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Which is why if humanity had empathy, it would be working on how to make smarter ants, so that they can learn more advanced geometry.
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I love that as a goal!

Perhaps indeed a better understanding of what intelligence really is would allow this sort of Uplift (as in Brin's books).

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A fellow Brin aficionado!
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It's quite possible ants understand a geometry more advanced than our own.
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What do you think we're doing?!
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Ant Intelligence will be next big thing in machine learning after this bubble bursts
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What’s optimistic or non-optimistic specifically about the machine having a system of mathematics beyond our comprehension within it? Why should we care about that in itself?
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In the first case, we'd still have a chance to take a glance at the frontier of discovery (even if ordinary human mathematicians had to spent years translating what metahumans achieved).

In the second case all human-level maths would be solved and what lies beyond would be always out of our scope.

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Why would this be optimistic? This sounds extremely negative to me…
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