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Hi All,
I've been doing some digging lately into the 3D geometric equivalents of the existing 2D Alchemical symbols and representations of Alchemical principles.
From a pictoral diagram showing the relationship and interconnections between the 4 elements of Earthly existence (E,W,A and F), the four principles that underlie them (being Hot/Cold and Moist/Dry) and the 3 of Universal nature (Sulphur, Mercury and Salt) it became apparent that when put into a 3 dimensional form the combination of groupings of 2 Elements that associate with each Universal element has a fourth version, one that was not shown, or hidden in the original diagram.
Putting it another way the diagram showed Fire is Hot and Dry; Water is Cold and Moist, Air is Hot and Moist and Earth is Cold and Dry.
It then showed Sulphur to be a combining or Fire and Earth elements, ie: H+D+C+D or HDDC; Mercury to be of Air and Water or H+M+C+M : HMMC and Salt to be of Water and Earth or C+M+C+D : MCCD. This misses the fourth combination, that of DHHM or Fire and Air thus giving 4 combinations of 2 groupings of 3 principles, which in total give 4 hot, 4 dry, 4 moist and 4 cold combinants.
All of the above can be reasonably well displayed in just 2 dimensions but as i mentioned, i've been digging into working out how to represent such information in a 'real' 3D world situation. This generally involves bringing in a new axis on which 2 extremes are equidistant from the common central point, and making circles into spheres, squares into cubes and triangles into tetrahedrons.
Tetrahedrons, having only four faces and four points, naturally allow for association with the Four Elements of 'square' (cubic) Earth but also associate with the 3 sided triangle. Curiously, while the faces of the tetrahedron only display angles of 60 degrees the interior of the tetrahedron as defined by it's side lengths perfectly contains the right angled X,Y and Z axes of trigonometry/geometry and, even more surprisingly, a tetrahedron can be constructed using ONLY right-angled connections of straight line segments! (in a 3 x 3 formation).
But i digress.
In attempting to locate in 3D space the 'boundary' between the two opposites of Hot and Cold as well as that of Moist and Dry so as to locate the 4 elements within and between them and by using a Tetrahedron to fix in place the 4 elements, the abscence of the missing 3rd boundary of separation showed up!
Hot/Cold are extremes along one axis of the 3 axes of 3D, Moist and Dry are two extremes along a second of those axes leaving the 3rd perpendicular to both of the other 2. I have defined the 2 extremes of this axis (what are effectively the 3rd Active principle pairing) as Solving and Coagulating (Solve Et Coagula).
Each side of the tetrahedron can then be seen to have it's own Principle about opposite sides of the tetraheron's centre: Heat, Cold, Moist, Dry and Solve (dissolution) and Coagulation (crystalization). To better visualise this concept it helps to see the tetrahdron standing not on it's base as is usual, but standing on one edge - this orients the 3D axes in the normal fashion.
Diagram attached '7 Elements' shows this more clearly.
Hot and Cold are above and below the central sphere 'Element' (centre or origin of the 3D axes); Moist and Dry are to the 'SE and NW', while Solve and Coag are to the 'NE and SW' respectively. The four points of the tetrahedron are colour coded: Red for Fire, Yellow for Air, Blue for Water, and Green for Earth. they also represent the 4 Cardinal compass points of N,S, W and E. Being located in the Southern Hemisphere I associate them as Fire and N (the Sun rises to my North!) Earth and S, Water and West (i have the Indian Ocean to my immediate West) and Air - East.
The diagram '6 Elements' is a preliminary effort which better shows the circular plane (neutral) boundary between each of the 3 principle pairings which are all at right-angles to each other. The yellow square is a 3D cube centred on the 3D axes in this version and the red line is one side of the tetrahedron (all 6 faces of the cube hold (in the diagonal) one side of the tetrahedron) which is expanded in the later version.