Purpose of Touching the Shadow

While classical science is based on knowing the object based on consciousness. 

Touching the shadow is based on self-awareness which is technically therapy. 

I basically observe how I am observing the object or other. The result of self-observation, if you wish, is not to know external objects, but eventually know and know via Self. This Self-archetype is according to Jung not anymore a psychological archetype, but what he calls Psychoid, which has been referred to in Jungian circles as a transcendental subject (E.F. Edinger). 

Put differently, one awakens to a deeper expanded experience of self. 

The result here is to get to know and experience deeper levels of self and via this a sense of reality, where self and other are not experienced as separate vis-a-vis the classical scientific approach, where a sense of separateness ensues to the world or object due to getting to know the object.