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Riemannian Manifold

Glossary of Spiritual Wisdom

Excerpts about Riemannian Manifold

Dimensions of Reality Seen as a Riemannian Manifold

Viewing our consciousness in terms of its dimensions, we see that it is not a three-or four-dimensional field, but a multidimensional manifold, a manifold in the sense that it is a dynamic structure of dynamic structures. This manifold is characterized by a nonlinear -- Riemannian -- geometry, in that all the dimensions open up to all the others in nonlinear ways. Even in ordinary human experience, we can be aware of many different levels of experience in a given moment... All our inner experiences are manifestations of forms within the manifold of our consciousness, where these forms are nothing but the very fabric of this consciousness morphing itself at particular regions. This view is not only a more faithful rendering of our inner experience, but clearly reveals the purpose of inner work. This purpose is realizing the awareness of the field of consciousness itself, which makes it possible for us to inhabit our inner field completely in all of its richness and freedom.

Manifest World Seen as a Riemannian Multidimensional Manifold

Reality is composed of many dimensions, all necessary for manifest forms and our experience of them. It also reveals their hierarchic functioning, which in turn points to the absolute as the apex or center of that hierarchy. It reveals the objective relation of the absolute to manifest reality as the center of a hierarchy of manifestation, and shows us that by descending into manifestation the absolute descends into an increasing number of dimensions. It also shows that this hierarchy of manifestation is not temporal or spatial, but ontological. The integrated dimension reveals the manifest world as a Riemannian multidimensional manifold, and shows the hierarchical relationships of the functioning of its various dimensions.

Morphing of the Inner Multidimensional Riemannian Manifold

The inner multidimensional Riemannian manifold is in a constant state of organic self-organization, not through one form passing and being replaced by another, but through morphing, by one form dissolving, melting boundaries, and this dissolution merging continuously into the emerging boundaries of a newly arising form. Dimensions interpenetrate each other, transform into each other, overlap with each other, coalesce and separate, all in a nonlinear, non-discontinuous manner. This continuously changing formation is similar to the morphogenic transformation that the human embryo goes through. From a nondifferentiated initial condition, forms arise to change again into new forms. Organs emerge, develop, and become parts of whole systems, which systems formulate themselves, self-organize, and then interrelate in a holistic way. By birth the basic form of the human body is crystallized, except for a few things like the sexual changes that occur later. The body still goes through changes and transformations after birth, but they are no longer morphogenic on the level of body structures and systems. The body basically grows by getting bigger and the basic forms attaining their adult shape and size. Not so with the soul. Morphogenic transformation is a fundamental property of the soul. Its cessation would be psychic death.

The Soul Can be Experienced as a Self-Organizing Riemannian Manifold

The soul is actually the prototype of self-organizing systems, which can be experienced directly as a self-organizing Riemannian manifold. Appreciating the characteristics of self-organization and autopoiesis can help us understand some of the difficulties we encounter in our inner journey of development. It shows that the flexibility and malleability of the soul are necessary for her self-renewal, for her to continue to function as an autopoietic system, rather than a machine. Consequently, the rigid and fixated structures created through ego development can be seen as barriers to the function of autopoiesis. For the soul to mature, she cannot retain the same structures that she develops at any particular stage of her evolution. To become attached to these structures, which is the hallmark of egoic life, means active resistance to self-renewal. The hallmark of egoic existence is the permanent identification with structures created in early life. Through this attachment to established structures the soul tries to remain in static equilibrium, antithetical to her nature of open non-equilibrium. She attempts to maintain order through fixation, which necessitates isolation, while her nature is to be open, which means she needs to find order through fluctuation, i.e., through change. Or as Jantsch puts it: “Autopoiesis and evolution, global stability and coherent change, appear as complementary manifestations of dissipative self-organization.” (Ibid., p. 44.) Hence, egoic life constitutes an attempt to turn the soul into a machine, a closed and relatively isolated system. The rigidity and fixity of the ego-self point to how the soul has become mechanical and isolated, and explains the primary reasons for its lack of vibrant living unfoldment. Furthermore, the second law of thermodynamics will impel the rigidly structured soul toward entropy, toward less order, more disorganization, and hence ultimately toward disintegration. This accounts for the continual suffering of ego life, and its hopeless and incessant attempts at balancing itself. Egoic life is bound to lead toward disorganization and breakdown, not renewal and evolution.

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