Even with full-blown space colonization, however, population growth can continue to be a problem, and this is so even if we assume that an unlimited number of people could be transported from Earth into space. If the speed of light provides an upper bound on the expansion speed then the amount of resources under human control will grow only polynomially (~ t3). Population, on the other hand, can easily grow exponentially (~ et). If that happens, then, since a factor that grows exponentially will eventually overtake any factor that grows polynomially, average income will ultimately drop to subsistence levels, forcing population growth to slow. How soon this would happen depends primarily on reproduction rates. A change in average life span would not have a big effect. Even vastly improved technology can only postpone this inevitability for a relatively brief time. The only long-term method of assuring continued growth of average income is some form of population control, whether spontaneous or imposed, limiting the number of new persons created per year. This does not mean that population could not grow, only that the growth would have to be polynomial rather than exponential.
@”different Jeff”:
Even with full-blown space colonization, however, population growth can continue to be a problem, and this is so even if we assume that an unlimited number of people could be transported from Earth into space. If the speed of light provides an upper bound on the expansion speed then the amount of resources under human control will grow only polynomially (~ t3). Population, on the other hand, can easily grow exponentially (~ et). If that happens, then, since a factor that grows exponentially will eventually overtake any factor that grows polynomially, average income will ultimately drop to subsistence levels, forcing population growth to slow. How soon this would happen depends primarily on reproduction rates. A change in average life span would not have a big effect. Even vastly improved technology can only postpone this inevitability for a relatively brief time. The only long-term method of assuring continued growth of average income is some form of population control, whether spontaneous or imposed, limiting the number of new persons created per year. This does not mean that population could not grow, only that the growth would have to be polynomial rather than exponential.
[from the WTA FAQ]