Trust the Process: Geomancy’s Hidden Shuffling Mechanism and its Reassuring Function - Alma Eliaz
Updated: 8 hours ago
In this blog post, I demonstrate that the medieval divination method of geomancy involves a hidden shuffling step, and explore the potential function of this secret validation mechanism.
Divination by sortition, also known as lot casting, has been used for millennia as a means of accessing higher realms and revealing hidden knowledge. It includes all methods that use random choice to uncover past or future events, gain secret knowledge and make decisions.
Different practices of lot casting use different instruments, including dice, cards, sticks, beans and animal entrails. While the instruments and methods vary, most of them will involve some form of shuffling: Shaking the dice before throwing, shuffling the cards before opening them, or mixing the beans in the sack before drawing a few out. Through this action the diviner both ensures and declares that the outcome is purely random.[1] Without shuffling, we might suspect that the outcome was deliberately chosen by the diviner so as to yield a desired answer.
Geomancy is one such form of lot casting. It was widely used in the Middle Ages throughout the Muslim empires and Latin Europe. Its Arabic name, ilm al-raml ('science of the sand'), attests to the fact that it was initially based on creating and interpreting marks made in sand. Later it was usually done with pen and paper. Medieval instructional treatises specify possible answers to different questions and show that geomancy was mostly used for decision-making. People would turn to geomancers for advice on matters such as buying land, embarking on a journey or deciding on an engagement. The answers were obtained through a long and complex process that required skill and expertise.[2]
The geomantic process consists of a sequence of steps. It begins with the drawing of sixteen random numbers, which were traditionally obtained by marking sixteen rows of dots, each with an arbitrary number of dots. It is this first step that defines geomancy as a form of lot casting. However, if a person consciously marks these dots, the process may not appear so random and could seemingly be manipulated. Although medieval geomancy manuals clearly state that the dots should not be counted while being made, it is only natural to suspect that geomancers could cheat by ignoring this rule to obtain the desired answer. Could they?
Not so easily, actually.
The reason is that one of the consecutive steps works as a shuffle, which makes it very hard to steer the result. Unlike in most methods, however, this step is neither visible nor performative, but hidden within the process. In fact, I only discovered it after I'd started experimenting with the method. As part of my research into the early use of geomancy in the medieval Jewish world, I tried to learn the method and put it into practice. My aim was to 'get to know it from the inside' to better understand my sources. While documenting my experiments, I once tried to demonstrate how a particular answer had been obtained. However, as I had only recorded the final chart, I could not work backwards to reconstruct the earlier steps. This means that, to produce a chosen outcome, one would have to know, and memorise, the entire sequence in advance. Geomancy, therefore, contains a kind of shuffling mechanism.
In order to understand how the shuffle works, we need to examine the process that leads to the creation of the geomantic chart, which is the final arrangement of figures to be interpreted.
As mentioned above, the first stage consists of making sixteen rows of dots. While drawing the dots, the geomancer should concentrate on the particular question whose answer is the object of the geomantic consultation. The dots should not be counted as they are made, allowing the hand to draw freely any number of dots on each row.
Once all the dots have been made, it is determined whether each row has an even or odd number of dots. If a row has an even number of dots, it is represented by two dots; if odd, by one. The dots are then divided into four sets of four, yielding four figures, each consisting of a column of four entries, each containing one or two dots.
These four figures are usually referred to as 'the Mothers' and are arranged in a line from right to left. From these four Mothers, all the rest of the geomantic chart is derived.
The fifth figure is formed by working from right to left and assembling the dots in the top row of the Mothers as a column from top to bottom. The sixth figure is formed in a similar way, but this time using the second row of the Mothers. Figures seven and eight are formed using the same principle. These four figures are called 'the Daughters'. I call this the transposition step: it can be viewed as a matrix transposition, with the four Mothers as a 4×4 matrix consisting of entries of either one or two dots. Reflecting this matrix along the diagonal from the upper right corner to the lower left corner leads to the creation of the matrix of the four Daughters.
From the eight geomantic figures thus obtained, four more are now produced by a binary operation that I call 'conjugation', and denote by (+). Two figures are conjugated by adding their dots level by level: an odd sum becomes one dot, an even sum two.
When this operation is applied to each adjacent pair of figures from right to left, a row of four new figures is produced. Conjugation is then applied to the adjacent pairs in this row, yielding two more figures, sometimes called 'Witnesses'. These two figures are then conjugated to produce the final figure, known as 'the Result' or 'the Judge'.
Once the first four figures have been obtained, the remaining figures are produced by either transposing a 4x4 matrix or performing the binary conjugation operation. As this process is fully algorithmic, the initial four figures (or the initial sixteen numbers) determine the final outcome.
Since a geomantic figure consists of four entries each of which can be one or two dots, there are a total of 2⁴ = 16 distinct figures. The geomantic chart is interpreted according to the meanings attributed to each figure and its position in the chart. Unlike the algorithmic process described above, which is fairly consistent over time and place, the rules for interpretation vary from tradition to tradition. Nevertheless, many traditions attach great significance to the last three figures, so I will use these to demonstrate a principle that applies to the whole chart: the geomancer cannot easily choose the outcome.
If we take the last three figures as our 'outcome', i.e. the signs that need to be interpreted, we can now try to reverse-engineer the process to obtain a desired triad. Reverse-engineering the conjugations is very easy. Each figure can be obtained through the conjugation of sixteen ordered pairs of figures. Each of these pairs can be produced simply by splitting the figure (at each level, a one-dot result can come from 1 (+) 2 or 2 (+) 1, and a two-dot result from 1 (+) 1 or 2 (+) 2). We just need to select one of these pairs and place it as the parents of the figure. This way, we can form the branches that split from each of the Witnesses until we reach the first row of Mothers and Daughters.
However, there we will face a problem, because there is almost zero chance that this process will produce the correct relationship between Mothers and Daughters.
The transposition step makes it almost impossible to reverse-engineer the correct steps that led to a certain outcome without laboriously computing many charts.[3] Consequently, it is almost impossible to know which initial numbers would produce a desired answer. In this sense, the transposition step works as a shuffle.
As noted, shuffling can both ensure and declare the credibility of a random process. To declare true objectivity, however, we would expect the shuffle to be visible to both the geomancer and the client. Yet, in geomancy, the shuffle is not obviously visible and was probably hidden from clients. How, then, should we understand its function? If clients cannot see that the figures are being shuffled, how can they trust the divination? To answer those questions, we must remember that, even if the shuffle is hidden from the client, skilled practitioners were probably aware of it. In this sense, the shuffle could play a role in building trust in geomancy.
The modern theory of the placebo effect emphasises the importance of trust in successful medical and other healing encounters. If we consider the geomantic encounter to be a form of consultation, trust may well have played a central role in its success.
In medicine, healing depends not only on the patient’s trust but also on the physician’s belief in the treatment, which is why double-blind methods are used to test medicines.[4] Applying the same logic to divination, the geomancer’s belief in the method would have mattered as much as the client’s. I suggest that the hidden shuffle had a reassuring function, directed towards the geomancer. Its untraceability, the geomancer’s inability to work backwards from a chosen result, made the method hard to manipulate. And because the geomancer could not control the outcome, a distance may have opened between him and the method, so that the answer seemed to originate from an external source. Whether this external source was understood as divine will or the internal mechanisms that govern nature, both of which were prevalent explanations for divination in medieval times, the complexity of the process could lend it credibility in the eyes of its practitioners.
While conducting research for my MA dissertation, I consulted two Hebrew geomantic texts found in MS Magliabechiano III.36, held at the Biblioteca Nazionale Centrale in Florence. Both texts, one attributed to Abraham ibn Ezra (1089–1164), and the other written by Mordechai Finzi (1407–1476), are practical treatises that provide instructions for casting and interpreting the geomantic chart. As my research involved both traditional philological analysis and practical experimentation, I became more aware of what was and wasn't present in the texts. For example, I noticed that certain steps in the process were missing, as were references to potential problems that could arise during it. The general untraceability of geomancy and the shuffling resulting from the transposition step were among the details not mentioned in these or any other medieval texts I know of. Nevertheless, I believe that the sources’ silence about the shuffle does not mean that medieval users were unaware of it. Studying the sources has taught me that pivotal elements of the practical process are sometimes absent from the written text. There are various reasons why information may be omitted, ranging from the intention to conceal and protect it, to a tradition of oral transmission that existed alongside textual transmission, not to mention copying errors and poor manuscript preservation.
Practical experimentation offers a first-hand perspective on historical knowledge systems and can help us to fill in the gaps. In this case, it enabled me to notice geomancy’s hidden shuffle and to see it as more than a technical curiosity. I suggest the shuffle may have provided geomancers with a subtle reason to trust a method whose results they could not manipulate.
Footnotes:
[1] On randomness as a basic element in the rhetoric of divination, see: Jørgen Podemann Sørensen, “The Rhetoric of Divination: A Comparative Approach.” In Theoretical and Empirical Investigations of Divination and Magic: Manipulating the Divine, ed. Jesper Sørensen and Anders Klostergaard Petersen (Brill, 2021), 42.
[2] On geomancy, see: Alessandro Palazzo and Irene Zavattero, Geomancy and other forms of divination (Sismel - Edizioni del Galluzzo, 2017).
[3] How many? There is only about a 1 in 32,000 chance that a process of reverse-engineering, which starts from a certain valid triad of Judge and Witnesses, will produce the correct relationship between Mothers and Daughters. It is worth mentioning that this number holds for the difficulty of working backwards from the answer. However, there is another route of trial and error, that works in the other direction as a 'forward search' where one simply starts from trying different sets of numbers until getting the desired result. In this case, it will take only 128 trials on average to reach a specific triad. This is, of course, far more feasible than working backwards, but since each trial requires the full computation of a chart, I would still argue that the shuffle acts as a considerable obstacle - without the transposition step, reverse-engineering would hit the solution on the first try.
[4] See: Fabrizio Benedetti, Placebo Effects: Understanding the Other Side of Medical Care. Third edition. (Oxford University Press, 2021), 9-10.
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