Dante, Einstein, and the curvature of spacetime

Dante, Einstein, and the curvature of spacetime May 15, 2020


Dante with Firenze
Dante holds a copy of his “Divine Comedy” in a fresco by Domenico di Michelino (1417-1491). With his right hand, he gestures toward a procession of sinners heading into Hell. Behind him on his right is Mount Purgatory, with repentant sinners toiling upward on its path. Behind him, to his left, is the city of Florence, including the dome of its cathedral and the tower of the Palazzo Vecchio. In the distance are the celestial spheres through which he will ascend during his tour of Paradise. Thus, all three books of the “Divina Commedia” — “Inferno,” “Purgatorio,” and “Paradiso” — are represented in this painting.
(Wikimedia Commons public domain image)


In a remarkable section (pages 77-88) of Carlo Rovelli, Reality Is Not What It Seems: The Journey to Quantum Gravity, translated by Simon Carnell and Erica Segre (Penguin, 2017), Rovelli, a prominent Italian theoretical physicist who currently directs the quantum gravity research group at the Centre de physique théorique in Marseilles, France, sets out to explain the nature of a “3-sphere” in order to help his readers grasp Albert Einstein’s vision of a universe that, given the curvature of spacetime, can be simultaneously finite and unbounded.


Such a universe is, I confess, very difficult for me to picture, but Rovelli probably does as good a job as it is possible to do.


Kabel does Firenze
The mosaic ceiling of the Baptistry of San Giovanni in Florence, in a composite image created by Matthias Kabel in 2011  (Wikimedia Commons public domain image)


Then, quite unexpectedly — even though he is an Italian physicist — Rovelli immediately proposes that the illustrious Dante Alighieri, Italy’s greatest poet, had already intuited a 3-sphere cosmos in the Paradiso, the third volume of his early fourteenth-century Divina Commedia.  And I must say that Rovelli makes a case for it.  (The idea isn’t original with Rovelli; he credits its initial “discovery” to an American mathematician by the name of Mark Peterson, in 1979.)  He connects it, too, to the interior design of the famous octagonal Baptistry of San Giovanni in Florence, which stands directly in front of the city’s remarkable Duomo or Cathedral.


Rovelli plainly admires Einstein enormously.  But he has just previously been explaining that Einstein’s mathematical abilities were not the great physicist’s strength.  Rather, what made Einstein amazingly unique was the power of his imagination.  It’s interesting, in that light, to see Rovelli go on to link artistic inspiration or intuition with that in the sciences, and to use aesthetic language to appreciate the insights of both a great physicist and a great poet:


I don’t know if the young Einstein had encountered the Paradiso during his intellectual wanderings in Italy, and whether or not the vivid imagination of the Italian poet may have had a direct influence on his intuition that the universe might be both finite and without boundary.  Whether or not such influence occurred, I believe that this example demonstrates how great science and great poetry are both visionary, and may even arrive at the same intuitions.  Our culture is foolish to keep science and poetry separated: they are two tools to open our eyes to the complexity and beauty of the world.

Dante’s 3-sphere is only an intuition within a dream.  Einstein’s 3-sphere has mathematical form and follows from the theory’s equations.  The effect of each is different.  Dante moves us deeply, touching the sources of our emotions.  Einstein opens a road towards the unsolved mysteries of our universe.  But both count among the most beautiful and significant flights that the mind can achieve.  (88)



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