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There are a lot of great answers here already, but I wanted to chime in with something that I felt was missing. If you want to show (not tell, as alluded to earlier in the Conrad / Kipling discuss...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/24158 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
There are a lot of great answers here already, but I wanted to chime in with something that I felt was missing. If you want to show (not tell, as alluded to earlier in the Conrad / Kipling discussion) that a culture has a different beauty standard, then that different standard should be represented in their cultural media. You mention in your post what the standard of beauty is in the US -- how did you arrive at that conception of what the standard of beauty is? Are people constantly talking about what is beautiful to them? Or, more likely, are people who match up with the standard of beauty more represented in media than people who don't? Wouldn't this be the same in the society you're writing about? Whatever means of cultural transmission the society you're thinking about uses, the standard of beauty will be represented in them. Paintings will feature people that meet the standard, professional or popular actors and dancers will exemplify the beauty standard, even bathroom signs might subtly reflect what that society expects people to look like. Have fun with it -- try to notice what everyday things subtly (and not-so-subtly) reinforce the beauty standards you've grown up with, and try to think of what would be analogous to those reinforcements in the society you're writing about. Overall, don't forget that while the characters in your story can represent and indicate the beauty standards of cultures, so can the objects.