Let us have a specific look at Namadev's proposed base-12 triangle as the foundation or basis for a 78-card deck.
Firstly, let me re-iterate that irrespective as to its historical merit, it is a geometrical insight which adds to the inter-relationship of the numbers used in Tarot's division which is suberb.
For the sake of ease of access, I have also attached a copy of Namadev's division of the base-12 triangle.
The 4x4 square and the 4x10 suits would have been without any doubt, to my mind, also thought about easily during earlier times as a square of base four (16) and four triangles of base four (each 10) - as indicated by the outer triangles by Namadev. For anyone which even plays a little with geometry, this would have come so easily as to have been 'obvious'.
Also, the 'tetractys' (or base-4 triangle) of ten points was well known - probably better than the base-4 square.
78, as a number, would likewise have been easily observed to have been a triangular number - and an important one, given its base is 12.
It
could therefore have been possible for someone to have also similarly discovered what has been presented by Namadev. However, the question is not whether others have likewise made this discovery, but whether it played a role in either the formation or the direction of tarot.
This is quite a separate matter.
If one reflects on a tetrahedron of edge-four, the total is not 22 - nor even 21, which would also have been quite significant - but rather 20 (base layer of 10 + next layer of 6 + next of 3 + top of 1).
Yet it is indeed fascinating that if one creates the simplest kind of 'template' for a construction, three triangles are sufficient (as given by Namadev). If each triangle has a base of four, this does indeed provide the 22 points.
But, again, was this a discovery which, if made earlier than by Namadev, came
prior to, or
subsequently to tarot's arousal?
For myself, the question has various layers itself.
On a mundane level, I suspect it is unlikely to have been noted by earlier neo-pythagoreans of the times under consideration.
On a
spiritual level, however, it was there all along - in the similar manner that the number
e existed prior to its discovery.
Tarot exhibits, then, a multifold mathematical aspect, of which we have the overall various allusions already made actually being there, without necessitating that those specific considerations were also historically important:
- line base 4 = 4 (suits)
- triangle base 4 = 10 (number in each suit)
- square base 4 = 16 (courts)
- pentagon base 4 = 22 (atouts)
- total: 4 x 10 + 16 + 22 = 78
With the additional interesting aspect being twofold: on the one hand the total being itself a triangular number of an important (and heavenly) numbered base; and that the pentagonal number can be altered in a manner demonstrated by Namadev to transcend its two-dimensional limitations and become, as a consequence, a three-dimensional tetrahedron - with again not only edge four, but with four faces (of necessity) arising from only three depicted ones.
If these
had been considered by early Tarot
creators, then, as the tetrahedron has only
twenty parts or points, would it not have maintained
two cards without number? Or is the other indicated by with-holding a
name!?
If there is Kabalistic influence in the deck, then it would also have undoubtedly been deemed important to want to maintain 21 (and only 21) out of the 22 numbered (yet also maintain the 22 in total), to achieve that other important and gate-opening triangular number (which utilises only the first three digits when written in Hindo-Arabic form),
viz, 231.
I read clearly - you must take responsibility for your words.