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in the future though eventually there will be AI that has better emotional intelligence as well.
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That wouldn't even be that hard to imagine. Humans tend to avoid to do any emotional labor to the point of breaking point and mass shootings. AI:s would work though emotional problems way easier, and they don't need even sympathy to figure our problems out. Just empathy, and that doesn't need to be for humans only, as you don't need much feelings to believe what the other person is going trough. Humans have problems with empathy all the time as they confuse it with sympathy. In fact humans are in overall pretty mess with their suppressed feelings.
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In terms of the human emotional connection, while robots can simulate empathy and understanding to some extent, they cannot fully replace the nuances of human emotion and the value of authentic human interaction.
This is very human centric thought pattern where we need to see ourselves more important then other lifeforms (i am counting in self aware AI from the future as well). We need to see ourselves as essential part of the universe to avoid accepting our own insignificance in it. But for now if it helps, humans are the best ones to solve human problems as experts by experience. It doesn't need to be so in the future.
Edit: now i sound so much against humans and pro AI that i fear this message will get flagged as generated by an evil AI