‘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.


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.




Rational forms of Divining.

The ancient Greek divinatory term Oionistic (from oio “thinking”, nous “understanding”, and hist “enquiry”) refers to the inductive art of the sane, those who inquire using the facility of human reasoning.  Many inductive or rational forms of divination have been compared with western scientific techniques.

Diviners are considered specialists who move from the boundless to the bounded.  They excel in insight, imagination and developed intuition.  During a divination they construct usable knowledge through linking diverse domains of representational information and symbolism.  It is the correct combination of inductive procedure and developed intuition that characterizes a good diviner.

The diviner’s individual creativity operates, jumbled with ideas, metaphors and symbols suggesting various possible interpretations.  Through the interaction of the client, these slowly give way to an ordered sequencing and to more limited interpretations, a technique not dissimilar to the psychoanalytical practice of free-floating attention.