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Now, I know this isn't the Sawi Culture, but the question asked for uncivilized. This was the first thing I thought of. To get to the question, I feel like society should not just give cultures like the Sawi the modern world on a platter all at once. I saw this because I came to Korea, and everything changed for me all at once. Everything I knew to be true, wasn't always true anymore. I can remember the first couple days I was in Korea I felt like I was suffocating because I couldn't read anything. I have always been a very word dependent person. Billboards, cleaning supply's, everything. So, when I moved to Korea and I couldn't read or recognize anything, it was really hard for me. I think this experience would be exponentially worse for cultures untouched by the modern world.
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The best way to introduce an uncivilized in my opinion would be to slowly increase the culture's knowledge. Dictionaries and translations of the language should be made before the culture is thrown into modern society. Social taboos such as cannibalism and incest might NOT be a problem for some cultures. While rare, they do exist. These cultures are not going to learn over night their entire way of life if frowned upon and must decease to exist. Cultures such as the Sawi found common products such as axe to be a revelation. Technology like computers, the internet, telephones, and other common wonders of the 21st century would be inconceivable to "uncivilized cultures." Cultures such as the Sawi should be introduced into their surrounding area, such as other similar tribes and nearby civilization. Then slowly branch out into their country and eventually international dealings. This process should take years, not days. Introducing a culture too fast would be like taking Pocahontas to New York City and telling her to have figure it out. Can you say, culture shock?
Something to be avoided with new cultures would be the exploitation of the people. Large companies should not be allowed to take advantage of new workers who would not know safe working conditions, fair wages, or issues dealing with slave labor. Everything is good in small doses right, except cigarettes.
So the key phrase in this is "slowly," as long as society does that, the undiscovered cultures should do just fine. Well, relatively speaking of course.