Sherical thinking presents layering of contexts to create new, original content. The elements - usually recognized / known and their semantics are combined to create new contextual content. The simplest way to describe the methodics of spherical thinking is to envision a sphere with many eliptical rings that rotate in different directions, similarly to an armillary sphere or "spherical astrolabe". 

image credit

image credit

The translation of the armillary sphere to spherical thinking constitutes the rings as trajectories that comprise countless "points" that represent units of a semantical corpus. Speaking metaphorically, the center - the axis of the rings would be the one point that can hold a mass of different semantical units together, the point would be logic, or an archetypal centre of ratio, the axis around which the semantical "bodies" rotate.

Crossing of the points placed on the different, moving rings would mean a creation of a new ring with a new "point" - the new semantical unit. If the semantical units are envisioned as a concrete contexts, their meeting translates into a summation or a different "operation", but the result is always a new unit based on the character of the previously combined contexts. 

Understanding the metaphorical interpretation of the device into the new methodics of thinking can provide an artist or a designer with infinite possibilities of imaginative or visual expansion based on the elements he is working with. 

The visual example of spherical thinking is The Birth of Church which much as explained, creates new semantics based on the widely known interpretations regarding the Catholic church.