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[Aion]

The paths of polarity as described by Ra are only somewhat relevant to such 'lodges' in that individuals may be drawn to one or other type of fraternity. I don't think it is true that positive goes to white and negative goes to black because there are many different perspectives and what is white to one may be black to another. I dont believe the idea of fraternal lodges is quite so simple, there are diverse groups and there are individuals. The idea of a collective black lodge seems especially unlikely since they are often not in to cooperation.

So, sure, these exist but they are more scattered than they seem. As for a 'third lodge', well, I will just say that many spiritual traditions work through the number 3. There are ever those who eventually.find the Middle Path.