The Geometry of Divination - The Power of Angles

The branch of mathematics that deals with the properties, measurement, and the relationships of points, lines, angles, surfaces, and solids is called geometry.
Fundamentally, our everyday experience of life is 3 dimensional, though that 3 dimensionality also includes one and two dimensional experience. We experience points, lines, planes or surfaces and volumes. Full stops or points such as at the end of that last sentence, a line when a word is underlined, the surface which is the page of this book in your hand, and volume is the box in which your geomancy cards and book arrived. These three dimensions are the simple experience of length and breadth and height. Each of these 3 dimensions are at a 90 degree or right angle to each other.

The Greek mathematician Euclid – known as the Father of Geometry – introduced the concept of a line. He defined it as “a breadthless length.” A line is created by a series of one dimensional points; is straight (meaning it has no bends); has no thickness; and extends infinitely in both directions.

If you take two lines at right angles to each other you  create a plane or flat surface. Something that has both length and breadth, a 2 dimensional surface, like the pages of a book. 

Then when we take another line at right angles to the surface, we invoke the third dimension of height (and volume), the thickness of this book if you close it. 

However, we can extend this model of right angles further by suggesting the possibility that if we were to make another line at right angles to that which created height (or volume) we would be invoking a fourth physical dimension. The problem with that concept is that there isn’t another line at right angles that isn’t either the length, breadth or height.

The possibility of a fourth physical dimension could be approached in a different way in that two points mark the boundaries of one line, four lines delineate one square, six squares create one cube, a numerical sequence of 2, 4, 6… which if continued would mean that eight cubes create a four dimensional figure, or shape, which will have an eight sided symmetrical aspects to four independent directions. Mental imagery will totally fail to create an image of such a shape. However, in mathematics this shape is called a tesseract or a four-dimensional hypercube. 

If we go beyond thinking in terms of ordinary mathematics and geometry and what we can do with numbers and shapes, and move into the mathematics and geometry of consciousness, we could postulate that there is a certain shift in perception at the point when there is a movement from the ordinary everyday perception of the three physical dimensions of the physical world into the next or fourth dimension. 

Whilst the everyday experience of life is three dimensional, we rarely think about it, or even perceive it as such, in any conscious way. Children explore this three dimensionality through relating vision to touch, they look at, are attracted to and then reach out and grasp objects near them, exploring them not just with their hands but also their mouth. They gradually build up a three-dimensional model of the world. As adults, one and two dimensional perceptions are not lost. In fact, two dimensional experience is rather more dominant in everyday experience. Many people have had the experience of being in a queue at a movie theatre and passing by simple two dimensional life size cardboard cut outs of the actors in the movie, and have found themselves startled, for a brief moment, thinking that the cutout was actually a real person. 

When learning to draw, we take a pencil and try to make a two dimensional representation of a three dimensional object on the paper. When looking at photographs, three dimensional shapes are rendered in two dimensions.  It is such a common experience that often people are referred to as two dimensional. Some people are even described as one dimensional when for example, they are obsessed by one experience in life. When looking at yourself in a mirror you know you have a three dimensional body that has both height and width but also depth, a front as well as a back. Yet you just see yourself in a two dimensional representation, and this two dimensional experience begins to dominate. 

It is easy to perceive, in everyday consciousness, a point, line or surface all at once. However, when it comes to a volume, such as a cube, it can only be perceived visually in one perspective at a time. To experience it fully, in its completeness, it has to be rotated by hand to see it from all sides and from different perspectives, in order to build up the representation of it in consciousness. If it is too big to hold then it must be moved around physically to get that complete experience, just as in a museum or gallery when an artifact or sculpture is viewed from all possible positions. 

The immediate perception of one and two dimensional objects, such as a point, line or surface, is the movement of visual perception up at right angles above them. Shamanically speaking, this is the eagle’s gift, perception itself moving into the third dimension. 

To perceive a three dimensional object all at once, would be to move perception into the fourth dimension. If a simple cube could be perceived all at once, both inside and out, from all perspectives, consciousness would have to move into the fourth dimension.

This movement of consciousness into the fourth dimension would not just allow the complete experience of physical space, in its totality, all at once, but as an aspect of that complete experience there would be the experience of the duration of the object, its birth or creation, and the duration of its existence and its destruction. In other words, fourth dimensional perception includes the experience of time. This fact lies at the heart of divination.