The Great Spirit (Wakan Tanka, Gitchi Manitou of Native American cultures) is a beautiful example of a non-theistic belief in an active, personal, non-anthropomorphic Deity that is intertwined with the fabric of the Universe itself on the large scale and yet is personally engaged with the web of living things and the world on an earthly scale. These cultures are not completely homogeneous, and there are a variety of creation mythologies that need not concern us as (in my opinion at least) these cultures have always been aware that their mythologies are myths, that their legends are legends, that their sacred stories are stories, and thus they have avoided the curse of socially enforced orthodoxy or any sort of insistence on “belief”. The myths themselves are intended and used as teaching stories that guide individual behavior in ways that support the individual and the community, not as metaphysical speculation. These religions also seem to lack the hellfire and damnation meme – the Great Spirit doesn’t punish people for being bad, doesn’t inflict eternal torment on people for “not believing in It”. In these cultures, a life out of balance with the Great Spirit, with the earth, with the community is its own punishment.
It is easy to over-romanticize these religions, and therefore important to remember that however successful they might have been within a community, pre-Columbian Native American tribal Stone Age cultures were many and were in more or less perpetual competition. Life was very close to the state of nature, and aspects of it were ugly, nasty, brutish, and short. Tribal wars were nearly ubiquitous and were very nearly ritualized. Torturing captives to death and ritual cannibalism were commonplace. Because each tribe had a personal, tribal vision of God, God naturally approved of all of these actions and indeed would sometimes help the tribe against their enemies. Life was filled with suffering as well as joy, and this intense mixture was the gift of the Great Spirit.
In post-Columbian times, the very process of romanticizing has, I suspect, injected memes of non-tribal Universalism into these tribal religions as what was a narrow and insular tribe has been submerged into the “tribe” of all of mankind. The concept of the Great Spirit as a somewhat nostalgic deity survives, but at this point tribal war, ritual torture and sacrifice, cannibalism, and all of the negative intertribal conflicts have faded.
So, is the concept of the Great Spirit compatible with the theorem above? If one takes the mythology literally, no. If one takes the actual spiritual practice, the personal view of the Great Spirit as a thing that is ubiquitous, a sort of a “life force” of the world itself, then maybe. Once again, there is an intuitional view of Deity that was pervasive in North America and clearly visible in their myths and sacred stories that all things were one with the Great Spirit, even as they manifested that spirit as Spider Woman, Buffalo Woman, the Old Man, as a creator who was often a trickster with a wry sense of humor who laid out the hills and covered them with trees and game and enemies to fight. All things had their own particular spirits, including the rocks, the hills, the trees, the animals, and of course the people. Were these spirits separate from and yet one with the Great Spirit? I have no idea, and given the number of pre-literate cultures involved and the evolution of their belief systems (especially after contact with the Christian Europeans who completely destroyed pre-Columbian intertribal society whereever they encountered it) I doubt that anybody really knows or that any single answer is universally correct.
Let’s give them the benefit of the doubt, and say that at the very least some of the cultures were developing an increasingly monotheistic and monist view of Deity at the beginning of the sixteenth century. Whether or not that view would ever have converged on the conditional pandeism proven in the theorem above on their own is a moot point, but to the extent that these religions survive in the modern world among Native American tribal groups, they are perfectly capable of incorporating this theorem into their current meme set now, should they choose to do so, without doing any great harm to the cultural mythology.