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.

The 528th digit of Pi

Gotfried Wilhelm von Leibniz

Two posts ago I mentioned that the best simple fractional approximation of the value of p is 355/113 = 3.14159292..., which was discovered in the West in the 16th century. Later, better approximations were obtained, but no longer in the form of a fraction, rather as the sum of a series. Several infinite series of terms are known whose sum is p. So it is enough to add a sufficiently large number of terms to obtain as many digits of p as we want, as long as we have time to do the sums. The first to propose one of these series was the French mathematician François Vieta. As his series was quite complicated, we give here the much better known series proposed in 1673 by the German mathematician and philosopher Gotfried Wilhelm von Leibniz:

The more terms we add of this series, the closer we will come to the value of p. The following table shows the advances made over time in the calculation of the successive approximations of this number, using different series, formulas or procedures.

Newton, the greatest scientist of our civilization

Isaac Newton

As I said in the previous article, in my biographical dictionary 1000 great scientists (1996) and an unpublished book, I proposed an objective quantification of the importance of different scientists, using measures such as the number of lines that various encyclopedias assign to each. Six scientists, one Greek (Aristotle), of whom we have already spoken, and five from the West (Descartes, Newton, Darwin, Freud and Einstein) were tied with the highest score in these studies. Among these five, is there one who can be considered the greatest scientist of our civilization?

In 1964 Isaac Asimov conducted another study (The Isaac Winners) on the relative importance of men of science, which resulted in a list of the 72 best scientists of all time, in his opinion. This list is simply qualitative and does not establish a relative order among the names that appear in it, although Asimov (again in his opinion) asserts that Isaac Newton, who happened to be his namesake, was the greatest scientist of all time.