Addendum on Squares

I first raised the qualitative issue with respect to mathematical interpretation through indicating that the square of 1 (2-dimensional) is clearly qualitatively different from the line segment of 1 (1-dimensional) though quantitatively the result is similar.

Further contributions then showed how the 2-dimensional qualitative structure is based on the complementarity of opposite (unitary) polarities that are positive (+) and negative (-) with respect to each other.

Now initially one might have difficulty in relating this to the quantitative geometrical notion of the square (of 1 unit).

However this complementary 2-dimensional nature can in fact be illustrated with reference to the geometrical square.

If one starts in one position - say - the top right hand corner and then goes around the square till one arrives back in the same position, this will require that the parallel lines of the square must be traversed in opposite directions (both horizontal and vertical).

So if the forward direction of one of these lines is + 1, then the reverse direction of the parallel line will be - 1.

Thus to draw the square geometrically in linear terms requires that both horizontal and vertical lines be drawn from two opposite directions!