Hint's of Bosch's Conjurer in Magician card variants

In past posts I have mentioned the possibility of a relationship, whether direct or indirect, between Hieronymus Bosch's 1502 masterpiece The Conjurer (my favorite Bosch by a mile) and the Tarot de Marseille -- particularly the Magician and Wheel of Fortune cards.

In the process of collecting various early versions of the Magician card (qv), I noticed a few hints that that influence or relationship may extend beyond the limits of the Marseille tradition. (Only a handful of fragmentary Italian decks predate The Conjurer, so direct influence is not out of the question.)

The Cary Sheet (Milan, 1550)

The magician on the Cary Sheet (a partial set of uncut and unpainted cards sometimes considered to be the "missing link" between the Italian decks and the Tarot de Marseille) wears fez-like headgear suggestive of Bosch's conjurer, as opposed to the wide-brimmed hat typical of the TdM. Bosch, the Cary Sheet, and the TdM all agree in putting two cups on the magician's table -- but on the Cary Sheet the cups are apparently inverted (narrow side up) as in the Bosch painting, while the TdM has the cups upright. The long object situated between the two cups on the Cary Sheet is hard to identify with any confidence. The TdM would lead us to expect a second knife, or a knife sheath, but it could just as easily be a magic wand of the type that appears in the same position in the Bosch painting. And if we really want to push things, doesn't that vaguely egg-shaped object in the far right corner of the table on the Cary Sheet look more than a little like Bosch's little frog?

Tarot de Paris (1650)

It's impossible to tell what's on the magician's table in the Tarot de Paris, but there are other potential links to Bosch. The general layout of the picture is similar: The magician is on the right side of the table, with spectators on the left, and a wall behind them. As in the Bosch painting, a dog hides unobtrusively in the shadow of the table. There is also a monkey, an animal which many people have mistakenly believed to be depicted in the Bosch painting, hiding in the conjurer's basket. (In fact it is an owl.) If modern art historians have made that mistake, the makers of the Tarot de Paris could easily have done the same. Again, the magician is depicted with fez-like headgear.

Mitelli's Tarocchini (Bologna, 1664)

The "magician" of Mitelli's Tarocchini would appear to represent a clean break with Tarot tradition, dispensing altogether with the conventional table-covered-with-gewgaws theme -- but don't the dog, the hoop, and the little cluster of spectators come right out of Bosch?

Minchiate al Leone (Florence, 1790)

The Minchiate al Leone has a very strange Magician card. The familiar cups and balls are notably absent -- and who are those two people standing beside the magician? It would be a strange position for spectators; are they his assistants? At any rate, the vaguely tent-like objects in the center and in the left foreground corner of the table remind me of the equally mysterious object in the center of the table in Bosch.

A gallery of early or otherwise historically important Magician cards

This is primarily for my own future reference, but I post it here because others may find it helpful as well. These are the highest-quality images I have been able to find for each of the cards. They are in something approximating chronological order, keeping in mind that most of the dates are estimates.

I am indebted to Andy's Playing Cards for providing innumerable leads, and to Tarot of Marseilles Heritage for many of the images of cards from that tradition. If I've missed anything important, please inform me in the comments.

(Note: The image of the Oswald Wirth card I had originally posted was incorrect. I replaced it with the correct one on November 23, 2019. The "restored" Jean Dodal card was replaced with the original on November 25, 2019.)

Visconti-Sforza (Milan, 1451)

Ercole I d'Este (Ferrara, 1473)

The Cary Sheet (Milan, 1550)

Jacques Viéville (Paris, 1650)

Jean Noblet (Paris, 1650)

Tarot de Paris (Paris, 1650)

Mitelli's Tarocchini (Bologna, 1664)

Jean Dodal (Lyon, 1710)

Pierre Madenié (Dijon, 1709)

Jean-Pierre Payen (Avignon, 1713)

François Héri (Solothurn, 1718)

Minchiate Etruria (Florence, 1725)

François Chosson (Marseille, 1736)

Jean-Baptiste Madenié (Dijon, 1739)

François Tourcaty (Marseille, 1745)

Rochus Schär (Mümlisvil, 1750)

Claude Burdel (Fribourg, 1751)

Nicolas Conver (Marseille, 1760)

Ignaz Krebs (Fribourg, 1780)

Jacques Rochias (Neuchâtel, 1782)

Grand Etteilla (Paris, 1788)

Minchiate al Leone (Florence, 1790)

Arnoux & Amphoux (Marseille, 1793)

Bernardin Suzanne (Marseille, 1839)

Oswald With (Paris, 1899)

Lequart "Arnoult 1748" (Paris, 1890)

Rider-Waite (London, 1910)

Crowley's Thoth (1938-1943, pub. 1969)

Dice and the Minor Arcana: Opsopaus's geometrical approach

In his article "Tarot Divination Without Tarot Cards" (qv), John Opsopaus proposes a system of correspondences between the 56 cards of the Minor Arcana and the 56 possible rolls of three dice. This is analogous to his systems for mapping the 21 trumps to the 21 possible throws of two dice -- but is necessarily more complicated because the Minor Arcana are structured in a way that the trumps are not. While the trumps are numbered in a linear fashion, the Minor Arcana are grouped into four suits, each of which has 10 numbered (or "pip") cards and four face (or "court") cards.

Just as 21 is a triangular number, 56 is a tetrahedral one. Since 10 is also a tetrahedral number, the pips of each suit can be assigned to the smaller tetrahedron at one of the corners of the larger one. Once this is done, there remain 16 points at the center, arranged in the shape of a truncated tetrahedron, and these can be assigned to the courts.

The diagram below (which is my own work but is based closely on Opsopaus) shows how the 6th tetrahedral number can be divided into four smaller tetrahedra (red, yellow, green, blue) and a truncated tetrahedron (purple). Purple points represent court cards, and the other four colors represent the four suits of pips.

This is a great way of dealing with the pips, but the problem is that the courts are also divided into four suits, and there seems to be no natural way of quartering our central truncated tetrahedron.

One way of dealing with the courts is to associate each of the court ranks with one of the suits -- which has traditionally been done by way of mapping both the court ranks and the suits to the four classical elements. One popular system is Kings/Clubs/Fire, Queens/Cups/Water, Knights/Swords/Air, Knaves/Coins/Earth.

Notice that our truncated tetrahedron is made up of four hexagons, each of which faces one of the four pip-tetrahedra. For example, in the diagram above, the top surface of the truncated tetrahedron is a hexagon, comprising the rolls {334, 344, 335, 345, 355, 346, 356}, and facing the red tetrahedron. If we assign the red tetrahedron to the suit of Clubs, say, which is associated with the court rank of Kings, then the seven rolls on the red-facing hexagon will correspond to the seven court cards which are Clubs and/or Kings. The roll 345, which is in the center and which thus belongs exclusively to the red-facing hexagon, corresponds to the King of Clubs. Each of the remaining six rolls is shared with one of the other hexagons. For example, the rolls 355 and 356 belong to both the red-facing and the blue-facing hexagons. If we assign blue to Cups, corresponding to Queens, then one of these rolls will be the King of Cups, and the other will be the Queen of Clubs; we can perhaps assign the higher toll, 356, to the former on the grounds that a King should outrank a Queen.

These examples are just examples. I have not yet thought out which tetrahedron should correspond to which suit or any of the other details. Nevertheless, Opsopaus's basic schema seems to have a lot going for it.