The left-hand photograph circulated on Twitter a few weeks ago and someone commented that “it looks Escheresque”. I found that fascinating: an apparently random natural phenomenon reminded someone of the mathematically composed artwork of the great graphic artist M.C. Escher.
We now know that there is a lot less “random” in the natural world than we thought there was roughly half a century ago. M.C. Escher (1898-1972) died before Mandelbrot published his work on fractal mathematics in 1979. Mandelbrot demonstrated that much of the apparent randomness that we observe in nature is the result of relatively simple mathematical relations, controlled by what is called a ‘strange attractor’. The best treaty on fractal mathematics and chaos theory for non-mathematicians is James Gleick’s ‘Chaos’. I read ‘Chaos’ more than 20 years ago and it completely changed my view on my work, my career and subsequently my life.
For many centuries before Mandelbrot people wondered “only” about symmetry in nature. Everyone observes symmetry and its exceptions, beginning with our own body which appears symmetrical but isn’t: two legs, arms, eyes, ears, lungs, kidneys but one mouth, esophagus, heart, liver, spleen, pancreas, bladder.
The foundations of crystallography and mineralogy are mandatory in every geoscience degree. We learn about molecular lattice structures and resulting crystal form. Depending on molecular lattice structure and resulting crystal structure, some minerals appear perfectly symmetrical, such as a cubic pyrite. At the other extreme is e.g. triclinic plagioclase, which is symmetrical in a more complex way.
Left: cubic pyrite. Right: triclinic plagioclase. (Wikimedia)
Maurits Cornelis (“Mauk”) Escher was fascinated, or maybe obsessed by ‘the systematic compartimentalization of space’ (in Dutch: “regelmatige vlakverdeling” as he wrote in a letter to his nephew Rudolf, a composer).
Mauk’s half brother was Berend Escher (1885-1967), an iconic professor of geology at Leiden University in the Netherlands, whose specialization was crystallography, mineralogy and vulcanology. Berend Escher was also the sole author of the next-to-last Dutch-language introductory geology textbook. The annual MSc-thesis prize, awarded by the Royal Netherlands Geological and Mining Society is named in his honour (full disclosure: I initiated the prize and was chair of its first jury but I didn’t name it).
‘Grondslagen der Algemene Geologie’ (Foundations of Introductory geology) by B.G. Escher, 1948 (my copy).
Berend Escher’s textbook doesn’t contain a chapter on crystallography nor one on mineralogy. As an expert in that field, he decided that this subject was too big for just a few chapters in a textbook and in 1950 he published a separate textbook entitled: “Algemene mineralogie en kristallografie” (“Introductory mineralogy and crystallography”). When I first published this post, I wrote that I don’t have a copy of that book nor had I ever seen it. My writer brother read my post and bought me the book! Here it is:
Did Berend and Mauk exchange thoughts on crystallography and mineral structure? I bet they did. I bet they wrote letters to each other, but if they did, I don’t know about them. We do know that Mauk was a letter writer, because I have a fascinating book with a collection of letters between Mauk and his nephew (Berend’s son) Rudolf Escher, a composer. And Mauk designed an ‘ex libris’ book stamp for his brother Berend, paying homage to his expertise on vulcanoes.
Left: Rudolf Escher and M.C. Escher “Beweging en metamorfosen, een briefwisseling” (‘movement and metamorphosis, an exchange of letters). 1985 – my copy. Right: Ex Libris for Berend Escher, designed by M.C. Escher
Mauk Escher explored symmetry in an illusionary manner his whole artistic life. This is not a treatise on that subject, which is too big for one blog post. I include only one illustration here. It is highlighted in “From 2D to 3D: I. Escher drawings crystallography, crystal chemistry and crystal defects” by Peter R. Buseck of Arizona State University, a downloadable 12-page document. Peter Buseck used Escher’s images to teach about symmetry by designing puzzles about them. Here’s one:
Left: M.C. Escher, 1942, Pattern #55 “Fish”. Centre: with lines indicating symmetry (drawn by me). Right: symmetry lines only, immediately showing 3-dimensionality.
I took crystallography and mineralogy at Groningen University in the Netherlands from professor Perdok, who impressed on us (among other things) “that a 2-dimensional space cannot be filled by pentagrams except by M.C. Escher”.
Mauk Escher’s oldest George was an engineer and moved to Canada early in his life. He donated his personal collection of his father’s works to the National Gallery of Canada, giving them one of the largest Escher collections in the world. At that occasion, he talked about his father. His two younger sons became geologists, Arthur in France and Jan in Switzerland.
Why do we continue to be so fascinated by Escher? For one thing, I think that it’s because he shows us something that science alone cannot show us in the same manner: beauty, wonder and unpredictability.
Which is why we always need more Art in Science.