Numerological Oddities

AUTHOR’S NOTE: I recently encountered a mathematical term that is new to me (not something that happens every day), although the concept isn’t: that of numerical aliquots, as in “the sum of the aliquot parts of an integer.”

I came across this in a discussion of the number Six as being an “aliquot sum” in that its constituent integers add up to the total of the number itself: 1+2+3=6. The same is true of the number Ten, in that 1+2+3+4=10, leading Pythagoras to observe that “the Ten is in the Four.” But this is perhaps nowhere truer than with the number Nine, for which all of the additions and multiplications, ad infinitum, reduce back to “9;” it’s an inescapable conclusion that Sallie Nichols likens to a “journey into self-realization,” in which the seeker (the Hermit) “must, in the end, return to himself.” However, in my model, Nine must inevitably resolve to One by way of Ten since that is the unitary root of all numbers and the earliest expression of Jung’s beneficial solitude.

I decided to lay out two sets of the Major Arcana in a pair of triangles, one ascending and the other descending (together forming a diamond), to see whether I might acquire any insights from the arrangement. The first group ran from One (the Magician) to Ten (the Wheel of Fortune), while the second one encompassed Twelve (the Hanged Man) through Twenty-one (the World). Each of these patterns contains nine internal triangles or triplets that contribute to the analysis. I removed the Fool as being of null value, and created a separate layout for Justice because it serves as the pivotal card between the two series. (All images are from the Albano-Waite Tarot, copyright of US Games Systems Inc, Stamford, CT.)

For the three numbers in each internal triplet that added up to 21 or less, I used “Theosophical addition” by summing the integers and selecting the associated trump as their “numerological counterpart” without reducing the totals any further. When looking at numbers over 21 for this purpose, I used “casting out nines” (and multiples of nine as necessary) because it offers more counterpart options than Theosophical addition and reduction. In this method, most of the higher triplets have a secondary, and sometimes even tertiary, counterpart that is the same one arrived at by normal reduction.

The total value of the cards in the first array is “55,” which reduces to “19” (Sun) by casting out nines and then to “10” (Wheel of Fortune), finally coming full circle to the Magician as “1” (first card in the series). In this group the Hierophant is the “interior force” that touches all of the other cards except the three points of the triangle. Thus, the Magician, the Chariot and the Wheel of Fortune enjoy a freedom of expression that the rest don’t. I have seen the equilateral triangle described as the source of rotational movement (producing the circle) when the three points are put into motion around the center, which makes perfect sense with these three cards.

The three angles and their numerological counterpart are numbered 1+7+10=18 (Moon).

The nine unique triplets with their numerological counterparts are:
1+2+3=6 (Lovers);
5+2+3=10 (Wheel of Fortune);
2+4+5=11 (Justice);
3+5+6=14 (Temperance);
4+5+8=17 (Star);
4+7+8=19 (Sun);
5+6+9=20 (Judgement);
5+8+9=22; 22–9=13 (Death);
6+9+10=25; 25–9=16 (Tower)

The cards in the second set total to “165,” which is “3×55,” making it a multiple of the first one. It reduces to “21” (World) by casting out nines and then to “12” (Hanged Man, first card in the series.) In this population, the Star provides the “interior force” communicating with all of the other cards except the three angular points. Therefore, the Hanged Man, the Devil and the World (Water/Earth/Earth) create their own passive and negative “power base” that stands apart from the uplifting positivity of Air.

The three angles and their numerological counterpart are numbered 12+15+21= 48; 48-(3×9)=21 (World). I see no reason to reduce this further.

All six corners sum to 66, an harmoniously balanced number that reduces to 12 by both Theosophical reduction and casting out nines, making the Hanged Man a central theme of this arrangement as the portal to trans-personal development. As the upper and lower points of the combined display, the Magician and the World add to 22, reducing to 13 by casting out nines, suggesting that Death is the gateway to evolution.

The nine unique triplets with their numerological counterparts are:
12+13+16=41; 41-(3×9)=14 (Temperance); 41-(4×9)=5 (Hierophant);
13+14+17=44; 44-(3×9)=17 (Star); 44-(4×9)=8 (Strength);
13+16+17=46; 46-(3×9)=19 (Sun); 46-(4×9)=10 (Wheel of Fortune); 46-(5×9)=1 (Magician);
14+15+18=47; 47-(3×9)=20 (Judgement); 47-(4×9)=11 (Justice); 47-(5×9)=2 (High Priestess);
14+17+18=49; 49-(4×9)=13 (Death); 49-(5×9)=4 (Emperor)
16+17+19=54; 54-(4×9)=18 (Moon); 54-(5×9)=9 (Hermit); 54-(6×9)=0 (Fool)
17+18+20=55; 55-(4×9)=19 (Sun); 55-(5×9)=10 (Wheel of Fortune); 55-(6×9)=1 (Magician)
17+19+20=56; 56-(4×9)=29 (Judgement); 56-(5×9)=11 (Justice); 56-(6×9)=2 (High Priestess)
19+20+21=60; 60-(5×9)=15 (Devil); 60-(6×9)=6 (Lovers)

The third array that includes Justice is where things get really interesting. By placing Justice at the center of a circle composed of the eight cards that form the “bases” of the two triangles and creating triplets from the diametrical opposites with Justice in the middle, every one of the subsets totals “33,” half the sum of the six corners. By casting out nines, this reduces to 15, the Devil. (I will add in passing that while researching the number “33” I learned far more about the Scottish Rite of Freemasonry than I ever needed to know.)

What is coming to light here is that the Hanged Man (Water), Death (Water), the Devil (Earth), the Moon (Water) and the World (Earth) are keynote cards to understanding the hidden meaning of these combinations. All of them are of negative and passive polarity, implying an inner significance that transcends outer reality. On the other hand, in A Dictionary of Symbols, J.E. Cirlot describes the diamond as a “material and active” principle, while the circle represents “Infinity, the universe, the All.” Although he doesn’t take it this far, inscribing the diamond within the circle with Justice at its center could be interpreted as an active inner life based on the judicious, pragmatic wisdom of Saturn in Libra that has important ramifications for outer reality. As a dominant Water and Earth personality (Scorpio/Cancer/Capricorn) with a prominent and well-favored Saturn, I can totally relate to this and might consider the combined set to be a form of personal sigil.

Originally published at http://parsifalswheeldivination.wordpress.com on October 28, 2023.