Native American Beliefs
I highly recommend the National Museum of the American Indian if you're in DC, And their websites got a lot of cool links too--including research materials. The whole third floor is given over to displays relating to the belief systems of these 8 tribes: the Pueblo, the Anishinaabe, the Lakota, the Quechua (Inca), the Hupa, the Q'eq'chi Maya, the Mapuche, and the Yupik. I don't want to over generalize and lump the beliefs of all these peoples together, but I did think I noticed some interesting similarities and differences with Western beliefs about the world--particularly scientific approaches.
All the tribes with the exception of the Quechua seemed to have as a primary symbol some version of a circle. The circles were divided by direction/season/color/stage of human life/associated animal spirit/virtue etc. So for instance, one part of the circle might represent East and Spring, and the color blue, and infancy... (not sure I'm remembering these exactly, but you get the idea). So there are those analogous connections and then there's also movement around the circle. I guess if you mapped it with one circle inside another and lines connecting the analogies, it would be a web.
Some had 7 directions, some five--almost all had one more direction than we generally do which was "center"--basically where the person is who is naming the directions. I could see one interpretation of this might be that this is unscientific--like a Ptolemaic universe versus a Copernican one--not acknowledging the independence of the movement of the heavens but always seeing in relation to the individual. But actually, I think there's something gained in acknowledging the subjectivity of the person doing the observation and that the objectivity of Western Science is it's own mythic belief in a way. Having people at the center includes them in the story instead of trying to separate them out. And that actually reminds me of kind of where we've wound up returning in quantum physics.
"... where we've wound up returning..."

Heh...
I guess that's what I was saying in a roundabout way. 
Interesting connection--I looked up "circuitous" and besides meaning roundabout it also means devious. And that reminded me of how trickster figures like Raven were seen as creators or benefactors of human beings.
There was also a picture of an Ourobouros (I can't remember from which tribe)--but didn't think I realized before how universal that symbol was.

Cafe at the museum
Not really about beliefs (though food and beliefs do go together in some way probably?) but the food at the museum was great! I wish I remembered all the ingredients in the main dish that I had--it had ancho chiles and corn and beans--but don't know what the sauce was. The hot chocolate was really thick and had some kind of chile flavoring. You didn't feel the chile heat as you sipped though, buta kind of delayed reaction in the throat. My brother thought this might be due to the kind of chile it was. I looked up chiles and couldn't find anything about that, but did find that dairy protects against that kind of chile burn, so maybe the milk/cream in the drink is what's producing the effect. The other thing I found out about chiles on this sight is that birds are immune to the effects so they recommend putting chile in your bird feeder if you want to keep the squirrels from eating. There's some good info on health benefits of capsaicin (the source of heat) too. About Hot Peppers
ETA: actually DL had a good summary of the health benefits of capsaicin here.