Arcologies

The Sun radiates about 400 trillion trillion Watts in all directions, and only a couple of billionths of it crosses Earth. There's a lot more radiant energy spreading out into the void waiting to be Dyson Swarmed. There's no way we're going to rocket launch billions to Mars, and there isn't another planet worth living on without unreasonable amounts of energy for Terraforming. But we are capable of rebuilding the atoms of Earth into much larger living environments - there are so many atoms it wouldn't mean destroying the Earth to do it. A Space Elevator doesn't need diamond nanowire, it could be built with enough steel chain. An orbital ring around the Equator would be enormous and would take approximately nothing of the Earth's matter to construct. Isaac Arthur's YouTube channel is full of speculation and plans for all kinds of possible or nearly-possible futures, as well as more distant dreams. e.g. the playlists: - "The future of Energy, Industry and Agriculture" - link - "Earth v2.0" - link - "Outward Bound" - near-Earth space exploration and living - link - "Visions of Earth" - arcologies, megacities, ecumenopolises, geoengineering, weather control - ▶ this video And somewhere in there, megastructures such as Dyson Spheres, ringworlds, etc.

Since you nerded out on this enough to do the math, you might actually be interested in this video. The only real bottlenecks to getting to these numbers are first, power and second the elevator conundrum. Solve for those and you can have quite a substantial population. Go big enough and the only bottleneck, if you want to stay a single planet species, becomes black body radiation. Check it out Archologies - Isaac Arther (28:43) ▶ this video

I thought I would add to this an interesting youtuber I've watched, and the idea of "Arcologies". The claim is that, a (current) skyscraper sized building that is a self sufficient ecology of human living space / food production, poking out one every few square miles, could support dozens of times our current earth's population and that heat, not space, is the real bottleneck for further growth[1]. Has some estimate calculations to back it up. [1] ▶ this video