MELENCOLIA I : The physics of Albrecht D¨urer

arXiv:physics/0602185 v1 27 Feb 2006

David.Finkelstein

∗

February 28, 2006

Abstract Besides its conspicuous early Renaissance scientific instruments and tools, D¨ urer’s engraving MELENCOLIA I also contains numerous apparently unreported concealments. Their decryption reveals heresies concealed in the work. The main one is encoded in the motto that has named the piece: Natural Philosophy is superior to Mathematical Philosophy and Theological Philosophy as a way to knowledge. Numerous secondary images demonstrate the relativity and ambiguity of perception and indicate that D¨ urer like Newton was a secret unitarian.

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Background

Many details of the MELENCOLIA I (1514) of Albrecht D¨ urer (1471-1528) seem to have been overlooked in recent centuries, and the meaning is in the details [6]. I report some of them here. My interpretations of some of these led to the discovery of others, giving me enough confidence to also make a stab at interpreting what I found. Mistakes in my interpretation undoubtedly exist but need not cast doubt on the observations themselves, which I bullet for reference. A better interpretation ought still to take these data into account. I have made an effort not to project my own views across half a millennium onto D¨ urer. The point is not what I see in the engraving but what D¨ urer expected his viewers to see. The philosophical views I read in the engraving and present below are not necessarily my own. They are selected from or extend those expressed in writing by D¨ urer and his acquaintances. Anyone can see the impressive angel sitting in the right foreground and the small winged serpent flying in the left background, like virtue and evil personified. A winged boy, or putto, a familiar convention of Renaissance art, perches between them on an up-turned millstone and intently inscribes a block. Paraphernalia of the arts and sciences clutter the scene in a significant pattern. The art historian Erwin Panofsky [19] saw the engraving as intensely autobiographical and read its melancholy as D¨ urer’s own frustration at the gap between artistic and divine creation. Frances Yates, historian of the Hermetic tradition, took its melancholia to be one that inspired creativity, ∗

School of Physics, Georgia Institute of Technology. [email protected]

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not mere depression, and read the engraving as a declaration of the harmony between microcosm and macrocosm: as above, so below [24]. The art historian Patrick Doorly sees it as an illustration for Plato’s Greater Hippias, a dialogue on beauty [4], with the angel melancholy because the artist cannot define absolute beauty. They pass over more than a score of individual concealments and paradoxes in the engraving: a key anagram, rebuses, Cabalistic gematria, puns, a Star of David, over a dozen hidden faces, two Jews blowing the ram’s horn, the entire figure of a kneeling warrior in Arab dress, and even the downfall of Babylon. There are references to Genesis, Revelation, Cabala, the Nicean Creed, and the D¨ urer family history. There are numerous demonstrations of the limits to human perception, and capital crimes that explains much of the concealment. These illuminate D¨ urer’s views on art, science, philosophy, and religion, and support some of the interpretations of others that I have just cited, but not all. The interpretations I cite do not mention the main point of the engraving. One element of this work is relativity in the broad sense, the study of how what we see depends on our viewpoint. D¨ urer uses perspective to construct several examples of relativity and ambiguity. It is not anachronistic to attribute this idea to D¨ urer, since he is one of the creators of descriptive geometry, which is precisely a theory of how the same object looks from different points of view, and is probably the first mathematical theory of relativity in the broad sense. He is significant in the history of the perspective technique, which the Romans and Greeks practiced and the Church suppressed as deceptive. D¨ urer carried “the secret of perspective,” as he called it, from Italy to northern Europe, and some say that his book on the subject founded the mathematical theory of descriptive or projective geometry, though this developed over centuries with growing rigor. Perspective, special relativity, and general relativity all rest on an understanding of visual perception and light, and so there are family resemblances among them. The apparent foreshortening of limbs in perspective and the apparent shortening of rulers and slowing of clocks in relative motion or in gravitational valleys are all effects of relativity in the broad sense. Where relativists today speak of light-cones, Leonardo and D¨ urer spoke of “pyramids of vision,” which are light-cones with time omitted, being made of paths of light in space rather than trajectories in space-time. They held that in perception one such pyramid diverges from the point observed, like a future light cone, and another converges to the the observing eye, like a past light cone. The perspective transformations of the graphic plane that we carry out when we shift our viewpoint are special cases of the transformations of space-time used later in modern relativity. Both are represented by matrices or tables of two rows and columns, with real or complex number entries respectively. Projective geometry is a playground for relativists and made D¨ urer an eminent mathematician of his time. That D¨ urer’s art can be programmatic is indisputable, for he literally encoded messages into another work of this period, leaving us message, code-book, and work. In 1514 — the year inscribed on this engraving — he had just finished his Triumphal Arch of Maximilian I , an elaborate eulogy of Maximilian assembled in several stages: 1. In the 2nd-4th century CE, a certain Horapollo wrote Hieroglyphica, a spurious rendering of the Egyptian hieiroglyphic symbols into Greek, centuries before the Rosetta Stone made a proper reading possible. This figures in MELENCOLAI I too. 2. In 1512/1513 Willibald Pirckheimer (1470-1530), D¨ urer’s learned best friend, Humanist, state councillor, and translator of Greek and Hebrew classics, translated the fictional Hieroglyphica from Greek into Latin. 3. D¨ urer illustrated Pirckheimer’s Hieroglyphica.

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4. Pirckheimer wrote out a eulogy of Maximilian I in plain Latin, still extant. 5. With the Hieroglyphica as his code-book D¨ urer encoded Pirckheimer’s eulogy word by word into an allegorical fantasy of dogs, goats, harpies, cocks, snakes, scepters and the like, making up the centerpiece of the Triumphal Arch [19]. The code-book and the clear message were also published, so the Triumphal Arch was an attempt to communicate, not conceal. Neither a plain text nor a code-book for MELENCOLIA I has been passed down to us, however, and we must resort to a kind of cryptography to deduce them. One might think that D¨ urer had something to hide. The message I find confirms this suspicion. MELENCOLIA I conceals more deeply than the Triumphal Arch. Some of its elements have been interpreted as slips of the artist and so seen but not read. Some viewers have suggested that D¨ urer did not know how to spell, since he misspelled the motto MELENCOLIA I; or how to draw a cube in perspective, since the polyhedron is not quite a truncated cube. There are indeed well-known limits to D¨ urer’s knowledge. Most famously, the astronomer Kepler pointed out that in D¨ urer’s work on measurement [6] he drew the ellipse produced by cutting a cone with a plane as egg-shaped, with its small end near the tip of the cone. I found a striking error in optics in this engraving. Nevertheless, to catch his meanings we must not underestimate his power with the burin, his skill in perspective, his devotion to precise language, and his acute observations of nature. We should remember that he was a humanist, knowledgable in mathematics, poetry, and antiquity as well as art, and that he argued philosophy hotly and on equal terms with a famous scholar like Pirckheimer and conversed with Erasmus. We should be aware of his impassioned criticism of corrupt ecclesiastical practices and his support of the Reformation. I was aware of none of these when I began this study, but they are indispensable for reading the engraving so I will state them briefly before we set out into the world of MELENCOLIA I . Like Leonardo, D¨ urer began his training under a goldsmith, namely his father, a Hungarian immigrant in Nuremberg. By the year on the engraving, he had made two historic visits to Venice, where he studied perspective and human proportion and developed a passion for geometry. Eventually he extended Leonardo’s work on beauty in a relativistic direction, using projective transformations to allow for different standards of beauty. D¨ urer brings us back to many beginnings. He did not have to please art critics to succeed because they had not yet been invented. The first published art criticism in history was actually the praise of this very engraving by Joachim Camerarius (1500-1574), a young friend of D¨ urer who watched him at work, translated his book on human proportions from German into Latin, and at the end wrote his eulogy, in which he declared that although D¨ urer’s art was great, it was the least of his accomplishments. D¨ urer was the first to publish in German a mathematical proof or a book on pure mathematics. He produced the first printed star-chart and the first printed map of the world as a sphere viewed from outer space. He shaped the German scientific language much as Leonardo did the Italian: by describing the processes of art and nature in ordinary language instead of flowery Latin, painstakingly picking out the prose ornaments and classical references that infested scholarly writing in his time. He was a brilliant and recognized originator in art too. He did the first known self-portrait and the first known specific landscape. He invented etching and some perspective drawing machines. He seems to have invented the modern artist, being the first to charge for his special talent instead of

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just billing for time and materials like Raphael or any house-painter of the time. His life mission seems to have been to sanctify art above artisanry and even above philosophy; to elevate graphic art to the status of music. Number lifted the medieval quadrivium of arithmetic, geometry, astronomy, and music out of the mundane and into the divine. So Leonardo, D¨ urer, and others sought to found art and beauty too on number. The concept of the Golden Rectangle, Leonardo’s famous drawing of a man inscribed in a circle, and D¨ urer’s books on descriptive geometry and body proportions are mementos of that search.

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Hidden faces

I had known MELENCOLIA I for many years when it caught my attention again in April 2004. On the internet, an anonymous donor posted a copy with a thin black outline of a face drawn on the polyhedron in the engraving sometimes called “D¨ urer’s Solid.” I chanced on this once and have never found it again. I went to my own copy and found at least the implication of a face that I had overlooked for decades. If we step back several paces from a good print and look at the shading of the front face of the Solid for a minute or so, we can see a woman’s face in profile. Or perhaps we construct it. There are three faces in the Solid and which you see depends on how you hold your head relative to the print. I will call these people A., B., and C. Solid. • A. Solid is a woman with her head erect. • B. Solid is a man with his head cocked 30◦ clockwise. • At the left edge of the face of B. Solid is a vee-shaped dimple in the stone that becomes the nose of C. Solid when we turn the picture on its left edge. I found C. Solid, smaller and more caricaturish than his two companions, some time after A. and B., but not by some careful search. I predicted his existence as described in what follows, and then found him at once. The existence of this triplet may have been known in the time of D¨ urer, but I do not find them mentioned by any modern writer on D¨ urer. We have to scan these hidden faces with some persistence before they emerge. They are subtle and draw much on our own perceptive process. We are not certain whether we see them or create them. I thought that the internet outline of A. Solid was an accidenal product of scanning or digitization until I realized that most of the left edge of her face has almost no physical correlate in the engraving. D¨ urer compels us to see it, when we look for it, by supplying chin and forehead lines and eye and nostril shadows, but we ourselves create the rest of the face as no point-by-point scanning process could. Part of the art behind these hidden faces is that they are ambiguous, deniable, and lie at the edge of perception. They are joint productions of the hand of the artist and the mind of the viewer, demonstrating D¨ urer’s mastery of both media. When we see one of the faces in this triplet we do not see the other two, because of elements they share. For example, A. and B. Solid share an eye-pit. Ambiguous faces are frequently reproduced, but I have never seen a triply ambiguous one before these, so these may not be well known today. They go beyond the familiar concept of relativity, in that each face in turn appears and disappears as we merely rotate our heads about the line of 4

sight. They show that what we see depends on our reference frame more than we ordinarily realize. Our innate face-detector is most sensitive by far to upright faces. These three faces also hide in the way watermarks do. We apparently filter out distracting lowcontrast images within a high-contrast one unless we consciously search for them. I have doubted the reality of some of these hidden faces but several circumstances reassure me: D¨ urer had extraordinary vision; what I see he saw more clearly. The anonymous donor saw one of the faces before me, and who knows how many of the others. I cannot find hidden faces in most of D¨ urer’s works but only in some. I verify the faces I see with other viewers. Ultimately I know these faces are not accidental random patterns in much the same way that you know that the words you are looking at now are not random selections of letters: They make more sense than random patterns do. On the other hand, in the end I cannot count the faces of MELENCOLIA I exactly. I have named 10 faces that are clearly intended, others are clearly unintended. nut there are a few intermediate cases that cannot be settled. Any noise, such as that produced by digitization, distorts or eliminates the intended faces and creates accidental ones. Our propensity to find faces is so strong that now I wonder why Schiaperelli saw canals on Mars and not a face as in the Moon. • Viewers of D¨ urer’s time may have seen most of these faces at once, alerted by the many hidden faces in earlier works of D¨ urer. His watercolor View of Arco has a cliff that clearly is also a famous scowling face. •His drawing of Arco hides three such unhappy faces in the landscape. • His engraving Der Spaziergang, or The Lady and the Gentleman, or Young Couple Threatened by Death (page 201 of [19]) has a remarkable secondary image of a male face formed of and looming over both the lady and the gentleman in question. Their heads are his eyes, her arm is his mouth. In this picture D¨ urer does not use the watermark technique but a kind of sleight-of-hand. The lines of the hidden face are all drawn in high contrast but other more expected forms divert us from the covert one. • In the 1494 drawing Orfeus der erst Pusaner (Orpheus the First Pederast) or The Death of Orpheus, a hidden face in the tree-top over Orpheus watches in astonishment as two Thracian women club Orpheus to death and a boy flees. Others have pointed out a significant hidden face in D¨ urer’s engraving The Knight, Death, and the Devil. D¨ urer portrays the Knight as spectacularly oblivious to Death and the Devil, though in all other such encounters in the work of D¨ urer, the knight engages evil in mortal combat. It is one thing to overlook an angel and a small demon as the Boy in MELENCOLIA I does; another to ignore Death and the Devil themselves as this Knight does. The Knight is generally said to represent the ideal Christian Soldier described by Erasmus (1466?-1536), who was a revered acquaintance of D¨ urer. So virtuous was the Christian Soldier that he was blind to the evil about him. On the other hand, D¨ urer wrote a fervent plea to Erasmus, still extant though perhaps never sent, to join with him and Luther in battle against the “Cave of Hell” and die a martyr’s death. Erasmus remained within the Catholic church and worked for reform instead of applying for martyrdom. For D¨ urer and his viewers, the unseeing Knight may also have represented Erasmus himself. In any case D¨ urer pays tribute to the Knight in a marvellous way that others have noted: • One sleeve of Death forms an agonized face smashed between the Knight’s two fists.

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The Knight may seem blind to Death but still punishes him. Eventually, Pirckheimer tells us, the high-minded D¨ urer would lament that the behavior of the Protestant clerics made even the Catholic clergy look respectable by comparison. • D¨ urer’s 1526 portrait Erasmus of Rotterdam has a gleeful hidden face high on the left sleeve of Erasmus. These examples indicate that the hidden faces are not all just puzzles and games. Some advance the story like a Greek chorus. When D¨ urer’s hidden faces look on and express emotion, they tell us how D¨ urer felt about the subject. For example, I suppose that the cliffs of Arco scowled because, as we now know, D¨ urer disapproved of some aspect of the Arco cathedral. We will find still more surprising and informative hidden faces in MELENCOLIA I . As for these three, the poses of A. and B. Solid are those of D¨ urer’s last portraits of his mother and father and so perhaps they fit well into Panofsky’s theory that this engraving is autobiographical. If so, then C. Solid might be D¨ urer the son. In his last portrait of his mother, D¨ urer shows her divergent strabismus, a family trait that he inherited known as the D¨ urereblick . The resolution of D¨ urer’s images may be too low for certainty but A. and C. Solid can be seen as strabismic.

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Rebuses

There are two rebuses in the engraving, and two in the D¨ urer coat-of-arms. These are clues to the central mystery. The famous D¨ urer monogram AD appears under the date 1514 on the edge of the stone slab under the angel. It seems to pun on Anno Domini. The capital A is also a rebus. To read it we need some family background. In 1455 Gutenberg printed his first Bible, Mohammed II, founder of the Ottoman Empire and conqueror of Constantinople, invaded Hungary, and a goldsmith named Albrecht, 23, left his village of Ajts in Hungary to finally resettle in Nuremberg. Ajto is Hungarian for door, or Th¨ ur in the German of the time, so Albrecht of Ajts became Albrecht Th¨ urer. Had he moved to England he could have become Albert Gates. He soon simplified the spelling to D¨ urer, a homonym in one dialect. He married his master’s daughter, Barbara Holper, and she had eighteen children. Three lived, inheriting his Hungarian nationality. One, Albrecht Junior, became the famous artistphilosopher-mathematician. His family coat-of-arms tells us much about his self-conception and opens the doors of this work. The coat-of-arms is topped with conventional symbols found in any dictionary of heraldry. Eagle wings mean fame and glory. A closed helmet in full profile declares D¨ urer an esquire, the lowest estate. A blackamoor at the top stands for heroic action by an ancestor in the Crusades. Its racism was common in the time and place, and recurs in MELENCOLIA I too. Below the cliches is a shield that carries specific family symbols. I point out two that are obvious. • A gateway with open doors can be read as a rebus for both “D¨ urer” and “Ajt´ os,” the family name and origin. This sent me looking for other rebuses. I did not have to look far. The gateway stands on a cloud, making it a gateway in the sky.

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It is easy to read this too. Coats of arms usually show off the pride of the family. The cloud should stand for some great personal accomplishment. To proclaim what he was most famous for, D¨ urer could simply have drawn his burin across the shield. But the burin is also a mere artisan’s tool, and D¨ urer’s life mission was to sanctify the artist above the artisan. He presumably knew that caelum, the Latin for burin, is also an ordinary word for “the sky, ” “heaven,” and “the heavens,” with the same root as our “celestial.” D¨ urer seized this heaven-sent opportunity to sanctify himself and his art. • The cloud in the D¨ urer coat-of-arms is a rebus that puts his family gates “at Heaven” (caelo) and at the same time says “I engrave” (caelo). The dative case of the noun is the first person present tense of the verb. The cloud is our second rebus. ”Gate to Heaven,” another reading of the coat-of-arms, became a common metaphor for the Roman Church itself. An educated person of the time might take this claim of divinity not as a sacrilegious display of ego but as a pious reaffirmation that we are made in the image of God. We will meet the D¨ urer gateway in the sky again in MELENCOLIA I . With D¨ urer’s coat-of-arms in mind, one now sees the oddly-formed A in his monogram as a gateway as well as a letter. The legs of the gateway are the uprights of the A, the lintel connects them at the top, and the stiffener just beneath the lintel is the cross-bar of the A. The cross-bar of D¨ urer’s A is peculiarly high for an A but for proper for a gateway. The polymorphic A-gate is our third rebus for the D¨ urer family, the first of several gates in the picture important for its interpretation.

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Gematria

The matrix of numbers set into the masonry wall like a window lattice is a magic square, meaning that it is made of consecutive numbers starting from 1 without omission or repetition, and every row, every column, and both main diagonals add up to the same number. Here that number is 34. This magic square is called a gnomon magic square because in addition its four quadrants, its four corners, and its central tetrad add up to the same number. In addition, the sum of any pair of numbers symmetric about the center is 17. The idea of the magic square and much of the cosmology in this engraving may have come to D¨ urer from Heinrich Cornelius Agrippa von Nettesheim (1486-1535), a prolific and controversial figure in the Florentine Neo-Platonist school, the original of Dr. Faust. Agrippa wandered Europe seeking royal support, never settling in one city as much as four years. He visited Nuremberg in 1510 with the manuscript of his De Occulta Philosophia, a compendium of astrology, alchemy, Cabala, and absurd propositions of biology, physics, and medicine, for example, that diamond destroys the magnetism of lodestone. He said that he studied the occult philosophy because it traced back to a secret divine revelation given at the same time as the open revelation of the Torah of Moses. In it Agrippa assigns a magic square to each of the seven “planets” then known, in both Arabic and Hebrew numerals, in the ancient order Saturn, Jupiter, Mars, Sun, Venus, Mercury, and Moon. This is the order of their periods, since the geocentric system gave to the Sun the heliocentric period of the Earth. These magic squares have ninth century Arab sources [19] but may be older. Agrippa omitted the 1-by-1 magic square [1] and there is no 2-by-2 magic square, so Saturn has a 3-by-3 table, Jupiter a 4-by-4 table and so on to the 9-by-9 table of the Moon. The number of 7

Jupiter is then 1 + 2 + . . . + 16 = 136, as the number of the Sun is 1 + 2 + . . . + 36 = 666. Agrippa warned that unshielded Saturn caused acute melancholia, a clinical mental illness, and prescribed wearing Jupiter’s Table as shield. Agrippa proved the virtue of Jupiter’s Table by gematria, a Hebrew numerology based on the fact that any letter of the Hebrew alphabet is also a number and that therefore every Hebrew word has a number, the sum of its letters. He found reassuring words in Jupiter’s Table by gematria. Some say D¨ urer borrowed Jupiter’s Table from Agrippa [19, 24]. • Here are the two magic squares: 4 14 15 9

7

16

6 12

5 11 10 16

1

3

2 13

5 10 11 12

8

9

2 3 13 Agrippa

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7 12

4 15 14 D¨ urer

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They have no row or column in common and D¨rer’s table lacks Agrippa’s protective words. D¨ urer borrowed the idea of the Table, perhaps, but he performed non-trivial permutations — not mere reflections of the whole table — that left it both magic and gnomon but changed the bottom line to the date 1514 of the engraving flanked by the Latin gematria for D A, matching the monogram and date at the bottom of the engraving. D¨ urer used the Table to perpetuate his name and the date, not to ward off melancholia. That he saw and used this combinatorial possibility tells us more about his vision and alerted me to other uses of the permutation principle and gematria in MELENCOLIA I . I found both. Pursuing the autobiography 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 spelling can be “Albrecht Dvrer, ” but this does not change the sum, since “v” would also replace “u” as letter 21. The summation of the whole table is 136 and is not under D¨ urer’s control. He would have separated the 1 from the rest of the table to make the sum equal 135 or “Albrecht Durer.” This prediction we can verify. • One wing of the angel has brushed the 1 and no other numeral in D¨ urer’s Table, blessing it, enlarging it, and raising it in a way that violates the conventions of realism. I did not see the enlarged 1 until I did the gematria and looked for it. The difference looks small to me, but D¨ urer had extraordinary vision for detail. It is a possibility that this holy 1 represents the Holy One. It is the 1× 1 magic square that Agrippa left out. Its size further distinguishes D¨ urer’s Table from Jupiter’s. The magic square thus carries D¨ urer signature twice, once in the bottom line and once in the total, next to the Holy One. It is easier to credit D¨ urer with such egotism after we see other instances. We have noticed one self-deification in his monogram and another in his coat-of-arms. For another example, see D¨ urer’s painting in the Alte Pinakothek of the Mourning over the Body of Jesus. The mourners form a triangle. The base of the triangle is the body of Jesus, and the body of the triangle is made up of mourners, looking down as symbolizes mournful melancholy. But the apex is D¨ urer himself, looking up. One moral of the magic square is so obvious that it is important to point it out again: Things are not what they seem in this engraving. What we see depends on our point of view. 8

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Bat

The chimera with head of mouse, wings of bat, and tail of serpent flies at us out of the engraving. In earlier works D¨ urer gives bat-wings and snake-tail to minions of the devil such as the dragon of St. George, suggesting that this is a demon, but Agrippa assigns the color black, serpents, and bats to the planet Saturn, so this could merely be a most Saturnian messenger, and the ambiguity could well be intentional. There are so many Agrippan elements in the engraving that I adopt the Saturnian interpretation and call this messenger the Bat. It carries the banner “MELENCOLIA I.” This clearly refers to the ancient Greek humor of melancholia, and likely to Agrippa’s revision of the teaching of the Florentine Neo-Platonist Marsilio Ficino (1433-1499). I summarize the language of the Spheres and Humors that seems to be used in this engraving [19, 24], capitalizing terms used in a now archaic sense. [1]. For a millenium and more, the West divided the world into three concentric Worlds of Spheres, the Terrestrial or Elemental, the Celestial, and the Supercelestial, Intellectual, or Spiritual. They were studied in Natural, Mathematical, and Theological Philosophy respectively [1]. Part of the Renaissance was the return to the subtler understanding of the Greeks, many of whom knew that the Earth moved. In this time of transition, I will suppose, Da Vinci and D¨ urer used a more physical cosmology in their science, while in their art they still used the naive Neo-Platonic cosmology of geocentric worlds because that was still the language that they shared with their viewers. The Terrestrial Sphere is our normal abode, angels and Platonic Ideas inhabit the Intellectual Sphere, and between the two lies the Celestial Sphere, made up of one sphere for the stars and many others to work the planets. Ptolemy used over 90 spheres in all, which are all lumped into the Celestial Sphere. Neo-Platonists analogously divided the human psyche into three Mentalities or Faculties specially suited to the corresponding Spheres [24]: Mens imaginatio, the Imaginative Faculty, empowers the artisan, the artist, and the Natural Philosopher to view arrangements of the four Elements in Space and Time, but nothing more. Mens ratio, the Rational Faculty, allows astronomers and Mathematical Philosophers to know when stars rise and set and thus through astrology it allows statesmen to know when kingdoms rise and fall. Mens contemplatrix , the Contemplative Faculty, enables Theological Philosophers to know angels and Plato’s Forms or Ideas. Their names vary considerably. Agrippa called them idolus, ratio, and mens respectively [18]. Ficino and Agrippa also kept the ancient Greek psychology of the four humors, one for each Element: blood for Air and the sanguinary temperament, yellow bile or choler for Fire and the bilious temperament, phlegm for Water and the phlegmatic temperament, and black bile or melancholia for Earth and acute depression. The black bile is a Greek myth invented to fit the mental state of acute depression into humor theory. There is no such stuff. Some said that the appendix secreted it, others the spleen; they secrete nothing. Astrologers associated Saturn, the slowest and darkest planet, with the least favorable humor, the black bile or melancholia; the worst mental state, depression, therefore called melancholia; the lowest Element, Earth; and the lowest people, understood to be those who work with or in the earth. Agrippa was a revolutionary astrologist while he practiced astrology and even after he rejected it

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[18]. He promoted Saturn from the lowest status among the planets to the highest, empowering him to inspire all three Faculties to their peak creativity, and transferred the demi-godlike geometers — “earth measurers,” after all — to the Saturnians. According to Agrippa, the truly inspired artist has a creative melancholia acting on the Imaginative Faculty [24]. D¨ urer was a revolutionary artist, aiming to promote art and artists from the lowest to the highest rank. Since artists are assigned to the Terrestrial Sphere of Saturn, this must have created a natural alliance between Agrippa and D¨ urer. Moreover both Agrippa and D¨ urer were humanists and admired Erasmus . Agrippa was a Hebraist, advocated simplicity and Bible-reading. These became part of both the Reformation and the Unitarian movement, but Agrippa himself remained in the Catholic Church. In the last phase of his life he hated astrology and was skeptical about all access to truth accept faith in the Bible. He offers us three increasingly reliable gateways to knowledge of God: the Book of Nature, the Book of the Law, and the Book of the Gospel. In the Book of Nature we see merely the creatures of God and use reason to deduce the existence and nature of God, but original sin clouds our souls and makes our reason unreliable. Reason even led to the original sin when Eve reasoned with the serpent. The Book of the Law and the Book of the Gospel, the two books of the Christian Bible, are the result of revelation and require only faith. His pessimistic work on the uncertainty and vanity of the sciences, and the superiority of faith in Scriptures and divine revelation to all the arts and sciences, including astrology, was written after his optimistic Occult Philosophy but appeared in print two years earlier. His self-contradiction is also built into MELENCOLIA I . Panofsky and Yates saw many Saturnian melancholic elements in the engraving, taking its melancholia in either the more depressive sense of Ficino or the more creative sense of Agrippa. They take it that D¨ urer accepted Agrippa’s philosophy at least for the purpose of this engraving. Indeed, much in the engraving supports this view or is at least consistent with it. Nevertheless while Erasmus, Agrippa and D¨ urer all took the Christian Bible as divine revelation, they took significantly different positions with respect to the Reformation. Erasmus remained loyal to the Church and distanced himself from Agrippa when Agrippa’s protest against the corruption of the monks who ran the Inquisition became radical [10]. D¨ urer left the Church to follow Luther, but if I read MELENCOLIA I correctly, it is more radical than anything we have from Agrippa or Luther. Also D¨ urer probably rejected astrology before Agrippa. In 1514 Copernicus (1473-1543) had not yet published his heliocentric cosmology, but the cardinal, mathematician, and philosopher Nicolas of Cusa (1401-1464) had quite demolished the Ptolemaic spheres. Leonardo had already written that the Earth moves, not the Sun, and that “those who have chosen to worship men as gods – as Jove, Saturn, Mars and the like – have fallen into the gravest error.” He had derided necromancers and excluded every trace of astrology from his intensely rational works on astronomy. There is a picture of the folly of Attention to the Stars in the Narrenschyff (Ship of Fools) of Brant (1494) [3], plausibly attributed to D¨ urer. It shows the astrologer-fool immersed in a motley flock of misshapen fowl flying in random directions, representing the products of the astrologer’s disordered mind. Birds were a common metaphor for thoughts. Martin Luther tacked his theses to a church door in 1517, and D¨ urer became an ardent follower at once. Luther specifically linked Agrippa’s Occult Philosophy with witchcraft, and Agrippa aroused ire when he defended a woman accused of witchcraft from her corrupt accusers. Agrippa eventually withdrew to a pious faith in God and the Bible. In view of the motto, the darkness of the engraving can be taken to indicate Saturnian melancholia. Some say that this motto names the angel diagonally opposite it. D¨ urer labels things unambiguously 10

in his other works. He puts his labels on or near the things labeled. The label is on the Bat or the whole scene, not the Angel. D¨ urer fills his engraving with Agrippan elements. I supposed that by giving the message “MELENCOLIA I, ” to the Bat D¨ urer identified the messenger as Agrippa delivering his theory of melancholy. Agrippa was such a charismatic figure that D¨ urer’s audience may have known at once who he meant by the Bat carrying Agrippa’s famous catch-word. Let us see how far this takes us.

6

Anagram

It seemed strange to me that D¨ urer would lower the tone of his classic Master Engraving with the lugubrious figure of the Bat,. There is also something off-key about the motto on the banderole of the Bat. Melancholia is transliterated Greek and also Latin for melancholy. The German is Melancholie. In no language is it melencolia. The spelling of the time was variable and phonetic, but this spelling is not quite phonetic either, for both the Greek and the German word have the guttural ch, different from any c sound. The encodings we have already found, the misspelling, and the cryptic extra letter suggested the possibility of an anagram to me. The odd choice of letters may have been constrained by a message that D¨ urer wished both to record and conceal. Agrippa could have put anagrams as well as gematria and magic squares into D¨ urer’s mind. They are all in his book on the occult philosophy. Anagrams, gematria, acrostics, and acronyms are among the techniques used to extract messages from biblical texts in the Baraita of Thirty-Two Rules of Rabbi Eliezer ben Jose the Galilean, who flourished in the second half of the second century C.E. and was cited importantly in later years. Such lore became more accessible to the Florentine Neo-Platonists, including Agrippa, an active Hebraist, when some of the Jews expelled from Spain in 1492 went to Florence. In any case, by the 16th century letter-permutation was a standard way to protect intellectual property. Writers of the time who solved an important problem could not guard their rights by publishing or patenting. The Royal Society and the system of scientific archives were still over a century in the future. Some protected their priority by permuting the letters of their solution and publishing the result together with the problem. Earlier Roger Bacon had scrambled the formula for gunpowder in this way in order to prevent the proliferation of this terrible weapon. Later Galileo would scramble his discoveries of the phases of Venus and the rings of Saturn. Mathematicians scrambled their theorems. The resulting meaningless jumble of letters declared on its face that it was a cipher. Sometimes it was misconstrued by a false rearrangement. In the next degree of concealment, the scrambled letters themselves spell a cover message, the anagram. This can conceal even the existence of a hidden message. “MELENCOLIA I” has done this well. Only the cover message has been read in recent centuries as far as I know. I decoded it as follows. Since so many D¨ urer’s already populate the engraving, it is a reasonable first guess that the motto might hide another signature, so I first went to D¨ urer’s family coat-of-arms to see how he might sign himself and found the caelo rebus already described by which D¨ urer represented his heavenly art. CAELO indeed fits into MELENCOLIA. The leftover letters promptly spell out LIMEN, commonly meaning gateway, a near-synonym for D¨ urer, as well as doorway, threshold, lintel, walls, house, home, boundary path, and limit, according to context. • MELENCOLIA is thus an anagram of LIMEN CAELO, literally “gateway at Heaven.” 11

The hidden motto thus combines the family name-rebus, D¨ urer’s art, and the D¨ urer coat-of-arms itself. This verifies the guess: The anagram is indeed another signature. Indirectly, it supports the interpretations that D¨ urer intended the clouds in the coat-of-arms as a symbol of Heaven, and did not intend to demonize Agrippa. The hidden phrase also applies to the dim archway in the heavens that frames the motto, and to other elements that we take up later. There are so many points of contact with the anagram and the engraving that I am pretty sure I have read it correctly. The overt message and image, both dark, cover a positive one. “Limen caelo” is as bright in spirit as “Melencolia” is depressive. It seems to tell us that Agrippa is or has a new gateway to Heaven. We must still figure out what that is. Possibly D¨ urer drew Agrippa with diabolical attributes to distance himself from Agrippa as Erasmus did. There are four living things in the engraving and only three Faculties. Someone has to be left out, and the Bat is the best candidate. I suppose that the role of the Bat is to carry the anagram into the picture, provide a cover story for it, and as Agrippa, alert viewers to the many Agrippan elements hidden in the engraving. It is not one of the Faculties.

7

Boy

The Boy — the root meaning of putto — is the central figure in several senses. The geometric central axis of the engraving is the vertical defined by the leftmost edge of the house. It passes almost exactly through the nearest eye of the Boy, a common way to indicate centrality in Renaissance art. The line of the comet, suitably extended, also strikes the Boy in the eye. One way to incorporate the I in the anagram is “Caelo limine” which can mean “I engrave at the edge” or “at the wall.” The Boy does all of these. • His instrument has a cross-bar at its top, and so is not a stylus as Panofsky said but a graver, the celestial burin again. His block is not a slate but a copper sheet or a block of wood. And he sits against a wall and on the edge of the stone disk as he engraves, as the anagram says. This could be a multiple coincidence, but more likely D¨ urer is making the Boy fit the anagram so we will know that the Boy is D¨ urer too. This supports Panofsky’s conclusion that D¨ urer meant this work to show many aspects of himself, but not that the Boy is the generic starving artist scribbling meaninglessly on a slate. It is the famous holy Engraver himself, at work with his heavenly Burin, perhaps with the creative frenzy that melancholia can inspire in the artist, as Yates said. Panofsky was misled by the paradoxical gloom of the work, which we must still understand. Yates, on the other hand, suggested that the Boy is D¨ urer engraving “MELENCOLIA I” itself, in a self-referential way. This is not consistent with projective geometry. It ignores the line of sight and the scale of the engraving. The Boy looks over his tablet directly at the Dog and his tablet is too small for “MELENCOLIA I.” The Boy is clearly engraving the Dog on his tablet. • Since Angel had her fools, I returned to the Boy to look for his wise men and found the face I call Mr. A. Boy in his blouse, between two straps.

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8

Mystery

One mystery that faces us is why all the mystery. D¨ urer could have explained his engraving for us. Leonardo made up many riddles, but he wrote the solutions next to them, protected only by his mirror-writing. D¨ urer and Pirckheimer left the key to the Triumphal Arch for us; why not the key to MELENCOLIA I ? In his essay on this picture, furthermore, Camerarius described the magic square full of numbers as a spider-web full of dead flies, ignored the many concealments, and omitted the religious and the scientific contents [13]. Why was he disingenuous? I hypothesized that D¨ urer and his friends were less than frank in order to evade the stake. The messages of the Triumphal Arch could be published in 1514, but the ideas in MELENCOLIA I must have been more dangerous, this theory goes; and yet they must already have had a market. In the times of this engraving, accusations of black magic and witchcraft beset magicians and natural philosophers alike. Agrippa was linked with the devil by Martin Luther (1483-1546). Agrippa may have influenced Servetus, who was burned in 1535, and D´avid, who was imprisoned and died in 1579 [10], both for the charge of “innovation” in religion. Eventually Agrippa renounced his major opus and adopted an uncritical fideism. There was ample reason for D¨ urer and his heirs to fear execution and preserve silence. This theory of a hidden heresy runs into a certain obstacle. In about 1498 D¨ urer executed and published a volume of fourteen woodblock prints of the Apocalypse. One of them, The Opening of the Fifth and Sixth Seals,, shows the wicked hiding from the vengeance that God takes for the blood of the saints. The wicked are the Pope, Cardinal, Bishop, Kaiser, and Kaiserin, the top of the whole hierarchy of the Catholic Church and the Holy Roman Empire. In another, The Battle of the Angels, he shows the imminent execution of the Pope by an avenging angel. So by the age of 27, 16 years before the date of MELENCOLIA I, D¨ urer — and his master Wohlgemut — had already stood against the hierarchy of the Church and killed the Pope and the Emperor in effigy. The heresy of this engraving must be even more criminal since he had to hide it. It must also have a market large enough to wear out the copper plate in making copies of this engraving. It must be a crime that the Protestants too would punish, since D¨ urer had already dismissed the Catholic threat. What was the crime of Albrecht D¨ urer? The answer to this question dawned on me slowly over a period of months but I could accept it only after answering easier ones.

9

Ladder

Any artist who put an endless ladder next to an angel, a house, and an up-turned stone in 1514 could be sure that the educated viewer of the time would see Jacob’s ladder, angel, house, and stone of Genesis 28. The unseen end of the ladder is in heaven. Ladders as gates of heaven occurred commonly in earlier art, including D¨ urer’s own. The most relevant verses are Genesis 28:12 And he dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven: and behold the angels of God ascending and descending on it. Genesis 28:17 And he was afraid, and said, How dreadful is this place! this is none other but the house of God, and this is the gate of heaven.

13

Genesis 28:18 And Jacob rose up early in the morning, and took the stone that he had put for his pillows, and set it up for a pillar, and poured oil upon the top of it. The house shows no door, so the ladder is the Gate of Heaven of the anagram and Genesis: another signature. Beth El, the House of God, is also the legendary site of the first house of worship of the God of Israel. Early on, therefore, the porta caeli of the Vulgate also became a metaphor for the Catholic church itself. We have found the limen caelo we were expecting, the predecessor of the limen caelo I , yet another hidden gateway. It suggests that the limen caelo I is a successor to the Church. This is at least consistent with the conversion of D¨ urer to Lutheranism, and hints at D¨ urer’s dread heresy and new gateway to Heaven. But if we jump to conclusions we will fall short.

10

House

The house too is meaningfully polymorphic. From up close we see two blank walls supporting a hodge-podge of instruments. The side wall does not seem much wider than the Boy leaning against it. It seems about the right thickness for an out-house or a chimney, not a residence. Its front wall extends indefinitely to the right and holds a bell, D¨ urer’s Table, an hour-glass, and a sun-dial. Its left edge bisects the picture to the millimeter. Its side wall holds a chemical balance. The bell-rope trails off the edge to our right, probably to clear the magic square. Step back several meters however and the picture changes. • Magic square and bell become a lattice window, the hour-glass a bay window, the scales a side window, and the out-house a full-sized house showing us three of its windows. Assembling familiar objects from unrelated parts in this way, for example, faces from fruits, or demons from vermin, was an optical illusion often practiced by artists of the era. Here there is allusion as well as illusion. If the house is what the sanctified instruments on its walls open into, it is the humanly perceptible universe, the entire physical cosmos. The ladder and the Angel have already told us that this is also the House of God, and the instrumental windows tell us that measurement and mathematics are a way of seeing into it. This is the declaration of Leonardo that all knowledge comes from experience, but D¨ urer clearly accepts the truth of the Scriptures as well. Then there is the curious matter of the door to the house. The curious matter, of course, is that there is no door to the house. The house that we see as we step back has several windows. The bell and the magic square become one window for arithmetic and music, an hourglass and a sundial turn into another window for time, and the scales turn into a third for weight. The Angel blesses all three windows with her wings. There is a distorted image in the hour-glass that by all the laws of optics should be the reflection of D¨ urer himself, standing before the Globe as he sketches: another signature. But nowhere do we see a door. When Mr. Door draws the House of God without a door he is likely making a statement. It is one of the major statements of the piece. If the house is indeed Reality, its doorlessness would mean that we have no direct access to absolute reality. This was a common idea by D¨ urer’s time, for example, from writings of Nicholas of Cusa and Erasmus already cited. D¨ urer could expect some of his viewers to make out this message at first sight. It recurs in modern physics in the limits to perception imposed so far by light-speed c and action-quantum ~, with more surely to come. Before D¨ urer did this engraving he had already written that the human mind cannot know absolute beauty, and in the picture he may be saying the same about absolute truth in several ways. We must not assume that he separated truth and 14

beauty, or intellect and emotion, as cleanly as some people claim to do today, especially if he expected a mathematical theory of both. From the Terrestrial Sphere we can look at divine reality but we cannot touch it. If it can be entered by the ladder, that is for the angels, we have seen. But D¨ urer makes no cut between the truth that we glean from measurements and that which we read from Scriptures. They form a seamless whole, except that the ladder reaches above the house.

11

Angel

The burin identifies the Boy as D¨ urer, but the Angel is probably D¨ urer too, sitting on and touching her name-tags, the D¨ urer monogram engraved on the edge of her stony seat and echoed in the magic square at her wing-tip. In the tripartite psychology of the times, the artist’s special Faculty is the Imaginative one, so the Boy is probably the Imaginative Faculty. Angel-wings indicate sanctity as eagle-wings represent fame. These sacred wings brush and bless the holy One in D¨ urer’s Table, the hour-glass, the scales, and nothing else in the picture. Apparently the Angel blesses the scientific instruments above the workman’s tools that litter the ground. She holds a sealed book and an idle pair of compasses. Most commentators also say that she is melancholy, and is even the spirit Melancholia herself. The motto on the banderole, the shadow on the Angel’s face, and the fist on her cheek all are indeed consistent with melancholia. But the hidden motto is not negative in mood but positive and in any case is attached to the Bat, not the Angel. Her wreath of Water-cress and Water-ranculus protect her from Earthy melancholia by their Watery nature [19]. The Angel’s expression is alert and focused, not soft and sad. Above all her gaze is not downcast, as was absolutely mandatory for portraits of melancholia, but elevated. Her pose more likely shows contemplation, as in Rodin’s Thinker, than melancholy. This and her wings say rather clearly that she is the Contemplative Faculty proper to the Intellectual Sphere.

12

Compasses

The compasses of the Angel test my assignment of Spheres and Faculties. Whenever the quadrivia are personified, Geometria is the one with the compasses. Since the Angel has the compasses, isn’t she, not the Bat, the Faculty of mathematical reason? To be sure, in a D¨ urer woodcut of 1504, The Astronomer measures a globe with compasses under a full moon, so compasses are also allowed in the Celestial Sphere, but this does not mean that the Contemplative Faculty can have them. Some say the Angel has measured the stone Globe that lies before the dog. But the Astronomer studies his globe intently while the Angel looks right past this globe, as she should if she is Contemplation and the globe is the the Terrestrial Sphere. Lines of sight matter in the work of a projective geometer. The Angel grasps only one arm of the compass and that near the point. She holds the compasses in a way unsuitable for ordinary use, which requires control of both points. She has no drawing board or table beneath it but seems to be sticking herself in the thigh. Since this is absurd we must look deeper. And lower.

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13

Arab and Jews

• The angel’s right knee, bright in the moonlight, is also the top of a hood worn by a bearded man whose head is cocked at about 30◦ counterclockwise, shown in profile with only one eye visible. Call him A. Angel. He has an aquiline nose and wears a black headband across his brow. Slowly we connect his face to a powerful shoulder, almost a hump back, on which Angel rests her elbow and compasses, and to his left arm, outstretched toward the saw-sword on the ground. The left foot of Angel, where it extends beyond her robe, is also his left hand, her toes are his fingers. In the other direction his shoulder leads us to his torso, waist, and knees. He is kneeling as he reaches for the sword blade. The Angel steps on the hilt with her right foot and pricks him with the point of the compasses in her left hand. His right hand is reaching up past his face to fend off the compass point that is evidently causing him discomfort. He kneels there covered from head to feet in an Arab burnoose. • He too is one of a triplet, the first that I found in the engraving, simply because it is the least hidden. To see the other two hidden faces, find a moonlit isosceles triangle next to the face of A. Angel, a lighter patch in the shading of the skirt directly below the Angel’s right knee. If we turn our head through 45◦ clockwise this time, we can see this lighter triangle as a spiral white horn leading to the dark line of a mouth in the face of a man in a skull-cap blowing a shofar, a ram’s horn, as is done on Rosh Hashonah, the Jewish New Year, in a full front view. I call him B. Angel. • There is a second older and hairier face blowing the same horn, whom I call C. Angel, shown in partial profile looking to the left with a hooked nose, a nasty expression, and a skull-cap. C. is looks like an anti-Semitic sterotype of a Jew. Young B. and old C. Angel share an eye. This triplet has higher contrast than the triplet of the Solid. They are hidden by sleight-of-hand, not the watermark technique. Their elements belong to a larger gestalt which compels us to give them a totally different interpretation. Again the people in the triplet can be seen only one at a time. We already read the Angel as the Contemplative Faculty of the theologians. D¨ urer seems to show by this triplet that her entourage includes Jews and Muslims as well as Christians. The sword for which the Muslim is reaching suggests that D¨ urer associated Islam with militancy. This is not palusible since Hungary was mauled by both Christian and Islamic combatants in the 15th century. Muhammed II, founder of the Ottoman Empire, took Constantinople in 1453 and launched a powerful counterattack on Hungary in 1455, the year in which Albert Senior left Ajt´ os. The attack was stopped by the forces of John Hunyadi, who became a Hungarian national hero. Since the fall of Constantinople was so epochal for Christianity, the viewers of D¨ urer’s day might have read A. Angel as Muhammad II. But then we would have no clue to whom D¨ urer might have meant by B. and C. Angel. The configuration makes more sense if the triplet represents the founders of the three monotheistic faiths of the time. This reading makes sense for the Faculty of the theologians and fits the scriptural reports that two of the founders were Jews of whom one lived to old age and one died young, and that the third was Arabian and a great warrior. The probability that these agreements are chance is not overwhelming so I pursue this possibility only. When D¨ urer unites these three figures in one triplet so that we can see only one at a time depending on our point of view, he represents them to be close in many respects. Since Moses and Muhammad were Prophets, D¨ urer would seem to assume the same for Jesus. I considered this unthinkable on 16

the basis of D¨ urer’s other works until I learned that Agrippa probably links D¨ urer to two founders of Unitarianism, Michael Servetus and Francis D´avid [10]. We have found the capital crime of Albrecht D¨ urer: innovation. Both Servetus and D´avid were charged with innovation and were sent to their deaths for this crime by Reformation courts, not the Roman Church. Being more explicit might have led D¨ urer to the same fate. If I read him correctly on this point, then most likely the downfall he shows would represent the overthrow of the hierarchy of the Roman Church, whom he had already slain in effigy. • In any case, now we see what the Angel is doing with her compasses. She is sticking the Arab. This violates realism, but D¨ urer left realism behind when his Angel raised the painted One in the magic square, so the violation has lost its shock value. I regret having to propose that D¨ urer sat her there with an innocent expression on her face as she pricks the Arab, but invisible attack is prominent in D¨ urer’s repertory. His Knight too seems oblivious to Death and the Devil but crushes one of them between his fists without visible feeling. The sneering cliffs around the Arco cathedral and much of MELENCOLIA I itself are acts of concealed aggression by D¨ urer himself against his targets. At least we can cast the Angel as the Contemplative Faculty with more confidence, now that we understand her anomalous compasses and her hidden faces.

14

Fools

This is a curiously domestic Angel. She is dressed as a housewife, complete with keys and purse hanging from her belt which D¨ urer says represent power and wealth, and she hides non-Christians in her garment. Only a fool would worship her, the artist seems to say. And there the fool is, a crude low-browed caricature hidden near her feet in the hem of her gown, next to D¨ urer’s monogram. Call him D. Angel. • We must turn the engraving about 60◦ counterclockwise to see D. best and then he looks to our right. His nose forms part of the bottom edge of the Angel’s robe. With no forehead, the caricature is so cruel that I suspected it was unintended. A powerful winged housewife with a low-browed fool in her hem does not seem to be a standardized symbol. • Actually it is. In a wood-cut Von Buolschafft (On Amours) attributed to D¨ urer. in the Narrenschyff [3], the winged woman of On Amours is Venus, the goddess of the fools of love, the most common variety of fool according to Brant. Her wings are those of an eagle signifying fame, not those of an angel signifying divinity. We know she too is a housewife because Brant calls her sarcastically “Frau Venus.” In MELENCOLIA I similarly we see Frau Angel, her housewife status conveyed now not by words but by purse and keys, hanging from her waist to the ground. (The Madonna by the Wall (D¨ urer 1514) also wears keys and purse, on short leashes.) “Frau” is evidently no term of respect for D¨ urer or Brant. These fools-in-winged-wives’-hems are clearly not accidents but part of D¨ urer’s artistic language. D¨ urer seems to say that the philosopher/theologian of the Contemplative Faculty is foolish, like one in love. This echoes and amplifies doctrines already expressed by Nicholas of Cusa in his On Learned Ignorance (1440) and Erasmus in his In Praise of Folly (1511), and later written down by Agrippa in his De uncertitudine et vanitate scientiarum (1526-1530).

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15

Globe

D¨ urer’s goddesses Fortuna and Nemesis both stand on globes, liable to roll in any direction at the least provocation, because Luck and Fate are unpredictable. Chance governs the Terrestrial Sphere, mathematical law governs the Celestial Sphere, and God alone knows what governs the Intellectual Sphere. Therefore D¨ urer’s Globe seems to represent the Terrestrial Sphere. It is indeed the lowest of the three stone objects in this picture, as if to confirm that they are D¨ urer’s version of the tripartite cosmology. D¨ urer, like Nicolas of Cusa and Leonardo, has replaced the naive tri-spherical geocentric Neo-Platonist cosmology by a tri-partite philosophy with three Faculties and Spheres that are no longer geocentric, concentric, or places at all.

16

Solid

D¨ urer seems to put his Solid in a place of honor. The artist stands before it, the ghosts haunt it, the motto might seem to name it, it balances the Angel in the composition. Yet it is bleak and sterile against the Angel, and its shape is subtly ambiguous. One looks for a deeper significance to enrich it and justify it artistically, or at least to understand its shape. A rhombus is a planar quadrilateral whose sides are all equal. A rhombohedron is a closed surface formed of six congruent rhombuses. Most people see the Solid as a truncated rhombohedron with its longer axis vertical [26]. If it represents any of the neo-Platonic Spheres, then its mathematical nature and its altitude in the picture suggest that it represents the Intellectual Sphere, the third realm, the abode of Platonic Ideas and angels. The ghosts in the Solid also support this conclusion, for this puts them in a philosophical Heaven. I tentatively adopt this hypothesis in what follows. If the two missing vertices were restored, they would seem to lie in a vertical line in space. The compulsion to see the figure as a truncated rhombohedron is irresistible. Only when a model or projection of such a solid is juxtaposed with the engraving does its untenability spring to the eye. In principle, however, one cannot determine the form of a solid from one perspective view. One can shift any surface point along the line of sight from the eye without changing its apparent location in the perspective view. Therefore there are many solids all having the same perspective view. The Reversing Staircase, the Necker Cube and the Cameo Intaglio exhibit this ambiguity. Sometimes other cues to the interpretation are so strong and unconscious that we cannot help inferring a particular solid. For example, it is hard not to see a perspective of a cube as a cube, or a perspective of a person as a person, even though intellectually we know the picture is ambiguous. The D¨ urer Solid is deeper than the illusions I mentioned, in that they are not like anything we see in nature, so it is not surprising that our visual system is not able to cope with them, while the D¨ urer Solid has two interpretations and looks real in both. If one views the Solid with head erect, one sees the hidden face of the woman on a truncated rhombohedron. If one views the Solid with head cocked to the right, one sees the hidden face of the man, on a nearly rectangular slab with two diagonally opposite corners trimmed, cocked and cantilevered back toward the horizon. I owe this second observation to Dr. Basimah Khulusi [15], who has constructed three-dimensional models to show that the rhombohedron theories do not fit in either view, and the truncated slab 18

does. Some speak of measuring the angles of the Solid from the engraving. These angles depend on secondary assumptions that are not forced on us by the engraving. One apparently invalid interpretation currently presented on the Web declares the acute angle of the rhombus to be a fifth of a circle, 72◦ . [26]. If one puts an actual model of the proposed solid, or a perspective view of such a model, next to the engraving, the mismatch is clear. If one compresses √ the engraving vertically by a factor of ϕ, its outline becomes square, and the Solid looks like a truncated cube, until one actually juxtaposes a true cube, or a perspective of one, for comparison. Another apparently invalid interpretation sees the same angle as close to 80◦ [17]. This results from measurements on the engraving assuming that certain lengths are show in true proportion. But there is no way to tell for sure from the engraving if a given length is shown in true proportion. This requires additional assumptions, usually made unconsciously and therefore irresistible. Moreover, if one juxtaposes a model of such a rhomobohedron with the engraving, the discrepancy is clearly visible. Before the engraving D¨ urer apparently made a rough sketch of the Solid that has survived, though it has been recognized as that only recently [23]. The sketch shows an irregular pentahedron inscribed in a circle. The apex angle in the drawing is indeed 79.5◦ ± .5◦ . The agreement with one interpretation of the engraving seems noteworthy.. The question remains: How did D¨ urer arrive at that angle? One notices that the circle in the drawing put forward by Weitzel was divided by a compass into seven equal arcs as if to inscribe a regular heptagon. There is no Euclidean construction for the regular heptagon but D¨ urer gives an excellent approximation to it in his course on measurement, without telling us that it is approximate. The vertices of the irregular pentagon seem to be five of the seven vertices of the heptagon. The two long edges of the pentagon are chords of the heptagon that connect the apical vertex to its next-nearest neighbors on each side, The remaining three edges of the pentagon are edges of the heptagon joining the remaining vertices. This would lead to an apical angle of 77.2◦ theoretically. The angle of 80◦ fits the engraving better. Leonardo had already undertaken a mathematical theory of beauty. That goal would occupy much of D¨ urer’s later years, and result in works on human proportions and on constructions of projections and perspectives with compass and ruler. D¨ urer’s study of human proportions is an amazingly dry gallery of stark outline drawings of standing human nudes and tables of anatomical dimensions to three decimal places. It may never have been of much use to artists, but it fulfilled other functions for him. Human measurements were to be the foundation of a geometry of beauty, as stellar measurements were the foundations of Ptolemy’s geometry of the heavens. Music was already divine and part of the quadrivium because it was considered mathematical. By providing a mathematical basis for art, D¨ urer hoped to sanctify the graphic arts as well. Possibly this belief in a mathematical art was only one aspect of a belief in a general mathematical wisdom, a mathesis. Then the Solid does not simply show off D¨ urer’s mathematical muscle, it represents the mathematical nature of the Intellectual Sphere, the divinely inspired mathesis that many sought, and its inaccessibility to human cognition. We will give it deeper meaning later. I propose that D¨ urer deliberately designed the Solid so that it was irresistibly misconstrued as a truncated rhombohedron when seen from one orientation, and as a truncated slab from another.

19

The Solid is a puzzle that is in principle unsolvable without another view. I suspect that is why the Angel is smiling.

17

Millstone

The most cryptic of the three stone things may be the wheel holding the Boy. Panofsky and Yates call it a grindstone and Doorly calls it a millstone. Its perimeter is broken while its face is smooth so it would make a passable millstone but a bone-rattling grindstone and likely Doorly is right. This is also the only stone in the engraving that could serve Jacob both as pillow and pillar. MORE Since we have argued that the stone Globe stands for the Terrestrial Sphere and the stone Solid for the Intellectual Sphere, by elimination it seems that the Millstone stands for the Celestial Sphere, the realm of Reason. Why D¨ urer would show the Celestial Sphere as a millstone is the next puzzle. This turns out to be an easy one. For centuries cultures as diverse as Babylon, Greece, Arabia, Scandinavia, and Rome had represented the Celestial Sphere by a millstone. The celestial millstone caused the precession of the equinoxes when it flew off its axis into the sea [20]. It makes a cameo appearance in the Icelandic legend of Amleth, the original Hamlet, and so Santillana and von Dechend called it Hamlet’s Millstone. In the Golden Age it ground out gold, in later, lesser times it ground out cheaper stuff such as sea salt and in our decadent age mere sand. The Scandinavian Amleth is as melancholy as Shakespeare’s Dane and D¨ urer’s Boy. I will point out an indication of the melancholy celestial millstone in Scripture too. The Boy-artist is the Imaginative Faculty and the Angel the Contemplative one, so by elimination the Dog is the Rational Faculty proper to the Celestial Sphere. Since a revolution is going on in this engraving, or perhaps two, some confusion in the seating is understandable, but the Faculties are out of place. The seated Angel, the Contemplative Faculty, is nominally of the Intellectual Sphere, the highest, but here she is grounded and lowest. The Boy, the Imaginative Faculty, is traditionally of the Terrestrial Sphere, but he is here esconced on the Celestial, fulfilling D¨ urer’s life dream. Perhaps the Dog, the Rational Faculty, is in his proper place, resting with open eyes between the two spheres, but he too is on the ground. D¨ urer has clearly promoted Natural Philosophy and demoted Theological Philosophy. We can read this as the Agrippan revolution, but it is also the scientific revolution. The Natural Philosopher observes matter in space and time, traditionally the lowest Sphere, yet thereby attains truth. The Experimental Philosophy is in the seating plan. Pace Yates, the balance between the Angel and the Boy, therefore, is not the Hermetic equality between the worlds above and below. That related the Terrestrial Sphere to the Celestial, not to the Intellectual Sphere represented by the Angel. “As above, so below” may well be Agrippa’s credo but it presumably is not D¨ urer’s. Like Da Vinci, D¨ urer had already mocked the idea that events in the sky foretold events on Earth. He had drawn and published maps of the stars above and the planet below that showed no similarity or correspondence.

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18

I

Some suggest that the “I” of the banerole refers to one third of the medieval tripartite universe, and expect that MELENCOLIA II and III were engraved and lost, or were at least planned. MELENCOLIA I is indeed one of three, but they all survive famously. They are the Master Engravings (Meisterstiche) of D¨ urer, all dated within a year of each other. The other two are The Knight, Death, and the Devil, and St. Jerome in His Study. They make a plausible triptych of the three Faculties, the artist, the statesman, and the contemplative. We know from D¨ urer’s records that when he made a present of MELENCOLIA I he often accompanied it with Jerome, never with the Knight. But this does not explain why one engraving bore its own caption and not the other two, and so does not explain the I . Another reading is natural for a mathematician like D¨ urer. Even in 1514, an “x primus” in a mathematical writing more often referred back to an earlier x than ahead to a later x secundus or x tertius. This would mean that D¨ urer was superceding the old gateway to heaven with a new one, limen caleo primus, and so was claiming innovation. I had to abandon this interpretation, which I held at first, not when I realized that innovation was a capital crime, but when I realized that D¨ urer and Agrippa did not consider themselves innovators but as renovators stripping away the innovations made by the Church. I propose that the ”I” indeed refers to a triple based on the three Neo-Platonic Spheres, namely the three Agrippan gateways to God of Natural, Mathematical, and Theological Philosophy, but we do not need to postulate lost engravings. This very engraving shows all three gateways and shows D¨ urer choosing gateway I, the Natural Philosophy that evolved into Physics. This is the I of MELENCOLIA I.

19

Comet

The bright light in the sky is a comet, not a nova, though it lacks the curved tail of the most traditional renderings. The NASA online collection of astronomical photographs shows comets quite like it. A comet is straight when it heads for the sun and sunlight pushes its tail out out behind it. It may be an illusion of perspective, but this comet seems to be pointing straight at the Boy, and at his near eye. The great comet 1471Y1 was first seen on Christmas Day in D¨ urer’s birth year, and D¨ urer wrote of seeing a comet himself in 1503. The physical natures of meteors and comets were not yet known in 1514. Galileo would still believe in the next century that comets and meteors were meteorological, weather of the highest atmosphere. Since the Bible has already explained many elements of the picture, let us search it for this one too. The answer is immediate and unique. The only blinding light in the biblical sky is the original light of the divine creation. Then the sky recalls the time in the Bible story after the creation of light but before the creation of the stars. This is a joyous occasion: Happy birthday, universe! The Light may represent Divinity itself, and divine revelation. Then the fact that the comet is heading exactly for the Boy suggests that he, not the Angel, the Dog, or the Bat, is chosen by God. Yet the tone is somber. The tension grows. But so does the ambiguity. This is a realistic comet. Nothing in the picture compels us to see it as

21

divine. It took me a long time to understand this engraving even with all these clues, because I could not figure out whether D¨ urer’s gateway to Heaven was mathematical or religious. This is a good example of the kind of projection to avoid in such a study. D¨ urer does not separate science and faith. On the right they entwine in the building and ladder complex. On the left, there is an unnaturally straight line from the comet or the light of God through the Intellectual Sphere of Mathematical Philosophy to the heart of the Terrestrial Sphere of Natural Philosophy. The Celestial Sphere is not in that line. It is old and damaged and out of service. The Dog is there instead.

20

Dog

The Dog is the last piece of the puzzle to fall into place. It had several possible interpretations. D¨ urer’s animals are among his finest works of art and science, and he had drawn at least three dogs in the year before that are still with us. A similar hunting dog in another work of D¨ urer is equally gaunt, perhaps as part of the training of the breed. Dog and hourglass are the only two components common to all three Master Engravings. Presumably hourglasses represent time and mortality. To me, dogs represent fidelity, to Agrippa love or flattery. There must be a better fit. This Dog lies rather too close to the line of Comet, Solid, and Globe for accident. He curls up just where the Celestial Sphere would lie in the old cosmology. The battered millstone has been lifted up on one edge and leaned on the House, and the Dog is where it used to be. The people associated with the Celestial Sphere were Mathematical Philosophers, astrologers, and kings. The connection of the dog to the Celestial Sphere is no more obvious than that of the Millstone. We know that when D¨ urer illustrated the Hieroglyphica, he learned to represent the ruler by a dog wearing the royal mantle on its naked body [14]. That is why in his Triumphal Arch D¨ urer so represented the Emperor Maximilian I. At the same time he also learned that the way to represent a prophet — one whose Rational Faculty is excited by Saturn, in the theory of Ficino and Agrippa — is by a dog. So the Dog — not the Bat, say — represents the Rational Faculty. This interpretation of the Dog fits all three Master Engravings at least loosely.

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Moonbow

I have never seen a moonbow but again NASA provides the picture and the Bible provides the caption. The only bow in the Bible sky is the “bow in the clouds” that Noah saw after the flood, a supreme example of divine revelation, direct communication with divinity. Genesis does not tell us whether Noah saw a rainbow by day or a moonbow by night. God’s memorandum to himself to send no more genocidal floods could have been either, but D¨ urer had no choice, once he set the scene in the dark of night. In Genesis, the light in the heavens and the bow in the clouds represent two of the greatest gifts of God, so the picture should be joyous, and yet it is dark. And ambiguous. Again. The viewer of any moonbow or rainbow lies on the normal to the plain of the bow passing through the bow center. D¨ urer’s watching eye should lie directly before the point of the horizon beneath the highest point of the moonbow. This is not exactly where he is located by the vanishing point of the building lines, which is under the eye of the Bat, but it is only several centimeters off. 22

The moon must lie on the same line, behind the viewer. It is therefore well to the left of center, like the viewer and the moonbow. But according to the shadows on the House and the face of the Angel the moonlight comes from well to the right of center, over the viewer’s right shoulder. This inconsistency in D¨ urer’s optics is of no import for the content of the engraving but sets an upper limit on D¨ urer’s knowledge of light.

22

Babylon

My Bible-searches for ladders, sky lights, and sky bows all bore fruit so I looked for D¨ urer’s Millstone in the Bible too. I found 11 millstones in the Christian Bible. The first ten serve as metaphors for livelihood or industry, and refer to no other element of the engraving so I put them aside. The eleventh and last is in Revelation. In the King James version: And a mighty angel took up a stone like a great millstone, and cast it into the sea, saying, Thus with violence shall that great city Babylon be thrown down, and shall be found no more at all. (Revelation 18:21.) At least three elements of the engraving appear here: the mighty angel, the millstone, and the sea. The millstone of Revelation is therefore a provisional candidate for D¨ urer’s millstone, the best in the Bible. But it is itself a puzzle. Tossing an arbitrary millstone into the sea is an oddly lame image for the downfall of Babylon, one of the great empires of Bible times. A bath would not harm a millstone and might do it good. But if the millstone of Revelation is again the Celestial Sphere, throwing it into the sea is the same astronomical catastrophe as Hamlet’s millstone rolling into the sea. It ends one world age and begins a new one [20], a simile fit for a a king even of Babylon. So I looked for Babylon and its downfall in the engraving. The engraving shows a city by the sea with ships in port. Over the left-most pan of the scales in the engraving, through a small triangle framed by ladder, house, and pan, we see a massif of flow-lines pointing toward the city, well-resolved in a full-size print if not in [19]. How could I have overloooked it? • There is a great wave looming high over the city, about to destroy it as prophesied in Revelation. Or the massif could be far up the coast beyond the city. The flow can be read in two ways due to the intrinsic ambiguity of perspective, which we at last begin to realize is always deliberate, the very point of the engraving, hammered home again and again until we could not miss it. The flow lines are then geological, not hydrodynamical. We cannot read the depth of the flow in the picture uniquely from one perspective view. The ladder hides connecting clues that might force one view or the other upon us. Now the engraving and the Biblical verse share Millstone, Angel, sea, Babylon, destruction, and even melancholy, for the verse I quoted is imbedded in a score that lament the destruction to come. If authors as far apart as those of Revelation and the Hamlet legend used the Millstone for the Celestial Sphere, then this usage may have still been current in D¨ urer’s time too. The connection we sketched in lightly between D¨ urer’s millstone and Hamlet’s is now less tenuous. Probably the millstones of Revelation, MELENCOLIA I, and the original Hamlet, separated by centuries, are one and all the Celestial Sphere, and this scene in the engraving probably refers to Revelation. The Biblical verse would then refer to the end of the Age of Aries and the beginning of Pisces, the next 23

after the writing of Revelation. If D¨ urer meant the metaphor seriously, he referred to the end of the Age of Pisces, and his Babylon might be the hierarchy of the Roman Church that he already so mistreated in his Apocalypse. In 1514 he was not yet disillusioned with the Reformation clergy as well, but Pirckheimer attested that both clergies eventually disgusted him beyond his tolerance.

23

Hexagram

D¨ urer was a descriptive geometer, practiced in constructing views of bodies from all sides and in reconstructing a body from its views. I therefore looked at the Solid from all sides, as he likely did, while I was searching for his meaning. • Viewed from the sky as a truncated rhombohedron, the ground plan of the Solid is a Shield of David framed in a hexagon.

T T  T b "  T b " " b  T " b  " b T b " T  b " b " T  " b T  " b  T  T T T 

T

The top and bottom triangles of the Solid project into the two crossed triangles of the hexagram. Perhaps D¨ urer truncated the cube, rather than some other regular solid, in order to create this hexagram. It would be anachronistic, however, to call this hexagram a Jewish star and to infer a certain philo-Semitism. Centuries earlier the Khazars of the Crimea had adopted the hexagram for their flag when they adopted Judaism, but in 1514 Nuremberg the hexagram was still mainly a magical device, an amulet, possibly referring to the Hebrews of the Bible but probably not to contemporary Jews. D¨ urer’s use was likely a Hebraism, not philo-Semitism. The Shield of David was called that because it was supposed to shield its bearer from evil spirits. It was more often found in churches than synagogues. A two-footed hexagram like D¨ urer’s ground plan is seen on a German altar of D¨ urer’s time. Some said the hexagram was the Seal of Solomon, and others the pentagram. Traditions firmed later that gave Solomon’s star five points to David’s six, and stood Solomon’s on two points to David’s one. Not long after D¨ urer’s death the Jewish community of Prague was granted the privilege of a flag and chose the hexagram, possibly because of its association with the Khazars, and this continued its evolution from magic charm to Judaic symbol. The Hebraism of both D¨ urer and Agrippa is conspicuous in their work. D¨ urer admired Jerome above the other founding fathers for Jerome’s greater familiarity with the Hebrew Bible [19]. In his several drawings of Jerome studying Latin, Greek, and Hebrew Bibles, D¨ urer invariably placed the Hebrew Bible above the others, and higher is holier. The Shield of David is a further Hebraism concealed in the D¨ urer Solid. Because we are so practiced at finding right angles in the world about us, had D¨ urer truncated a true cube, we would have seen it as such in any view. Stretching the cube made the figure triply 24

ambiguous, and demonstrated our inability to reach truth through our senses. Circumcising it Hebraicized it, connected the new gateway to heaven with the Hebrew Bible. His stereotypes of the Jew and the Arab make it clear this hidden Shield of David is a Hebraism, not philo-Semitism, and this again aligns him with Agrippa.

24

Space and time

D¨ urer uses the vertical dimension on his plate in a traditional way. Higher is holier. Jacob’s angels get to heaven by climbing a ladder. Angel and Boy have equal divinity because they have equal altitude. The tools of artisans litter the ground, they are profane, while the instruments of science and mathematics hang carefully on the wall nearer to the sky, they are more sacred. The horizontal dimension is time. It is cut neatly in half by one edge of the House. The cut separates the new and old gateways to Heaven, which use the Rational and Contemplative Faculties. Yet all three Spheres of the cosmos and all four actors in the drama are to the left of the dividing wall of the House, though perspective puts the Boy and the Angel on the right-hand half of the paper. All the instruments of science are on the right-hand side. The crucible is no exception. If it were an instrument of alchemical science, as I thought at first, it would be elevated, but it is on the stone floor. Only perspective puts it high on the paper, above all other tools; perspective and filial feelings. This is further indication that Doorly read this correctly, This crucible is not an instrument of science but a remembrance of D¨ urer’s goldsamith father. The near eye of the Boy lies just on the center line. D¨ urer the artist-scientist withdraws from the schism about him and does his inspired work. Perhaps the vanishing points tell us how to hang all three Meisterstiche as a triptych on three walls of one room: Jerome on the wall to our right, Knight on the wall before us, and MELENCOLIA on the wall to our left. Then the horizontal axis can be time passing from right to left as in Hebrew writing. Perspective provides a third dimension of depth into the scene along the line of sight. D¨ urer seems to use this expressively too. On the right side our view is blocked by the House and on the left there is an unlimited vista. It seems that perspective depth in the picture is the familiar metaphor for depth of vision.

25

Melancholy

The light and the bow and even the destruction of the city of evil are good news, and yet the picture is set in the gloom of night. D¨ urer has even transformed the rainbow of the common understanding into a moonbow. The comet illuminates nothing and hides the stars. Only the moon behind us lights the scene and creates the shadows and the moonbow. What might have been a sunny prophesy if Leonardo were speaking is dark as night. While Leonardo and D¨ urer were both mathematically ambitious, they differed importantly in their outlook. Leonardo wrote confidently of “a complete knowledge of all the parts, which, when combined, compose the totality of the thing which ought to be loved.” Leonardo was the rational optimist. D¨ urer on the contrary said shortly before this engraving, “But what absolute beauty is 25

I know not. Nobody knows it but God.” The darkness of the setting and the multiple ambiguities of the Solid suggest that after all D¨ urer did not expect humanity to attain the supreme mathesis that optimists like Ramon Llull had expected and even claimed to have attained. He expressed this pessimism in the engraving atmospherically, by omitting the door of the House of God, and by numerous skillful demonstrations of ambiguity and relativity. The most unambiguous aspect of this engraving is its ambiguity. D¨ urer wants us to know clearly that we cannot know. The Solid is a truncated rhombohedron with vertical axis or a slab tilted toward the horizon. There are three faces hidden in the Solid or none. The city is to be destroyed or not. The Angel is good or evil, the Bat too. The house has windows or not. The melancholy is inspired by the inaccessibility of the absolute, or by the influence of Saturn, or because the Celestial Sphere is off it axis. What we see depends on how we look at the scene and what we expect. Most of the elements of this engraving that we have discussed here are intentionally ambiguous, either in meaning or form. If we cannot believe what we see, what can we believe? This questioning occurs famously in the First Meditation of Descartes (1596-1650), who cites optical illusions as a reason for his method of universal doubt. It seems that MELENCOLIA I anticipates Cartesian doubt. And its response has a mathematical element that anticipates the Mathesis Universalis of Descartes. The ideal of a complete mathematical theory of beauty lies on the same long line of distinguished fantasies of mathematical wisdom as the number mysticism of Pythagoras and Plato, the Ars Magna of Ramon Llull (whom Agrippa studied) and Giordano Bruno (who studied Llull and Agrippa), the vision of Mathesis Universalis that Descartes and Leibniz shared, and the Ars Combinatorix of Leibniz. D¨ urer does not doubt the existence of absolute beauty but despairs of knowing it. The Boy withdraws from both philosophy and astrology, ignores theory, and observes Nature. Years after 1514, D¨ urer like Agrippa explicitly abandoned the search for absolute truth and beauty as futile and hopeless, crying out, “The lie is in our understanding, and darkness is so firmly entrenched in our mind that even our groping will fail” [Panofsky 1971]. In 1517 D¨ urer was still optimistic enough to join with Luther. The engraving seems to come from a later more despairing phase of D¨ urer’s life. This suggests to me that the date on the engraving is an afterthought, chosen to agree with the bottom line of the magic square and the death year of his mother. One can also suspect the date because in 1514 Luther had not yet linked Agrippa to witchcraft and the demon image might have been obscure. This reasoning is somewhat circular, and only further historical data will break the circle. The engraving should indeed be read as an illustration, as Doorly says, but of D¨ urer’s own lament and credo. Its night is our benighted ignorance. Its darkness is the darkness “firmly intrenched in our mind.” The mystery of the Solid, crafted to be insoluble, is one of many metaphors in the engraving for our inability to see the Absolute Truth from our limited perspective. In acknowledging the limits of human knowledge, D¨ urer went a step beyond the more optimistic Leonardo toward modernity. As Panofsky and Doorly said, the melancholy is D¨ urer’s over the limit of human art and understanding. And as Yates said, it is also the Saturnian melancholy that inspires artistic creation. The posthumous publications of D¨ urer on measurement and on human proportions show that he never quit searching for a mathematical theory of beauty and truth based on measurement rather 26

than abstract speculation, but it became relativistic. He included a variable horizontal scale-factor transformation in order to represent human beauty of the lean, average, and plump variety as the reference frame of the artist requires.

26

Trinities

The triplets of the Angel and of the Solid, both in the theological realm, would likely be read by viewers as references to the Doctrine of the Trinity. It is not clear at first whether D¨ urer means triplication to imply divinity. The fool provides a useful indicator for this. If he is a triplet, D¨ urer does not intend triplets to be divine as opposed to human. Following this reasoning I returned to the engraving and looked at the fool from another angle. • It was then easy to see faces E. and F. Angel superimposed on D. D. in profile looks to our right, E. in full face looks slightly to our left; and F. in profile looks upward and to our left. I originally found C. Solid in the same way. I looked in vain for such triplets in the other figures of this engraving or in other works of D¨ urer. The fool of Frau Venus too is single, not three-faced. This supports two inferences at once. The triplets refer to the Doctrine of the Trinity, and the Angel and Solid alone belong to the Spiritual Sphere. It seems probable that Drer introduced these three relativistic triplets in order to reform the Doctrine of the Trinity. He shows one individual with three aspects, not three entities and one at the same time. This puts D¨ urer closer to Unitarianism than Trinitarianism. This is not completely absurd, it seems, due to at least three circumstances. First, since he agrees with Da Vinci that knowledge comes through the senses, and since the Doctrine of the Trinity comes more from the Council of Nicea (325) and faith than from direct observation, it would not be surprising if an independent thinker like D¨ urer had doubts about the Trinity by 1514. Second, the Hebraism of Agrippa might also stimulate a revision of the Trinitarian doctrine. Gell´erd proposes that Agrippa provided the Transylvanian Unitarian D´avid with some of his epistemology [10]. Panofsky and Yates make it clear that Agrippa influenced D¨ urer’s thinking. It seems possible that the charismatic Agrippa inspired D¨ urer too to express the unitarian tendencies we find in MELENCOLIA I. Michael Servetus, traveling in Germany, published his historic unitarian treatise De trinitatis erroribus, perhaps the first, in 1531 at Hagenau, only 100 km from Nuremberg. The publication and this engraving close enough in space and time to suggest that unitarian thoughts were part of a local Zeitgeist, perhaps inspired by Agrippa, though in 1531 he was publishing his occult philosophy at last in Antwerp. Once we look for unitarianism in the engraving, it is easy enough to find. The Deity is shown here as the single point of light that is also the comet. In his Landauer altarpiece, on the contrary, D¨ urer presents each member of the Trinity as a fully conceived independent entity in itself, represented by a dove, an old man, and a young man on a cross, and indicates their unity by the convention of arranging them in a vertical straight line. In Melencolia I instead he presents a relativistic kind of trinity more natural to a descriptive geometer. Each of the members of such a triplet is not a

27

different and separate individual but a different aspect of one unity. This representation captures the impossibility of seeing three separate things where there is only one in a way that the Landauer altarpiece cannot. D¨ urer’s heresy is at least threefold if I see it correctly. First, he shows the same Contemplative Faculty that serves Christian theologians as serving Jews and Muslims too. Secondly, as Boy he declines the traditional ways to knowledge of the Contemplative and Rational Faculties for the way of the Imaginative Faculty, the way of artists and artisans and natural philosophers. “All that is in the mind comes through the senses.” Finally, he suggests that the three entities of the Trinity are One seen from three viewpoints. This engraving instantiates what Yates said about this transitional moment in the evolution of science. No sharp line yet separated the cultures of the old magic, the new natural philosophy, and religion. This is the brief era when the closest thing to physics was natural magic, the natural was still emerging from the magic, and the Bible was more trusted than our senses. D¨ urer shows a single divinity connected to the human world through the realm of pure mathematics. He demonstrates multiply that relativity keeps us from the absolute. He shows how this fills him with melancholy, and how this melancholy inspires the frenzy of artistic creation and natural philosophy that we see before us.

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Disclaimer

The views expressed by this engraving are not necessarily mine. D¨ urer seems to find that relativity is a melancholy science. Many poets, philosophers, artists, and even some scientists, express sadness, pain, or nausea over losing the absolute, and many still continue to seek it. I do not.

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Acknowledgments

I thank an anonymous donor (§2) for starting me on this study. It would have been impossible without the studies on MELENCOLIA I by Erwin Panofsky and by Francis Yates and works on Agrippa by Judit Gell´erd and by Charles Nauert. I have also drawn on the study of Hamlet’s millstone by Giorgio de Santillana and Hertha von Dechend, on a study of MELENCOLIA I by Patrick Doorly, on a study of Hamlet by Stephen Greenblatt. The heraldry dictionary of Cecil Wade helped me to read D¨ urer’s coat-of-arms. I benefited from gematria on the website of the Aiwaz Gallery, though our arithmetic and interpretation differ. My thanks go to Roy Skodnick for introducing me to the work of Yates; to Prof. Heinrich Saller for the print of MELENCOLIA I that triggered this process; to Rabbi Mario Karpuj for reminding me that Jacob’s ladder is the original gate of heaven; to Prof. Shalom Goldman for stimulating, informative, and encouraging discussions, the reference to Yates on D¨ urer, and the meaning of the Magen David in the Renaissance; to Dr. Basimah Khulusi for generous helpful discussions, models of the D¨ urer Solid, the asymmetric interpretation of the Solid, and the reference to Von Buolschafft; to Danny Lunsford for refining the Schreiber construction of D¨ urer’s Solid and for the reference to http://meteoros.de/halo/halo1.htm; to Carla Singer for her expertise in art history, including the 28

reference to Mantegna; and to Shlomit Ritz Finkelstein, for lively discussions, help with Torah and Descartes, and useful expository suggestions. An earlier stage of this study was published in The St. Ann’s Review, whose reviewer improved the paper.

References [1] Agrippa von Nettesheim, Heinrich Cornelius: 1531. Of Occult Philosophy, digital edition, ed. Joseph H. Peterson, http://www.esotericarchives.com/agrippa/agrippa1.html. Based on the translation of ”J.F.”, printed by Moule, London (1651). [2] Agrippa von Nettesheim, Heinrich Cornelius: 1530. De incertitudine & vanitate scientiarum & artium atque excellentia verbi Dei declamatio. Antverpiae : Grapheus, 1530. OCLC: 22080834. [3] Brant, Sebastian. Narrenschiff (Ship of Fools). Illustrated by A. D¨ urer. Basel, 1494 (first edition). Translation by Alexander Barclay: Ship of Fools, Pynson 1509. Rhyming translation by E. H. Zeydel: Ship of Fools. Columbia University Press, 1944, reprinted by Dover Publishing Co., 1962. Espeically Chapter 13, On Amours. As of June 1, 2005, the site http://www.loc.gov/exhibits/treasures/images/wb0013.1s.jpg shows the woodcut Von Buolschafft mentioned in §11. [4] Doorly, Patrick. D¨ urer’s Melencolia I : Plato’s Abandoned Search for the Beautiful. The Art Bulletin88, 255 (2004) [5] D¨ urer, Albrecht. The works of D¨ urer mentioned in this paper are reproduced in [19] and are found online in internet galleries. Such presentations are good enough to verify the features mentioned in this paper, but when we are verifying the secondary images, the beat between the raster of the presentation and the shading of D¨ urer combines with our propensity to see faces and creates artifacts that should not be taken seriously. Commercially available art prints create no such problems. [6] D¨ urer, Albrecht. Vnderweysung der Messung mit dem Zirckel un Richtscheyt in Linien, Ebnen und Gantzen Corporen, Vol. 1-4. Nuremberg 1525. Republished with English translation of Walter L. Strauss, revised, on compact disk. Editor, anonymous. Commentator, David Price. Octavo Editions, Oakland CA, 2003. [7] Erasmus, Desiderius, of Rotterdam. In Praise of Folly. Translated by John Wilson. Dover Thrift Editions. 1991 [8] Finkelstein, David Ritz. Melencolia I: D¨ urer Decoded, The St. Ann’s Review , 2004. [9] Galileo Galilei, Dialogue on the Great World Systems. The Salisbury translation. Revised, annnotated, and with an Introduction by G. de Santillana. University of Chicago Press (1953) [10] Gell´erd, J. Francis D´avid’s Epistemological Borrowings from Henry Cornelius Agrippa of Nettesheim. w3.enternet.hu/sandor64/cffr/papers/agrippa.htm [11] Goldman, Shalom. God’s Sacred Tongue: Hebrew and The American Imagination; also http://uncpress.unc.edu/booksT-6957.html. For the concept of Hebraicism.

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[12] Greenblatt, Stephen. Will in the World: How Shakespeare Became Shakespeare. Norton (2004). On Hamnet and Hamlet. [13] Heckscher, William S. Melancholia (1541). An Essay in the Rhetoric of Description by Joachim Camerarius. In: Frank Baron, ed., Joachim Camerarius (1500-1574). Beitrge zur Geschichte des Humanismus im Zeitalter der Reformation. Essays on the History of Humanism During the Reformation. Humanistische Bibliothek, Abhandlungen 24 (Munich, 1978): 32-103 [14] Horapollo Niliaci. The Hieroglyphics of Horapollo. Boas, George, translation and introduction. Princeton University Press 1993. [15] Khulusi, Basimah. Personal communication. [16] Lunsford, Daniel. Personal communications concerning the D¨ urer Solid and Ratio (2004). [17] MacGillavry, C. The polyhedron in A. D¨ urer’s engraving Melencolia I. Nederl. Akad. Wetenschap. Proc. Series B 84, 287-232 (1981). [18] Nauert, Jr., C. G. Agrippa and the Crisis of Renaissance Thought University of Illinois Press, Urbana, 1965. [19] Panofsky, Erwin. The Life and Art of Albrecht D¨ urer . Princeton University Press, 1971. The standard work. It reproduces the D¨ urer works mentioned here. [20] Santillana, Giorgio de, and Hertha von Dechend. Hamlet’s Mill: An Essay on Myth and the Frame of Time. Gambit, 1969. Argumentation for the astronomical interpretation of all myth. [21] Peter Schreiber. “A New Hypothesis on D¨ urer’s Enigmatic Polyhedron in His Copper Engraving Melancholia I.” Historia Mathematica 26, 369-377, 1999. [22] W. Cecil Wade. The Symbolisms of Heraldry or A Treatise on the Meanings and Derivations of Armorial Bearings. London: George Redway, 1898. [23] Weitzel. H. A further hypothesis on the polyhedron of A. D¨ urer’s engraving Melencolia I. Historia Mathematica 31 (2004) [24] Frances A. Yates. The Occult Philosophy in the Elizabethan Age. London ; Boston : Routledge & K. Paul, 1979. Especially chapter 6. [25] http://gallery.euroweb.hu/html/d/durer/ shows all the D¨ urer works I mention. [26] http://mathworld.wolfram.com/DuerersSolid.html describes and names the D¨ urer Solid. [27] http://meteoros.de/halo/halo1.htm is a remarkable gallery of portrayals of heavenly phenomena like moonbows and moon halos, including several from D¨ urer’s time.

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