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You can do the maths yourself!
The present population of the world weighs, conservatively, about
2 x 10*8 (200 million) tons.
This figure is doubling every 50 years. .
The planet earth weighs approximately
3 x 10*21 (3 sextillion) tons.
So, before the year 4200 AD (broadly, as far in the future as, say, the birth of Julius Caesar is in the past), the human race will weigh more than the entire planet Earth does now...
which is clearly impossible....
unless we choose very seriously to control ourselves,
- or let our governments control us (which only the Chinese have so far dared),
- or allow our children to be killed in massive wars (two world wars didn't much dent the growth),
- or give the world to monsters like Stalin and Hitler (who hardly got started),
- or suffer a catastrophic pandemic (660 years since the last of these that had a real impact),
- or let global warming, pollution or other act of a vengeful God do the job for us...
In passing: if we could launch 100 spaceships a week, each carrying 10,000 people...
the population would still rise; just not so fast. So escape isn't an option. .
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