Impossible Objects: Messing With Your Brain Since 1934

There are many reasons to check out optical illusions: to challenge your mind, to remind yourself that "things aren't always what they seem", or just pass a few minutes of Friday office time. They've always fascinated artists as well, and impossible objects, a well-known type of illusion, are at the center of an interesting case of art-influencing-science-influencing-art.

The first well-known intentional impossible object was created by a young Swedish student named Oscar Reutersvärd in 1934. Intentional is an important term here - impossible objects previously occurred in art when the artist committed errors due to a lack of perspective skill. Reutersvärd, impossibly bored during a Latin lecture, began to doodle a six-pointed star shape and surrounded it with 3-dimensional cubes. Fascinated by illusions, Reutersvärd defied traditional perspective by selecting a "magic cube" (#6 in the image below) and tucking it behind another cube instead of overlapping it. This sort of "half-tuck" (similar to the Moebius Strip's "half-twist") completes the impossible triangle design.

Reutersvärd's thought process; the completed design featured on a Swedish postage stamp. | Via Sandlot Science & Cargo Collective

Reutersvärd continued to experiment with impossible objects throughout his life, producing over 2500 isometric projections.

By the 1950s, the much more famous artist M.C. Escher had already created several impossible prints and became fascinated with the simplicity of Reutersvärd's triangle. Escher's work and writings on impossible constructs were exhibited in Amsterdam in 1954 and were viewed by a young conference-going mathematical physicist named Roger Penrose. The inspired Penrose began to experiment with his own impossible art and went on to co-author a paper, "Impossible objects: a special type of visual illusion" with his father Lionel. Penrose expanded upon the impossible triangle to create other objects, including the "Penrose stairs", in which each section of steps is correct but inconsistently connected to create a staircase that would be theoretically impossible to climb. The paper was published by the British Journal of Psychology in 1958, and Penrose was sure to send Escher a copy.

The Penrose triangle, essentially a solid version of Reutersvärd's; the Penrose stairs. | Via Wikipedia

Here's where the creativity cycle becomes circular. Escher was re-inspired by Penrose's work on the subject and went on to create two of his most endearing late works, Ascending and Descending and Waterfall, in 1960 and 1961 respectively. The earlier print is a direct artistic implementation of the Penrose stairs, while Waterfall features an impossible watercourse consisting of two stacked Penrose triangles.

Ascending and Descending; Waterfall | Via M.C. Escher Company BV

Fifty years later, many are still fascinated by these objects. A well-known triangle sculpture exists in East Perth, Western Australia. Viewed from the steps leading up to it, the installation indeed looks like a Penrose triangle, but walk around it and you'll see that…well, it just doesn't look right, proving its impossibility.

Should you be so enamored with impossible objects that you'd drool over owning one, a Dutch 3-D printing company called Shapeways began producing Reutersvärd-style triangle models in 2011. The company also makes neat (extremely dorky?) accessories, including Penrose triangle necklaces and Moebius napkin rings.

Hey, holiday shopping is in full swing - maybe pick one up for the "impossible" people on your list.