Jupiter Square, Magic Square

I’ve become interested in the mathematical idea of the magic square. I learned about this idea from Dürer’s print Melencolia I. A magic square appears over the angel’s shoulder, below the bell. The rule of the magic square of numbers is that the digits in any direction of rows, top to bottom, left to right, right to left, diagonally, or in the four center squares, etc., always add up to the same number. In the case of Dürer’s magic square next to the angel of melancholy, the 4 numbers in the patterns of combination always add up to 34. The idea is that this mathematical table engages with the protective astral influences of Jupiter as a way to combat the dark anxiety and melancholic effects of the planet Saturn. Jupiter’s shield of balance and order can block the destructive chaos rays of Saturn.

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I have a lengthy but very interesting quote to follow from the book Perfection’s Therapy, An Essay on Albrecht Dürer’s Melencolia I, by Mitchell B. Merback:

“Why, then, has Dürer been credited with such a singular focus on the astrological? Why else but the electrifying presence of an object directly concerned with mitigating the debilitating power of the illness — the famous “Jupiter square” (mensula lovis), the sixteen-celled numerical chart that Dürer has set into the wall behind Melancholy. Confronting the viewer directly, it goes unseen by the seated genius, who nevertheless seems to reach absentmindedly toward it, her folded left wing just overlapping the bottom of its frame. Just as suggestively, the chart is aligned vertically with the bell, close enough for the bell pull to graze its upper right corner as it dips down, neither slack nor taut, past the picture’s edge. In this subtle choreography of contacts, separations, overlaps, and infinitesimal proximities we have another example of Dürer’s knack for intimating the hidden sympathies between things. The vignette anchored by the magic square is perhaps the most appealing of the engraving’s zones, a pictorial metaphor for the object’s cosmic power of attraction.

Melencolia’s magic square has attracted more than its share of attention from mathematicians, symbol hunters, code breakers, philosophers, astrologers, and other adepts of the esoteric — and for good reason. Each row of numbers counted in any direction (vertically, horizontally, diagonally) adds up to thirty-four, as do the numbers in the cells of the four outer corners; the four center cells; the groups of four assembled from the two inner cells of the top and bottom lines and two inner cells of the left and right column, respectively; each corner group of four; and so on. Islamic mathematicians had developed this branch of number theory as early as the seventh century, and it may have entered Europe, along with other aspects of Arabic astral magic, through the court of Alfonso X of Castile (1221-84). In all likelihood, the design of Dürer’s sixteen-cell square derives from the occult philosophy of Agrippa von Nettisheim, for whom magic and mathematics were intimately connected. In Agrippa’s conception, “formal and rational numbers” represent divine ideas, distinguishing them from the “natural numbers” used in the secular world of commerce. The former stand in the closes possible relation to truths beyond the sensible world precisely because they have no counterparts in observed nature.

Some have taken the “magic constant” of thirty-four in Dürer’s square to be symbolic of Christ’s years on earth as a man. Others have discerned numerological meanings both far-flung and obvious: the engraving’s date, for example, 1514, which is visible in the lower row. This was also the year Dürer’s mother died (17 May), making the magic square, in the view of some commentators, emblematic of the whole scene’s allegedly mournful mood, therefore commensurate with its — again, alleged — function as a consolation in grief.

Building on the work of Giehlow, Warburg identified the Jupiter square as an astrological talisman of the kind recommended by Ficino for use by fellow scholars in warding off the ill effects of Saturn (himself a victim of dark anxiety, Ficino’s horoscope showed Saturn in the ascendant position). As a “magic image,” its purpose is to counteract the pernicious effects of one planet by attracting the healing power of another — in this case, the deity’s “joyful” nature works to dispel “all worries and fear,” as Panofsky would later write, vaguely concurring with the opinions of his predecessors.

Does the therapeutic potentiality of Melencolia come down simply to this? In the exegetical perspective common to Giehlow, Warburg, and Panofsky, the magic square symbolizes the neutralization of those rays that bring the darkness associated with melancholia and acedia, “lightening” those states to become the melancholia generosa associated with genius. As Ficino has asserted, only the right combination of the two planetarty influences can produce melancholic philosophers who embrace their destiny as children of Saturn, men “whose minds are truly withdrawn from the world”. But only Warburg had the imagination to understand the square also in narrative terms, as the marker of a kind of astrological peripeteia, a triumphant reversal in the melancholic’s struggle against Saturn’s influence. And most significantly, he conceived this as a victory set in motion by thought itself. That account we must now quote in full:

Dürer shows the spirit of Saturn neutralized by the individual mental efforts of the thinking creature against whom its rays are directed. Menaced by the “most ignoble complex,” the Child of Saturn seeks to elude the baneful planetary influence through contemplative activity. Melancholy holds in her hand, not a base shovel…but the compass of genius. Magically invoked, Jupiter comes to her aid through this benign and moderating influence on Saturn. In a sense, the salvation of the human being through the countervailing influence of Jupiter has already taken place; the duel between the planets, as visualized by Johannes Lichtenberger, is over; and the magic square hangs on the wall like a votive offering of thanks to the benign and victorious planetary spirit.

Magical imagery in the virtual world that Dürer’s print conjures up, in other words, moves beyond symbolization to serve as an active relay for the psychic mobilization of Jupiter’s aid, and then finally as a token of its efficacy. On this basis, Warburg, breaking with Giehlow, could declare the engraving a Trostblatt, a comforting image, since the victory of the thinking being over Saturn’s dark power has already taken place.”

  • Excerpt taken from pg 156-159 of Perfection’s Therapy by Mitchell B. Merback

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Melencolia I (B. 74; M., HOLL. 75)*engraving  *24 x 18.8 cm *1514
Melencolia I, Albrecht Dürer, 1514

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