Roger Penrose: A Life Of Science In Platonic Aesthetics

The awarding of the 2020 Nobel physics prize to Roger Penrose has come late, but, as it is said, better late than never.

As early as 1998, physicist John Wheeler wrote about Penrose in a volume celebrating his life and work:

At that time, the dominant and favoured speculation about the origin of the universe was the "steady-state theory" – of which Sciama was a strong advocate. However, the discovery of the cosmic background radiation changed the status of the theory.

As early as 1927, Monsignor Georges Lemaître, a Catholic priest and astronomer, had formulated based on Albert Einstein’s theory of general relativity a ‘big bang’ origin of the universe – which, of course, was not favoured among physicists at the time.

The identification of the cosmic microwave background radiation changed all that. It strongly favoured the big-bang scenario.

Penrose writes in the preface to his book Cycles of Time: An Extraordinary New View of the Universe:

In 2010, Penrose unveiled a new cosmological model that he called "conformal cyclic cosmology" (CCC).

Penrose explains in The Basic Ideas of Conformal Cyclic Cosmology:

A caveat is needed here. These cosmological models are based on strong mathematical formalism and deeply penetrating cerebral work that can only be compared with the Puranic tapas. They are not fanciful flights of wild imagination.

An attitude that goes like "this is already in our scriptures" can impair our ability to experience the beauty of such models and the real challenges they present for the advancement of human knowledge.

It is true that Hindu cosmology is far richer than most traditional cosmologies in conceiving almost all possible scenarios – from cyclic to parallel universes. But ultimately, what will matter is how much of this civilisational treasure chest is used in emboldening our physicists and mathematicians in their odyssey of expanding and deepening our understanding of the universe.

Another important contribution of Penrose is the Penrose tiling – ‘the most well-known set of aperiodic tiles.’

Penrose inherited a love for recreational mathematics from his father, the late geneticist L S Penrose. Senior Penrose's ‘Penrose ladders’ is depicted in artist M C Escher’s famous lithograph ‘Ascending and Descending’.

Son Roger studied the tiling of a pentagon, which cannot provide tiling in a plane. He chose to study the gaps between pentagons in these attempts. He tried to fit in smaller pentagons in these spaces.

Interestingly, he used the golden mean properties of the triangles within the pentagon in creating his tiles. At last, the tiles he arrived at are called Penrose tiling.

Given that the Hemachandra-Fibonacci numbers play an important role here, it would be interesting to see if these exist in our traditional designs including kolams.

Penrose tiling is used in the study of crystal structures.

The discovery of Penrose tiling in nature has led to the question that if they were present already, why were they not observed by science before they were arrived at by the mathematician. One answer that has now become a cliché in the circles of philosophy of science is that science cannot see if it does not have the language to describe what it sees.

Penrose is famous for his work on consciousness too. In fact, he is known in advanced popular science circles more for his work on consciousness than for his achievements in physics and mathematics. Here, he belongs to the non-computational school, which views consciousness as non-algorithmic.

In his book The Emperor's New Mind, Penrose strongly rejected the reductionist computational model of mind and consciousness, crisply stated by Marvin Minsky as minds are computers made of meat.

The book is interesting not only for the repudiation of the computational model of consciousness but also for the advocacy of a real universe.

One should remember that in the continued legacy of the Bohr-Einstein debates, Penrose stands with Einstein. He argues for a physical universe and Platonic realm. He would like to imagine that "the interesting and profound mathematical ideas somehow have a stronger existence than the uninteresting or trivial ones".

In The Emperor’s New Mind, Penrose reverses this question:

Penrose is not a monist. He does not consider these two realms to be the same despite his sympathy for such a view. He weaves a grand tapestry in which consciousness, tiling of crystals, and the underlying structure of the universe all get connected.

The human mind is non-algorithmic and, hence, a computational model of artificial intelligence can never achieve certain mathematical tasks that only a human mind is capable of. This is because, according to Penrose, Gödel's theorem makes mathematical understanding fundamentally non-algorithmic.

A critic of Strong AI, Penrose says "science is a great deal more than mere mindless computation".

In Shadows, Penrose points out the bigger picture – of how quantum physics is changing the way we look at consciousness and do the neuroscience of consciousness.

While "the study of neuroanatomy, of neurological disorders, psychiatry, and psychology has told us much about the detailed relationship between the physical nature of the brain and our mental conditions", yet without quantum mechanics and relativity changing the way we view the fundamental nature of reality, "we shall be stuck within the strait-jacket of an entirely computational physics, or of a computational cum random physics".

Penrose's work in the field of consciousness is in collaboration with Dr Stuart Hameroff, professor of Anesthesiology and Psychology, and director of the Center for Consciousness Studies at the University of Arizona.

Here too the contribution of Penrose and Hameroff should be recognised as pioneering in what is now fast becoming an important field – quantum biology – though one needs to be cautious to avoid new-age pitfalls.

In the Penrose-Hameroff hypothesis, consciousness is produced because of 'objective reduction'. This happens at the spatial dimension of 10^-33 cm and at a time scale of 10^-43 seconds. With an increased number of participants, these reductions evolve and ultimately create the subjective experience. Penrose ingeniously connects this reduction with the Platonic realm because, according to him, objective reduction happens with constraints of 'Platonic values', which are inherent in the Planck-scale space-time geometry.

The quoted passage is stopped there because of the length constraint. However, the entire passage, as it goes into the intricacies of simplicity, accuracy, and aesthetics, should be abridged and made a part of curricula for not only graduate science students but also for students at the high school and undergraduate levels.

It is important to see that for Penrose, mathematics is deeply intertwined with the Platonic philosophy of the Greeks. The way science and ancient philosophy have interacted in the West is a good example of what a good grounding in traditional philosophies can do for the exploration of science.

Unfortunately, despite being nominated multiple times for the Nobel prize, he was not awarded it. But the greater tribute to his legacy would be to create a curriculum where – whether in the arts or science, humanities or literature – Indian Darshanas can inspire and motivate students to further human knowledge and enable humanity to prosper in peace.