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25 March 2017
Morning Sedition

"Moping Melancholy, and Moon-Struck Madness."

"Melencholia I" by Albrecht Dürer

"Melencholia I", Albrecht Dürer, 1514, 9 1/2 x 7 3/8 inches (24 x 18.5 cm) (various museums)

I hold that the perfection of form and beauty is contained in the sum of all men.

— Albrecht Dürer, Four Books on Human Proportions, 1528

I first encountered Albrecht Dürer's "Melencolia I" twenty-five years ago, when I was in high school. (I remember seeing it in Science, not the JAAS journal, which I also leafed through, but in their magazine designed to compete with Scientific American.) Since then, I've thought about it from time to time, but never dug into exactly what all the symbolism meant.

A few weeks ago I was thinking about Dürer again — he was a very smart and accomplished fellow, and his accomplishments include inventing etching (hey, baby, want to come up and see my etchings?), making numerous advances in art, and creating a mechanical device for accurately drawing perspective — and was inspired to again dig out Melencolia I for a look. That led me to some searches for the symbolism — an option that was not easy twenty-five years ago — and after doing so I was inspired to write it up.

I spent a bit of time digging out Webpages and papers on Melencolia I, and have only included the ones with detailed analysis, and those not in the realm of the delusional, spiritual, or occult. The "The Melencolia Code" by David Finkelstein, a physics professor at Georgia Institute of Technology, has the best writeup of the lot, so I'll be quoting extensively from him. This isn't to say he's correct, just that he summed up the arguments cogently and succinctly. I won't write up all of the symbolism, just enough to give you a flavor for the piece.

The Melencolia I (1514) of Albrecht Durer (1471-1528) might be the most studied engraving ever made, and it influenced European art for centuries. It represents science well before Newton. Many riddlers have tried to decode it. The art historian Erwin Panofsky saw in it Durer’s own melancholy frustration at the gap between artistic and divine creation. Frances Yates, historian of the Hermetic tradition, took its melancholia to be an inspired creative fever, not sadness at all, and read the engraving as a declaration of the harmony between microcosm and macrocosm. The art historian Patrick Doorly sees it as an illustration for Plato’s Greater Hippias, a dialogue on beauty; the angelic melancholy represents the inability to define absolute beauty. Long before I heard of their studies, I saw in it a feeling about science that I could not quite read. Was the angel truly melancholy? If so, was it for knowing too little? Or too much? Is the angel dreaming of a Final Theory? Isn’t she actually smiling slightly? What is the joke?

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 3

The Name and the Bat

"Melancholia I" by Albrecht Dürer

To unscramble it [the name Melencolia I] I proceeded as follows. Since so many Durers, father, mother, and repeated son, already hide in the engraving, I guessed that the motto might hide another. This amounts to a prediction. To test it I went to Durer’s coat of arms to see how he might depict himself. There I found if I did not invent the caelo rebus by which Durer represents his art. CAELO indeed fits into MELENCOLIA. The leftover letters quickly arrange themmselves into the common noun LIMEN, commonly meaning gateway, doorway, threshold, lintel, walls, house, home, boundary path, and limit, according to context. MELENCOLIA then decodes to LIMEN CAELO, gateway in heaven. This describes the Durer coat of arms itself quite accurately, fulfilling the prediction that the anagram hid a name for Durer. It indirectly supports the rebus theory of the coat of arms. It also applies well to the dim archway in the heavens that frames it, and will acquire further meaning as we go.

The speed with which this prediction checked out suggested that I read Durer correctly. The proposition before us is that Durer constructed the motto MELENCOLIA I from the covert one LIMEN CAELO I, put melancholic elements and the mooonbow to fit them, and added the hell-bat to signal that the cover message was ironic.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 11

The Solid

"Melancholia I" by Albrecht Dürer

There are observations about the geometrical figure to the right of Melencolia. Geometrically, the polyhedron is simply a cube or rhombohedron which has been truncated at the upper vertex. Somebody has proposed that the shape is a very elaborate optical illusion. It is made to appear as though it is a truncated cube, with 90 degree angles, but in reality, it has no 90 degree angles at all. Panofsky describes it simply as a "truncated rhomboid." It is possible to proportion it so that the vertices project onto a 4-by-4 square grid like that of the magic square (T. Lynch, "The geometric body in Durer's engraving Melancholia I," Journal of the Warburg and Courtauld Inst., pp. 226-232, 1982.). Schreiber (P. Schreiber, "A New Hypothesis on Durer's Enigmatic Polyhedron in His Copper Engraving 'Melencholia I'," Historia Mathematica, 26, pp. 369-377, 1999. ) proposes that it comes from a rhombohedron with 72-degree face angles, which has been truncated so it can be inscribed in a sphere....and on and on.

"Dürer's Polyhedra" by George Hart

Dürer's solid is the 8-faced solid depicted in an engraving entitled Melancholia I by Albrecht Dürer (The British Museum, Burton 1989, Gellert et al. 1989), the same engraving in which Dürer's magic square appears, which depicts a disorganized jumble of scientific equipment lying unused while an intellectual sits absorbed in thought. Although Dürer does not specify how his solid is constructed, Schreiber (1999) has noted that it appears to consist of a distorted cube which is first stretched to give rhombic faces with angles of 72°, and then truncated on top and bottom to yield bounding triangular faces whose vertices lie on the circumsphere of the azimuthal cube vertices.

"Dürer's Solid" Mathworld

What triggered my own new interest in Melencolia I and Durer were two faces that I found hiding in the polyhedron in April 2004. Anyone who steps back several paces from a good print and focuses on the shading of the front face of the polyhedron patiently for a minute or so, will soon find or construct a face, either a man with his head cocked to the right or a woman with her head erect. Both are there, at di erent angles and scales, apparently waiting to be seen for centuries. Some viewers see the man first and some the woman; one cannot see both at once. Both disappear if we come too close. Digitizing and reducing the engraving for the internet sometimes outlines one of the faces crisply, bringing it completely out of hiding. That is how I found the woman by chance and was drawn into this study. Absent such electronic aids, the faces emerge from the polyhedron slowly the first time but are inescapable thereafter. They are subtle and draw much on our own perceptive process, so that as we see them taking shape, we are not entirely clear whether they are really there or are our own projections. One can resolve these doubts to some extent. We may note that we cannot find such faces in all of Durer’s shadings. We can verify the faces we see with other viewers. We may assume that Durer’s vision was more sensitive to variations of shade than most, and infer that if we see these faces then so did Durer, and therefore they are part of his intention.

In 1604, long after popular demand had worn out Durer’s original copper plate, the Dutch engraver Jan Wierix (ca. 1553-1619) produced a new engraving of Melencolia I from scratch, so to speak. In order to distinguish his copy from the original he left out a flourish between “Melencolia” and “I” in the motto. Less publicly, he also systematically changed both hidden faces to hidden devil’s masks. By this change he left a secret sign that he saw the hidden faces and rejected what they stood for. This convinces me that they are not of my creation. And later they will lead us to the function of the polyhedron.

...

One can read the surface of the polyhedron in three ways: as blank, as a woman’s face, or as a man’s face. This is the only such triple image I find in Durer’s work. The two hidden faces resemble somewhat Durer’s last portraits of his mother and father, and have the same poses. Durer’s father died in 1507 at the age of 75 and a Durer portrait shows him beardless at 70, but five years is enough for the small beard on the hidden face of the man. Durer did his last portrait of his mother two months before her death and Melencolia I soon after. There is not enough detail in the hidden faces for positive recognition but since the ages, poses, and general features match, and the picture has already been recognized as autobiographical, perhaps they represent his mother and father. They have another function that I will point out later. They are part of a joke that Durer is playing on us.

I am less certain of a third hidden face. The black axle-hole in its center of the millstone might pass for a silhouette profile of a lean young man, presumably Albrecht again. Unlike the two parental ghosts, this hidden face reverses figure and ground, a common way to hide faces at the time.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Pages 5-6

The Magic Square

"Melancholia I" by Albrecht Dürer

We need not look far [to find the meaning of the magic square]. The sum of the whole table is 136. Pursuing the autobiographical hypothesis, I computed the Latin gematria for “Albrecht Durer,” ignoring the non-Latin umlaut. The sum is 135. Since there is no “u” in the Latin alphabet, the name should really be “Albrecht Dvrer, ” but this would not change the sum, since “v” would then replace “u” as letter 21 of the alphabet. There is a significant discrepancy of 1 between 135 and 136. One must separate the 1 from the rest of the table to make the sum “Albrecht Durer.” This amounts to a prediction: that Durer did so. Returning to the engraving to check this prediction, we see that he made the 1 unmistakably taller than all the other numerals, as I did in transcribing the Durer Table above. This again di erentiates the Durer Table from the Jupiter Table. In addition, one wing of the angel brushes the 1 in the table, and only that numeral, verifying it divinity.

By splitting the sum into 136= 1 +135 Durer again puts himself into his own Table, next to God. The magic square provides two more Durer signatures within a symbol of the divinity of mathematics.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 9

The Comet

"Melancholia I" by Albrecht Dürer

The great comet 1471Y1 was first seen on Christmas Day in Durer’s birth year, and Durer wrote of seeing a comet in 1503. The physical natures of meteors and comets were not yet known in 1514. Even Galileo would still believe that comets were formed from atmospheric vapors leaving the Earth. But da Vinci already mocked the idea that events in the sky foretold events on Earth, and so did Durer.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 21

The Balance (Scales)

"Melancholia I" by Albrecht Dürer

The balance is one of the few scientific instruments in the picture. They all hang on the wall and the artisan tools litter the yard, as the experimental philosopher is sanctified above the craftsman. The scales hang on the side wall between the angel and the putto, level and balanced. One dish touches the putto, the other the angel. There is a balance between putto and angel, first literally, there it hangs between them, and then metaphorically, they have equal weight in some sense; perhaps equal divinity. The putto-angel equation seems to be a literally central message of the engraving. This fully supports Yate’s interpretation of the triumphant artist and of a balance between the Intellectual and Terrestrial spheres represented by the angel and the putto.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Pages 14-15

The Angel

"Melancholia I" by Albrecht Dürer

If she had melancholia, it would have to be the creative form of the humor, not the depressive. In fact she is visibly not creating. Her compasses are held in a way that puts them out of service. Her book is sealed. The unresolved tension between her positive expression and attitude and the apparently negative legend is part of the hold that the engraving has on us.

She looks at nothing in the scene. The polyhedron, the putto, and the dog are directly to her right, and the globe is beneath her line of sight. She looks up out of the frame, right past what is going on in the sky behind her, meteor, hell-bat, moonbow and all. This is consistent with her representing the faculty of Contemplation that connects its user to the Intellectual Sphere of Forms and angels. What the angel is doing is remarkable. She is doing nothing.

I propose that her main function in this engraving is that of the knight between Death and the Devil: to ignore evil. She sees nothing and does nothing. She is unlike the putto, who studies the dog intentlly and draws it. But neither see the bizarre night sky.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 14

Sources and Further Reading

  1. "Dürer's Solid" Mathworld
  2. "The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology
  3. "The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology (CitizenArcane copy)
  4. "Dürer's Polyhedra" by George Hart
  5. Melencholia I, Albrecht Dürer, 1514, Metropolitan Museum of Art

Oh, and since I know you were wondering, the title line is from Paradise Lost, by John Milton, (book XI, l, 485). I'll leave you with one more thought:

Gone is the mystical mathetic vision of absolute truth, the perspective of infinity, but also the self-deification and the gloom. Both halves of the picture live on Earth. Knowledge, with all its limits, is no longer a light in the night sky but a record of actual experience.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 22

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