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Zero. The hotter the planet gets, the more water evaporates from the oceans, which condenses into clouds, which reflect sunlight, which cools the planet.

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According to statistical mechanics, even boltzmann brains have a higher probability than zero.

I find your absolute certainty disturbing.

Earth is 4.5 billion years old. A runaway, climate chain-reaction hasn't happened yet.

I find your lack of faith disturbing.

I think you're confusing a complete boil-off of the atmosphere with a slightly less extreme event that simply eliminates 90% of life on the planet, which has in fact happened before

I think you're conflating a "runaway feedback loop" with "a slightly less extreme event that simply eliminates 90% of life on the planet," which says nothing about whether it was caused by a runaway feedback loop.

Therefore, by this logic, zero percent chance... qed

So, how many billion years more would it take to convince you that it's not going to happen? If earth is 4.5 billion years old, that's already more than 25% the age of the universe.

What does the evidence show? Are you willing to believe the evidence?

As I said before, I think you're confusing a complete boil-off of the atmosphere with a slightly less extreme event that simply eliminates 90% of life on the planet, which has in fact happened before

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