I was watching "The Omega Glory" last night. The only way the ending makes sense is if there was an early joint American-Chinese colonizing effort that was thrown way across the Galaxy by a temporal wormhole, depositing them a couple thousand years in the past. That's the only way to make them a lost colony and have enough time for the society to develop as we saw.
No. Basic to TOS was an idea that I remember as being fascinating to me as a kid... the idea that, given precisely identical conditions, identical planets with identical geography and/or culture could arise independently in very widely separated parts of space. With NO contact whatsoever between them... but the starting conditions have to be identical. There is a name for the theory in Trek. I've forgotten it.
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Now, the biggest reason for it was as a cost-cutting measure to make Trek feasible to produce... but Trek, being a smart show run by smart creative people, came up with a justification that got my imagination racing when I was young. The idea was often the most interesting thing about any episode in which it was used.
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Latter day Trek viewers approach Trek in a cynical way, sometimes, assuming stupid reasons, or no reasons, for things happening in stories. They're used to product television. Give Gene R, Gene C, and company some credit. They made a point of thinking these things through.
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No, they weren't just casually throwing Earths at us as if it never occurred to them that space wasn't filled with Americans. No, it wasn't a matter of throwing space cowboys or space Romans at us without the slightest justification, expecting us all just to accept anything in the name of an hour's diverting entertainment.
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Someone else will have to mention the name of the theory, please...