The calculation presumes that at one point in time we will reach the carrying capacity of Earth. It makes no assumptions about when that happens, what the popul

The calculation presumes that at one point in time we will reach the carrying capacity of Earth. It makes no assumptions about when that happens, what the population is at that point or what technology is available at that point. It could happen because we run out of production space for food or that there are no longer enough plants to handle human carbon dioxide production, it could happen in 50 years with essentially the same technology as today or in 5000 years with very advanced technology, it could happen at 10 billion people or at 10 trillion people. But there is such a limit at which it becomes impossible to support more people on Earth - the ultimate limit is having so many people that the heat produced by the bodies alone raises the temperature to the point that humans can no longer exist. With a population growth rate of 1 % per year the population doubles every 70 years. 2685 years are about 39 doubling periods which means that the population will increase by a factor of 549,755,813,888 over this time and if we needed on Earth at the beginning we then need that many Earth-like planets or the entire Milky Way under my assumptions of 400 billion stars and one inhabitable Earth-like planet per star. This assumes no further or at least only negligible technology advances over those 2685 years, i.e. we do on the new planets what we did on Earth when the carrying capacity of Earth was reached, but which we assumed was the best thing possible at that point in time. Exponential growth is really that bad and 1 % per year is a pretty high growth rate. We could never have sustained such a growth rate for extended periods. We only surpassed 1 % per year in the early 20th century, before that it was a lot lower. My entire point was to demonstrate that exponential growth with 1 % per year is so huge that it would grow beyond any realistic resource limits in pretty short time. Decreasing the growth rate by a factor of 10 to 0.1 % per year will only increase the doubling time by about a factor of 10 and we would still reach the carrying capacity of the Milky Way in relatively short 26,728 years. Stabilizing the population at some point is really the only option, exponential growth can not possibly work besides with growth rates that are essentially zero.