The distinctive apparatus of Western geomancy is the shield chart, and its structure is worth setting out, because it is what separates the art from simply drawing a figure and reading it.
The four Mothers
The practitioner generates four figures in the manner described elsewhere. These are the Mothers, and they are the only figures produced by chance. Everything else is derived from them by fixed rules.
The four Daughters
The Mothers are set side by side and read across instead of down. The four Fire rows of the four Mothers, taken together, form the first Daughter; the four Air rows form the second, and so on.
This is a transposition of the matrix. No new information enters. The Daughters are the Mothers rearranged.
Nieces, Witnesses, Judge
The remaining figures are produced by pairwise addition. Two figures are combined row by row: where the two rows have the same value the result is a double point, where they differ it is a single point.
- The eight Mothers and Daughters combine in pairs to give four Nieces.
- The four Nieces combine in pairs to give two Witnesses, the Right and the Left.
- The two Witnesses combine to give the Judge.
Fifteen figures in all, of which four were generated and eleven were calculated.
The check that makes it a discipline
The Judge is the answer to the question, and here the system does something that most divinatory methods do not: it contains an arithmetical check on its own validity.
Because of how the additions work, the Judge must always be a figure with an even number of points. Only eight of the sixteen figures qualify. If the calculation produces an odd Judge, an error has been made somewhere in the chart, and the reading is invalid and must be redone.
The system can tell you that you have got it wrong. That is a rare property, and it is the reason geomancy was taken seriously by people who took arithmetic seriously.
The later houses
A further development distributed the fifteen figures across the twelve astrological houses, producing a chart readable by the methods of horary astronomy. That layer is later than the shield and is where geomancy borrowed most heavily from astrology.
Practitioners have argued ever since about whether the house chart added anything the shield did not already contain.