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SciArt of the Day: Hyperdimensional Suffering


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Corpus Hypercubus by Salvador Dalí

As our month of SciArt of the Day winds down, I had to share this image. For me, this is a touchstone of what makes wonderful science-art: marrying metaphors from past and present, science and myth.

The idea that art and science represent two cultures, as C.P. Snow described is a curious one. Art, or more accurately Fine Art , is a relatively recent phenomena. What we study in this history of fine art from ancient Egypt, Greece and Rome were not borne from the same impetus of fine art. Most were forms of worship and story-telling. Objects from antiquity we now call art served functions different from the decorative, challenging and growing culture of navel-gazing and mash-ups that post-modernism has become.

So: art. Beginning with the Renaissance, and re-injected with vigor during the Enlightenment, the two human activities of art making and scientific exploration have not been so far from each other. But Snow’s idea still holds sway. He may have been lamenting the supposed gulf between science and the humanities, but he widened it further than it ever had been before.  I’ve sat in excellent art history lectures about Cubism and Surrealism that neglect to mention the physics of the day, or Symbolist lectures that ignore the artists’ fascination with the deep ocean.

Dalí’s Christus Hypercubus. This painting and this artist need to be rescued from the tut-tutting in academia. It needs to be rescued from stoner dorm-room walls and blacklight.

Let’s start with the crucifix. What we’re looking it you’ll note, is a boxy object with the “t” going across two axis. This is what Charles Howard Hinton described as a tesseract, and is sometimes known as a hypercube (though there can be other varieties of that).

If you take a typical 3-dimensional cube like a box and unfold it, you get a “t” shape, a cross. The flat cross-shape exists in 2 spatial dimensions. Now, if you were to try and imagine a cube in 4 spatial dimensions (which you can’t but its fun to try!) and unfolded this 4 spatial dimension cube, you would be left with a series of cubes in a “t” shape, but with 2 crossbars at right angles like the one in the painting above. This is sometimes known as an unfolded hypercube, a cube that exists in 4 dimensions, unfolded to fit into our 3, much like a box can be unfolded into a flat 2 dimensional cross.

The idea that a god exists in more spatial dimensions that our own was popularized in some ways by the novel Flatland by E.A. Abbott, published in 1884. In it, a 3-dimensional being can escape a 2-dimensional jail simply by stepping over the 2-D lines that form the walls. To the 2-dimensional people, this would appear as magical, miraculous trickery.

Dalí has used this knowledge of spatial physics, revived and popular in the wake of Einstein’s publication of the general theory of relativity, to demonstrate the idea of the demi-god Christ as existing and suffering pain which is beyond our dimensional understanding. In Western Christian culture, the 2 symbols of the cross and Jesus on the crucifix are often used interchangeably. Rather than attempt to depict the human body of Christ in multiple spatial dimensions, Dalí opted to show the cross as an unfolded example of those higher dimensions.

The incidental connection between the torture-device’s shape (which is based of course on human anatomy), coupled with the unfolded hypercube gives the idea of a godlike-being powerful, metaphorical resonance in a way Biblical passages never could. Using math as metaphor, Christ’s suffering is taking place on a plane of existence we cannot quite envision.

Math + myth = sublime sciart.

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Crucifixion / Corpus Hypercubus / Christus Hypercubus by Salvador Dalí

1954, presumably oil on canvas, located at the Metropolitan Museum of Art in New York (though not yet in the Google Art Project).

The sparse, unhelpful Wikipedia page about this image.

Tesseracts on Wikipedia.

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All through September here on Symbiartic, we’ve brought you a new SciArt of the Day image to challenge perceptions on what science communication and education can look like. Have you enjoyed the series? Leave a comment, or tell us on Twitter!

Glendon Mellow About the Author: Glendon Mellow is a fine artist, illustrator and tattoo designer working in oil and digital media based in Toronto, Canada. He tweets @FlyingTrilobite. You can see Glendon's work-in-progress at The Flying Trilobite blog and portfolio at www.glendonmellow.com. Follow on Twitter @symbiartic.

The views expressed are those of the author and are not necessarily those of Scientific American.





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