The 2020 Nobel prize in physics to Roger Penrose had a seemingly curious motivation: “for the discovery that black hole formation is a robust prediction of the general theory of relativity”. Indeed, the recipient did not discover or formulated the concept of black hole. Neither he was among the founders of general relativity. What did he do about “robustness” then, to deserve such an honor? As far as general relativity, Penrose is mostly known as the namesake of a conjecture about the minimum amount of matter that can be contained in a given portion of space-time; however, he never proved mathematically his conjecture, that was proven only 25 years later in 2001 by Hubert Bray, and independently by G. Huisken and T. Ilmanen (although in 2015 Sheldon Cooper from Big Bang Theory TV series claimed to be still working on its definitive solution).

To understand the importance of Penrose’s contribution, a good starting point is to read his 1972 Nature paper (Black holes and gravitational theory, vol.236, p.377-380), in which he gave a very much understandable description of black hole physics, at a time in which no one could even dream of seeing one. The problem was that general relativity contemplated the existence of two singular solutions: one at the center of a celestial body, the other at a special value of the radius. While the latter was shown to be an artifact of the coordinate system, the r=0 singularity was the one that suggested the final stage of the gravitation at a single point, the black hole. The only theoretical model that detailed the gravitational collapse was the Oppenheimer-Snyder solution, which however required a perfect spherical symmetry. What would happen if the system was only slightly non symmetric? Clearly, there would be no reason for all the matter to converge radially in a singularity.

It is interesting to note that black holes are not peculiar to general relativity. Already in 1793, the amateur astronomer John Michell had written an article suggesting that for a very massive celestial body the gravitational attraction could be so strong that no even light could escape it. And in 1798, the mathematician Pierre-Simon de Laplace calculated that it would take a star of the same density as the Earth but with a radius 250 times the Sun, to attract the light onto itself. For this calculation, Laplace used a formula like 2mG/c2>R, taken straight from Newtonian gravity and with c the speed of light, which however is identical to the formula derived from Einstein’s theory (R being called in this case the Schwarzschild radius). In his Nature paper, Penrose goes so much in depth in describing the physics of black holes, including many effects from general relativity, such as curvature anisotropy and rotation, so as to make observable predictions that would definitively prove the existence of such objects, notably the suggestion that a black hole swallowing matter would emit gravitational waves. Events of this type have been recorded for the first time in January this year, by the LIGO and VIRGO detectors.

It has been said by some that maybe a part of this 2020 Nobel prize should have gone to Stephen Hawking. Some more opinionate colleagues went as far as to suggest that given the rule-of-3 for sharing the prize, the Committee was waiting for either one to die, between Penrose and Hawking, the latter having quite a higher probability given his unfortunate physical conditions. The claim is not true. In fact, Hawking himself gave ample credit to Penrose for the idea of the “closed trapped surface” in his 1965 PRL (Occurrence of singularities in open universes, Phys Rev Lett 15, 689), which came out just a few months after the key Penrose’s paper of the same year (Gravitational collapse and space-time singularities, Phys Rev Lett 14, 57), where the closed trapped-surface concept was depicted with such a nice sketch drawing that the Nobel committee could reuse it almost unchanged. The trapped surface is a topological notion that Penrose introduced just to eliminate the issue of spherical symmetry in the gravitational collapse: in such a weird surface of arbitrary shape, outgoing light rays converge to a single point, that is the r=0 origin of the coordinates, instead of diverging to infinity like for an ordinary sphere. As a consequence, the time progression will take an observer inevitably to the singularity, where time (and his life) will end.

As it turns out, numerous Penrose’s claims to fame (besides being an open critic of multidimensions, string theory and cosmic inflation) could easily rest also on several other beautiful pieces of work that he did in mathematical physics. A puzzling one relates to the popular M.C.Escher’s “infinite ladder” print of 1960, which was reportedly inspired by a Penroses’ (father and son) paper of 1958 appeared in the British Journal of Psychology (apparently, physics journals had refused to publish it). According to F. Hallyn (Metaphor and Analogy in Sciences, 2000) it could have been a client of Escher in 1959 the one who pointed the artist at Penroses’ graphic work. However, Escher himself had already made other “impossible stairs” prints, at least ten years before that, see for example “House of stairs I” and “Gravity” (enclosed figure), in which Escher invented a peculiar world in which simultaneous gravity fields apply independently in orthogonal directions. Sometimes, artist’s intuition precedes science…

I must confess that I have never been a big fan of the later Penrose, anyway. I find intellectually unsatisfactory, and ultimately quite boring, his overstated Platonism in science. One of his most recent ideas is a “theory” about the supposedly quantum origins of consciousness, which he elaborated with Stuart Hameroff, an anesthesiologist. No one quite knows what to make of this theory, which has no experimental support and is almost certainly wrong, but since Penrose is the famously brilliant math&phys guru (and now even one who got a Nobel) one cannot just dismiss their theory single-handedly.

To finish on a fun note, the best anagram I could make with the letters in “Roger Penrose” is a curious mix of Latin and English: Eros porn rege

A black hole of consciousness

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