Enrico Fermi Paradox

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There are 30 or so galaxies in our local group. None of them have been observed to exhibit signs of galaxy-wide Type III colonization.

There are, at least, 100 billion planets in a galaxy on average. 10 billion are estimated to be in the habitable zone and orbiting a sun-like star.

That's 300 BILLION such planets in our local galaxy up. If just 0.1% of said planets harbor life, that's 300 million planets with life on them. If just 0.1% of life-bearing planets develop intelligent and technological societies then there should be around 300,000 planets with civilizations like ours. If just 0.1% of said planets with civilizations like ours reach the Type 3 stage then that's 300 civilizations with Type 3, galaxy-colonizing capabilities.

Any way you look at it, we should have detected a Type 3 civilization in our local group by now. The fact that we haven't points to the rare earth hypothesis being true.

We are the only intelligent life in the cosmic horizon. Note I said COSMIC HORIZON, not the observable universe or the entire universe (whatever that means anyway).

If there is ANY life similar to ours then it is almost certainly outside of our cosmic horizon and we will never detect or interact with them in any way. For all intents and purposes, we are alone.

Q.E.D.