It is reasonable to say that Humans have not been around for 200,000 years

"The author never suggests that this same analytical approach can be used to extrapolate population growth throughout the ages." This is true. The first link I gave only gave the doubling numbers for the past three centuries. But using this data there would be an impossible amount of people right now if the doubling rates have been the same. That said, the rates are most likely not the same. That is why I raised the doubling years to 75 years and then to 2,000 years. And the truth is, as I stated in round one, the amount of people would still be way to high. The population would literally have to double every 6,250 years in order for humans to have the same population we have now (as my second link showed). "It is estimated that the average life span of hominids on the African savanna between 4,000,000 and 200,000 years ago was 20 years." Whether that is true or not is open to debate. Your wiki link does not give much information as to how this information was collected and it only has about five lines of information on the subject (those hominids aren't even people right?). But the main problem is that I am not interested in what supposedly happened between 4,000,000 and 200,000 years ago. My concern is about people that lived 200,000 plus years later when your rates no longer matter. People living (if this happened) to the age of 20 years during 4,000,000 years ago makes no difference on the people that lived 200,000 years ago. See what I mean? "Roughly multiplying 40,000 centuries by 50,000 to 500,000 individuals per century, yields a total of 2 billion to 20 billion hominids, or an average estimate of about 10 billion hominids that lived during that approximately 4,000,000 year time span.[1]" But actually, this new information creates more problems for you. If 10 billion hominids lived during the 4,000,000 -200,000 years period...then you are going to have even more people (descendants of the 10 billion) added to the impossible amount of people that would have existed from 200,000 years till now. "Life span: It is estimated that the life span of the average person in the ancient world was approximately 20 years. Assuming that humans at that time were able to reproduce approximately 40%* of that life span, this would mean that the average person would have about six years to reproduce." But again, this debate is on the people that supposedly lived 200,000 years ago and not on the ancient world (4,000,000 years ago). So you still have a huge problem. The people existing 200,000 years ago would have doubled to an impossibly high number as stated in round one and the decedents of the people in the ancient world would only add to that number. "Once again, I will point out that there is no real data to substantiate the numbers definitively. However, archaeological evidence which includes the fossil records suggests that a much lower rate of population growth is more likely." The amount of people would have to double every 6,250 years in order for your numbers to work. That isn't even including the ancient world. That is highly unlikely as my second link demonstrated. "This is a topic that requires a more detailed debate and isn't the topic of this one. I would be happy to engage in that debate with the caveat that I am a physicist. A challenger would have to be up on the mathematics and history of these developments." I do not know to much about the dating methods except that are used with certain assumptions about the world that may or may not have been true thousands of years ago. "In conclusion, the evidence provided by my opponent in no way validates the assumption that all populations have doubled at any particular rate." Not quite true. I did show the rates for the past three centuries and using that information I made hypothetical scenarios about the doubling rates in the past. And we found out that 2,000 years would not have even been enough time for a population to double 200,000 years ago. "The linearity alone of that assumption is highly unlikely " nothing moves in a straight line forever." The problem is that the current rates of population growth do not even come close to supporting the humans existence 200,000 years ago. "The available data is insufficient to draw conclusions about previous population growth." Based of what we know about our population, 2,000 years would be plenty time for any population to double. But humans would need to double over 6,000 years in order for humans to have existed 200,000 years ago. And unless there were constant catastrophic events for the majority of humans existence, the numbers do not add up. Therefore it is in fact reasonable to say that humans have not existed for 200,000 years. The data does not make sense since the numbers of humans would be to high and hence it is certainly reasonable for a person to say that humans did not exist that long ago.