A Curious Note About the Geomantic Joys

[sdi]

I was pondering the Joys of the Geomantic Figures and realized something interesting: Mercury and Venus cannot rejoice together. This is because the first mother's head must be latent if Mercury rejoices, the first daughter's head must be active if Venus rejoices, and these cannot occur simultaneously. (Weren't violetcabra and I just talking about this yesterday?)

I was curious if such a relationship held for any other pair of planets, and so I wrote a computer program to examine every geomantic chart and see which pairs of planets either always or never rejoice together. It turns out there is exactly one other possibility: the Sun and Jupiter also cannot rejoice together.

The analysis for this is a little more involved. Let's name the boolean variables that make up the mothers as follows: A B C D for the first mother, E F G H for the second mother, etc.; the daughters are the transpose of these: A E I M for the first daughter, B F J N for the second daughter, etc.; and finally, the nieces are the XOR of their parents: A⊕E B⊕F C⊕G D⊕H, etc.; as in the following shield chart:

D H L P	C G K O	B F J N	A E I M	M N O P	I J K L	E F G H	A B C D
C⊕D G⊕H K⊕L O⊕P		A⊕B E⊕F I⊕J M⊕N		I⊕M J⊕N K⊕O L⊕P		A⊕E B⊕F C⊕G D⊕H
⋯				⋯
⋯

We will focus on the head and neck lines of the ninth house (where the Sun rejoices) and the eleventh house (where Jupiter rejoices). First, please note that the Solar figures Fortuna Major and Fortuna Minor always have identical head and neck lines, while the Jovial figures Acquisitio and Laetitia always have different head and neck lines. Therefore, if there is a Solar figure in the ninth house and a Jovial figure in the eleventh house, then A⊕E=B⊕F [eq. 1] and A⊕B≠E⊕F [eq. 2]. However, if we add B⊕E to both sides of eq. 1 and cancel, we get A⊕B=E⊕F [eq. 3]. Eqs. 2 and 3 cannot both be satisfied, therefore the Sun and Jupiter cannot rejoice together. ∎

Comments

[boccaderlupo]

I know literally zero about Geomancy, but might be interesting to cross-reference these with the "contraindications" of the planets in the Picatrix (if you have it), and if I am reading you right.

Axé

[sdi]

Thanks for this; I'll have to dig up a copy of the Picatrix and see.

[tunesmyth]

Fascinating, and worth meditating on! I guess you could cheat out a Mercury Venus double joy if you were to allow Caput to count as Venusian or Jovian when necessary, though this may be a dubious thing to do. Either way, still there would be no way have both Solar and Jovial joy together, as the head and neck lines of Caput are different.

Also, can I steal your letter table at some point? It shows very clearly something that I have wanted to be able to explain concisely but always needed a lot of words to describe.

[sdi]

I am not yet certain if Caput can be used in place of Venus in these context: I haven't seen the case occur, as far as I know! As I wrote a little while back, I suspect not—I think there's a compelling argument that Caput has it's own joy elsewhere—but that's speculative.

As for the table, yes please! I disclaim all copyrights to everything I post.

[sdi]

Yesterday, I had a chart where Cauda was in the twelfth and was so mighty that it should have been counted as rejoicing, I think. So I have at least a little evidence that the planetary figures used for the joys matches those used for planetary company. Still in need of more data to be sure...