TheOtherDave comments on Convincing ET of our rationality - Less Wrong
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I'm reminded of the hoary old anecdote about the primate intelligence researchers who put a chimpanzee in a room with a collection of intelligence-testing toys to see what it would do, and when they peek through the keyhole all they see is a chimpanzee eye watching them.
Which is to say, I doubt that my primary goal in this situation would be to convince them of my rationality, but rather to learn as much about them as I could.
That said... no, I don't think I could communicate much of anything reliable without the benefit of common language, culture, psychology, or biology.
Funny story, but it raises a good point. Perhaps an expression of curiosity would be enough to convince them of our worthiness.
On the other hand, that doesn't seem to have convinced us about the chimpanzees.
For what it's worth, the chimps have me convinced.