However, directions of geometric deformations of strain packages (quantum of matter and energy) are not supposed to be within three spatial dimensions. Our strain packages bulge out (or dent in) perpendicularly to three-dimensional space, as if a knot on the surface of a balloon bulges out from the two-dimensional surface of the balloon.

Eventually, geometric deformation (curvature and torsion) may oscillate and be symmetric on the spatial plane. In such a case, a complete strain package has two points that do not have (vertical) displacement per cycle of oscillation. Hence, deformation of strain package crosses spatial plane twice like a wave. Strain packages (photons) with such a deformation have symmetric wave function, and they have an integer spin.

Figure 10.1 Sine curve, two intersection points with plane for each oscillation

On the other hand, deformations of localized strain packages (knots and vortexes) bulge out (or dent in) perpendicularly to three spatial dimensions. In such a case, a strain package touches a spatial plane from a single point for each intrinsic circulation in the confinement volume. These strain packages have antisymmetric wave functions, since their geometric deformations are located towards either inside or outside the spatial plane (½ spin).

Figure 10.2 Deformation is either on top or on the bottom of the spatial plane. There is a single intersection point for each deformation

Hyperdirection is an inwards or outwards direction, which is added as an additional dimension to the three-dimensional space, as if spatial locations are divided into two alternatives (inside or outside the spatial plane). In fact, hyperdirection is the deviation from spatial directions to time dimension.

According to our hypothesis, the spin property of a strain package is the direction of the axis of circulation of the constant intrinsic flow (of the expanding space) in the confinement volume. However, this direction covers the hyperdirection, too. Thus, it adds an additional dimension (hyper-dimension) to the spatial directions.

Hyperdirection of the geometric deformation has very important consequences and leads to another important physical property: exclusion principle.

According to Geometric Generalization, three-dimensional space is closed (spherical), and its inwards and outwards directions differ, like the inside and outside of the two dimensional surface of a sphere. In physical reality, the difference between the inside (past) and the outside (future) is based on the direction of the expansion of space (time dimension), and it eventually forms the basis of the charge concept.