When we reach the symbological level of neomathematical language we begin to consider the various symbological patterns of mathematical and neomathematical forms. Ifwe have a symbol that stands for a mathematical entity, say F, then we are accustomed to mappings between F onto other mathematical symbols, say G, We also name the mappings, either by associated spaces or directly through the pair, FG; but in any case we may also use a symbological symbol, such as R, to represent the mappings, as in the example, FRG.

More generally, mathematics is a mixture of purely mathematical expressions, such as FRG, and of the ordinary language. Let us for the moment leave the ordinary language parts in place and concentrate on variation in the purely mathematical symbology.

Following is a series of symbological variations

The principle of symbological variation is that each variation in symbolic form corresponds to a variation in the meaning of the symbol.

A possible use of symbological variation is as a forcing method of introducing new possibilities of meaning, much like neomathematics in general.

Here is an example which mixes physics, metaphysics and mathematics. Let the symbol

represent the solution to a Schrodinger equation (the wave function, which is more commonly rpresented by the Greek letter psi),

and let the empty set be represented by

Now we may form the symbological variation

which might be taken to symbolize a transition between being and nothing.

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Copyright(c) Joe Staley 1998