific American in August 1976, written by J.J. Callahan and entitled The curvature of space in a finite universe. This article compares Newton's universe (finite, non-homogeneous, Euclidean and with one center), Leibnitz's (infinite, homogeneous, Euclidean and without a center) and Einstein's (finite, homogeneous, non-Euclidean and without a center). By adapting to Euclid's plane geometry, the first two can be represented by graphic models as those in the attached figure.