Math + Art = The Purist Expression of Impossibility

Blogger’s Note: What you are about to read is my very longwinded answer to the oft-asked query, “What does your tattoo mean?” The fact that a $50 sub-dermal injection of ink I got as a 21st birthday present to myself happens to perfectly encapsulate the Project S.T.E.A.M. objective through the marriage of art and math is just icing on the [birthday] cake.


My decision to treat myself to a Penrose triangle tattoo on the inside of my right wrist as a 21st birthday present was not made lightly. I ultimately chose the design because it spoke to me on multiple levels. First, because I am a fan of M. C. Escher, who used similar impossible objects in his optical illusion artwork; second, because I am an advocate for embracing the absurd. Mathematical physicist Roger Penrose was inspired to design his triangle after attending a lecture Escher gave at the 1954 International Congress of Mathematicians. At the conference, the Dutch artist presented his work on translational symmetry; Escher translated (see what I did there?) Euclidean geometry into art with his awe-inspiring tessellations.

Penrose was “absolutely spellbound” by Escher’s artwork, and set out to create a visual representation of “impossibility in its purest form” – the Penrose triangle.

Roger Penrose, and his psychiatrist father, Lionel, wrote about the younger Penrose’s triangle for the British Journal of Psychology in 1958. The Penroses sent a copy of their article to M. C. Escher, who went on to incorporate the impossible object into his 1961 lithograph, The Waterfall.

The Waterfall seems to depict a violation of the law of the conservation of energy, as the water appears to flow in a continuous loop, simultaneously cascading down a waterfall that rotates a waterwheel, which in turn, (pun intended, as always) looks as if it propels the water along a channel that is presented as level, but must be on an incline, as that is the only way for the water to rise enough for it to create the waterfall. Just as Penrose, once inspired by Escher, went on to play muse to the Dutch artist in return, The Waterfall continuously feeds back on itself.

Contemporary artists continue to draw inspiration from Penrose’s triangle. The Impossible Triangle is a sculpture that was created by artist Brian McKay and architect Ahmad Abas. Located at the center of a roundabout in Perth, Australia, what appears to be simply an abstract sculpture reveals itself as a Penrose triangle when viewed from the correct angle.

Writer and director Christopher Nolan is another modern artist whose creativity was stimulated by the inspired (intended, again) collaboration of mathematician, Penrose, and artist, Escher, (a match made in S.T.E.A.M. heaven). In Nolan’s 2010 sci-fi thriller Inception, “extractors” perform daring heists and corporate espionage in the dreams of their intended targets. Ellen Page plays an architecture graduate student recruited to design dreamscapes. In the video clip below, Joseph Gordon-Levitt’s Arthur describes the advantages of the Penrose staircase to Page’s Ariadne.

Top: Escher’s “Ascending and Descending” Bottom: the Penrose staircase from “Inception”

Inspiration and art are endlessly engaged in relentless pursuit of one another, both rising and falling in equal measure, much like Escher’s Ascending and Descending. Even as one creation inspires another, which in turn inspires a third, art always seems to revolve around basic, central themes. The creations of Roger Penrose, Maurits Cornelis Escher, Brian McKay, Ahmad Abas, and Christopher Nolan share more than inspiration drawn from an impossible triangle; they are all searching for the best method to express “impossibility in its purest form.”

photo by Javier Begazo, January, 2011

photo by Javier Begazo, January, 2011

…what you just read is my very longwinded answer to the oft-asked query, “What does your tattoo mean?”


One thought on “Math + Art = The Purist Expression of Impossibility

  1. Pingback: My Mind, Undermined | Project S.T.E.A.M. TV

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