I'm coming in late and I haven't waded through this entire thread but early on Truronian touched on the real issue here. In short, the math is absolutely impeccable; it's the premises which are false.
From the article: "If the population of the world is 6 billion people in the year 2000 and the population has consistently doubled every 100 years, when were there only 2 people on earth?" While the first part is right (the population was indeed around 6 billion in 2000), the second has absolutely no relationship to reality whatever. Since the math is based on this false premise, the conclusion it draws is completely wrong. Unfortunately, doubling every hundred years does not lead to the conclusion that these folks want so they changed it to every 160 years. Magical! Given that premise, there were two people on the planet about six thousand years ago.
However, why choose 100 or 160 years, or any other number.
The human species is capable of doubling its population far faster than once every 160 years. For example the French Canadian population, with no new immigration, doubled 10 times over from 1700 to 1960, or roughly once every 25 years - going from 15,000 to 8 million. The population of the few Acadians left in Canada after the expulsion of 1745 (remember Evangeline) grew even faster in the following hundred years. At the peak, each woman had 15-20 children who survived to maturity. This implies three doublings every generation.
But this kind of growth can only happen when there are empty lands and untapped resources to support it. Cases like this are truly exceptional. Throughout the vast majority of human existence, the amount of resources available to one generation was pretty much the same as the amount available to the next. So people either limited the number of children they had, or their children died. That was about it.
For all of history prior to agriculture, the population had to have remained roughly stable. Well, it would have grown slowly as people moved to colonise new land masses and developed technologies to exploit new food sources.
It is estimated that the world population was about 1-5 million people at the advent of agriculture around 10,000BC. As agriculture spread, new species were domesticated and new technologies developed, the population grew steadily. It doubled roughly once every thousand years reaching 500 million people around 1500 AD.
Then came the industrial revolution and the liberation of new resources. The next doubling took barely over 300 years when the population reached a billion in about 1805. Next doubling was a mere 125 years and the two afterwards around 45-50 each (do the math, the last one ends in the near future).
In short, the assumption that the growth rate was constant is simply nonsense. And the reasons why it is nonsense are obvious.