Geomancy · Method
How a shield is made
A geomantic shield consists of fifteen figures. Four of these are cast and eleven get worked out, and the working is arithmetic so plain that it can be done on paper in a minute and checked by anybody who knows the one rule. This page is that rule, and the eleven consequences of it, set out one move at a time.
Each step below is quoted from Of Geomancy in Robert Turner's English of 1655, with this study's plain English underneath it and marked as ours. The quotes are cut out of the transcription by a script rather than typed, so the spellings are the printing's: foure, Matres, Coadjutrices or Testes.
1. What a figure is
A geomantic figure is four lines, one above another, and each line carries either one dot or two. That is the whole of it. There is no picture to learn and nothing to copy: a figure is four bits of information, and two figures are the same figure if and only if all four of their lines agree.
Four lines of two possibilities each is sixteen arrangements, so there are sixteen figures and there cannot be a seventeenth. That is not a doctrine about the art; it is a fact about the number four, and it is the reason this site can prove its table of figures rather than ask you to trust it. The extractor that reads the sixteen out of the 1655 printing refuses to write its file unless all sixteen arrangements come out exactly once.
first it is to be knowne, that all Figures upon which this whole Art is founded are onely sixteen, as in this following Table you shall see noted, with their names
In plain English The art has sixteen figures and no more. Four lines, each of one dot or two, is sixteen arrangements exactly — so the table of them can be checked rather than trusted.
Eight of the sixteen have an even number of dots and eight have an odd number, and that division matters later: only the eight even ones can ever be a Judge. The sixteen figures lists them all with their planets.
2. Casting the four Mothers
Make a row of points — in sand, on paper, with a stick, with a pen — without counting them as you go. Not counting is the point: the row is supposed to end where your attention ends. Then make three more rows under it. You now have four rows of an unknown number of points each.
Count each row. If it came out odd, it leaves one dot; if even, two. Four rows therefore give four lines, and four lines are a figure. Do this whole thing four times over to make sixteen rows in all — and you have four figures. Those four are the Mothers, and they are the only chance in the entire shield.
- 13 points — odd leaves one
- 9 points — odd leaves one
- 8 points — even leaves two
- 11 points — odd leaves one
And now we come to speake of the manner of projecting or setting downe these Figures, which is thus; that we set downe the points according to their course in four lines, from the right hand towards the left, and this in four courses: There will therefore result unto us foure Figures made in foure severall line; which foure Figures are wont to be called Matres: which doe bring forth the rest, filling up and compleating the whole Figure of Judgement
In plain English Make four rows of points, right to left, without counting them; do that four times over. Each row's parity gives one line, so each course of four rows gives one figure. Those four figures are the Mothers, and they are the only part of a shield that is cast.
Two details of that passage are worth keeping. The rows are made from the right hand towards the left, which is the direction a shield is read in too: the first Mother sits on the right of the top row, not the left. And the four figures are called Matres because they bring forth the rest — the name is a description of what they do, not a title.
Nothing in the printing says the points must come from a person rather than from anything else, and it says outright that it does not matter where or how they are made. What it does say is where the answer is supposed to come from.
Another power there is that doth direct and rule this Lot or Fortune, which is the very soule it selfe of the Projector, when he is carried to this work with some great egresse of his owne desire, for this Art hath a naturall obedience to the soule it selfe, and of necessity hath efficacy and is moved to that which the soule it self desires, and this way is by far more true and pure; neither matters it where or how these points are projected
In plain English What makes the cast answer, in this account, is the mind of the person casting — so the manner of making the marks is left open, and the book says outright that it does not matter where or how they are made.
3. Turning them into Daughters
Write the four Mothers side by side and you have a four-by-four grid of lines. Read it down its columns instead of across its rows and you get four more figures: the Daughters. The first Daughter is the first line of each Mother, top to bottom; the second Daughter is the second line of each; and so on.
This is a transposition and nothing more. No points are cast, no information is added, and the sixteen lines of the Daughters are the very same sixteen lines as the Mothers, turned ninety degrees. That is worth being clear about, because it is what makes the Judge behave later on.
| Mother | Line 1 | Line 2 | Line 3 | Line 4 |
|---|---|---|---|---|
| Mother 1Puer | · | · | ·· | · |
| Mother 2Amissio | · | ·· | · | ·· |
| Mother 3Albus | ·· | ·· | · | ·· |
| Mother 4Populus | ·· | ·· | ·· | ·· |
| Read down | Daughter 1 The lesser Fortune | Daughter 2 Lætitia | Daughter 3 Conjunctio | Daughter 4 Lætitia |
Of these foure Matres are also produced foure other secondary Figures, which they call Filia, or Succedents, which are gathered together after this manner; that is to say, by making the four Matres according to their order, placing them by course one after another; then that which shall result out of every line, maketh the Figure of Filiae, the order whereof is by discending from the superior points through the mediums to the lowest
In plain English Set the four Mothers side by side and read them downwards instead of across. The four Mothers' first lines are the first Daughter, their second lines the second Daughter, and so on. The Daughters add nothing new: they are the same sixteen lines, transposed.
Turner calls them Filia, or Succedents. The second word is astrological, and the printing gives two different house layouts for these eight figures: the common one, which fills houses one to eight in order, and then his own, which puts the Mothers on the four angles and the Daughters on the four succedent houses — the second, the eleventh, the eighth and the fifth. Neither is drawn here. This section stops before the houses.
4. Adding two figures
Everything from here to the bottom of the shield is one operation, done seven times. To add two figures, take them line by line. Add the dots in the pair of lines. If the total is odd the new line has one dot; if it is even it has two.
Since a line is only ever one dot or two, there are four cases and they collapse to a shortcut that is easier to do in your head: alike makes two, unlike makes one. Both shown here, because the shortcut is the consequence and the counting is the rule.
| First line | Second line | Points | Leaves |
|---|---|---|---|
| · | · | 2 — even | ·· two |
| · | ·· | 3 — odd | · one |
| ·· | · | 3 — odd | · one |
| ·· | ·· | 4 — even | ·· two |
By the combination or joyning together of the two Figures according to the rule of the even or uneven number in the remaining points of each Figure
In plain English This is the whole of the arithmetic, and the only operation in the art: add two figures line by line, and ask of each pair of lines whether the total is even or odd. Even leaves two dots, odd leaves one.
Worked through once
Mother 1 (Puer) added to Mother 2 (Amissio), which is how the first Niece of the example below is made:
| Line | Mother 1 | Mother 2 | Points | Leaves |
|---|---|---|---|---|
| 1 | · | · | 2 — even | ·· two |
| 2 | · | ·· | 3 — odd | · one |
| 3 | ·· | · | 3 — odd | · one |
| 4 | · | ·· | 3 — odd | · one |
The result is ☊ Dragons head. Notice that an addition throws information away — several different pairs of figures give the same sum — which is why a shield narrows as it descends and why the Judge is one figure rather than fifteen.
5. Nieces, Witnesses, Judge
Eight figures are now on the table. Add them in pairs, in order, and four more appear: Mother 1 with Mother 2, Mother 3 with Mother 4, Daughter 1 with Daughter 2, Daughter 3 with Daughter 4. This site calls those four the Nieces; the printing gives them no name of their own at all, and identifies them only as the ninth, tenth, eleventh and twelfth houses.
And these 8 Figures do make 8 Houses of Heaven, after this manner, by placing the Figures from the left hand towards the right: as the foure Matres do make the foure first Houses, so the foure Filia doe make the foure following Houses, which are the fift, sixt, seaventh, and eighth: and the rest of the Houses are found after this manner; that is to say, out of the first and second is derived the ninth; out of the third and fourth the tenth; out of the fifth and sixth the eleventh; and out of the seventh and eighth the twelfth
In plain English The eight figures now on the table are combined in pairs, in order, to make four more. This site calls those four the Nieces; the printing gives them no name of their own, and identifies them only as the ninth, tenth, eleventh and twelfth houses.
Add the Nieces in pairs and two figures are left: the Witnesses, which this printing calls the Coadjutrices or Testes. The right-hand one carries everything the Mothers came to and the left-hand one everything the Daughters came to. Add those two and one figure is left. That is the Judge — or, in Turner's word, the Index of the whole Figure.
After the same manner there are produced out of the last foure Figures; that is to say, of the ninth, tenth, eleventh, and twelfth, two Figures which they call Coadjutrices or Testes; out of which two is also one constituted, which is called the Index of the whole Figure, or thing Queried
In plain English The four Nieces are added in pairs to make two figures — the Witnesses, which Turner calls the Coadjutrices or Testes — and those two are added to make one. That last figure is the Judge, which this printing calls the Index of the whole figure.
The whole descent, on one example
Four Mothers of this site's own choosing — Puer, Amissio, Albus, and Populus — carried all the way down. Turner's own worked example is printed as a plate and this study has not transcribed it, so these four are ours and are named rather than implied.
Cast — four Mothers, then their Daughters
- Puer Mother 1 · House 1
- Amissio Mother 2 · House 2
- Albus Mother 3 · House 3
- Populus Mother 4 · House 4
- The lesser Fortune Daughter 1 · House 5
- Lætitia Daughter 2 · House 6
- Conjunctio Daughter 3 · House 7
- Lætitia Daughter 4 · House 8
Nieces — each the sum of the two above it
- ☊ Dragons head Niece 1 · House 9
- Albus Niece 2 · House 10
- Rubeus Niece 3 · House 11
- ☋ Dragons taile Niece 4 · House 12
Witnesses — the Coadjutrices, or Testes
- Aquisitio Right Witness
- Amissio Left Witness
Judge — the Index of the whole figure
- Via 4 dots — even, as a Judge must be
Cast a shield does the same to four figures of your own, and will walk you through all twelve moves one at a time.
6. Why the Judge is always even
The oldest check in the art is that a Judge with an odd number of dots is a mistake. It is usually taught as a rule to remember. It is not a rule; it is a theorem, and the proof is two sentences long.
- The Daughters are the Mothers transposed, so the sixteen lines of the Daughters are the same sixteen lines as the Mothers. Everything in the shield is built by adding those thirty-two lines together in pairs, and each of the sixteen distinct lines appears exactly twice.
- Adding line by line keeps the parity of the total. So the parity of the Judge's dot-count is the parity of every cast point counted twice — and twice anything is even.
Eight of the sixteen figures have an even number of dots, so only those
eight can ever be a Judge. The other eight can never appear
there, in any shield anybody has ever cast or ever will.
spec/services/geomancy/chart_spec.rb checks this the brute
way, over all 65,536 possible casts of four Mothers, because a proof
written in a comment is a proof nobody re-runs.
7. Where arithmetic stops
Everything above is arithmetic. What follows it in the book is judgement: the first twelve figures are read as the twelve astrological houses, the question is assigned to the house it belongs to, and the figures are weighed against each other. Turner then adds a step of his own that he calls the secret of the whole art.
But here we shal give you the secret of the whole Art, to find out the Index in the subsequent Figure, which is thus: that you number all the points which are contained in the lines of the projections, and this you shall divine by twelve: and that which remaineth project from the Ascendant by the several Houses, and upon which House there falleth a final unity, that Figure giveth you a competent Judgement of the thing quesited
In plain English Turner's own further step: count every point in the projection, divide by twelve, and count the remainder round the twelve astrological houses from the Ascendant. The house corpus is now present; this numerical technique is preserved as his additional instruction, not treated as a replacement for reading the figures and Judge together.
Those materials are now available without being collapsed into a verdict. Houses and meanings carries the twelve topics and all 192 figure/house relationships. Disputed attributions keeps the two sign lists and three elemental schemes in separate columns. The app does not choose between them, and it does not manufacture an automatic answer from judgments Turner says must be weighed together.