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Mean Phase of Sample Matter

Simplicial 3-Complex of Elements



Among the elements is there a sensible relationship that somehow takes the shape of the tetrahedron?  Possibly.  Consider the shape itself, its parts and their boundaries.  For example, the space inside the pyramid has a boundary made of four triangular sides, representing the four elements.  Between every two sides there is a line segment, representing a substance having qualities of both the particular elements; e.g., between earth and water there is mud.  Each line segment has two endpoints, and they are representing two opposing extremes of the substance.  The figure has four vertices, and another way to interpret them is as a lack of quality; since every element has only three corners, there is a fourth corner at a distance from each.  Opposite fire is cold, and so there is also dryness for water, compactness for air, and a sort of fluent vortex for earth.  For instance, mud therefore ranges from being compact to being cool, dust ranges from being dry to being cool, steam ranges from being compact or thick to being vortical, etc. Notice that one extreme doesn't exactly oppose the other, but rather there is more the possibility of one quality dominating the other.

After some thinking, I find a problem with making the vertices each a lack of something rather than a positive quantity.  The assignment is problematic because there would be no constant value signifying two lacks at once in homogeneous coordinates.  The solution is to put each element at a separate vertex and to consider a sample of fixed mass.   Each face of the tetrahedron becomes the lack.  Alternatively, in a higher-dimensional space there may be a way to keep the complex as it were.  If, for example, add mass itself as a dimension and construct the pentachoron, and there might be a possibility.  A little more reflection and pondering are necessary to be sure of it.



Categories : mathematical

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