Last month, Robert Lawrence Kuhn interviewed eminent British mathematical physicist Sir Roger Penrose on a number of topics, including the influence of surrealist artist M. C. Escher (December 9, 2022/32:00 min).

Here is a transcribed selection from the second part of the discussion in Part 1 above*, beginning around the 12-minute mark, with some notes:

Robert Lawrence Kuhn: We talked about the impossible Penrose triangle which really opens up another area of your life in terms of visual representations of remarkable things. Penrose tiling really new ways of thing of seeing visual representation of fiery fundamental geometric and algebraic transformations and things. But what I wanted to ask you is, as you
developed that you had this interaction with the artist M.C. Escher, which yielded some very famous work that he did. What’s the real story behind that? I’ve seen a lot of different versions.
(12:55)

Note: M. C. Escher (1898–1972): “In addition to eventually becoming a lauded international artist with mounted exhibitions, Escher was embraced by mathematicians and scientists, as much of his heavily researched, precise output embodied or explored concepts around geometry, logic, space and infinity.” – Biography.com

Roger Penrose: Well, the real story was that — I think it was my second year as a graduate student in Cambridge and the International Congress of Mathematicians is being held in Amsterdam in the Netherlands. I and a friend of mine decided we would go to the international Congress and I remember going to this and being very puzzled by many of the lectures which I barely understood. But one of my lecturers was Sean Wiley. (13:25)

I remember I was getting on a tram and he was just getting off and he had in his hand this catalog. I said what on Earth is that? It had a picture of Escher’s Night and Day, with the birds flying one way in the other way — and I was absolutely stunned by that. And he said, I’m sure you’d be interested. There is this exhibition in the van Gogh Museum by this artist, M.C. Escher. (13:43)

Roger Penrose: So I went to this exhibition. I was completely bowled over and went away thinking that I would like to do something impossible myself. I remember being struck by one called Relativity, I think, where gravity is in three different directions and you have people walking upstairs in different ways. (14:04)

An animation of Escher’s Relativity (1953):

Roger Penrose: A quite incredible picture and I came away thinking, let me try and do something impossible which I hadn’t quite seen in the exhibition. I was thinking of roads and rivers and bridges which went off and did impossible things and I simplified it down to this — what people call a tri-bar — which was this thing, three rods at right angles like this. And it’s impossible but you could draw a picture of it. (14:29)

Note: Escher’s mathematical art was all the more remarkable because he had no formal training in mathematics:

*Note: The discussion between Penrose and Kuhn continued over several segments of Closer to Truth. Here are Part 2 and Part 3. More interviews with Sir Roger here.

You may also wish to read: Nobelist Roger Penrose talks about his impossible triangle. At Closer to Truth, the mathematical physicist explains to Robert Lawrence Kuhn how he understands the relationship between mathematics, the mind, and the physical world. Penrose attempts a minimalist position when defending the reality of both mathematics and the mind in a world where many believe that only the physical exists.