Hi Tornapart,
"A few statistics.... they say man was about a population of 1 million about 10, 000 years ago. There are about 4 generations (for arguments sake) in 100 years. So to get from 2 people doubling each generation (going by the bacteria illustration), that would be roughly 20 generations. At that very slow rate it would take only 500 years to reach a million. We are talking about 500,000 years, a thousand times longer!"
I'm not sure if this is the correct way to look at the math. I tend to think of population as hour glass with a hole also in the bottom. You add to population by giving birth to children and subtract by having people die. If the rate of birth and death were in perfect balance it would not matter how many generations you had the number would not go up.
To make the number go up, you need a rate of birth that exceeds the rate of death. If you had a perfect 50-50 split between male and female and they all were mated, all pairs would need to produce at least two children to keep the population from declining. If instead a few produced 3 and most produced 2, then it could increase. So you need to think in terms of all the variables that could impact the birth rate -- for example polygamy could increase it, but polyandry (where a woman has more than one husband) could decrease it. If either men or women are compelled to spend a lot of time in pursuit of something other than sex, then birth rates would decline. Then you would need to think of all the things that could impact death rate, including things that kill humans before they are old enough to reproduce.
The very odd thing about this argument is the theory of evolution actually faces the other problem. The theory of evolution demands time and reproduction bumped up against selective pressures. Thus if the rate of reproduction is too slow the time variable becomes a problem. Darwin tackled this directly in Origin of Species by working out rates of reproduction for elephants. His conclusion was there is indeed enough time available even with animals that take a long while to reproduce.
Cheers,
-Randy