Tom McFarlane in The Integral Sphere: A Mathematical Mandala of Reality presents a dynamic mathematical mandala which can be seen as an integral model of reality. In contrast with conventional two-dimensional mandalas, the mandala described here is a sphere in three (or more) dimensions. Moreover, through a process of breaking the perfect symmetry of the three-dimensional sphere and then projecting the sphere onto a plane, the sphere is related to conventional linear, planar mandalas and unfolds their implicit archetypal structures. For example, a mandala with many similarities to Ken Wilber's Four Quadrant model of the Kosmos is unfolded as a special case of the spherical mandala. A four-dimensional integral sphere also contains Wilber's nested spheres as a special case. Higher dimensional spheres can be used to represent additional aspects of existence. The paper also shows how the present model provides a tool for facilitating complex thinking with fundamental categories, revealing how they interpenetrate and transform into each other.

oroboros commented on the word integral sphere

Tom McFarlane in The Integral Sphere: A Mathematical Mandala of Reality presents a dynamic mathematical mandala which can be seen as an integral model of reality. In contrast with conventional two-dimensional mandalas, the mandala described here is a sphere in three (or more) dimensions. Moreover, through a process of breaking the perfect symmetry of the three-dimensional sphere and then projecting the sphere onto a plane, the sphere is related to conventional linear, planar mandalas and unfolds their implicit archetypal structures. For example, a mandala with many similarities to Ken Wilber's Four Quadrant model of the Kosmos is unfolded as a special case of the spherical mandala. A four-dimensional integral sphere also contains Wilber's nested spheres as a special case. Higher dimensional spheres can be used to represent additional aspects of existence. The paper also shows how the present model provides a tool for facilitating complex thinking with fundamental categories, revealing how they interpenetrate and transform into each other.

June 28, 2008