Human Extinction

Well no one (realistically) knows how to stop climate change period anyway. All the serious solutions are political or economic impossibilities. the most we'll ever get is weak legislation from politicians wanting to look like they're doing something. We're just gonna have to get used to the new equilibrium, whatever it may be.
 
Could advances like bio-fuels or solar power help to avoid that fate?

The problem with Solar is the panels is that there's a limit. The sun generates only 1,000 watts per square meter (well, that reaches the surface of the earth). A nuclear power plant is around 4,000 square meters. We don't capture 100% with solar panels, but if we did, we could generate around 4 Million Watts in the same space. A small nuclear power plant generates 1,027 Million Watts in the same area. And it doesn't have downtime. Solar would be able to sustain small groups of people, but nowhere near the current population. I mean, I guess you could do solar until you rebuilt civilization.

If you could develop algae or something that create oil or natural gas, sure. But that would require space too.
 
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And it doesn't have downtime. Solar would be able to sustain small groups of people, but nowhere near the current population.

This is correct for Earth or planetary-based installations. For space habitats, good solar panels orbiting the star directly can provide continuous energy input. This is one of the rationales for the Dyson Swarm concept (ie, the original and most feasible variant of the Dyson Sphere); once you pay the fixed costs for getting material into orbit and you thus have the self-sustaining space infrastructure, it would be relatively easy to convert asteroids into self-sufficient rotating habitats. This is a far more optimal solution than settling Mars or other plaentary/sub-planetary bodies, since you can tailor such habitats perfectly to human life.
 
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