I have a question that I fear may raise some objection to the fact that it has been posted here, but I cannot think of a more appropriate place to pose it. I am not a mathematician; I'm a historian, and I am working on piece of prose writing that discusses the way in which an anthropologist from the early 20th century defined the idea of what a "culture" is. The idea here, of course, is that cultures can be defined differently, and in my work I want to argue that this anthropologist described cultures as "manifold" objects.
The question is to what extent is this description metaphorical and to what extent is it literal. In language, the definition of a manifold that I am interested in is the idea that a manifold is a whole thing with many distinct parts. I'm wondering, however, if the mathematical concept of a manifold may expand in important ways on this idea. What I'm wondering is what is a manifold object in mathematical terms.
My sense is that a manifold object in math is a way to talk about a space or an object that is continuous and yet which extends in dimensions that go beyond those that humans can with their basic senses (which are confined to euclidean space?) perceive?
I'm sure this definition falls harshly on many of your ears, but that is exactly why I am writing here. How can I understand/describe this concept in prose writing better? Am I completely off in my understanding? Any help would be wonderful!