‘Geomantic’ figures as fourth dimensional vectors

The fourth dimension is an abstract concept derived by generalizing the rules of three-dimensional space.  It has been studied by mathematicians and philosophers for almost two hundred years, both for its own interest and for the insights it offered into mathematics and related fields.

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The figures are generated by applying the rules of vectors and coordinate geometry to a space with four dimensions.  A vector with four elements, such as the geomantic figures, can be used to represent a position in four-dimensional space.

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‘The revealer of secrets’

 

The revealer of secrets

Possibly from Damascus (Syria), AD 1241-42

This unique instrument ‘calculates’ patterns of dots with different ascribed meanings, related to the planets, four elements, the signs of the zodiac and parts of the body.  Many scholars have written about geomantic divination, but there are no references to an instrument such as this.  One Arabic term for geomancy is ‘ilm al-raml (‘the science of sand’); originally, the patterns were created when the geomancer traced dots with a stylus across a board of sand or dust.  The geomancer then inspected and interpreted the dots, deriving further patterns, and eventually a result or forecast for his customer.  This instrument provides a mechanical means of tracing the dots and developing further patterns.  The rectangular tablet features a series of sixteen dials, each turning to display a domino-like pattern in the small window above.  Hence the inscription on the instrument’s face:

I am the revealer of secrets; in me are marvels of wisdom and strange and hidden things. But I have spread out the surface of my face out of humility, and have prepared it as a substitute for earth. […] From my intricacies there comes about perception superior to books concerned with the study of the art’ [of geomancy].

To use the device, the customer or the geomancer turns the first series of four dials, creating four dot patterns for interpretation.  From these four, the geomancer then derives a further twelve patterns, using the following dials to record each stage.  The semi-circular panel at the bottom provides ‘meanings’ for the final derived pattern, and the customer receives an answer to his question (‘should I marry X?‘, ‘will my business venture succeed?‘, etc.).

The triangular handle and ring at the top of the panel are features usually found on astrolabes.  This suggests that the craftsman, Muhammad ibn Khutlukh al-Mawsili, was also a maker of astrolabes, but there are no known astrolabes bearing his signature.  ‘al-Mawsili’ shows that Muhammad ibn Khutlukh came from Mosul in northern Iraq, a city famous for its accomplished metalworkers in the first half of the thirteenth century.