"Free green" energy, e.g. fusion, is problematic for that reason. Any such energy has to go somewhere, and the earth is a (large) black body radiator.
Absolutely true.
The amount of solar energy that hits the Earth is approximately 173,000 terawatts. Our current average global energy consumption is around 20 TW. So we are adding 0.01%.
According to the Stefan-Boltzmann law the total black body radiation from an object is proportional to the 4th power of its absolute temperature. So a 0.01% (10-4) increase in radiation requires a 10-16 increase in temperature.
As Earth's average surface temperature is around 15º C (288 K), current human energy output will, at equilibrium, raise the temperature by 0.0000000000000288º C.
That figure overstates the temperature increase by whatever proportion of human energy use consists of capturing and immediately using solar energy i.e. solar, wind, and biofuels.
That statement was made in the context of presuming continual (economic) growth at the historic rate. Hint: exponential growth for a long time[1].
Please read the reference I gave with that statement. Here it is again: https://dothemath.ucsd.edu/2012/04/economist-meets-physicist/
[1] Economists and politicians infamously can't get their head around what exponential growth means; engineers really ought to understand it instinctively!
Yes, I read it.
"The upshot is that at a 2.3% growth rate (conveniently chosen to represent a 10× increase every century), we would reach boiling temperature in about 400 years."
After 400 years, under this assumption, we would be using 10,000 times more energy than at present i.e. 200,000 TW, or yes approximately the same amount of energy as received from the sun. So a doubled energy budget to reject thermally needs 1.19x the current temperature (288), or 343 K (70 C).
That's not boiling but it would indeed be unpleasant.
But I'm not at all sure I accept the 2.3% total energy growth rate.
Between the years 1000 and 2000 the average population growth rate was 0.3%. The previous 1000 years more more like 0.05% per annum. In the 1960s and 1970s population grew at 2% a year, since 2000 it's been under 1%, and everyone seems to agree the population growth rate is going to hit 0% or even negative in the coming decades.
So population growth has been a fairly significant component of energy use growth, and that's going away.
We are left with per-capita energy use growth.
I really really don't see how per capita energy use is going to grow exponentially.
Let's concentrate on the 1st world. We can assume the 3rd world will in time catch up to the 1st world, per capita, but that's a one-off. The world per capita energy use is about 21,000 kWh/year. NZ and Austria (not Australia) are around twice that, the nordic countries, Russia, Australia are around 3x (I assume mostly heating/cooling of buildings), USA nearly 4x and Canada 5x. UAE and Singapore are 7x and 8x, Qatar is 11x (or 3x the USA).
Where is energy use growth over the current usage of Qatar going to come from?
The article discusses food. I can't see how we're going to want exponentially more expensive food. We're certainly not going to eat exponentially more calories. Beef is supposedly the most energy-intensive food (at least major food). Ok, so everyone starts eating the finest steaks 3x a day. What then?
Once all your buildings are kept at your preferred 21 C or 23 C or whatever all year, in every climate ... what then? A/C gets more efficient, insulation gets better.
Gadgets? I dunno. Most things except TVs are getting smaller, with less material in them.
Transportation? Modern cars and airliners are, roughly speaking, equally efficient per passenger km, and are getting better. Even if we all start travelling anywhere in the world in 90 minutes by rocket, the energy use of a rocket trip (to anywhere) is similar to flying between Los Angeles and Sydney. We all start commuting to work or shopping on the opposite side of the planet by rocket? Ok. That's a lot higher energy use on transportation than today -- a daily circumnavigation of the Earth is 1000x more distance (let's call that energy) than today's typical 10k miles / 15k km driven -- but I don't see how it can increase beyond that. The article is assuming we're staying on this one planet, right?
Airlines do already exist. Before COVID we reached around 1000 km of annual airline travel per capita -- or around 10,000 km per person in the 1st world, roughly similar to the level of travel by car.
At the moment transportation is about 25% of total global energy use. Under the assumptions in the last paragraph (or anything remotely close to them) it could come to dominate. But even it has absolute limits on a per capita basis. And I don't think it will ever get anywhere near that 1000x current 1st world levels. One world trip per month, maybe, not daily. So, 15x current average levels, increasing total per capita energy use to around 4x current levels.
So again: where is long term exponential per capita energy use going to come from?