The earth could probably support 100+ billion people at reasonable comfort levels with slightly better technology as long as we give up the idea of life outside of zoo's.
That said, past experience has demonstrated the Human population can easily grow at 5% per year. At that rate it's doubling every 15 years. Trying to double the universes food supply every 15 years is just not possible indefinitely.
PS: 2^n is crazy. It takes less time than you might think before the mass of humanity is growing faster than a sphere expanding at the speed of light could support.
Uh, the current growth rate is around 1% per year, and it's decreasing as countries enter the first world. That's a doubling every 70 years. See https://en.wikipedia.org/wiki/Population_growth
We've got a lot of efficiency left in terms of agriculture as well, so there isn't much reason to think reaching the carrying capacity of the planet is a particularly pressing issue. The amount of food that we already grow that we don't eat roughly 1/3 already, and the vast majority of land doesn't contribute to agriculture.
The counter argument goes something like this. Let's double every 1,000 years for the next 1,000,000 years that sounds easy.
Let's see that's only 7billion * 2^1,000 or err ~7 * 10 ^ 310 people. Hmm, there are only ~10^83 atoms in the observable universe. I guess they must be really tiny people.
So, yea it's not a problem in right now and probably not for a long time yet. But, as soon as you start doubling something has to give.
The top of the curve can be unpleasant. It doesn't have to be.
The worst is when population goes past carrying capacity and then crashes. That's when you get mass die-offs.
Population can settle down at carrying capacity simply through reduced birth rates matching up with death rates. That's the situation we see in much of the western world, with better availability of birth control etc.
Every part of the curve faces that sort of instability. The number of crops actually growing isn't particularly higher than the number needed to sustain the population, and we can't just spin up enough food for billions of people even if we do have plenty of land to do it on.
With humanity, "carrying capacity" is unlikely to be food-limited.
The large number of overweight Americans is a huge pool of excess food and takes a lot of extra daily calories to maintain. As is the large number of livestock being produced and all that corn ethanol etc.
The top of the curve removes that as we can't pay for the inefficiency's of livestock or the extra daily calories to be overweight and feed 50+ billion people.
"carrying capacity" is set by a lot more factors than just food.
Human population is expected to level off at 10-13 billion based on factors relating to social organization, not the 50+ billion that could theoretically be fed.
Replace food with water, land, etc and you get the same instabilitys. Social factors at the limits can easily lead to war, revolution, and or the breakdown of society.
sure, but you don't need to be at the limit to have that sort of instability. It becomes a bit more pronounced when there's less leeway, but it's not different in kind, only a little bit in magnitude.
That said, past experience has demonstrated the Human population can easily grow at 5% per year. At that rate it's doubling every 15 years. Trying to double the universes food supply every 15 years is just not possible indefinitely.
PS: 2^n is crazy. It takes less time than you might think before the mass of humanity is growing faster than a sphere expanding at the speed of light could support.