Two kinds of dice were used in classical antiquity: dice proper (kuboi, tessarae), which are virtually identical to six-sided modern dice, and knucklebones (astragali, tali), which have four sides (Halliday 205-15, esp. 213-15; David 1-7; Ore 193). For divination, five astragali were rolled, and the resulting combination was looked up on a four-sided pillar, many examples of which survive in more or less fragmentary form (e.g., Sterrett "Epig.", "Wolfe"; Kaibel). It so happens that the number of possible five-astragali throws is 56, exactly the number of Minor Arcana, and that the throws were listed on the tablets in four "suits" (two of 15 throws, two of 13; see Halliday 213n3). When dice are thrown for divination, the number of possible throws of three dice is also 56 (Minor Arcana), and the number of throws of two dice is 21, the number of Major Arcana (excluding the Fool).
This correspondence would be remarkable if it were coincidental, and it therefore suggests that the Major Arcana derive from divination with pairs of dice, and the Minor Arcana from triples of dice (or quintuples of astragali). Additional evidence can be found in a system of meditation developed around 960 CE by Bishop Wibold of Cambray, in which 56 virtues were associated with the throws of three dice (Kendall 2-4). Also, in the fifteenth century, when the Tarot first appears, we find a number of poems setting out the meanings of the 56 throws (Kendall 11; see, e.g., Kraemer). In truly Cabalistic fashion, San Bernadino's sermon of 1423 draws an analogy between the 21 rolls of two dice and the 21 letters of the (medieval) Roman alphabet (Kendall 4) - that is, ours without J, V, W, Y, Z.
Unfortunately I cannot take credit for this important insight; Gertrude Moakley (p.42, n.9) attributes it to the statistician Maurice G. Kendall (1956). This is particularly annoying since I have been piecing together and translating astragalomancy tablets, and the significance of the number 56 should have been obvious to me! In mathematical terms 21 is the sixth Pythagorean triangular number, the Hexaktys, and 56 is the sixth Pythagorean pyramidal number (the base of which is the Hexaktys). The total number of Tarot cards, 78, is the twelfth triangular number. The Pythagorean Tetraktys is, of course, the fourth triangular number.
There is, so far as I know, any record of the correspondence between dice throws and Tarot cards. Nevertheless, I've listed a throw of two dice for each Major Arcanum. This is based on the observation that in ancient dice games numerically higher rolls (usually) beat numerically lower ones, and on the assumption that the higher numbered die corresponds to the row of the triangular number. There are two obvious way the 21 Major Arcana (Magician to World) correspond to the rolls, both of which reflect the structure of the Major Arcana (as will be explained later):
A correspondence between the Major Arcana and throws of three astragali is discussed later. There are also correspondences between the Minor Arcana and throws of three dice or five astragali. The charts are presented in an Appendix (Tarot Divination Without Tarot Cards), where practical techniques of dice divination are discussed.
This is perhaps an appropriate time to show the relationship between the Ferrara order, Pythagorean number theory, and the Water Hexactys. Write the third triangular number:
The remaining rows of the Water Hexactys show the structure of the remaining Triumphs (see next section):
Note that in the Fire Hexaktys, the King of Misrule is row 1, Tr. Love is rows 2 and 3, Tr. Virtue is row 4, Tr. Time is row 5 and Tr. Eternity is row 6. Thus, when a pair of dice are rolled, if the numerically greater die is an ace, it's the King of Misrule; if it's deuce or trey, it's the Tr. Love; if a cater (4), it's the Tr. Time, etc. Conversely, in the Water Hexactys, with some adjustments, row 1 is Tr. Love, row 2 is Tr. Virtue, row 3 is Tr. Time, rows 4 and 5 are Tr. Eternity, and row 6 is the World. In this case, the numerically smaller die indicates the triumph (ace = Love, deuce = Virtue, etc.). In both cases, 1.Magician, 10.Wheel, 11.Old Man and 21.World are somewhat independent of the Triumphs, since they are the Tetrad of Transformation, the Lords and Ladies of Chance and Necessity (discussed in the next section).
There is a similar correspondence between the Triumphs and the 20 throws of three astragali. (Here we set aside 21.World for reasons that will be apparent in the next section.) In antiquity the four sides of an astragalus were assigned the values 1, 3, 4 and 6 (ace, trey, cater and sice). We will see that if a throw contains an ace but not a sice it's in the Tr. Love; if it contains both an ace and a sice it's the Tr. Virtue. In the remaining cases there are no aces: if it contains at least two treys or a trey and a cater, it's Tr. Eternity; otherwise it contains two caters or at least two sices and it's Tr. Death. Here are the first two triumphs, Love and Virtue, arranged in the Fire Hexactys:
The position of a trump in the Hendecad is obtained by reducing the isopsephos value to the range 1-11. This reduced isopsephos value is computed as follows: Start from the rightmost digit, and alternately subtract and add the preceding digits; add 11 if the sum is negative or zero; subtract 11 if it's more than 11. (Alternately, the reduced value is the remainder after dividing the isopsephos value by 11.) The procedure is actually easier than it sounds:
Finally there are two Ogdoads, each comprising four pairs of cards, one pair for each suit. The first Ogdoad, which is ruled by the Lord and Lady of Chance, contains the Personal Triumphs. Each pair comprises a male and a female, which I call the Master and Mistress (of the Wand, Pentacle, etc.). Here it is:
The second Ogdoad, which is ruled by the Lord and Lady of Necessity, contains the Universal Triumphs, and each pair comprises a Second and a First (in that order) - think of them as junior and senior. The First (senior) usually ranks over the Second (junior) and follows it in time, though sometimes they are equal and alternate in time (e.g. Sun, Moon):
One Soul, yet two, sets out and knows no bound;
Two Lords, two Ladies turn the Cosmos round;
Eight Couples march in Triumph to the Goal;
These all together make the Arcane Whole.
By two and twenty Signs the Truth is found.
The meaning of the trumps can be illuminated by placing them on the 21 lines that connect 7 poles, as indicated in the accompanying diagram. The two lower diagrams show the relation of the seven poles to the planets in the order used by the Chaldeans and Greeks, and the order of planets assigned to the days of the week.
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Last updated: Sat April 20, 2019