Dürer’s solid

Updated: Sep 30, 2020

In 1514 the German artist Albrecht Dürer created a fascinating copper engraving. We see among many other things a display of scientific instruments, a ladder, a magic square, a little chubby child with wings and a mature angel, a flying bat holding a banner with the title 'Melencolia I'. At the base of the ladder we find a huge geometrical object that seems to play with perspective. This video explains the various elements that Dürer used to compose this masterpiece...

As I wrote last February the Dutch artist Armando (1929-2018) reflected on Dürer's strange geometrical object with a series of dry needles. However beautiful these sheets might be, his cubes don't quite resemble the geometry of Dürer's object. A fact that Armando almost seems to acknowledge, naming the edition 'Melancholie' 2004. It seems that Armando is not just referring to Dürer, but possibly also to his own emotional state. It looks to me as if Armando scratched his burin deep into the copper plate just to notice how his cubes almost bounced off the sheet in a wild stubborn escape...

After 500 years of study and numerous interpretations, Dürer's etching still speaks volumes. You might even say that I actually gazed exactly like Dürer's angel yesterday after the Governmental press conference on the new corona measures. March this year when the crisis reached the Netherlands, some early dissident voices made me rather skeptical about a lot of things in the media. Thank god I had my studio and my daily walks to preserve a certain level of calmness. For me personally it was a done deal when our national institute of health (RIVM) publicized their official mortality overview. All of a sudden the yearly influenza death-count plummeted from the usual 6200 / 6800 cases to 404 cases, at the same time we had roughly 6300 mortalities attributed to corona virus. You do not need to be a medical specialist to draw your conclusion but nobody seems to care. Metaphorically speaking, reason and logic left the world as I thought it was, a fundamental shift into the unknown had taken place.

Back in my studio again, at first I thought Dürer's object was simply a cube with two edges truncated, that is chopped off, leaving behind two triangular faces. Alas, how often I turned my cube and watched carefully, it did not really resembled the original shape. It would be the easy way out to think that Dürer simply made a mistake, not uncommon in 1514 when the laws of perspective where just explored. The trouble is that Dürer wasn’t the sort of guy to make mistakes with perspective, so hence the underlying shape simply can't be a cube.

There have been quite a few studies over the years correcting the perspective in various ways to compute what the angles of the object must be, they all reached different conclusions. Since we can't turn Dürer's polyhedron around at our will, we have to settle with an educated guess.

Gradually in the process of cutting and pasting my cardboard items, while contemplating the current state of the corona idiocy, I thought of creating a new machine that would include a half-burnt stump of driftwood, a slow horizontal moving background with typical Dutch clouds, a blackened miniature landscape and an enormous dark gray polyhedron á la Dürer. Unlike Dürer, I will make sure that my polyhedron rotates slowly, revealing all it's corners and sides. That's the benefit of making machines, a pleasure not to think lightly of.

For my Melancholy Machine I prefer the Polyhedron developed by US mathematician and artist George Hart. Mister Hart points out that geometrically speaking the Dürer’s solid is simply a cube or rhombohedron which has been truncated at the upper vertex. His website can only be described as vast oceanic and it is wholeheartedly recommended by me.