Melencolia100311

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THE GNOMONS OF MELENCOLIA IVersion of 2010.01.01

David Ritz Finkelstein

Georgia Institute of Technology

c©2010

This supercedes arXiv:physics/0602185.

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Figure 1: MELENCOLIA I.0, A. Durer, 1514

Chapter 1

THREE GATES TO HEAVEN

Albrecht Durer’s 1514 engraving MELENCOLIA I (sic), has been anicon and conundrum of German culture for centuries. It seems to saymuch, but what? I propose here that it is an elaborately encryptedmanifesto of Humanism and the impending Scientific Revolution, withinnocuous overt meanings and dangerous covert ones.

In particular it recognizes relativity as a limit to our knowledge ofabsolute truth. An important part of its message is that what we see isnever the thing as it really is but our own unreliable reconstruction. Itwould be inconsistent with the message itself to claim that the messageis unambiguously clear

We see Durer’s engraving with eyes of our own times, but to min-imize the resulting misreadings I confine my interpretations to viewsalso expressed in:

• His other works and writings, especially his coat-of-arms and thetwo extant states of the engraving MELENCOLIA I whose differ-ences clarify his intentions.

• Works and writings of Leonardo da Vinci, who worked on the MonaLisa in Florence while Durer studied perspective in Venice.

• The Bible.

• The De Occulta Philosophia of Agrippa, who carried his manuscriptto Nuremberg, Durer’s home, in the year before this engraving.

• The Hieroglyphica of Horapollo, which Durer had illustrated earlier,and then had used as code-book in a major allegorical work of thepreceding year.

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4 CHAPTER 1. THREE GATES TO HEAVEN

• The Ship of Fools of Brant, some of which Durer illustrated.

The process of trial and error converges to an interpretation thatseems to fit more elements of Durer’s work —over 50 at last count,subliminal and hidden as well as visible——with fewer assumptionsthan others I have seen. Some of these elements have been reportedby others, especially the subliminal face I call Ghost I [?], and thesubliminal Wave [?, ?]; I capitalize my proper names for the objects inMELENCOLIA I.

1.1 Anagram

The clue that catalyzed this study is the subliminal face of an oldwoman in the Solid, noted by many. It suggested that there mightbe other hidden content, and I turned my attention to the eponymicMotto that appears on a banderole. Actually, the motto is “MELEN-COLIA§I”. The stylized S that I transcribe as § is lighter than theother letters, and is significant in the interpretation, though usuallyignored.

Melancholia is transliterated Greek for melancholy and black bile.A Latin form is melancolicus ; the German, Melancholie. the Italian,Malinconia. Durer himself uses the etymologically reasonable formMelancolia in a title-page woodcut of 1503. In no language do I findthe spelling melencolia. It is odd even for Durer and the unstablespelling of the time. Could the Motto be an anagram?

Heinrich Cornelius Agrippa von Nettesheim (1486-1535), a prolificand controversial figure of the Florentine Neo-Platonist school, couldwell have put anagrams, melancholy, magic squares, and gematria (soonto come) into Durer’s thoughts. They are all in his Occult Philosophy ,and he visited Durer’s Nuremberg in 1510 — four years before thisengraving—with its manuscript. They are also among the techniquesused to squeeze new meanings out of old texts in the Baraita of Thirty-Two Rules of Rabbi Eliezer ben Jose the Galilean, who flourished inthe second half of the second century C.E. and was cited importantly inlater years. Jews expelled from Spain in 1492 who settled in Florencebrought this lore to Florentine Neo-Platonists like Agrippa, who wasan active Hebraist.

1.1. ANAGRAM 5

In any case, by the 16th century letter-permutation was a standardway to protect intellectual property. The Royal Society and the systemof scientific archives were still to come. Writers who solved an impor-tant problem could not guard their intellectual property by publishingor patenting. Some protected their priority by permuting the letters oftheir solution and publishing it with the problem. Earlier Roger Baconscrambled the formula for gunpowder in this way in order to preventthe proliferation of this terrible weapon. Later Galileo would scramblehis discoveries of the phases of Venus and the rings of Saturn. Mathe-maticians scrambled their theorems. The resulting meaningless jumbleof letters declared on its face that it was a cipher. Sometimes it wasmisconstrued by a false rearrangement.

In the next degree of concealment, the scrambled letters themselvesare used to spell out a cover message, the anagram. This can hidenot only the message but even the existence of the message. If themotto MELENCOLIA I is an anagram, it has worked. Only the covermessage seems to have been read in recent centuries. It was decryptedas follows.

Panofsky, a major authority on Durer, declared the engraving to beintensely autobiographical [?]. I tentatively supposed that the mottorepresented Durer himself. To see how he might describe himself I wentto his coat-of-arms (1490, 1523).

The 1523 version has his famous monogram and the year at topcenter. Next come cliches one finds in any dictionary of heraldry [?]:a blackamoor for heroic action in the Crusades by an ancestor; eaglewings, for fame and glory; a closed helmet in full profile, for the estateof esquire, the lowest. A shield below these cliches bears his familialcoat-of-arms, the only image in the coat-of-arms specific to the family.

� The coat-of-arms shows a gateway with open doors.This is self-evidently an ideograph for both “Durer”, the family

name, and “Ajtos,” the Hungaran town of origin. This sends one look-ing for other ideographs. One is near at hand:

Coats-of-arms usually display the pride of the family, some greatpersonal accomplishment. Durer, the world-famed engraver, shouldhave drawn a burin on his arms, or the word “burin” itself. But theLatin for burin is caelum. Unexpectedly, caelum, like coelum, is an


Durer_herb.jpg (JPEG Image, 499x595 pixels) http://upload.wikimedia.org/wikipedia/commons/5/54/Durer_herb.jpg

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Figure 1.1: Durer’s coat-of-arms.

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ordinary word for “the sky”, “heaven”,“the heavens”. Caelus is also aPlatonistic name of God [?]. It has the same root as our “celestial.”Thus caelo means “to Heaven”, “to God”, and “I engrave”. Durer couldnot resist the pun. The gateway stands on a cloud, and so is in the sky.

� The Durer coat-of-arms is an ideogram for “Gateway to Heaven”.� It is also a rebus for “Durer” and “burin”.“Gateway to Heaven” was and still is a common metaphor for the

Roman Catholic Church itself.Gates of Heaven appear again in MELENCOLIA I itself. The Durer

monogram AD, exhibited at the top center of the 1523 coat-of-arms andat the bottom right corner of MELENCOLIA I, is one of them. At firstglance it is a pun on Anno Domini , but it is also an ideographic logo.The flat-topped A is a gateway as well as a letter, its legs are theuprights of the gateway, and a lintel sits on them and connects them.A stiffener just beneath the lintel is the crossing of the A, rather highfor an A but proper for a gateway. The D between the uprights of theA echoes the Doors between the uprights of the Gateway in the Durercoat-of-arms.

One life-mission of Durer was to achieve for the graphic arts the di-vine status granted in his time to music, which was part of the quadriv-ium. In Durer’s coat-of-arms he symbolized the divinity of art by thepunning caelo rebus.

CAELO also fits into MELENCOLIA, and the leftover letters thenspell out LIMEN, one of whose common meanings is gateway. This toomay be taken as a self-reference to the name Durer and the gatewayin the Durer coat-of-arms. Limen also means gate, doorway, thresh-old, lintel, walls, house, home, boundary path, and limit, according tocontext.

� The unscrambled motto can be LIMEN CAELO I, “Gateway toHeaven I”, a reference to the Durer name, city of origin, coat-of-arms,and familial arts.

The §-symbol and the “I” in the Motto reappear later.Panofsky was right, we have another signature. Its unscrambling

took much less time than it takes to tell, making me feel that I mightbe conversing with Durer, not just with myself. The unscrambled Mottoalso confirms the interpretation that Durer intended the clouds in the


coat-of-arms as a symbol of Heaven. It also could describe the dimarchway in the heavens that frames the motto, and other elements ofthe engraving that we take up later.

The overt message and image, both dark, thus cover a luminous one.“Limen caelo” is as optimistic as “MELENCOLIA” is depressing. Andyet the picture is dark. It seems to offer a gateway to Heaven, but ithas not yet told us what that is.

Some suggest that the “I” of the banderole refers to one third ofthe tripartite neo-Platonic cosmology, which was described by Agrippa,consisting of the Elemental Sphere, the Celestial Sphere, and the Intel-lectual or Angelic Sphere. They expect that “ MELENCOLIA II“ andIII were engraved and lost, or were at least planned. MELENCOLIA Iis indeed one of three, called the Meisterstichen or Master Engravingsof Durer, dated within a year of one another. In chronological orderthey are St. Jerome in His Study , The Knight, Death, and the Devil ,and MELENCOLIA I.

The series indeed suggests the neo-Platonic cosmology. The Mottopresumably refers to the ancient Greek humor of melancholia, the blackbile (melan cholia). It has been suggested that it also refers to, and evenendorses, a revolutionary variation on the humor theory then being cir-culated by Agrippa [?]. The evidence that Durer had access to Agrippais circumstantial but is accepted by Panofsky and Yates. Neo-Platoniccosmology figures strongly in MELENCOLIA I, so a brief summary iscalled for.

Today cosmologies are revised drastically every century or less. TheNeo-Platonic cosmology permeated and dominated the language andthought of the previous millennium as no cosmology has since. It con-sisted of three Worlds:

1. World I is the Terrestrial or Elemental World, our material abode,made of the four elements distributed in space and time.

2. World II is the Celestial World above, the locus of astronomicalobjects, with one rigidly rotating crystal sphere holding the fixedstars, and as many other spheres as necessary for the sun, themoon, and the planets; Ptolemy used over 90 ancillary spheres.

3. World III is the Spiritual or Intellectual World outside the Celestial

1.1. ANAGRAM 9

World, the place for Angels and the Platonic Ideas.

Neo-Platonists divided the human psyche into three corresponding Men-talities or Faculties specially suited to these Worlds [?].

1. Mens imaginatio, the Imaginative Faculty, empowers the artisan,the artist, and the Natural Philosopher to view arrangements ofthe four Elements in Space and Time, but nothing more.

2. Mens ratio, the Rational Faculty, allows astronomers and Mathe-matical Philosophers to predict when stars rise and set and throughastrology allows statesmen to predict the rise and fall of empires.

3. Mens contemplatrix , the Contemplative Faculty, enables Theologi-cal Philosophers to know about angels and Plato’s Forms or Ideas.

The names for the three Worlds vary. Agrippa also called themidolus or imaginatio, ratio, and mens respectively [?]. With the threeWorlds Agrippa and other neo-Platonists associated three Gateways toknowledge of God, three Books of wisdom, and three Philosophies:

1. Gateway I is Natural Philosophy, which reads the Book of Nature::

2. Gateway II is Mathematical Philosophy, which reads the HebrewBible::

3. Gateway III is Theological Philosophy, which reads the ChristianGospel.

In Book I we see merely the creatures of God, not God, Agrippa wrote.We may use Reason to deduce the existence and nature of God, butoriginal sin is supposed to clouds our souls and make our conclusionsunreliable. But Books II and III are the result of revelation and requireonly faith. Gateway III was the surest according to Agrippa.

Neo-Platonism also kept the ancient Greek psychology of the fourhumors, one for each Element: blood for Air and the sanguinary tem-perament, yellow bile or choler for Fire and the choleric temperament,phlegm for Water and the phlegmatic temperament, and, last but least,black bile for Earth and the melancholic acute depression. This ancienttheory occupied Durer’s imagination in 1514 [?]. It survives today inour vocabulary for temperaments.


Melancholia, the black bile, does not exist. It is a Greek myth,invented to fit the mental illness of acute depression into the humortheory. Some said the appendix secreted it some the spleen; neithersecretes anything.

Ficino (1433-1499), the Florentine humanist and astrologer, had as-sociated Saturn, the slowest, darkest planet, with the black humor,melancholia; with the lowest Element, Earth; and with the lowest peo-ple, earth workers. As astrologer, the younger Agrippa was a revolution-ary. He elevated Saturn from the lowest planet to the highest, arguingthat Saturn is highest from the Sun and most sedate. He attributed toSaturn the power to inspire all three Faculties to their peak creativity,and transferred even the demi-godlike geometers—“earth measurers,”after all—to the dominion of Saturn, among farmers, miners, and ditch-diggers. Marlowe’s Faust is said to have been based in part on Agrippa.

Whom the Motto labels is not completely clear. Most assume thatit labels the Angel sitting opposite the Imp in the sky. But in his otherworks Durer puts his labels on or near the things labeled. Most likelythe Motto labels what bears it, the Imp.

This leads me to tentatively identify the Imp with the then well-known champion of Melancholia, Agrippa von Nettesheim. Some of hisbiography seems relevant to this engraving:

Agrippa wandered Europe for much of his life, seeking royal sup-port, making enemies, and fleeing them, leaving centers of intellectualferment behind [?]. His De Occulta Philosophia is an encyclopedic com-pendium of astrology, alchemy, Cabala, biology, physics, and medicine,largely false and easily refuted by experiment. It claims, for example,that the touch of a diamond demagnetizes magnetite [?]. (It does not.)But he also wrote a tract on the natural superiority of women overmen, and defended a wealthy widow against witchcraft charges by cler-ics seeking her fortune. Not long after this engraving, Martin Luther(1483-1546) linked Agrippa with the devil.

In 1531 a plague broke out in Antwerp. The doctors left but Agrippastayed to tend the sick. When the doctors returned, to recover theirwealthy patients they filed charges against Agrippa for practicing medicinewithout a license. Agrippa fled once more.

In his later years he said that he had studied the occult philoso-

1.1. ANAGRAM 11

phy because at one time he believed that it traced back to a secretdivine revelation given by God at the same time as the public divinerevelation of the tablets of the Torah. He remained in the CatholicChurch and eventually adopted an uncritical fideism, abjured astrol-ogy, and doubted all access to truth but faith in the Bible. His work onthe uncertainty and vanity of the sciences, exalting faith in Scripturesand divine revelation over all the arts and sciences, including astrology,retracted hisOccult Philosophy but appeared in print earlier.

Panofsky and Yates saw many Saturnian melancholic elements inthe engraving, in either the depressive sense of Ficino or the creativesense of Agrippa. They inferred that Durer adopted Agrippa’s esotericphilosophy at least for the purpose of this engraving.

This does not do justice to Durer as mathematical scientist, nat-uralist, and artist, or as follower of the teachings of Leonardo. Yes,MELENCOLIA I uses the language of neo-Platonism, but there was noother. It is more radically Humanistic and rationalistic than Agrippaor Luther. Agrippa, Erasmus, and Durer all took the Gospel as di-vine revelation, but they chose different ways through the Reformation.Agrippa’s protest against the corruption of the monks who ran the In-quisition has beed radical [?] but he stayed within the Roman Churchand retreated into a passive fideism. Erasmus remained in the RomanChurch but also became a leader of Christian Humanism and distancedhimself from Agrippa. Durer left the Roman Church to follow Luther.

Durer probably rejected astrology years before Agrippa came toNuremberg, still an astrologist. In 1514 Copernicus (1473-1543) hadnot yet published his heliocentric cosmology, but the cardinal, mathe-matician, and philosopher Cardinal Nicholas of Cusa (1401-1464) hadlong demolished the Ptolemaic spheres, and Leonardo had already writ-ten that the Earth moves, not the Sun, and that “those who have cho-sen to worship men as gods – as Jove, Saturn, Mars and the like –have fallen into the gravest error.” Leonardo had derided necromancersand excluded astrology from his intensely rational works on astronomy.Similarly, a 1494 caricature of the folly of “Attention to the Stars” plau-sibly attributed to Durer in the Ship of Fools of Brant [?] shows theastrologer-fool immersed in a motley flock of misshapen fowl flying inrandom directions, perhaps representing the the astrologer’s disordered


thinking.Durer must have had strong mixed feelings toward Agrippa, adopt-

ing Agrippa’s keyword as Motto of the engraving, and yet depictinghim as an Imp of Satan. Both men were engaged in raising the statusof the First World to at least equal the Third, for their own reasons.This could be an expression of the Humanism that was then in theair. But Durer left the Catholic Church, and Agrippa withdrew into itinstead.

Martin Luther nailed his theses to the church door in 1517, andDurer soon became an ardent follower. Agrippa aroused Luther’s irewhen he defended a woman accused of witchcraft from her corruptaccusers, and Luther specifically linked Agrippa’s Occult Philosophywith witchcraft. Durer looked to the future for knowledge and Agrippato the past.

The three Master Engravings of Durer correspond to inspired ge-niuses of the Three Worlds. Jerome exemplifies Faculty III, and Agrippa’sBook III lies open before him. Likely the Knight represents Faculty IIas a statesman. And MELENCOLIA I exemplifies Faculty I, showingthe Boy artist reading Agrippa’s Book I. Other symbols in MELEN-COLIA I can be plausibly assigned to one of the three neo-PlatonicWorlds or Faculties.

� The full Motto “MELENCOLIA§I” is an anagram of LIMENCAELO §I, meaning both “The First Gateway to Heaven” and ”I en-grave Gateway I”.

We see why only one of the three master engravings bore its owncaption: Durer advocates Gateway I, not II or III. And this supportsthe “I” interpretation of Boorsch and Orenstein [?].

Another usage of “I” would also have been natural for a mathe-matician like Durer. Even in 1514, an “x primus” in a mathematicalwriting, including Durer’s, referred back to an earlier x and did notimply a later x secundus or x tertius. This is true Durer’s own math-ematics too. Then the Motto would mean, however, that Durer wassuperceding the old Gateway to Heaven with a new one, thus claiminginnovation. This would have provided the capital crime that wouldaccount for all this concealment, but Durer’s writings indicate that hedid not consider himself an innovator but a renovator stripping away

1.2. DURER THE RELATIVIST 13

the innovations made by the Church.We do not need to postulate lost engravings of the three Worlds to

explain the Motto. MELENCOLIA I itself shows all three Faculties,Worlds, and Gateways to Heaven:

For Durer, Natural Philosophy still meant making precise and beau-tiful records of nature and knowing and obeying the laws of perspectiveand structure. The Boy presumably represents the Imaginative FacultyI choosing Agrippa’s Gateway 1, the Natural Philosophy that evolvedinto Physics and Chemistry.

Gateway II is the way of Mathematical Philosophy and the Prophet,represented by the Dog. Yes, the Dog, if you find this as unlikely as Idid. More on this later.

Gateway III, the way of Theological Philosophy, is the contemplativeway of the Angel; who is mocked.

1.2 Durer the relativist

To read the messages it helps to know the writer.Durer is one of the inventors of relativity in the broad sense. This

is no anachronism, merely a recognition that relativity has long roots.Durer was famed as mathematician and philosopher as well as artist,and was one of the creators of descriptive geometry, the theory of howone object in space looks from various points of view. His descrip-tive geometry is probably the first mathematical theory of relativityin the broad sense, and it has a family resemblance to all subsequentrelativities. Durer is a significant figure in the history of the perspec-tive technique, which had been practiced by the Romans and Greeks,suppressed by the Church as deceptive, and reconstructed by the ar-chitect Filippo Brunelleschi (1377-1446). Durer traveled to Italy tofind what he called “the secret of perspective” and brought it back tonorthern Europe. Some say that his book on the subject founded themathematical theory of descriptive or projective geometry, though thistheory developed over centuries with growing rigor.

Perspective theory, special relativity, and general relativity are allbased on how light propagates, and so they share striking family re-semblances. Limbs foreshorten in perspective, rulers shorten and clocks


slow when they move relative to us or when they stand between us andlarge masses. These are all relativistic effects in the broad sense. Rel-ativists today speak of “light cones,” but Leonardo and Durer alreadyspoke of “pyramids of vision”, light cones with time omitted, made upof light paths in the space of the artist rather than light trajectoriesin space-time. Leonardo and Durer dealt with perception by posit-ing one such pyramid diverging from the point observed, like a futurelight cone, and another converging to the observing eye, like a pastlight cone. The perspective transformations of the graphic plane thatwe carry out when we shift our viewpoint, and the transformations ofobserver orientation and velocity in modern special relativity, are bothrepresented today by 2×2 matrices—tables of numbers, real or complexrespectively—making projective geometry a still useful playground forrelativists today. Durer uses his deep understanding of perspective toconstruct ambiguous puzzle pictures within the picture, presenting therelativity of perception and the existence of optical illusions as a majorlimit to human understanding.

Again, Durer relativized Leonardo’s project for a mathematical the-ory of absolute beauty, by specifying projective transformations relatingrelatively thin, medium, and plump standards of human beauty.

1.3 Durer and Leonardo

Like Leonardo, Albrecht Durer the younger began his training undera goldsmith: his father. By 1514, the date on MELENCOLIA I, hehad made two historic visits to Venice, where he studied perspectiveand human proportion and developed a passion for geometry. DuringDurer’s first visit to Venice (1505-1507), Leonardo finished the MonaLisa (1503-1506). He worked on her mainly in Florence, but took herwith him wherever he traveled, and never parted with her while helived. I will point out signs of her influence in MELENCOLIA I soit may be that Durer saw her; and in that case Durer and da Vinciprobably met. Leonardo’s influence has been remarked in other workof Durer.

Durer brings us back to many beginnings. The art critic had notyet been invented in his time. The first published art criticism was

1.3. DURER AND LEONARDO 15

the praise of MELENCOLIA Iby a young friend of Durer, JoachimCamerarius (1500-1574), who watched Durer at work, translated hisbook on human proportions from German into Latin, and at the endwrote his eulogy, declaring that although Durer’s art was great, it wasthe least of his accomplishments.

Durer may have invented the modern artist too, by charging for hisgenius, instead of merely for time and materials like a house-painter orhis contemporary Raphael.

Durer produced the first printed map of the world as a sphere viewedfrom space, and accompanied it by the first printed star-chart, whichviewed the celestial sphere from inside. He was the first to publisha mathematical proof or a book on pure mathematics in the Germanlanguage instead of Latin. He shaped the German scientific languagemuch as Leonardo did the Italian: by insisting on plain, ordinary lan-guage instead of flowery Latin, systematically weeding out the proseornaments and classical references that permeated scholarly writing inhis time.

He was a brilliant and recognized originator in his art too. His wasthe first known self-portrait and the first known specific landscape. Heinvented etching and two machines for drawing perspective.

Durer main goal seems to have been a sanctity above mere artisanryfor the graphic arts, comparable to that of the medieval quadrivium ofmusic, geometry, arithmetic, and astrology. What lifted these activitiesfrom the mundane into the divine was number, so Leonardo, Durer,and others sought to found art and beauty too on number. The GoldenRectangle, Leonardo’s famous drawing of a man inscribed in a circle,and Durer’s books on descriptive geometry and body proportions aremonuments of that quest. So is MELENCOLIA I.

To read the covert message of MELENCOLIA I it is importantto know that Durer was a Humanist in his interests in mathematics,science, poetry, and antiquity, and moved in Humanist circles. Heargued philosophy hotly and on equal terms with the famous Humanistscholar Willibald Pirckheimer (1470-1530), his best friend and landlord;and conversed with the Humanist Erasmus. He passionately criticizedcorrupt ecclesiastical practices. He ardently supported the Reformationin its first years and lamented its failings in later years.


1.4 Durer’s origins

Durer’s family background figures significantly in this engraving.In 1455 Muhammad II (Mehmed II), founder of the Ottoman em-

pire, having just conquered Constantinople, invaded Hungary, and Al-brecht Durer’s father, a goldsmith of the same name, 23, left the villageof Ajtas (or Eytas) in Hungary. Eventually Albrecht Senior resettledin Nuremberg. Ajto is Hungarian for door, Thur in the German of thetime, so Albrecht of Ajtas became Albrecht Thurer; Thurer can mean“of Door” (of Ajto) in the way that Frankfurter means “of Frankfurt”.Had he moved to England he might have become Albert Gates. Hesoon simplified the spelling to Durer, a homonym in one dialect. Hemarried his master’s daughter, Barbara Holper, and they had eigh-teen children. Three lived, the brothers Endres (Andrew), Albrecht,and Ajtas or Hanns. Albrecht, Jr. remained a Hungarian national inNuremberg all his life.

1.5 The Triumphal Arch

Durer’s immediately preceding work, The Triumphal Arch of Maximil-ian I , is intensely programmatic and ideoglyphic, and so prepares us forMELENCOLIA I. It, its key, and its clear Latin version are all availableto us. It evolved in four stages:

1. Around the fifth century, Horapollo Niliaci, an Egyptian gram-marian from Phanebytis under Theodosius II (408450 AD), claimedto render 189 hieroglyphs into plain everyday Egyptian [?]. A Greektranslation of his work, yphica, was found in the fifteenth century, andwas widely believed until, centuries after Durer, the Rosetta Stone dis-credited most of Horapollo’s interpretations, but not all.

2. In 1512/1513 Willibald Pirckheimer, Durer’s learned best friend,neighbor, landlord, Humanist, state councillor, and translator of Greekand Hebrew classics, translated Hieroglyphica from Greek into Latin.Durer illustrated this translation and it was widely disseminated. Itproviding a new graphic vocabulary that refreshed the visual arts ofEurope.

3. Pirckheimer wrote a Latin eulogy of the Holy Roman Emperor

1.5. THE TRIUMPHAL ARCH 17

Maximilian I, patron of scholars and artists and specifically of Durer,who illustrated writings of Maximilian himself.

4. Finally Durer translated Pirckheimer’s eulogy word by word intoglyphs like dogs, goats, harpies, cocks, snakes, and scepters in the cen-terpiece of the Triumphal Arch, using the Hieroglyphica as code book.For example, since Hieroglyphica states that the ancient Egyptians rep-resented a king by a dog with an ermine stole, Durer drew the goodEmperor Maximilian as a dog wearing a stole. I cannot make outwhether he did this with tongue in cheek.

The text, key, and wood-cut of the Triumphal Arch all survive. Wedo not have the clear text for MELENCOLIA I but we seem to haveall the keys.

Without the overall interpretation, it is easy to overlook significantelements in MELENCOLIA I or take them for slips. Some suggestthat Durer did not know how to spell his motto, and indeed its spellingis strange; that he did not know how to draw a cube in perspective,since the Octahedron is not quite a truncated cube; that he did notknow how to make clean corrections, and indeed there are blurs andfragments in the Magic Square.

There are well-known limits to Durer’s knowledge, to be sure. Mostfamously, the astronomer Kepler pointed out that Durer drew the el-lipse that is produced when a plane cuts a cone as egg-shaped, with theend nearer the tip of the cone smaller than the other end [?]. Thereis also a subtle error in optics in MELENCOLIA I, pointed out in duecourse. More to the point, Durer declared that there are ultimate limitsto all human knowledge, including his own. He demonstrates this inthe engraving itself.

Nevertheless, to catch his meanings we should begin by recognizinghis unparalleled power with the burin, his mathematical skill in per-spective, his dedication to precise language, and his acute observationof nature. The peculiar spelling of MELENCOLIA I, the odd shape ofthe Octahedron, and the curious blur and other anomalies in the MagicSquare, among other things, are all meaningful in his philosophy, sci-ence, and art.


1.6 Mystery

Durer could have explained his engraving for us. Leonardo made upmany riddles, and he wrote the solutions next to them, protected onlyby his mirror-writing. Durer and Pirckheimer left us the key to theTriumphal Arch; they could have done the same for MELENCOLIAI. In his essay on this picture, furthermore, Camerarius avoided all itsmany concealments. He described the Magic Square as a spider-webfull of dead flies and omitted the religious and scientific messages. [?].All this lack of openness calls for explanation.

I propose that Durer and Camererius were less than open in theirpublic expressions to avoid the stake. In their times religious thought-police persecuted both the old magic and the new sciences with accu-sations of black magic and witchcraft. Both Catholic and Protestantofficials jailed or burned people convicted of the mortal crime of “in-novation”. The Geneva city council condemned the Unitarian MichaelServetus to the pyre as late as 1553. There was ample reason for Durerand his heirs to whisper their dissent. Yet the market for this engravingwore out its copper plate. It would be surprising if its hidden messagewere not well known in its time, and if no transmission to later timestook place. At least there are negative indications of such an under-standing in the copy of MELENCOLIA I by Wierex discussed later.

MELENCOLIA I was not Durer’s first foray into dissent, moreover;not at all. In about 1498 Durer published fourteen woodcuts of theApocalypse. One of them, The Opening of the Fifth and Sixth Seals ,shows the wicked hiding from God’s vengeance. The wicked are thePope, Cardinal, Bishop, Kaiser, and Kaiserin, the top of the hierarchyof the Catholic Church and the Holy Roman Empire. Another, TheBattle of the Angels , shows the imminent execution of the Pope byan avenging angel. So by the age of 27, 16 years before the date ofMELENCOLIA I, Durer—with his master Wohlgemut— had alreadytestified against the hierarchy of the Church and publicly killed thePope and the Emperor in effigy. This verifies that Durer could expresscontroversial views in his art. It suggests that the views lurking in thisengraving were criminal, since he hid them so well that they remainedunread by scholars for nearly five centuries. We can also infer that they

1.7. THE IMP 19

would incense Protestant officials especially, since Durer had alreadyflaunted Catholic law. What was the crime of Albrecht Durer? It isnot visible on the surface of MELENCOLIA I.

1.7 The Imp

A black creature with head of mouse, wings of bat, and tail of serpentflies at us out of the engraving. It sports a Banderole with the Motto“MELENCOLIA§I” that gave the engraving its name. Since it carriesa message, it is a messenger, literally an angel, a dark one to balancethe light one on the other side of the engraving. Since it seems smallfor a demon, call it the Imp. I tentatively identified it with Agrippa.

If Durer accepted Agrippan teachings, at least for this engraving,it seems unlikely that he would represent Agrippa as a demon. TheHieroglyphica gives a less-than-damning meaning for a bat, but the Impis not a bat. Let us take it that Durer represented Agrippa as an Impin order to demonize him, both for his astrology and his adherence tothe Church of Rome. Then the Imp is not carrying a message from thedivine light in the heavens behind him but fleeing the light, seeminglybearing his motto, but actually the anagrammatical manifesto that wehave already unscrambled. If Durer is telling us that Agrippa, like thisMotto, concealed covert humanism beneath overt melancholy, then heis accusing Agrippa of hypocrisy.

1.8 The Octahedron

Durer seems to put his Octahedron—the name given this solid by Fed-erico [?] — in a place of honor. The artist stands before it and it bal-ances the Angel in the composition. Yet it is bleak and sterile againstthe Angel. One looks for a deeper significance to justify it artistically,or at least to understand its puzzling shape, which has no simple name.

A rhombus is a planar quadrilateral whose sides are all equal. Arhomboid is a closed surface formed of six congruent rhombuses. Allthe descriptions I have encountered see the Octahedron as a truncatedrhomboid with its longest diagonal vertical [?].

If it represents any of the Neo-Platonic Worlds, then its geometrical


nature and its altitude in the picture place it in Intellectual World III,the abode of Platonic Ideas and angels. The Ghosts in the Octahedronalso support this conclusion, for it puts them in philosophical Heaven.I adopt this interpretation in what follows.

If the two missing vertices of the Octahedron were restored, theywould seem to lie in a vertical line. One sees the Octahedron as asymmetrically truncated rhomboid with a vertical axis of three-foldsymmetry.

In principle, however, one cannot determine the form of a solid fromone perspective view. One can shift any surface point along the lineof sight from the eye without changing its location on the paper inthe perspective view. Therefore many solids have the same perspectiveview. The Reversing Staircase, the Necker Cube and the Cameo In-taglio famously exhibit this perspectival ambiguity. It is an importantlimit to our knowledge of the world. For example, a map of the starsgives us no inkling of how far they are.

Sometimes other cues are so strong and unconscious that we cannothelp inferring a particular solid. For example, we must see a perspectiveof a cube as a cube, and a perspective of a person as a person, eventhough intellectually we know the perspective is ambiguous. The DurerOctahedron is subtler than the illusions I have mentioned, in that theyare merely ambivalent, while the Durer Octahedron is at least trivalent:

View the Octahedron with head erect, and one sees a truncatedrhomboid.

View it with head cocked to the right and one sees a nearly rectan-gular slab with two diagonally opposite corners trimmed, cocked andcantilevered back toward the horizon.

Turn the engraving on its side, and one sees another form of Oc-tahedron. I do not recall another optical illusion that assumes threeshapes as we turn it.

Some claim to measure the angles of the Octahedron from the en-graving. This is impossible. These angles depend on implicit assump-tions that are not deducible from the engraving. This impossibility isthe point of the Octahedron. We can never know its true shape.

If one compresses the engraving vertically by a certain factor—thesquare root of the Golden Ratio—its frame becomes nearly square, and

1.8. THE OCTAHEDRON 21

the Octahedron might pass for a truncated cube; but only until oneactually juxtaposes a true cube, or a perspective of one, for comparison.

One acceptable interpretation sees a truncated rhomboid with theapical angle close to 80◦ [?]. If one juxtaposes a model of such a rhom-boid with the engraving, the match is good [?].

Before the engraving Durer made what seems to be a rough sketchof the Octahedron, though it has been recognized as that only recently[?]. The sketch shows an irregular pentagon inscribed in a circle. Theapex angle in the drawing is 79.5◦± .5◦, close enough to Macgillavray’sinterpretation.

The sketch also shows what seems to be a regular heptagon. Theirregular pentagon is inscribed in the heptagon by omitting two verticesof the seven, separated by one vertex between them. There is no wayto make a regular heptagon by Euclid’s methods, but Durer gives asimple approximation in his posthumous work on descriptive geometry.Theoretically, the sharpest angle of the inscribed pentagon is threefourteenths of a full circle, or about 77.1◦. Perhaps Durer merely copiedhis imprecise sketch, for the exact angle is unimportant for the illusion,as long as it is close to a right angle but not too close.

Leonardo had already undertaken a mathematical theory of beauty.That goal would occupy much of Durer’s later years, and result in hisworks on human proportions and on how to construct projections andperspectives with compass and ruler. Durer’s study of human propor-tions is an amazingly dry gallery of stark outline drawings of standinghuman nudes, with tables of anatomical dimension ratios to roughlyone part in a thousand.. The human measurements were to be thefoundation of a geometry of beauty, as stellar measurements were thefoundations of Ptolemy’s geometry of the heavens. Music was alreadydivine and part of the quadrivium because it was considered mathe-matical. By providing a mathematical basis for art, Durer hoped tosanctify the graphic arts as well. Possibly this belief in a mathematicaltheory of art was only one aspect of a belief in a general mathematicalwisdom, the mathesis universalis of Leibiz to come.

I propose that Durer designed the Octahedron to be multiply am-biguous, irresistibly construed as a truncated rhomboid in one orien-tation, as a truncated slab in another, and as something else from yet


another. For this reason he had to both stretch the cube and truncateit. Neither alone would have created an ambiguous solid, for we areready to see cubes in any orientation. The exact angles of the Octa-hedron are then immaterial as long as they are not too close to rightangles, which might force themselves upon our perception in any ori-entation. The Octahedron is a puzzle that is intentionally unsolvable.It does not simply show off Durer’s mathematical muscle. It declaresthat if the Intellectual World has a mathematical design, this design isinaccessible to us.

1.9 Angel

Angel-wings mean sanctity, eagle-wings fame. The sacred wings ofMELENCOLIA Ibless the hour-glass, the scales, the numeral 1 in theDurer Table, and nothing else in the picture. The Angel thus seems tobless the scientific instruments above the workman’s tools that litterthe ground. She holds a sealed book and an apparently idle pair ofcompasses. She cannot be using the compasses as compasses when sheholds them as she does, nor has she a suitable working surface.

Some commentators say that she is the spirit Melancholia herself.The Motto, the shadow on the Angel’s face, and the fist on her cheekare indeed consistent with melancholia. But the hidden motto is notnegative in mood but positive and in any case is attached to the Imp,not the Angel. Her wreath of water-cress and water-ranculus protecther from Earthy melancholia by their Water nature [?], so she cannotbe melancholy according to Agrippa himself. The Angel’s expression isalert and focused, not soft and sad. Above all her gaze is not downcast.Downcast gaze and down-turned corners of the mouth may be innatephysiological responses to melancholia, transcending culture and lan-guage, and were mandatory for portraits of melancholia. The Angel’sgaze is elevated, and her lips are not clearly drooping. The engravinghas two states, which I call MELENCOLIA I.0 and MELENCOLIAI.1. Comparing them reveals some of the engraver’s intentions. In ME-LENCOLIA I.0 there is a small upward line at the near corner of hermouth that can be read as a smile or not. The far corner lips is almosthidden by the turn of her head, so that only a trace of smile, if any, is

1.9. ANGEL 23

Figure 1.2: The Angel smiles; or doesn’t. MELENCOLIA I.1, detail.


visible there. The whole meaning of the Angel’s expression, of the An-gel as a whole, and of the entire engraving is controlled by that almostimperceptible trace of the burin, creating a high-intensity critical pointfound elsewhere in Durer’s work. In MELENCOLIA I.1 the Angel hasa darker face. The place where her lip turns up in MELENCOLIA I.0is solid black in MELENCOLIA I.1. This does not mean that she isnot smiling, but leaves it for us to decide. MELENCOLIA I.1 is moreserious in tone than MELENCOLIA I.0 but also more ambiguous.

The ambivalent smile of the Angel would seem to be Durer’s homageto the ambivalent smile of La Gioconda. Leonardo finished the MonaLisa, presumably in Florence, during the time that Durer lived andstudied in Venice. The Mona Lisa smile is wry. Her lips curl upwardmore on her left side than her right, so that the viewer oscillates rest-lessly and irresistibly between two interpretations. This is sufficientlyunusual in portraiture that when Durer’s angel too has an ambiguousexpression it is fair to look for influence. It is easy to find some once welook for it. The bird’s-eye view of background watery landscape in theMona Lisa was an innovation of Leonardo, demonstrating his masteryof perspective. Durer adopts such a perspective for the background ofMELENCOLIA I. There is no direct evidence that Durer ever saw theMona Lisa but neither is it excluded, and others have considered itlikely that Durer saw works of Leonardo. Since he had traveled for amonth from Nuremberg across the Alps to Venice to study Italian per-spective for over a year, it would have been natural to cross the smallermountain between Venice and Florence to see the great master of per-spective. The engraving supports this supposition with its distinctivefacial expression and background.

The two expressions differ significantly, however. We do not doubtthat La Gioconda smiles with at least half her lips. We see them clearly.Only what she feels puzzles us. But we can never see clearly whetherthe Angel is smiling or not. If she moved her sleeve by a millimeter orturned her head by a degree the ambiguity would dissolve. Durer posedher so that the Angel’s expression could be taken as serious or smilingdepending on the expectation of the viewer. This is not a picture of afacial expression as much as a picture of ambiguity itself.

The pose shows contemplation, as in Rodin’s Thinker, not melan-

1.10. COMPASSES 25

choly. This and her wings suggest that she is the Contemplative Facultyproper to the Intellectual World of Gateway III, Theological Philoso-phy. Let us see how this interpretation fits the rest of the engraving,and why Theological Philosophy is smiling, if she is.

1.10 Compasses

Whenever the quadrivia are personified, Geometria gets the compasses.Since the Angel has the compasses, some say that she is Geometria.In a Durer woodcut of 1504, however, The Astronomer measures aglobe with compasses under a full moon, so compasses also occur inthe Celestial World. Durer’s compasses do not define their bearer.

Some say the Angel has measured the stone Globe that lies beforethe dog. But the Astronomer studies his globe intently while the Angellooks right past this globe into space; as indeed she should if she isContemplation or Theological Philosophy and the globe is the Elemen-tal World. Lines of sight matter, especially in the work of a projectivegeometer.

To use compasses one must control both points at once, either byholding the apex or both grasping both points. The Angel grasps onlyone arm of the compass and that near the point, and she has no drawingboard or table beneath the point, so she cannot use them as compasses.If anything, she seems to be sticking herself in the thigh and smiling.Since this is absurd we must look deeper. A few centimeters will do.

1.11 Four Ghosts

There seem to be a score of subliminal faces in this engraving groupedin five quartets. Some fit into the decryption I offer but most I cannotidentify. None of the main points of the decryption I offer depend onthese subliminal images.

I call such images subliminal because they wait just below the limenor threshold of perception, and also as a subliminal reference to thelimen of Durer. They are also called secondary images. The termsubliminal itself is a subliminal reference to Durer. The root limen canmean threshold, lintel, gate, or limit. The name Durer itself can mean


Figure 1.3: Ghosts 1, 2, and 3

“man of the door” or “gateway”, and Durer presented himself that wayin his coat-of-arms. Gates and doors dominate MELENCOLIA I.

Schuster sees this subliminal face as a frightening death-head [?].But it might also be a memorial to Durer’s mother, who died in theyear 1514 of the dateline. Some see Durer’s last portrait of his motheras malicious, but it can also be seen as an accurate record of the familialamblyopia known as the Durerblick, and of the physical consequencesof bearing eighteen children and losing fifteen of them.

Three other subliminal faces lurk in the upper pentagonal face ofthe Octahedron. I looked for them only after I noticed other groupingsof faces into quartets in the engraving. I call them the four Ghosts.Which we see depends on how we turn our heads relative to the print,for our remarkable propensity to find faces in hiding is sharply tunedto upright faces.

� First Ghost is the woman in profile with her head erect, alreadymentioned.

� Second Ghost is a bearded man with his head cocked 30◦ clockwise,roughly parallel to the Ladder.

� Third Ghost appears when we stand the picture on its left edge.At the left edge of the face of Second Ghost is a vee-shaped dimple inthe stone that becomes the nose of Third Ghost.

� Fourth Ghost is a younger bearded man seen in full profile lookingto our left with his head upright, to the left of First Ghost.

I found Third and Fourth Ghosts some time after First Ghost and

1.11. FOUR GHOSTS 27

Second, but not by careful search. I inferred them on grounds de-scribed below and then found them. The poses of First Ghost andSecond Ghost are those of Durer’s last portraits of his mother and fa-ther and so perhaps they fit into Panofsky’s view that the engraving isautobiographical. Then Third Ghost might be Durer the Son. In hislast portrait of his mother, Durer shows her divergent strabismus, thefamilial Durerblick . Third Ghost seems wall-eyed too.

We have to scan these subliminal faces, also called secondary images,for some time before they emerge. They are subtle, ambiguous, andstrain our perception; especially Third Ghost. Do we see them or createthem? Most of the left edge of the face of First Ghost has almost nophysical correlate in the engraving. Durer compels us to see it, whenwe look for it, by supplying chin and forehead lines and eye and nostrilshadows, but we ourselves have to create the rest of the face.

Subliminal faces are ambiguous, lie at the edge of perception, andare eminently deniable. They are joint productions of the hand of theartist and the mind of the viewer, demonstrating Durer’s mastery ofboth media. When we see one of the faces in this quaternity we donot see the other three, mainly because they share some elements. Forexample, Second Ghost and First Ghost share an eye-pit.

We are remarkably apt at imagining faces where none are intended:in a bush, in the Moon, or in maps of the ocean floor. I may havefallen into this trap here. Some viewers see few of these subliminalfaces; others see some that I do not. Similar variations happen amongviewers of random-dot stereograms, where the images are intended.

Subliminal faces are common in Durer’s work, but scanning, digiti-zation, or lithography may create accidental ones and distort or destroythose actually there. I have dutifully tried to suppose that the sublim-inal faces in MELENCOLIA I are imaginary, and report only thosethat I cannot dispel. Durer kindly organized the faces into significantlylinked quaternities, I find.

There are famous two-valued faces, like the one called “The Ladyand the Hag.” Roger Penrose made a trivalent optical illusion, his Im-possible Triangle, any corner of which can be seen as a right angle. Iknow no other quadrivalent illusions in art, however.

Durer’s five subliminal quaternities go beyond the familiar kind of


relativity, the change in visual appearance under rotation that turns ↑into ↓. Each face appears and disappears as we merely rotate it aboutthe line of sight. To see one at all we have to be in the right referenceframe. It seems likely that the Ghosts are there to demonstrate thatperception is unreliable. Durer hides them as paper-makers hide water-marks. Our perception adjusts itself to the largest range of brightnessthat is present. We filter out distracting low-contrast background inbrightness within a high-contrast image.

Jan Wierix (1549-1615), known as the Flemish Durer, made fromscratch (so to speak) an engraving that is also called MELENCOLIA Iand is usually described as a copy [?]. Wierix actually retained almostall the superliminal content but revised the subliminal content sub-stantially. In particular, Wierix eliminated at least two faces of everyquaternity and substantially changed some of the surviving faces andother details, in a way that erased the subliminal message of Durer’swork. The Wierix Motto lacks the §of Durer’s. The erasures seemstoo systematic to be chance. Wierix read Durer’s covert message andedited it out.

Viewers of Durer’s time may well have seen these faces easily andquickly, alerted by the many subliminal faces in earlier works of Durer.We mention some as precedents and to provide practice in face detec-tion.

The most spectacular demonstration of Durer’s wizardry with illu-sion is his engraving of Der Spaziergang , or The Lady and the Gen-tleman, or Young Couple Threatened by Death. A brilliant subliminalimage of a male face forms out of and looms over the young couple.Their heads form his eyes, her arm his mouth. The gentleman’s plumedhat becomes a flaring eyebrow of the subliminal face. In this pictureDurer does not use the watermark concealment technique but a kindof bricolage. Several overt forms have to be broken into pieces by ourperception and reassembled to make the covert one.

His watercolor View of Arco has a cliff that scowls famously. Hisdrawing of the same Arco hides three such angry faces in the landscape.

In The Knight, Death, and the Devil Durer portrays the Knight asspectacularly oblivious to death and the devil, though in other suchencounters in the work of Durer, the knight engages evil in mortal

1.11. FOUR GHOSTS 29

combat. The Knight is generally said to represent the ideal ChristianSoldier described by Erasmus (1466?-1536), so virtuous that he wasblind to the evil about him. Erasmus was a revered acquaintance ofDurer.

On the other hand, Durer wrote a fervent plea to Erasmus, perhapsunsent, to join with him and Luther in battle against the “Cave ofHell” and die a martyr’s death. Erasmus remained within the Catholicchurch and worked for reform instead of applying for martyrdom. TheChristian Soldier and the unseeing Knight may both have representedErasmus himself for Durer.

In any case Durer pays the Knight a subtle tribute. Others havepointed out one of the subliminal faces in The Knight : Part of thegarment of Death forms a subliminal agonized face smashed betweenthe Knight’s two fists. The Knight may seem blind to Death but stillbattles him. A second subliminal face watches the Knight from therocks of the hillside.

Eventually, Pirckheimer tells us, the high-minded Durer would lamentthat the behavior of the Protestant clerics made even the Catholicclergy look respectable by comparison, and there is indication thatDurer never lost his high regard for Erasmus: Durer’s 1526 portraitErasmus of Rotterdam has a gleeful subliminal face high on the leftsleeve of Erasmus.

The most outrageous subliminal face in Durer’s work seems to lurkin St. Jerome in his Study. The rays that seem to emanate from Jeromealso emanate from a faint well-formed face in the shadows on his baldcranium.

These examples show that Durer’s subliminal faces are not just vir-tuosity or puzzles. They advance the story like a Greek chorus, oftentelling us how Durer felt about the subject. For example, I suppose thatthe cliffs of Arco scowled because the Humanist Durer disapproved ofpractices connected with the Arco cathedral, a vivid graphic use ofthe pathetic fallacy. The Young Couple suggests Durer and his 15-year-old bride Agnes soon after their marriage, just before Durer leftplague-stricken Nuremberg and his new bride for Italy, where he metwith their neighbor Pirckheimer. Then Death hiding behind the tree isthe plague, and the bulbous-nosed beetle-browed figure that unites the


Couple could be the powerful Pirckheimer.

1.12 Four Theologies

� The Angel’s right knee, showing a bright triangular patch in themoonlight, is also the top of a hood worn by a man, shown from headto foot.

He is the largest subliminal element in the engraving. His profile iscocked at about 45◦ to the left and he looks downward. He has a fullblack beard, an aquiline nose, Arab attire, and a black headband acrosshis brow. He will be our Fourth Theologian. His face eventually leads usto his powerful shoulder, on which Angel rests her elbow and compasspoint. His left arm reaches toward the saw/sword on the ground. Theleft foot of the Angel, where it extends beyond her robe, is also hisleft hand, and her toes indicate his fingers. In the other direction hisshoulder leads us to his torso, waist, and knees. The Angel steps onthe hilt with her right foot as though to foil his effort. Now one cansee what the Angel is doing with her seemingly useless compasses.

� She is sticking the Fourth Theologian.His right hand, which doubles as her spindle, reaches up past his

face as if to fend off the sharp point.This reminds us that Durer’s parents may have been fleeing the

invasion of Muhammad II, judging by when they left Ajtas. I am re-luctant to suggest that Durer’s Angel half-smiles as she surreptitiouslypricks The Fourth Theologian, but his Knight too seems oblivious toDeath and the Devil as he crushes one of them between his fists. Thesneering cliffs around the Arco cathedral are acts of concealed aggres-sion by Durer himself. We can cast the Angel as the ContemplativeFaculty with more confidence now that we understand her anomalouscompasses and her subliminal faces.

The Fourth Theologian is the last member of another quaternity.For another, find a lighter triangle in the shading of the dress directlybelow the Angel’s right knee, a moonlit isosceles triangle next to theface of the Fourth Theologian. Turn your head through 45◦ clockwisefrom the vertical to see this lighter triangle as a ram’s horn.

� It leads to the dark line of a mouth in the face of a man in a

1.12. FOUR THEOLOGIES 31

Figure 1.4: Four Worships. MELENCOLIA I detail.

skull-cap, seen in a full front view.He is blowing the ram’s horn, as is done on the Jewish New Year.

Call him Third Theologian.� In the same view as The Young Jew is an older and hairier sub-

liminal face in partial profile looking to the left with a hooked nose, asour expression, and the same skull-cap; call him Second Theologian.

Second and Third Theologians share an eye in shade and the ram’shorn.

� First Theologian is a dark face to the left of the others, the onlyone looking to our right, wearing a hood composed of the same part ofthe Angel’s robe as the hood of Second Theologian.

This quaternity in the Angel is hidden by both the bricolage andthe watermark techniques. Its elements belong to a larger Gestalt,the robe of the Angel, which leads us to give them a totally differentinterpretation. Again the four faces can be seen only one at a time.

We have already read the Angel as the Contemplative Faculty of thetheologians. Durer seems to say by this quaternity that her entourageincludes pagans, Jews, and Muslims as well as Christians, and thatContemplation does not lead all her practitioners to one absolute truth.

The serrated sword for which the Fourth Theologian is reaching sug-gests that in this engraving Durer associated Islam with militancy. Thisis plausible. Hungary had been mauled by both Christian and Islamic


combatants in the 15th century. The first response of Muhammad II tothe Crusades was barely stopped by the forces of John Hunyadi, whobecame a Hungarian national hero thereby. Later the Ottoman Empirewould envelope Buda and briefly reach Vienna. Since the fall of Con-stantinople was so epochal for Christianity, Durer might conceivablyhave had its conqueror Muhammad II in mind.

But since Muhammad II was more warrior statesman than theolo-gian, a more plausible original for the Fourth Theologian is the ProphetMuhammad himself. This suggests that the four overlapping faces un-der the Angel consist of an unidentified polytheist, followed by Moses,Jesus, and Muhammad, the founders of the three major monotheisms,drawn in chronological order, but from left to right. This would beproper company for the Contemplative Faculty of theologians.

Although it is possible that all these agreements are due to chance,I tentatively associate the faces of this quaternity with four Theologies.

Why all these quaternities? By repeating the pattern Durer helpsus find all his faces. Why fours and not, say, threes, I cannot say.

Subliminal faces in other works of Durer are erect. Subliminal facesincline only in this engraving, leading us to examine it from variousangles. This forces us to see the Octahedron change its apparent shape,and perceive a central message of the engraving: Absolute Truth isnot available to us, only relative truth. Here again Durer parts fromAgrippa, who finally finds Absolute Truth through his Gateway III.

1.13 Four Fools

This is a curiously domestic Angel. She is dressed as a housewife, com-plete with keys and purse hanging from her belt which Durer says repre-sent power and wealth, and she attracts Christians and non-Christiansalike. Only a fool would worship her, the artist seems to say.

� And there the fool is, a crude low-browed subliminal caricaturelurking near her feet in the hem of her gown, next to Durer’s monogram.

Call him First Fool. We must turn the engraving about 60◦ counter-clockwise to see First Fool best and then he looks to our right. His noseforms part of the bottom edge of the Angel’s robe. He has a mustacheand curly hair. He is so demeaning that I hoped at first that he was my

1.13. FOUR FOOLS 33

Figure 1.5: Four Fools 1,2 3 4

misreading, not Durer’s intention. But a powerful winged housewifewith a similar fool in her hem also resides in a woodcut attributed toDurer in the Ship of Fools of Brant [?], in Chapter 13, “On Amours”(Von Buolschaft)). There the winged housewife is Venus, the goddessof the fools of love, the most common variety of fool according to Brant.. Venus’s eagle wings signify fame. We infer that she is a housewifebecause Brant calls her “Frau Venus” and she wears a purse and keys.The caricature in her hem is crude, but since it recurs it is probablypart of Durer’s graphic language.

Evidently the Angel too is presented as a housewife, not in so manywords this time but by her purse, keys, and spindle dangling down herdress from her left knee. The Madonna by the Wall (Durer 1514) alsowears the keys and purse of a housewife. Durer seems to say that theTheological Philosophy too attracts fools.

Are the quaternities of the Theologies and the Ghosts echoed here?Let us look for more Fools.

� It is easy to see the larger face of Second Fool looking at us andslightly to our left.

Second Fool shares curled hair with First Fool.� Third Fool is looking upward and to our left and has a body, a

complete arm with a mitten-like hand at his side, a leg, and the purse


of the Angel.� Fourth Fool stands upright to the left of the others, wearing a robe

from head to ground, looking almost right at us.

1.14 Purse and Keys

The keys and purse of the Angel are the only elements in the engravingwhose meaning has been left for us by Durer. They stand for power andwealth. But while his Madonna and his Venus wear their purses andkeys at the waist, the Angel drags her purse on the ground. Likely thismeans that fiscal power profanes theology, for Durer was a passionatecritic of clerical corruption.

1.15 The Millstone

The most opaque and mysterious of the three stones in MELENCOLIAI is the stone wheel on which the Boy— the putto— perches. Panof-sky and Yates call it a grindstone and Doorly calls it a millstone. Itsperimeter is broken, its face is smooth. It would make a passable mill-stone but an oversize bone-rattling grindstone, so likely Doorly is right.This is also the only stone in the engraving that could serve Jacob firstas pillow and then as pillar, if he could raise it.

Since the stone Globe stands for the Elemental World of NaturalPhilosophy, Gateway I, and the stone Octahedron for the IntellectualWorld of Theological Philosophy, Gateway III, by elimination it wouldseem that the Millstone should somehow stand for the Celestial World,the realm of Reason and Mathematical Philosophy, or astrology, Gate-way II. This representation would have to be obvious to his intendedviewers as well. It was not to me.

Question: How is the Celestial Sphere like a Millstone?Answer: They both turn slowly about a nearly fixed axis.In olden times there were few such objects, and the millstone is the

most common. For centuries before Durer, cultures as diverse as Baby-lon, Greece, Arabia, Scandinavia, and Rome represented the CelestialSphere by a millstone. Later, Galileo would too: “Next, applying thisreflection about the millstone to the stellar sphere, ...” [?].

1.15. THE MILLSTONE 35

In a widespread myth, the celestial millstone wanders off its axis intothe sea, presumably the Milky Way. This represents the slow precessionof the equinoxes from one house of the zodiac to another [?]. Santillanaand von Dechend called it Hamlet’s Millstone because it is mentionedin passing in the legend of Ambleth, the original Hamlet, as retold bySaxo Grammaticus in the late 13th century.[?]. Saxo was first printedin Paris in the very year 1514 of MELENCOLIA I, indicating that thetrope of the celestial millstone was still alive in Durer’s day.

According to the myth, in the Golden Age the millstone ground outgold. That is, in the good old days the stars were propitious. In later,lesser times it ground out salt, making the ocean undrinkable. In ourdegraded age it produces sand and the terrible maelstrom, whose namepreserves the myth. The fault is in our stars, not in ourselves.

Saxo’s Amleth and Shakespeare’s Dane share with Durer’s Boy thethemes of melancholy, parental Ghosts, and dynastic overthrow, be-sides the millstone. This suggests that Durer and Shakespeare bothtransmuted personal grief into the Agrippan creative melancholy thatinspires great works, Durer mourning his mother Barbara, Shakespearehis son Hamnet, and that both infused their ensuing creation withSaxo’s tale of familial bereavement; whether independently or not Icannot say [?].

The Faculties are drawn as out of their proper spheres, but sincea revolution is going on in this engraving, some seating rearrangementis understandable. The seated Angel, the Contemplative Faculty, isnominally of the Intellectual World III, the highest, but Durer has putTheological and Natural Philosophy on the same ground level. Thisshould be interpreted with caution. In the usual neo-Platonic hierarchyit would demote Theological Philosophy, but the revolutionary neo-Platonism of Ficino and Agrippa inverts the value scale. In givinghighest powers to Saturn, it ennobles the Earth as well.

The Boy, as the Imaginative Faculty, is properly of the ElementalWorld I, but here he perches his rump on the Celestial World II, thehighest of the three Faculties. Durer has elevated Natural Philosophy:above Theological Philosophy on the paper; and with eyes on the samelevel according to the laws of perspective, for the line of their eyespasses through the vanishing point. The natural philosopher observes


matter in space and time, traditionally the lowest World, but therebyapproaches God. The impending scientific revolution is in the seatingplan.

The Boy watches passively and draws what he sees. We know thatDurer himself did experiments, since he invented drawing aids and etch-ing, but he has not made them part of his philosophy or his Boy. Theevangelist of experiment, Francis Bacon, has yet to be born.

The equality between the Angel and the Boy, therefore, is not theHermetic equality between the Worlds above and below, as has beensuggested [?]. The Hermetic doctrine of the Faustian magus suggestsa magical influence of the higher levels of a hierarchy on the lower. Itclashes in spirit and letter with the rationalism, Humanism, and mod-esty of MELENCOLIA I. When Durer rolls away the Celestial Sphere,he eliminates the Hermetic above and below and unifies the heavensand the earth, preparing the way for Newton. Hermetic doctrine re-lates the Elemental World to the Celestial, and becomes irrelevant whenthe celestial millstone is taken out of service. “As above, so below” maywell have been Agrippa’s credo at one time but it is not Durer’s. LikeLeonardo, Durer caricatured the idea that events in the sky foretoldevents on Earth. He prepared and published printed maps of the earthand the celestial sphere as globes. They are realistic maps of the starsabove and the planet below and indicate no similarity or correspondencebetween them. The unity of Elemental and Celestial Worlds that Durersymbolizes by rolling away the Millstone does not hark back to HermesTrismegistus but looks forward to Newton.

1.16 The Dog

The Dog was especially obscure to me from the start. MELENCOLIAI, The Knight , and Jerome each have a dog and an hour glass. Theirhour-glasses remind us that life is brief. What do their dogs mean?

The Dog of MELENCOLIA I dozes rather too close to the straightline of Comet, Octahedron, and Globe for accident. He is just wherethe Celestial World would lie in the old cosmology. Someone rolledthe battered Millstone away and leaned it up against the House andthe Dog lay down in its place. The geniuses of the Celestial World

1.16. THE DOG 37

were the Mathematical Philosophers, astrologers, statesmen, kings; theconnection of the Dog to the Celestial World was even less obvious tome than that of the Millstone. To us, dogs represent love and fidelity,to Agrippa, they represent love or flattery, but to Durer, somehow, theyrepresented the Rational Faculty of Agrippa’s World II. We may inferthis by elimination and guesswork, but we also have to understand howDurer’s viewers could have understood this on sight.

To read this Dog I first looked at Durer’s other dogs. He had drawnat least two in the year before that are still extant, in the TriumphalArch and the Hieroglyphica. The dog drawn by Durer for the Hiero-glyphica is like the one in MELENCOLIA I, and some take it for asheep.

In his Triumphal Arch Durer represented the Emperor MaximilianI as a dog with a stole, as the Hieroglyphica required. Returning tothe Hieroglyphica we learn that the Egyptians represent a prophet by adog, “because the dog looks intently beyond all other beasts upon theimages of the gods, like a prophet.” [?]. For whatever reasons, the Dogis actually a prophet, a worker of the Celestial Sphere; an astrologer.

Reading the language of Hieroglyphica is trickier than writing it. Be-sides a prophet, Horapollo’s naked dog can also represent an embalmer,the spleen, odour, laughter, sneezing, and rule. Apparently one goesby context. I think this Dog means the prophet. Others have opted forthe spleen, influenced by humoral psychology, but this does not fit assnugly. The main people associated with the Celestial World and withinspired Rational Faculty, according to Ficino, are the prophets and thekings. The Hieroglyphica represents both by dogs, naked or stoled. SoDurer obediently represented them accordingly on the Triumphal Archand in MELENCOLIA I.

The dog as the Rational Faculty of the Celestial World fits all threeMaster Engravings rather well. The dog of Jerome can sleep soundlybecause Jerome’s melancholia inspires his third Faculty, theology, nothis second, astrological prophesy. According to traditional Catholicapologetics St. Jerome did not believe in astrology. The Boy’s Dogrests with half-closed eyes because his Celestial World is out of action.The Knight’s dog runs beside the Knight because the Knight concernshimself with affairs of state, with inspired Faculty II. The Knight may


well be Erasmus, who believed in astrology [?]. Now the three dogs fitthe Three-World interpretation of the Master Engravings.

There remains the matter of how dogs come to represent prophetsfor Horapollo. Horapollo was, after all, writing about the hieroglyphs.Some hieroglyphs show gods with the head of a dog or a jackal, such asThoth, the god of writing, and Anubis, the god of embalming. Durer’sdogs might be a trace of Thoth in European culture.

1.17 Wave

Bible-searches for the Ladder, the Comet, and the Moon Bow all borefruit so following the same hermeneutic rule I looked for the Millstonein the Bible. Of about a dozen millstones in the Bible, all but two aremetaphors for livelihood or industry and refer to no other element ofthe engraving, so I put them aside. Matthew 16:6 seems irrelevant tothe contents of the engraving. That leaves Revelation 18:21:

And a mighty angel took up a stone like a great millstone, andcast it into the sea, saying, Thus with violence shall that greatcity Babylon be thrown down, and shall be found no more atall. (King James)

The engraving and this sentence of Revelation share the mighty angel,the millstone, the sea, and even melancholia, for Revelation imbeds thismillstone in a score of verses lamenting the destruction to come. Themillstone of Revelation is therefore a reasonable candidate for Durer’smillstone, and the only one in the Bible.

But now that we look at it, the millstone of Revelation is as puzzlingas Durer’s. Babylon was the great empire of the ancient world. Amore cosmic image than sinking a millstone—say, sinking a mountain—would show how great a force would destroy Babylon. A more domesticimage—say, crushing a wine-cup—would show how easily God coulddestroy Babylon. But a millstone is neither here nor there. Anyonecan sink a millstone in the sea, and it does the millstone no harm. Theangel of Revelation seems merely peeved with Babylon, if we take theaccount literally.

On the other hand, if the millstone of Revelation too were the Ce-lestial World, throwing it into the sea would be a cosmic disaster, the

1.18. FOUR DESTROYING ANGELS 39

same one as Ambleth’s millstone rolling into the sea, the wobble in thecelestial sphere that ends one world Age and begins another [?]. Nowthis is a metaphor fit for an emperor.

Any Biblical reference to the celestial millstone might have to becryptic, because it is a vestige of the Babylonian astrology that Abra-ham fled. The separation of the waters below from the waters aboveby the firmament of the celestial sphere in Genesis seems to be anotherbiblical trace of the ancient Three-World cosmology.

If Durer is referring to this verse then one might look for Babylonand its downfall in the engraving too. The engraving indeed showsa subliminal Wave destroying a port City [?, ?]. Over the left-mostpan of the Scales, through a small triangle framed by Ladder, House,and pan, a closely spaced system of fine parallel wavy lines flows frombehind the House leftward into a great Wave that looms high over thecity, about to crash down on it and wipe it out.

The Wave too is ambiguous. It can also be merely the shorelinebeyond the city, not looming over the city at all. Then the lines aremerely geological strata, not water. We cannot tell whether they arenear the city or far from one perspective view. The ladder hides con-nections that would force one interpretation or the other. If the shorehad a smooth C-shaped curve we would tend to see it as horizontal, butthe visible shoreline is oddly straight and vertical on the canvas, evok-ing our propensity to recognize vertical lines. Durer has also shadedthe Wave darker than the remote hills, to separate them. He forces usto choose between seeing this line as a vertical wave or as a horizontalshoreline on insufficient evidence.

On perceiving this I realized at last that this recurrent perspectivalambiguity was not a weakness of Durer’s art but a main point of theengraving, driven home again and again until even I could not miss it.

1.18 Four Destroying Angels

In MELENCOLIA I.0 the ambiguous vertical shoreline-or-wave-frontframed between the fourth and fifth rungs of the ladder can also beseen as a face of a man or woman. Then it is not hard to find afull quaternity of Destroying Angels of Babylon in the Wave. They


Figure 1.6: Destroying Angels. MELENCOLIA I.1 detail.

1.19. LADDER 41

are present but reworked in MELENCOLIA I.1 so there can be littledoubt that they are intentional. The most evident change is in thelip line of the leftmost Destroying Angel, whose profile is the shorelineor wavefront. With a single slant stroke of the burin Durer changedfrom a smile of Schadenfreud in MELENCOLIA I.0 , to a frown inMELENCOLIA I.1, as might better befit a Destroying Angel. Threeprofiles parallel to the first complete this quaternity. To their rightswims a fish, endorsing the wave theory.

Now the engraving and the verse of Revelation share Millstone, An-gel, Sea, Port, Destruction, and Melancholy. This also reinforces theconnection we sketched in lightly between Durer’s millstone and Ham-let’s. I infer that the millstones of Revelation, MELENCOLIA I, andAmbleth, in different centuries and continents, all represent the Celes-tial World, and that Durer’s Millstone refers to Revelation as his Cometrefers to Genesis.

The Biblical verse would have referred to the end of the Age ofAries and the beginning of Pisces. Durer must have referred to theend of Pisces and the beginning of Aquarius. Since Durer had alreadyexecuted the hierarchy of the Church in absentio in his Apocalypse, hemight have meant the same by the destruction in MELENCOLIA I.Then this picture is in the future tense, as Jerome is in the past andthe Knight in the present. This suggests how the triptych should hang.Jerome is on the right, the Knight in the center, and Durer himself onthe left, facing the future more than the past. Read from right to left,of course.

1.19 Ladder

Any artist who put an endless Ladder next to an Angel, a House, andan up-turned stone in 1514 could be sure that the educated viewer ofthe time would see Jacob’s ladder, angel, house, and stone of Genesis28. The upper end of the Ladder is unseen, so it may be in heaven,but it is surely not the ladder of Durer’s crucifixion scenes. Laddersas gates of heaven occurred commonly in earlier art, including Durer’sown. The most relevant verses are

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 Godascending and descending on it. King James Bible, Genesis28:12

And he was afraid, and said, How dreadful is this place! thisis none other but the house of God, and this is the gate ofheaven. And Jacob rose up early in the morning, and tookthe stone that he had put for his pillows, and set it up fora pillar, and poured oil upon the top of it.King James Bible,Genesis 28:17-18

So the ladder is the Gate of Heaven of Genesis and also of the coat-of-arms; another signature, through the Durer coat-of-arms. Beth El, theHouse of God, is also the legendary site of the first house of worship ofthe God of Israel. Early on, therefore, porta caeli, the Gate of Heavenin the Vulgate, became a metaphor for the Catholic Church itself. SinceDurer criticized the Church strongly, it is doubtful that he referred tothe Church here, and more likely that he recaptured the metaphor forhis own use.

1.20 House

The house too is semantically polymorphic. From up close we see twoblank walls supporting a miscellany of instruments. The side wall doesnot seem much wider than the Boy leaning against it. It seems aboutthe right thickness for an out-house or a chimney, not a house. Its frontwall extends out of the scene to the right and holds a Bell, a Table ofnumbers, an Hour-glass, and a Sun-dial. Its left edge bisects the pictureto within a millimeter or two. Its side wall holds a chemical balance orScales. The Bell-rope trails off the edge to our right. Step back severalmeters or squint and the picture changes.

� Table and Bell together become a lattice window, the Hour-glassa bay window, the Scales a side window, and the out-house a full-sizedhouse showing us three of its windows.

The Angel blesses all three windows with her wings. There is noproblem assigning them to the Three Worlds: The Scales Elemental,the Sun-Dial Celestial, the Table Intellectual.

1.21. MAGIC SQUARE 43

Assembling familiar objects from unrelated parts in this way, forexample, faces from fruits, or demons from vermin, was an optical il-lusion often practiced by artists of the era. Here there is allusion aswell as illusion. If the house is what the sanctified instruments on itswalls open into, it is the humanly perceptible universe, the physical cos-mos, Agrippa’s Book I. The Ladder and the Angel have already told usthat this is also the House of God, and the instrument-windows tell usthat music, measurement and arithmetic look into it. Leonardo wrotethat knowledge comes from experience, and Durer draws what Agrippawrites, that scientific experience leads to God. This juxtaposition ofscience and religion is inconsistent with Church teaching of the time,which provides only one Gateway to Heaven and Absolute Truth, butit is consistent with Durer’s known Humanism.

1.21 Magic Square

The Table of numbers set into the masonry wall in MELENCOLIA Ilike a window lattice is a magic square, meaning that it is filled withconsecutive numbers starting from 1 and every row, every column, andboth main diagonals add up to the same number. In a 4 × 4 magicsquare that number must be 34, one quarter the sum of the integersfrom 1 to 16. This is a gnomon magic square, meaning that besidesbeing magic, its four quadrants, its four corners, and its central squareadd up to the same number as the rows and columns.

Usually a gnomon is a pointer or indicator, especially of a sundial,but a carpenter’s square and the figure made by removing one quad-rant of a rectangle were also called gnomons, presumably because theytoo look like a pointing hand. This magic square is called gnomon, Iimagine, because removing a quadrant leaves a figure that resembles acarpenter’s square. In addition, the sum of any pair of numbers sym-metric about the center of this square is 17.

In his Occult Philosophy Agrippa assigns a magic square—then calledsimply a table — to each of the seven “planets” then known, in the an-cient order of Saturn, Jupiter, Mars, Sun, Venus, Mercury, and Moon.This is the order of their apparent periods about the Earth; in the geo-centric system the Sun acquires the heliocentric period of the Earth.


He gave each table in both Arabic and Hebrew numerals. These magicsquares have ninth century Arab sources [?] but may be older.

Agrippa omitted the 1-by-1 magic square [1] — reserving it for God?— and there is no 2-by-2 magic square, so the Table of Saturn is 3-by-3, the Table of Jupiter is 4-by-4 and so on to the 9-by-9 Table of theMoon. The number of Jupiter is then 1 + 2 + . . . + 16 = 136, as thenumber of the Sun is the 1 + 2 + . . . + 36 = 666 of biblical fame,raising the possibility that the nine planetary tables are older then thebiblical passage about the Number of the Beast. Agrippa warned thatunshielded Saturn caused acute melancholia, a clinical mental illness,and prescribed wearing Jupiter’s Table as shield. Agrippa proved thevirtue of Jupiter’s Table by gematria, a Hebrew numerology based onthe fact that any letter of the Hebrew alphabet is also a number andthat therefore every Hebrew word has a number, the sum of its letters.He used gematria to find reassuring Hebrew words in Jupiter’s Table.

As a child I wondered why such squares were called magic. TheOccult Philosophy answers this question: They were used as magicaltalismans. For example, Agrippa prescribed wearing the Jupiter Ta-ble to ward off the melancholy influence of Saturn. Some say Durerborrowed Jupiter’s Table from Agrippa [?, ?]. But Jupiter’s Table andDurer’s Table are different: Durer performed permutations on Jupiter’sTable that left it both magic and gnomon in the arithmetical sense. Heinverted it and he interchanged the two middle columns. Why did hedo this? Such changes by the artist are both puzzles for us to solve andclues to the solution.

The Bible, Agrippa, and Horapollo desert us here. But there is aplausible reading: thanks to these permutations, Durer’s Table echoesthe date-line below. Durer’s bottom line is 4 15 14 1, the date 1514of the engraving, flanked by Durer’s initials in Latin gematria, theA = 1, B = 2, . . . code. Durer’s transformation trivially leaves thesquare magic; that it leaves it gnomon, however, is a special propertyof this Table. It tells us something about Durer’s mind that he sawthis possibility in the Jupiter Table.

And we experience the gap between his thought and ours in thefact that he looked for such numerological possibilities. It transportsus to an era before the Newtonian concept of a mathematical theory of

1.21. MAGIC SQUARE 45

Figure 1.7: Durer’s Table (version 1)

4 14 15 1

9 7 6 12

5 11 10 8

16 2 3 13

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

Jupiter’s Table Durer’s Table


nature. I diffidently suggest that for Durer this kind of accord betweenthe Table above and the monogram date-line on the rock below was anintimation of an accord between divine mathematics above and secularreality below, a goal for the Natural Philosopher. It is his glimpse intothe future through Gateway I. The examples of a mathematical theorythat he could build on, like the Pythagorean musical scale, Ptolemaicastronomy and his own descriptive geometry, aimed at such arrangedmatches between mathematical and observed harmonies, not just pre-diction. Galilean and Newtonian ideas of a law of motion were still acentury in the future; we should not expect them of Durer.

The 5 in the Magic Square has a puzzling background. There seemto be two numbers superimposed. Most say that Durer made an im-perfect correction. We search MELENCOLIA I.1 in vain for traces ofthe alleged error that Durer made in MELENCOLIA I, clearly Durerknew how to make clean corrections. It is safer to ask what he wishedto convey by this blur.

In fact such blurring image-duplication was used at the time toconvey motion. The horse of the Knight has two hoofs on one foot; thespinner in the Velasquez painting Las hilanderas (The Spinners, circa1657) has six fingers on one hand. The fingers and hoof are the mostrapidly moving elements of their pictures, the artist duplicated them toshow this. Xeno taught that something in motion cannot have a definiteposition; Durer and Velasquez believed him. They show motion in astatic medium by putting the object in two positions.

Therefore the duplicated 5 is probably spinning in its box. This isconfirmed by the fact that the foremost 5 is upside down and the dimhindermost one is upside up. Our three sources have not yet explainedthe meaning of this motility to me; but Agrippa, the most likely source,has many volumes. It is too easy to find meanings for it; the questionis what Durer meant.

Other characters in the Magic Square are significantly distorted.The 5 in the number 15 is more like a capital S. Both sixes in theMagic Square are actually the medial form of the lower case S still inuse in Durer’s time. The inverted 5 has a minute but clear serpent’shead, jaws gaping and forked tongue protruding. These will be easierto read after we compare the two states of this engraving.

1.22. MELENCOLIA I.1 47

1.22 MELENCOLIA I.1

The two states of MELENCOLIA I differ in many ways, most conspic-uously in the fine details of the Durer Table. In MELENCOLIA I.0 ,displayed on the internet (for example) by the Fine Arts Museums ofSan Francisco, the numeral 9 in the Magic Square differs from Durer’susual 9 by a wriggle in its tail that makes it more like a question markthan a numeral. In MELENCOLIA I.1 however, shown on the internetby the British Museum, the 9 is reversed, more S than 9.

There are several changes in the faces too. In MELENCOLIA I.0the left side of the Angel’s lips (our right) ends in an upturn, eitherof the lip-line or a sleeve-line. In MELENCOLIA I.1 this part of theengraving is simply blackened. MELENCOLIA I.1 also reworks someof the robe of the Angel and the Wave. I return to these changes andothers in due course, since they indicate Durer’s intentions.

1.23 Door

Then there is the curious matter of the door to the House. The Housethat we see as we step back has several windows but nowhere do we seea door. When the Door-man draws the House of God without a door,we should pay attention. He is likely making a statement.

It seems to repeat the major melancholy statement of the piece.The House of God has no doors, we can look in but we cannot enter.Absolute truth is inaccessible to humanity. The ladder is presumablyfor the angels.

The inaccessibility of absolute truth was a common idea by Durer’stime. It was taught by Nicholas of Cusa and Erasmus, already cited,and would reappear in the writing of Vico in the next century. Durercould expect viewers to make out this message at first sight. BeforeDurer did this engraving he had already written that the human mindcannot know absolute beauty. In this picture he seems to be sayingthe same thing in several ways. We must not assume that he separatedtruth and beauty as cleanly as some claim to do today, especially sincehe expected a mathematical theory of both. When science is supposedto consist of mirroring nature then Durer’s rabbit and Audobon’s birds


must count as great science as well as art.

1.24 Boy

� The Boy’s writing instrument has a crossbar at its top, and so is nota stylus or a piece of chalk as some say, but a graver, the celestial burinagain. His block is therefore not a slate but a copper sheet, or possiblya block of wood. He is engraving, not drawing.

The Boy’s eyes are disturbing under magnification. I cannot seethem as both looking in the same direction. His left eye could belooking toward the Globe, while in MELENCOLIA I.0 a ring of whitein his right eye gives the strong impression that the Boy looks directlyas us with that eye wide open. MELENCOLIA I.1 changes the ringof white into a more naturalistic crescent of white, but the Boy is stilllooking outward with his right eye and downward with his left.

Durer himself had amblyopia. The Boy then carries two distinc-tive attributes of Durer, his burin and his amblyopia. Durer drew hismother’ wall-eyed, like Third Ghost, but the Boy is cross-eyed.

As Panofsky said, Durer meant this work to show many aspects ofhimself. As Yates said, the Boy is Durer at work in the creative frenzythat melancholia can inspire in the divinely gifted artist [?]. But hisBurin and his strange eyes indicate that he is not a generic starvingartist scribbling meaninglessly on a slate after all [?].

The Boy is the central figure in several senses. The geometric centralaxis of the engraving is the vertical defined by the leftmost edge of theHouse. It passes almost exactly through the nearest eye of the Boy, acommon way to indicate centrality in Renaissance art. The line of thecomet suitably extended also strikes the Boy’s left eye.

Yates suggested that the Boy Durer is engraving MELENCOLIA Iitself in a self-referential way. The Boy’s copper plate seems too smallfor that suggestion to be taken literally, and it does not fit the Three-World cosmology. In the tripartite psychology of the times, the artist’sspecial Faculty is the Imaginative one, that of the Natural Philosopher,so the Boy represents Natural Philosophy and the Imaginative Facultytoo, as the Angel represents Theological Philosophy. Then he shouldbe looking at the Globe, the world of the four elements in space and

1.25. FOUR FRIENDS 49

time, as Gateway I requires. And so he is; at least with one eye.According to this theory, Durer has represented himself with his

rump on the Celestial Sphere. I cannot read this as a sign of respectfor Mathematical Philosophy, which was then mainly astrology, as aGate of Heaven. It rather reinforces the message of the anagram, rec-ommending Gateway I, not Gateway II or III.

1.25 Four Friends

� if we cock our heads about 30◦ to our left, we can see or imaginean erect face peering from behind the Boy, in the part of the blousebillowing out between two straps.

I call him First Friend. His head is bounded on our right by thecurve of the Boy’s gown between the straps and is looking downwardtowards the viewer’s left. The Boy’s gown, where it passes over theMillstone, forms two near right-angles that look like a small book, andFirst Friend seems to have a hand on it. That and the robe trailingbehind him make First Friend look clerical or at least scholarly.

First Friend too is part of a possible quaternity in MELENCOLIAI.0 that Durer substantially reworks in MELENCOLIA I.1.

� To see the profiles of Second Friend we should stand the engravingon its left edge. The fringe of the Boy’s garment then becomes the profileof Second Friend.

� Third Friend is the Boy’s left upper arm.� In MELENCOLIA I.0 Fourth Friend is the Boy’s right lower leg.� In MELENCOLIA I.1Fourth Friend is a smaller better-formed

head set into the Boy’s right knee, touching the Boy’s engraving block.

1.26 Scales

On the side wall of the House hang a pair of chemist’s scales. Extended,their lines pass through the vanishing point, so the Scales are balanced.Perspective causes the line of the pans on the paper to slant slightly up-ward toward the vanishing point, and the line of the suspension slightlydownward. One pan brushes the Boy, the other the Angel. I think wecan say that Durer has established a balance between Natural Philoso-


phy and Theological Philosophy, unlike Agrippa’s fideism. The line ofthe eyes of Boy and Angel also goes through the vanishing point. Theyhave exactly the same altitude, that is, holiness.

1.27 Globe

Chance governs the Elemental World, mathematical law governs theCelestial World, divine law governs the Intellectual World. Durer’sgoddesses Fortuna and Nemesis both stand on globes, liable to roll inany direction at any impulse, because Luck and Fate are unpredictable[?]. Therefore Durer chooses a Globe to represent the Elemental World.

It is indeed the lowest of the three stone objects in this picture, asit should be if they represent the Three Worlds. Durer, like Nicholasof Cusa and Leonardo, replaced the naive tri-spherical geocentric Neo-Platonist cosmology by a tri-partite philosophy with three Facultiesand Worlds that are no longer geocentric, concentric, or even places atall. And here he has retired the Celestial World.

1.28 Moonbow

I have never seen a moonbow but again NASA provides the picture andthe Bible provides the caption.[?] is an on-line gallery of portrayals ofheavenly phenomena like moonbows and moon halos, including severalfrom Durer’s time. The only bow in the Bible sky is the “bow in theclouds” that Noah saw after the flood, a supreme example of divinerevelation, direct communication with divinity. Genesis does not saywhether Noah saw his bow by day or by night. Durer had no choiceonce he set the scene in the dark of night. In Genesis , the light in theheavens and the bow in the clouds represent two of the great gifts ofGod, so the picture should be joyous, and yet it is dark and ambiguousagain.

The viewer of any moonbow or rainbow lies on the normal to theplane of the bow that passes through the center of the bow. Durer’swatching eye should therefore lie directly before the horizon point be-neath the highest point of the moonbow. This is not exactly where heis located by the vanishing point of the building lines, which is under

1.29. COMET 51

the eye of the Imp, but it is only about a centimeter off.When we look directly at a bow in the clouds, the light source must

lie directly behind us, and very likely Durer knew this from personalexperience. The artist is standing before the Imp, a bit to the leftof the center of the Bow. Therefore to make such a bow the moonshould be behind him and slightly to his left. But according to theshadows on the House and the face of the Angel the moon is behindthe artist and well to his right. This optical inconsistency seems tohave no meaning, but we need not try to believe that Durer made amistake in his depiction of nature. Had he followed natural law thebow would have been far out of the picture to our left. He wanted toshow shadow on the Angel’s profile to at least suggest melancholia, andGod’s promise in the sky to express faith and inspiration, a physicallydifficult or impossible combination in any one view. I suspect that hedeliberately sacrificed optical truth for a greater artistic one, knowingthat few would notice or care.

1.29 Comet

Though it lacks the curved tail of the most traditional renderings thebright Comet in the sky is a comet, not a nova. The NASA onlinecollection of astronomical photographs shows comets quite like it. Acomet is straight when it heads for the sun and sunlight pushes its tailout behind it.

The great comet 1471Y1 was first seen on Christmas Day in Durer’sbirth year, and Durer wrote of seeing a comet himself in 1503 [?, ?].The physical natures of meteors and comets were not yet known in1514. Leonardo believed, and Galileo would still believe in the nextcentury, and our very words still reflect their belief, that meteors weremeteorological, weather of the high air, and comets too.

Since the Bible has already explained other elements of the picture,let us search it for this one too. The answer is swift and unique. Theterms “comet,” “shooting star,” and “falling star” do not appear. Thereare three cases of a star that falls in Revelation, but they do not fit thepicture especially. The only blinding light in the biblical sky is theoriginal light of the divine creation. Then the starless sky would recall


the time in the Bible story between the creations of light and the stars.The Comet would then represent divine creation and divine revelation.

The Hieroglyphica has no comet, but it has a star, another glyphfor God. I see no way to decide whether Durer had Revelations inmind or the Hieroglyphica when he drew the Comet/Star, but the twointerpretations are consistent, even mutually supportive. The comettail points quite accurately at the Boy’s head. This suggests that Godis singling him out for illumination, above the representatives of theother two Gates to Heaven; and presumably his viewers would see itas an emblem of the Reformation doctrine that divine illuminationrequires no priestly intermediary.

The Creation is a joyous occasion: Happy birthday, universe! Thenews is good but the tone is somber. The tension grows. And so doesthe ambiguity. This is a realistic comet. Nothing in the picture compelsus to see it as a symbol.

It took me some time to proceed further with this engraving evenwith all these clues, because I could not figure out whether Durer’sGateway to Heaven was mathematical or religious in nature. This is agood example of the kind of projection to avoid in such a study. Firstof all, Durer does not separate science and faith. On the right theyentwine in the building and ladder complex. On the left, there is anunnaturally straight line from the comet or the light of God throughthe Intellectual World of Mathematical Philosophy to the heart of theElemental World of Natural Philosophy.

The Celestial World is not on that line, however. It is old anddamaged and out of service. The Dog remains, idle, dozing. Durergraphically reduced the three Worlds to two in this engraving. AsLeonardo had explicitly said, the terrestrial and celestial worlds are runby the same laws, and are actually one. The Hermetic doctrine was,“As above, so below” but Durer – and possibly Humanist philosophy –dissolved the absolute separation between above and below. The newastronomy saw Earth and stars as made of similar stuff governed bysimilar laws.

1.30. HEXAGRAM 53

1.30 Hexagram

Durer was a descriptive geometer, practiced in constructing views ofbodies from all sides and in reconstructing a body from its views. Itherefore looked at the Octahedron from all sides, searching for hismeaning. He likely did the same, for he invented the representation ofsuch polyhedra as nets of polygons [?].

� The ground plan of the Octahedron viewed as a truncated rhom-boid from a certain viewpoint is a Shield of David framed in a hexagon.

The top and bottom triangles of the Octahedron project into the twocrossed triangles of the hexagram. Perhaps Durer 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 Jewishstar and to infer any philo-Semitism. Centuries earlier the Khazars ofthe Crimea had adopted the hexagram for their flag when they adoptedJudaism, but in 1514 Nuremberg the hexagram was still mainly a mag-ical device, an amulet and talisman, possibly referring to the Hebrewsof the Bible but not to contemporary Jews[?]. The Shield of Davidwas called that because it was supposed to shield its bearer from evilspirits, and it was more often found in churches than synagogues. Atwo-footed hexagram like Durer’s ground plan is seen on a Germanaltar of Durer’s time. Some said the the Seal of Solomon was the hex-agram, and others the pentagram. Traditions firmed later that gaveSolomon only five points to David’s six, and stood Solomon’s star ontwo points but David’s on one. Not long after Durer’s death the Jewishcommunity of Prague was granted the privilege of a flag and chose thehexagram, already associated with the Khazars, and this continued itsevolution from magic charm to Judaic symbol. If Durer used it, it waslikely as a Hebraism, not philo-Semitism.

Hebraisms are conspicuous in the works of Durer and Agrippa. Hu-manists like Durer admired Jerome above the other founding fathersfor Jerome’s greater familiarity with the Hebrew Bible [?]. In his sev-eral drawings of Jerome studying Latin, Greek, and Hebrew Bibles,Durer invariably placed the Hebrew Bible above the others, and higheris holier. His stereotypical caricature of the Second Theology corrob-orates that the Hexagram beneath the circumcised rhomboid was not


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Figure 1.8: The Hexagram in MELENCOLIA I

philo-Semitism but Hebraicism. It connects the Intellectual Sphere, theHeaven of Humanism, represented by the resulting Octahedron, withthe Hebrew Bible, as Agrippa did.

1.31 Space

Durer uses the vertical dimension on his plate in a traditional way.Higher is holier. Jacob’s angels get to heaven by ladder. Angel andBoy have equal divinity because they have equal altitude. The toolsand nails of artisans are on the ground because they are mundane,belong to the Elemental World, while the instruments of science andmathematics hang nearer to the sky because they are holier, belong tothe Intellectual World.

It is doubtful that Durer grounds the tools to disrespect them. Ifthe cross is holy then so are its Nails, and they are there among thetools. Rather he elevates the Elemental World as Agrippa elevates theplanet Saturn and its Humor to the highest status. Durer puts hisfather’s Crucible in that World, and himself too, as the inspired artist,the Boy.

The horizontal dimension is cut in half by the left-most wall of theHouse. Because the viewpoint is on the far left, it is not obvious at firstthat all three Worlds of the cosmos and all four actors in the drama areto the left of the dividing wall, and the House of God and the Bell-ringer

1.31. SPACE 55

are to its right.The division of the space of the scene by the median plane seems

meaningful and non-random enough to be Durer’s intention. The pointof view of the artist on the extreme left masks this clean cut by dis-tributing elements of both halves of space on both halves of the paper,but all the Biblical and Intellectual elements are on the right-hand sideof the median wall, and all the tools and nails are on the left-hand side.

The weighing Scales are ambiguously located, hanging on the divid-ing wall itself. This detail fits our interpretation. Space and time wereimmaterial and therefore considered spiritual. Mass—“body” is theroot meaning — was material, not geometrical and therefore not spiri-tual; it was not defined in terms of space and time until four centurieslater, by Albert Einstein. For Durer mass belonged to a lower Worldthan time, and perhaps to the natural philosopher, not the theological.I suggest that this is why the scales are to the left of the House of Godbut not the hourglass or bell.

The crucible is no exception. If it were an instrument of alchemicalscience, as I thought at first, it would be elevated, but it is on thestone floor, so it is merely a tool of the goldsmith. Only perspectiveputs it high on the paper, above all other tools; perspective and filialfeelings. This is further indication that Doorly read this correctly. Thiscrucible is not an alchemical instrument but a remembrance of Durer’sgoldsmith father, who died in 1502. Its position to the far left gives usone point on the time axis. The House of God puts Biblical times onthe right.

The Octahedron is as opaque as stone. Durer shows it hiding thelight of Heaven from the inhabitants of the Elemental World, the Globe.The opacity of the Octahedron in the left-hand side of the pictureis a counterpart to the doorlessness of the House on the right-handside. Neither mathematical nor theological philosophy can bring usknowledge of absolute beauty-truth.

The division of the picture by time agrees with its division by Gate-ways, since Durer took the occult philosophy represented by the Impon the left to be later than the theological philosophy and Scripturerepresented by the House on the right.

The near eye of the Boy lies on the center line of the paper, making


him the center of attention, but he too is left of the median plane.Durer the artist-scientist takes Agrippa’s Gateway I to Heaven, not hisGateways II and III.

Perspective provides a third dimension of depth into the scene alongthe line of sight. Durer seems to use this expressively too. On the rightside our view ends in the House and on the left there is an infinite vista.It seems that perspective depth in the picture is the familiar metaphorfor depth of vision.

1.32 Bell-ringer

All the mortal creatures in the engraving are on the left-hand side ofthe median plane. The only one on the right-hand side is the Bell-ringer, off stage, invisible. There can be little doubt about Who ispatiently, patiently holding the bell-rope, as though conducting theHarmony of the Spheres, and not to be graven. Perhaps Durer foundmore truth/beauty in this invisibility than in Michelangelo’s Cistinevisualization.

1.33 Melancholy

The light and the moon-bow and even the destruction of the city ofevil are good news, cause for joy, and yet the picture is set in thegloom of night. Durer has even transformed the rainbow of the commonunderstanding into a moonbow. The comet illuminates nothing. Onlythe moon behind us lights the scene and creates the shadows and themoonbow. What might have been a sunny prophesy for Leonardo isdark as night for Albrecht Durer.

While Leonardo and Durer were both mathematically ambitious,they differed importantly in their outlooks. Leonardo wrote confidentlyof “a complete knowledge of all the parts, which, when combined, com-pose the totality of the thing which ought to be loved.” Leonardo wasthe rational optimist. Durer on the contrary said shortly before thisengraving, “But what absolute beauty is I know not. Nobody knowsit but God.” The darkness and the multiple ambiguities suggest thatafter all Durer did not expect humanity to attain the supreme mathe-

1.33. MELANCHOLY 57

sis that optimists like Ramon Llull expected, and even claimed to haveattained; and that he felt this as a great bereavement. He expressedthis pessimism in the engraving atmospherically, and by omitting thedoor of the House of God, and by numerous skillful demonstrations ofambivalence and relativity.

The most unambiguous aspect of this engraving is its ambiguity.Durer tells us clearly that we cannot know anything clearly. The Oc-tahedron is a truncated rhomboid with vertical axis, or a slab tiltedtoward the horizon. There are four subliminal faces in the Octahedron,or none. The city is to be destroyed, or not. The Angel is sad, orsmiling; the Imp is good or evil. The house has windows, or not. Themelancholy is sadness inspired by the inaccessibility of absolute beautyand the fall of the Celestial World from its axle; or it is creative frenzyinspired by Saturn. What we see depends on us as well as where welook. The elements of this engraving that I have discussed here aredeliberately ambiguous in meaning or form or both.

What can we believe if we cannot believe our eyes? This question-ing occurs famously in the First Meditation of Descartes (1596-1650),who cites optical illusions as a first reason for his method of univer-sal doubt. MELENCOLIA I anticipates this Cartesian doubt. AndDurer’s response to this doubt has a mathematical element that antic-ipates the Mathesis Universalis of Descartes, but already corrects it byaccepting the limitations to human knowledge.

The ideal of a complete mathematical theory of beauty lies on thesame long line of distinguished fantasies of mathematical wisdom as thenumber mysticism of Pythagoras and Plato, the Ars Magna of RamonLlull (whom Agrippa studied) and Giordano Bruno (who studied Llulland Agrippa), the vision of Mathesis Universalis that Descartes andLeibniz shared, and the Ars Combinatorix of Leibniz. Durer does notdeny the existence of absolute beauty/truth but despairs of knowingit. The Boy withdraws from both theology and astrology and observesNature.

Years after 1514, Durer like Agrippa explicitly abandoned the searchfor absolute truth and beauty as futile and hopeless, crying out,

“The lie is in our understanding, and darkness is so firmly in-trenched in our mind that even our groping will fail” [Panofsky


1971].

Durer expressed his pessimism about attaining absolute truth in hisengraving some years before he put it into writing.

The night of the engraving is our benighted ignorance. Its darknessis the darkness “firmly intrenched in our mind.” The mystery of theOctahedron, crafted to be insoluble, is one of many metaphors in theengraving for our inability to see the Absolute Truth from our limitedperspective. His chosen Gateway in Heaven is Natural Philosophy, inspite of its limitations. In acknowledging the limits of human knowl-edge, however, Durer took a step toward modernity beyond the moreoptimistic Leonardo.

The posthumous publications of Durer on measurement and on hu-man proportions show that he never quit working toward a mathe-matical theory of beauty and truth based on measurement rather thanabstract speculation, but his concept became more relativistic, to thedegree of including a variable horizontal scale-factor transformation inorder to represent human beauty of the lean, average, or plump varietyas the reference frame of the artist requires.

Agrippa inverted the primary meaning of Melancholia just as Ho-rapollo inverted the social status of the dog, the bat, and the serpent,making the lowest the highest. By using the ephemeral and counterin-tuitive languages of Agrippa and Horapollo, Durer defies our ordinaryrules of interpretation, making the work surreally ambiguous but alsocontributing to its remarkable endurance. This melancholia does notlead to death but to its transcendent opposite, a form of immortality,exhibited by the engraving itself, vibrant after five centuries. Actuallyno one in the engraving is merely sad. The overall darkness of the en-graving expresses Agrippan melancholia, not pure depression but alsocreative ecstasy, perhaps not just of the Boy but also of the Bell-ringer.

Durer records that when he made a present of MELENCOLIA Ihe sometimes accompanied it with Jerome, but never with the Knight .This pairing makes sense if the recipients were Protestants. For obviousreasons, Protestants could venerate Jerome but not Erasmus. Jeromehad criticized clerical corruption to the point of endangering himself,was a celebrated Hebraist, and was a close friend of Origen of Antioch,who is said to have held the Universalist doctrine, anathema to the Ro-

1.34. FLOURISH 59

man Church, that ultimately everyone is saved. Erasmus, on the otherhand, remained loyal to the post-Nicean Roman Church and believedin the value of astrology as a hermeneutic art [?]. This theory requiresonly that Durer gave the prints in question mostly to like-minded peo-ple.

1.34 Flourish

A certain Flourish separates the two words “MELENCOLIA” and “I”of the banderole, a stylized S that I render as §.

In 1604 the Flemish engraver Jan Wierix made a version that isusually called a copy. He omitted some subliminal elements altogether,modified some into fiendish masks, converted the entries in the DurerTable to mere numerals, and deleted the significant §, apparently cre-ating a bowdlerized version fit for pious Protestant viewers.

The same flourish stands before the Knight’s dateline and appearsin reverse following the date in Durer’s 1504 “Adam and Eve”. Likelyall three have the same meaning. Perhaps it is reversed in one case sothat it always faces what it modifies.

The numbers in the Magic Square are determined by its 4 × 4 sizeand the date line 1514. Once the bottom line is chosen the rest is nolonger under Durer’s control and so probably carries no information.However Durer still controls the orthography of the numerals. Actuallythere are eight orthographically deviant numerals in the Table of eachversion by Durer, and only one in the Wierix version. Seeing them iseasy now because they call attention to one another:

� The numeral 1 that stands by itself is brushed by the Angel’s wing,and enlarged and elevated relative to all the other 1’s, as though blessedby the Angel.

� The 4’s are not only numerals but also palm leaves folded intocrosses.

� Both 5’s are inverted [?]. Durer ordinarily makes his 5 as we dotoday.

� One 5 has circular striations and a faint image of a numeral inits background.

� The two 6’s are more open and overhanging than Durer’s usual


6’s, more like σ’s than 6’s.� The 9 is open and curly in MELENCOLIA I.0. Its lower end is

sinuous, with two bends more than the the usual 9. Durer ordinarilymakes his 9 as we do today.

� The 9 in MELENCOLIA I.1 is reversed [?], more like a sigmathan a 9, and is less sinuous, but still has a serpentine reverse curve inits tail.

� The 0 in MELENCOLIA I.1 is a serpent with its own tail in itsjaws. The 0 in MELENCOLIA I.0 has less detail.

Durer’s precision suggests that these small variations are significantand require interpretation.

When an S appears before a date in Durer’s work, it stands forSalus , or Salvation [?]. Durer prefixed the dates of the Knight and ofthe 1504 “Adam and Eve” with S’s as if to say “In the year of God1514” or “1504”. The S also occurs in reversed form as the Flourishfollowing the date in“Adam and Eve”.

The Greek alphabet has three forms of our S, the medial (and ini-tial) form σ, the final form ς, and the capital Σ. Two lower-case formsoccur in early English manuscripts and printing. Today the final formhas replaced the medial, but both forms are still in common use inDurer’s time and both occur in Durer’s own writing in (say) the ban-derole of his drawing Orfe der erst Pusaner . The prefix to the date ofAdam and Eve is S. The variant forms of the numerals 5 and 6 in theMagic Square can be read respectively as forms of final S and medial S(approximately, σ). One has the eyes and tongue of a Serpent profile,another shows a Serpent’s face head-on, so each refers to God twice,once as abbreviations for “Salus” and once as the Serpent ideogram forGod found in the Hieroglyphica. The two variant 5’s and the Flourishin the banderole are instances of the medial S. The two variant 6’s areσ’s, which are also medial S’s. Durer’s form of S before the date 1504in Adam and Eve is the one most convincingly similar to the 6’s in theSquare. The variant 9 is a reflected form of the final S, and deservesspecial attention. The otherwise mysterious variant of 9 after the name“Albert” in Adam and Eve may be seen as the medial s in the lowerleft-hand corner of the plaque, overturned.

I propose to read all these occurrences of S as salus or salvation, like

1.34. FLOURISH 61

the Knight’s S, and even as “God”, especially when they are serpents aswell. Their meanings are further modified by context. The 9 followingAlbrecht’s name in Adam and Eve would then be another claim ofpersonal divinity.

The 1 in Durer’s Table and the “I” in the Motto are likely synony-mous, the Flourish in the Motto serving like the Angel’s wing in theTable to show sanctity. The Flourish in the anagram then declares thesancity of Gateway to Heaven I, Natural Philosophy. This was capitalheresy.

We thus cover all 10 graphic anomalies in “Melencolia I”, plus one inthe “Knight” and two in “Adam and Eve” with one hypothesis: Theydepict God. Combined with the Wave and the twenty subliminal faces,they make “Melencolia I” densely pro-science, pro-art, pro-religion, andanti-Church.

As though to verify this interpretation, Jan Wierix in his 1605 ver-sion of MELENCOLIA Isystematically modified Durer’s work:

He eliminated the ambiguous Wave. He deleted the Flourish. Hereduced the magnification and elevation of the solitary 1 in the MagicSquare. He flattened the 4’s and eliminated their folds, so that they areno longer solid crosses but mere numerals. He corrected the 5 withinthe date in the Magic Square. He corrected the 6 not touching the datein the Magic Square. He retained the variant 5 touching the date inthe Magic Square like the S of the Knight. He retained the variant 6prefixed to the date in the Magic Square like the S of the Knight. Heretained the variant 9 before the date in the Magic Square.

Wierix thus stripped the engraving of six heretical subliminal ele-ments and retained two conforming ones. The subliminal versions ofthe covert message are gone. Even the anagram has been cleansed.This suggests that he wished to make a version suitable for ProtestantFlanders. If we suppose that he could have eliminated each of thesenine features as likely as not, the probability of doing all this by chanceis 2−9 = 1/1024.

Wierix also modified the subliminal faces. He almost eliminated allfour Ghosts, replaced the quaternity of Friends by one cadaverous face,and eliminated First Theologian, the skull-cap of Second Theologian,and First Fool. No quaternity or trinity remained when he was through.


He also eliminated the ambiguous smile of the Angel. His Angel isunmistakably serious, even sad, consistent with the overt message.

I conclude that probably some form of my interpretation of thesenine graphic elements was still alive in 1605 and known to Wierix; Ihave merely revived it, not invented it.

These interpretations of the wandering S’s and crosses make senseonly if there were viewers who would understand them. Since the doc-trines of “Melencolia I” are part of the Humanist tradition, most likelythe initiates were Humanists, especially Durer’s best friend, WillibaldPirckheimer.

1.35 Serpents

After writing the above I realized that I had noticed but not understoodthe sinuousity of the 9 in MELENCOLIA I.0and examined the figuremore closely, to find that it is a rather detailed serpent.

� The top of the 9 in the Table has a Serpent’s head curled insidethe loop of its body, with two eyes looking directly at us, a mouth-line,and a forked tongue.

In MELENCOLIA I.0 I must cock my head about 30◦ to the leftto best see this face with its two eye-dots. In MELENCOLIA I.1the9 is reversed, the serpent’s face is upright, and the eyes have grownfrom miniscule dots into discs, all serving to make the Serpent moreconspicuous.

� The numerals 6 in the Durer Table are also serpents, with headand forked tongue at their lower end. These are the most minute ofthe subliminal structures. The forked tongues are conveyed by twoscratches of the burin.

� The numeral 0 in the Durer Table of MELENCOLIA I is a Ser-pent eating its tail, the Ourobourous. The eyes are drawn only in ME-LENCOLIA I.1.

The Serpent in the 9 seemed to refute my then current interpreta-tion. I had deduced that the S was a sign of the Highest, while theSerpent was the lowest of the low. But within the hour I rememberedthat I had experienced this inversion before, first with the Dog andthen with the Imp. I went back to Horapollo and looked up “Snake.”

1.36. THREE GNOMONS 63

Nothing. Then “Serpent:”

They symbolize the Almighty by the perfect animal, againdrawing a complete serpent. Thus among them that whichpervades the whole cosmos is Spirit. ([?], Book I, Symbol 64)

So the Serpent in the Table does not wreck the interpretation but sup-ports it.

There is no clear indication in MELENCOLIA I that Durer differedwith Christian orthodoxy on the divinity of Jesus; it seems to be aHumanist manifesto, not a Unitarian one. The first known Unitarianpublication came more than a decade after this engraving.

In this theory, Durer hides the Bell-ringer in obedience to the com-mandment about graven images but shows the Serpents and the Eaglebecause they are not images of God but merely glyphs.

We see that the Magic Square is riddled with defects, such as in-verted, backwards, or otherwise distorted numerals. I suggest that theseimperfections were meant to disqualify this engraving for the talismantrade, which still flourishes. Not only did Durer disdain the magicarts, it would have been dangerous to be suspected of practicing them.Most of the distortions inject symbols of God into the Magic Square,as though to fend off accusations of devil worship.

1.36 Three Gnomons

I thought I had exhausted the symbols in MELENCOLIA I until I no-ticed that Durer provided a gnomon in and of each World. The gnomonof the Elemental World is the Carpenter’s Square on the ground. TheCelestial World has the mathematical Gnomon Magic Square. The In-tellectual Sphere has the Gnomon of the sundial, the highest elementof the engraving. The meanings of the Gnomons correlate with thelocations and the Worlds. There is no problem finding a reasonableguess at Durer’s intention. The Greek root of gnomon, em gnome,means judgment. Durer would seem to indicate that the engraving isgnomonic, points to knowledge, and of three kinds.

Today dropping something on the ground deprecates it. In MI theground is high in the picture, as a result of the strange perspective,


and perhaps high in esteem, since it holds the Sphere of the Earth,the Crucible of his father, the Nails of the Cross, and the tools of thecraftsman; including a carpenter’s Gnomon, a symbol of the knowledgeof the First World. How Durer arranged the three Gnomons on hiscopper plate may show how he allocated them to the three Worlds, nothow he esteemed them.

1.37 Summation

There are several main ideas beneath the surface of this engraving:The Motto “MELENCOLIA§I”, in its overt form, and the general

gloom of the picture, refer to the melancholy of those who strive invain to define or create absolute truth and beauty. This limitation ofknowledge inspires a melancholia in the Boy that is not depression buta frenzied and sanctified creativity.

Unscrambled, the Motto becomes LIMEN CAELO I, probably refer-ring to Agrippa’s Gateway to Heaven I, Natural Philosophy. Durer setsNatural Philosophy, based on the observation and portrayal of nature,ultimately in mathematical terms, and Theological Philosophy, basedon the Holy Scriptures, on one level as Gateways to Heaven. The cre-ative thinkers of the early sixteenth century did not separate art andscience as neatly as those of the twenty-first; when Durer sanctifiesartistic depiction he sanctifies scientific observation as well. NaturalPhilosophy is not a sure Gateway to Heaven, as the various perspec-tival ambiguities demonstrate. But neither is Theological Philosophy,as shown by the three warring sects in her skirt. And MathematicalPhilosophy, meaning then astrology, is not even in the running: Durerdiscards the Celestial Sphere, the middle world of the Neo-Platonictriple cosmos, together with astrology, the Mathematical Philosophy ofAgrippa, and puts the astrologist-dog of Horapollo to sleep.

The three gnomons further clarify Durer’s intentions. He does notmean to discard any of the three paths to salvation. He wishes to raiseNatural Philosophy to the level of sanctity of Theological, and while heshows contempt for the astrologer, he puts Mathematical Philosophy,represented by the gnomon magic square, almost at the top of his world.

This is, I propose, a Humanist manifesto of the impending Refor-

1.37. SUMMATION 65

mation, the scientific revolution, and Natural Philosophy, still withinthe neo-Platonic world view.

Durer anticipates Descartes’ universal doubt based on the existenceof optical illusions, and also Descartes’ two-fold world of matter (theElemental World of res extensa) and mind (the Intellectual World ofres cogitans), but he is already beyond Descartes in recognizing thatour mathematical models can never exactly match reality, that becausefallible perception is the source of all our knowledge, our knowledge isrelative, not absolute.

We read these messages in this engraving in its grand overall struc-ture, its fine details, its ambiguous perspective projections, its quadri-valent subliminal elements, its orthographic variants, and its anagram.

Some of these messages were capital crimes in the time and place ofDurer. This would account for the concealments in the engraving. Yetthe concealments are not mere self-protection, as I assumed at first.The multiple ambiguity does not merely cloak the message, it also isthe message.

“The lie is in our understanding, and darkness is so firmlyintrenched in our mind that even our groping will fail.”

For Durer and MELENCOLIA I, the world still has a unique meaning,but God alone knows what it is. with The pervasive ambiguity ofMELENCOLIA I and its recruitment of the viewer, are postmodernaspects of a 16th century work of art.


Chapter 2

DISCLOSURE

I disclose here some of my own still developing views on these topics ofDurer. They undoubtedly influence my interpretation.

The idea that an eternal universal Law hides behind the veil of ever-surprising life experience can be traced in the west to the formula ofPlato that Logos + Doxa = Episteme, and to the pre-Socratic Par-menides, who also split knowledge into Logos and Doxa.

It persists today even though we understand better the evolution-ary process that produces mathematics and physics out of raw nature.Likely there is a neurological base for this division, Doxa correspondingroughly to the stimulus and Logos to the conditioned response whichemerges out of many stimuli. The glorification of the lessons of ex-perience as eternal Law seems to admit explanation on a higher level,that of culture, but certainly does not follow from experiment, nor isit necessary for science. Some of the Neo-Platonic cosmology referredto in MELENCOLIA I still lingers on today as the belief, both inspir-ing and crippling, that Nature is a mathematical system. In the firstphysics class I taught, I told my students that physics is not the searchfor the laws of nature but for the Law of Nature, a lesson I learnedfrom Einstein that influenced me greatly for years, and may also haveconsiderably impeded my research. I did not know I was transmitting avestige of the perennial philosophy. I hope I did no permanent damage.

The doctrine of Leonardo and Durer that all knowledge comes fromthe senses is forerunner of the scientifc revolution, a revolt against theperennial philosophy. Both artiscientists took pains to conceal thisdoctrine from hostile viewers. We have seen it expressed in MELEN-COLIA I by the relative position of the artiscientist putto and the

67

68 CHAPTER 2. DISCLOSURE

theological angel, and by the exaltation of art, mathematics, and thephysical sciences. The limits to knowledge expressed by MELENCO-LIA I and major thinkers of the time are milder than today’s limits.We are required to suspend belief today not merely in our ability toperceive absolute reality but in the existence of such an absolute. Ourpredicament as students of nature therefore seems less melancholy thanDurer’s, since we know that we are not deprived of anything that everexisted, and the loss of mechanical certainty goes with an access tounderstanding and control.

The Renaissance doctrine that all knowledge comes through thesenses can be taken too simplistically. It takes a much prior knowledgeto convert what comes through our senses into a little new knowledge.Some of this may be hereditary, such as the vital procedural knowledgesof how to breathe, suckle, develop, and learn to speak. We are not neu-tral receivers of sensory impressions but have feelings, vested interests,and theories. When we study nature, and even when we merely look atan engraving, the neural traffic from the brain to the eye is a significantfraction of the opposite traffic. Descriptive geometry is an importantbeginning but is still too passive to be a useful metaphor for scientificobservation. His attitude toward experiment differs from that of Plato:he hangs its instruments on the House of God. But the appreciation ofits power is still in the future.

Durer, Kepler, and Einstein wanted to know the creative mind ofGod, at least metaphorically:

“I want to know how God created this world. I am not in-terested in this or that phenomenon, in the spectrum of thisor that element. I want to know his thoughts; the rest aredetails.” (Attributed to Albert Einstein)

This inspiring metaphor is an insidious form of the mathetic fallacy.Such beliefs led Kepler to his Platonic-solid model of the Solar System,a thoroughly mistaken theory, and blocked him from appreciating thebeauty of the three laws that he found more empirically, and that arestill named after him. It led me to set out to read nature much as I setout to read MELENCOLIA I, but less successfully.

When I began my own research I took it for granted that it would

2.1. ACKNOWLEDGMENTS 69

pass though three stages: I would first find or form a theory in whichI could at least potentially believe, then compute some of its conse-quences, and finally compare them with experimental data; then Iwould return to stage 1 for an improved version. After about fortyyears I could not help noticing that I was still at the first stage. It maybe, I begin to surmise, that physics is not the project of replacing oneeternal faith by another, but replaces the method of faith by a differentone, the method of experiment. I had looked for a final theory, but afinal theory makes about as much sense as a final experiment or a finalsong; and this can be taken as a vital sign, and as a source of joy at leastas much as melancholy. The quest for the final theory has stimulatedimportant and fruitful work, but the concept derives from misplacedfaith like Kepler’s, not from experiments like Galileo’s, Rutherford’s,and Hubble’s. It seems inconsistent with the quantum theory, which,like any cookbook, leaves most of the universe by far—the experimenterand the environment of the experiment—almost undescribed.

Durer despairs because he sees his task as the true representationof nature, and recognizes this as hopeless. Since we know that truerepresentation is non-existent, due to the interactive aspect of percep-tion, it cannot remain our goal. It is simplistic to suppose that sucha complex institution as physics serves but one function; now that theidea of physics as the mechanical representation of nature has fallenaway, truer functions step forward. Physics is still a key element inthe survival strategy of the human race, and is still an outlet for theancient human need to converse with something larger than ourselves.Nature is among other things an evolutionary process that births us,our purposes, and through us, our theories, which are all like the Celes-tial Sphere, millstones that eventually slip off their axles and are rolledaway, to be replaced by fresh ones that work better.

2.1 Acknowledgments

This study would have been impossible without the works on “ME-LENCOLIA I” by Erwin Panofsky and by Francis Yates and the stud-ies of Agrippa by Judit Gellerd and by Charles Nauert. The heraldrydictionary of Cecil Wade helped me to read Durer’s coat-of-arms. I

70 CHAPTER 2. DISCLOSURE

thank Dr. Basimah Khuleusi and Prof. Bill Branch for their inter-pretations of several elements of MELENCOLIA I, some of which Iultimately accepted. Khulrusi pointed out the reference to Jesus in thefour nails of the engraving, and made a convincing model of the Octa-hedron that established the angle 89.5◦ for one interpretation, amongnumerous other contributions; Branch pointed out that the numeral5 in the Magic Square was upside down and that the 9 was back-wards, and brought up the Ouroubouros. I noted some numerologyattributed to Durer on the Web site of the Aiwaz Gallery though fi-nally I did not accept it. My thanks go to Roy Skodnick for introducingme to the work of Yates; to Prof. Heinrich Saller for the print of “ME-LENCOLIA I” that triggered this process; to Rabbi Mario Karpuj forreminding me that Jacob’s ladder is the Biblical gate of heaven; toProf. Shalom Goldman for stimulating, informative, and encouragingdiscussions, the reference to Yates on Durer, and the meaning of theMagen David in the Renaissance; to Danny Lunsford for the referenceto http://meteoros.de/halo/halo1.htm; to Glenn Michael for a refer-ence [?]; to Carla Singer for lending me her expertise in art history,including the reference to Mantegna; to Aria Ritz Finkelstein for thereference to Velasquez and her discovery of the subliminal Jesus-facein Jerome; to Dr. Ernst Theodor Mayer for references to Pico andthe millstone in Matthew; and to Shlomit Ritz Finkelstein, for livelydiscussions, help with Torah and Descartes, and useful expository sug-gestions. A first stage of this study was published in The St. Ann’sReview, whose reviewer improved the paper [?]. A later stage was sub-mitted for publication with Dr. Khulusi [?].

Bibliography

[1] Heinrich Cornelius Agrippa: Of Occult Philos-ophy, digital edition, ed. Joseph H. Peterson,http://www.esotericarchives.com/agrippa/agrippa1.html. Basedon the translation of De occulta philosophia libri tres (ThreeBooks About Occult Philosophy) translated by ”J.F.”, printedby Moule, London (1651).

[2] Suzanne Boorsch; Nadine M. Orenstein (1997) The Print in theNorth. The Age of Albrecht Durer and Lucas van Leyden. TheMetropolitan Museum of Art Bulletin, Vol. 54 No. 4 (Spring 1997)pp. 1+13-60.

[3] This was kindly pointed out to me by Bill Branch in a privatecommunication. Prof. Branch also suggested the Ourobourous inconnection with MELENCOLIA I.

[4] Brant, Sebastian. Narrenschiff (Ship of Fools). Illustrated by A.Durer. Basel, 1494 (first edition). Ship of Fools , Alexander Bar-clay, translator, Pynson, 1509. Rhyming translation, Zeydel, E.H. Ship of Fools. New York: Columbia University Press, 1944;reprinted by Dover Publishing Co., 1962.

[5] Brosseder, Claudia. The Writing in the Wittenberg Sky: As-trology in Sixteenth-Century Germany. Journal of the History ofIdeas 66:557-576 (2005).

[6] Conway, William Martin. Literary Remains of Albrecht Durer.London: University Press, 1899, pages 142-143.

[7] Doorly, Patrick. Durer’s Melencolia I : Plato’s Abandoned Searchfor the Beautiful. The Art Bulletin88, 255 (2004)

71

72 BIBLIOGRAPHY

[8] Durer, Albrecht. Vnderweysung der Messung mit dem Zirckel unRichtscheyt in Linien, Ebnen und Gantzen Corporen, Vol. 1-4.Nuremberg 1525. Republished with English translation of WalterL. Strauss, revised, on compact disk. Editor, anonymous. Com-mentator, David Price. Octavo Editions, Oakland CA, 2003.

[9] Einstein, A. MORE

[10] Eisler, Colin. Review of Jane Campbell Hutchison, Albrecht Drer:A Biography. Renaissance Quarterly , 45: 163-166, 1992

[11] Erasmus, Desiderius, of Rotterdam. In Praise of Folly (1511).Translated by John Wilson. Dover Publications, 1991.

[12] Fine Arts Museums of San Francisco. http://www.thinker.org/provides much of the cited art with enough zoom to show thedetails mentioned.

[13] Federico, P. J. “The Melancholy Octahedron,” Mathematics Mag-azine, 45:30-36, 1972.

[14] Finkelstein, David Ritz. Melencolia I: Durer Decoded, The St.Ann’s Review , 2004.

[15] Galileo Galilei, Dialogue on the Great World Systems . The Salis-bury translation. Revised, , annnotated, and with an Introductionby G. de Santillana. University of Chicago Press (1953)

[16] Gellerd, J. “Francis David’s Epistemological Borrow-ings from Henry Cornelius Agrippa of Nettesheim. ”w3.enternet.hu/sandor64/cffr/papers/agrippa.html

[17] Goldman, Shalom. The Sacred Tongue; alsohttp://uncpress.unc.edu/booksT-6957.html. For the conceptof Hebraicism.

[18] Greenblatt, Stephen. Will in the World: How Shakespeare BecameShakespeare. Norton (2004). On Hamnet and Hamlet.

[19] Heckscher, William S. Melancholia (1541). An Essay in theRhetoric of Description by Joachim Camerarius. In: Frank Baron,ed., Joachim Camerarius (1500-1574). Beitrage zur Geschichte

BIBLIOGRAPHY 73

des Humanismus im Zeitalter der Reformation. Essays on theHistory of Humanism During the Reformation. HumanistischeBibliothek, Abhandlungen 24 (Munich, 1978): 32-103

[20] Horapollo Niliaci. Hierogrlyphica. Translated in The Hieroglyphicsof Horapollo. Boas, George, translation and introduction. (Prince-ton: Princeton University Press, 1993.)

[21] Mysterium cosmographicum de admirabili proportione orbiumcoelestium. (1596). Translation: The secret of the universe = Mys-terium cosmographicum / Johannes Kepler; translation by A.M.Duncan ; introduction and commentary by E.J. Aiton ; with apreface by I. Bernard Cohen. [Mysterium cosmographicum. En-glish] (New York : Abaris Books, 1981.)

[22] Dr. Basimah Khulusi. Personal communication.

[23] Finkelstein, D. and B. Khulusi,MELENCOLIA I . Submitted forpublication.

[24] Lunsford, Daniel. Personal communications concerning the DurerSolid and Ratio (2004).

[25] MacGillavray, C. “The polyhedron in A. Durer’s engraving Melen-colia I. ” Nederl. Akad. Wetenschap. Proc. Series B 84: 287-232,1981.

[26] Mathworld, http://mathworld.wolfram.com/DuerersSolid.htmlso describes the Octahedron.

[27] Menand, L. The Metaphysical Club: A Story of Ideas in America.New York: Farrar, Straus, and Giroux, 2001.

[28] Nauert, Jr., C. G. Agrippa and the Crisis of Renaissance ThoughtUrbana: University of Illinois Press, 1965.

[29] Nicholas, of Cusa, Cardinal, 1401-1464. Of Learned Ignorance(1440) translated by Germain Heron; with an introd. by D. J.B. Hawkins. (London : Routledge & Paul, 1954)

[30] Panofsky, Erwin. The Life and Art of Albrecht Durer . Prince-ton University Press, 1971. The standard work. It reproduces theDurer works mentioned here.

74 BIBLIOGRAPHY

[31] Penrose, R. The Road to Reality (New York: Knopf, 2004). Abrilliant exposition of contemporary Platonism, the antithesis toour thesis.

[32] Pico della Mirandola, Giovanni. Canzona d’amore composta perHieronymo Benivieni cittadino Fiorentino, secondo la mente eopinione de’ Platonici (1486). Transl. A Platonick Disourse uponLove. E. G. Gardner (ed.). Merrymount Press, Boston (1914), pp.9, 34.

[33] Santillana, Giorgio de, and Hertha von Dechend. Hamlet’s Mill:An Essay on Myth and the Frame of Time. Gambit, 1969. Argu-mentation for the astronomical interpretation of all myth.

[34] Saxo. Gesta Danorum. Translation: Davidson, H. E. and Fisher,P. Saxo Grammaticus: The History of the Danes (Cambridge:Cambridge University Press, 1979)

[35] Schuster, Peter-Klaus. MELENCOLIA I: Durers Denkbild.(Berlin: Gebr. Mann Verlag, 1991).

[36] Peter Schreiber. “A New Hypothesis on Durer’s Enigmatic Poly-hedron in His Copper Engraving Melancholia I.” Historia Math-ematica 26, 369-377, 1999.

[37] Serveto, Miguel (Michael Servetus). De Trinitatis Erroribus (Onthe Errors of the Trinity). Hagenau: John Setzer, 1531

[38] Wade, W. Cecil. The Symbolisms of Heraldry or A Treatise on theMeanings and Derivations of Armorial Bearings . London: GeorgeRedway, 1898.

[39] Yates, Frances A. The Occult Philosophy in the Elizabethan Age.London ; Boston : Routledge & K. Paul, 1979. Especially chapter6.

[40] Yates, Frances A. Giordano Bruno and the Hermetic Tradition.Chicago: University of Chicago Press, 1964.

[41] Weitzel, H. “A further hypothesis on the polyhedron of A. Durer’sengraving Melencolia I.” Historia Mathematica 31, 2004.

BIBLIOGRAPHY 75

[42] http://antwrp.gsfc.nasa.govapodap010704 shows a photograph ofa real moonbow.

[43] http://gallery.euroweb.hu/html/d/durer/ shows all the Durerworks I mention.

[44] http://meteoros.de/halo/halo1.htm is a remarkable gallery ofportrayals of heavenly phenomena like moonbows and moon ha-los, including several from Durer’s time.

Melencolia100311

Documents

de occulta philosophia

fine arts museums

impending scientic revolution

make clean corrections

called secondary images

king james bible

intellectual world iii

gnomon magic square