For 1-dimensional subsets, the concept of *Frenet torsion* is intuitively
related to the twisting of the thread that approximates any given space curve.
For 2-dimension subsets, note that a twisted tube is different from an untwisted
tube, and leads to the concept of a *distribution parameter* in the
differential geometry of surfaces. For 3-dimensional subsets in space-time,
things becomes more complex, for now the concept of *Topological Torsion*
leads to visual topological defects, the production of lines of intersection,
and separated parts. Topological Torsion does not exist in less than three
dimensions. Topological torsion is a "point defect" in three
dimensional spaces, and a line "defect" in four dimensional spaces.

Topological Torsion cannot be zero in a chaotic dynamical system. In
hydrodynamic systems a non-zero value for the helicity density is a signature of
topological torsion. In space time, the helicity density, V .curl V/(V.V), is
the fourth component of the Torsion Current.

The arguments above apply to a 4 dimensional variety, like space time, but the
concepts can be extended to N forms dA^dA... and N-1 forms A^dA...