Two Approaches to Tarot Triangulation: The Quintessence and the Midpoint
AUTHOR’S NOTE: There is a technique used in navigation and surveying called “triangulation,” the technical definition for which, in its simplest form, is “the process of determining the location of a point by forming triangles to the point from known points.” While navigation encompasses distance as well as direction and position and surveying only defines a set of coordinates, figurative triangulation can be brought to bear on the relationship between any two cards in a tarot reading regardless of how far apart they are as a way to add depth to the narrative in the form of a third “derived” card (or, as we shall see, two cards). I should also mention that, while the processes here are mathematical, the results should be interpreted fluidly as in any storytelling scenario involving several cards.
As I apply it, this symbolic extrapolation yields another set of factors that can serve as a summary or overview harmonizing the interaction that might occur between the initial pair at two distinctly different junctures, one arrived at by the quintessence calculation and the other by midpoint determination; the former stands out as mystically impressionistic in an archetypal sense while the latter is more rationally discernible and utilitarian in its emphasis. (It’s worth noting that any such harmony may not be immediately apparent via a cursory comparison of the “textbook” meaning of the two original cards to the third one in each instance; deeper contemplation will often be necessary, and the last section of this essay offers some insights on that.)
I’ve occasionally been scolded by traditionalists in European (mainly French) cartomancy, who insist that the quintessence calculation should only be used with the tirage en croix (aka “French Cross”) and is not applicable to any and every haphazard subset of cards out of the 78. My personal position is that I will employ all techniques in the diviner’s toolbox that yield results, and the universal quintessence is among them. For those unfamiliar with it, the method involves summing the numerical values of the cards in a reading and then, if necessary, “reducing” the total to a number that fits within the range of the 22 trump cards; the trump that matches the derived number becomes the “quintessence,” which is read as a symbolic synthesis of the contributing cards at a more profound level of abstraction. I sometimes use it to suggest long-term consequences.
There are several caveats to consider in this calculation. The main one is that only the practice of “casting out nines” (subtracting increments of nine) can produce zero (which most of us ascribe to the Fool); the more conventional “Theosophical” reduction (that is, adding together the digits of any result higher than 22) will never generate zero. Historically-inclined practitioners get around this by renumbering the Fool as 22, in line with the assumptions of earlier Continental occultists, in which case Theosophical reduction works just fine as far as it goes. I prefer to leave the Fool as zero in my own work, so I like casting out nines.
The second caution is that some time ago a mathematician of my acquaintance performed an analysis of Theosophical reduction and found that it generates a bell curve in which the lowest and highest of the trumps are never selected as the quintessence, a failing that defeats the purpose of the calculation. Casting out nines can significantly minimize this potential by offering two possible “quint” cards for the reader to choose between, a two-digit trump higher in the sequence and a single-digit, lower-numbered one.
The third and last point of contention is that some writers tell us that, because they are unnumbered, the court cards should be excluded from the calculation. I strongly disagree since I believe all of the cards on the table should participate in the roll-up; otherwise we are once again diluting its purpose.
The other “triangulation” method involves finding the numerical midpoint between the two cards in question and treating the card at that location as the “harmonizing” agent. I once wrote an essay on this subject that you can refer to for more detail. I’ve streamlined the determination by creating a table that lays out all 78 cards, and all you have to do is count the intervening cards, divide by two and add the result to the lower one in order to locate the target card (with one further consideration that you will find in the previous essay, linked below).
Now for the philosophical discussion. If we look at it from a Pythagorean point-of-view, the geometric relationship between any two cards is linear; it doesn’t matter which one we place first in the line because the flow of energy between the cards is reciprocal and compensatory from one end to the other and back again, resembling an electrical circuit or the arc of a swinging pendulum that only achieves equilibrium very briefly at what we might call the “bottom-dead-center” of its travel. By adding a third oblique point, we create a two-dimensional planar surface (aka a “triangle”) that increases the possible range of interpretation for the original pair, such that we can come down somewhere in the middle by “shading” the combined meaning of the three according to the relative potency of the cards.
With two diagonal features to factor in (quintessence and midpoint) we wind up with a diamond array instead of a triangle. In thinking about it, I would place the quintessence card — the more abstract of the two — above the horizontal connecting line as the archetypal theme of the reading and the more literal midpoint card below it as the situational undercurrent. If we start with a three-card line reading and “triangulate” by both methods from the two end cards we will have a five-card pattern with a vertical line centered on the middle card of the original pull, which serves as the focus around which the rest of the reading revolves. It is probably best to illustrate this graphically.
I performed a random, three-card pull to demonstrate my thinking and came up with an imaginary narrative to explain it. The Focus Card was the 10 of Cups (“Satiety” or self-indulgent excess) and the contributing cards were the 10 of Disks (“Wealth,” 74 of 78) and the Knight of Cups (“Fire of Water,” 50 of 78).
The 10 of Cups suggests that the querent is suffering a state of emotional dyspepsia, possibly over some kind of monetary indulgence shown by the 10 of Disks, which Aleister Crowley defined in part as “the futility of material gain.” (I’m reminded of the old Alka-Seltzer commercial in which a distraught man in obvious discomfort moans to his wife “I can’t believe I ate the whole thing,” to which his wife replies tartly “You ate it, Ralph.”) Perhaps the querent in this case over-committed himself financially (10 of Disks) and is regretting his loss of liquidity (10 of Cups). The Knight of Cups could be his spiritual advisor (the proverbial “wet blanket”) giving him the bad news but also offering him an unpalatable way out shown by the two “summary” cards, without which this is a fairly innocuous scenario.
The sum for the 10 of Disks and the Knight of Cups is 24, which reduces by “casting out nines” to 15, the Devil as “Quintessence Card.” The “Midpoint Card” between the Knight of Cups (50) and the 10 of Disks (74) is the Prince of Swords (62). I’m reading the pair as showing that draconian measures will be necessary for the man to right his listing financial ship: the Devil is holding the whip and rubs his nose in the distasteful reality and the Prince of Swords is the Devil’s “hatchet-man,” perhaps proposing where any “dead-weight” ballast might be trimmed.
This individual is clearly caught in a bind of his own making and won’t escape unscathed. He might as well get his hand-wringing behind him and move on. However, because the Devil (as Capricorn) is elementally compatible with the Earth and Water cards, we could say that the “fix is in” and he will receive little resistance in rewriting the script, with no need to rely on the incisive but painful tactics of the Prince of Swords. The projected outcome has a Faustian feel to it that might warrant a cautionary mention.
Footnote: I used the Thoth Tarot (copyright of US Games Systems Inc, Stamford, CT) to perform this reading. For those who favor the Waite-Smith deck, the Thoth Knight of Cups corresponds to the RWS King of Cups as the fourteenth card of its suit, and the Thoth Prince of Swords equates to the RWS Knight of Swords as the twelfth card.
Originally published at http://parsifalswheeldivination.wordpress.com on April 28, 2024.
