Simbola is not mathematics and mathematics is not a language. It might be a provocation to think this but we will come back later to this prediction. For now we like to intruduce you into some simple logical operations. First we define the operations. Think about the results.

The next row shows the results. You might agree in this.

The next operation will also lead to a valid result in Simbola.

In this operation you take away the little left circle. You have no optical information whether a vertical bar exists behind 00 or 01 or 02 (square,reverse triangle, triangle) or not. By counting the number of different visible shapes you only can assume that 2 layers are free. If there would be a vertical bar behind the square, it would be invisible (like Schrödingers cat).

It might be helpful to see Simbola here more like a house with seven floors than a collection of numbers. You can add or subtract floors (= shapes), but the layers do not represent values that can be offset.

The space could be notated as space[0001020304].

Lets step back to the first simple operation. Question: Would be any other result be possible? Answer: Yes. In the first operation the little centered circle could be behind the big ciclye. So in fact the representation of the result of this operation could be the big circle.

If this is seen as a valid result, Question: How many possible results are valid for the second operation?

Space A[09] + Space B[03] = Space C[0903] or Space C[0309] (first operation)

Space A[03] + Space B[0201] = Space C[030102] or Space C[030201] or Space C[020301] or Space C[020103] or Space C[010302] or Space C[010203] (second operation)

However, the user decides on the result. In his choice he deliver the choosen vectors.

Rules:

When adding spaces, all combinations of all visible shapes, distributed and limited over the possible seven layers in the target space are valid, independent of their ability to be seen in the result space.

When substracting all visible shapes of the minuend space disapear in the result space. All visible shapes in the subtrahend space without a pair in the minuend space are disapearing too.

Shapes in the foreground are emphasized and are considered important. Background shapes are considered less important. The arrangement by the user also expresses his prioritization.

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