Sorry for bumping this thread after so much time, but it appears that the OP didn't get an actual answer so I'm giving it a shot:

mathmannix wrote:OK, so I was originally going to post this in response to the latest What-If, but then I reconsidered, and this seemed like the safest place to put this.

Not looking for a debate at all, so just think of this as fictional science. Actually, what I'm really interested in is the math here, but I don't really know how to begin to calculate it, which falls under the social sciences, or so I'm guessing, anyway. All I really know is the exponential growth model (N=N

_{0}e^{kt}), and I don't think it applies, but maybe I'm wrong and it does.

Hypothesis: let's say that the Human population was bottlenecked to a total of 8 in the year 2348 BC (4004-1656, as calculated

here). With the current population of just over 7.2 billion, as shown on the various

population clocks. How can we estimate how many people have ever lived?

Surprisingly, the proposed bottle-neck at 2348 BC won't really affect the grand total by much.

First, let's get one common misconception straightened out: Going up from 8 people to (say) 100 million shouldn't take more than a few hundred years. If we assume each couple to have 4 kids who reach adulthood (which is really conservative, given the proposed scenario) that means that the population doubles every generation. It takes 24 doublings to get you from 8 to 100 million so:

24 doublings x 1 generation/doubling x 20 years/generation = 480 years.

Now to be even more conservative, let's double this number and give a full 1000 years for the population to grow.

If we assume an upper bound of 100 million people as the average population for the period of 2348 BC - 1348 BC and also assume a generation length of 20 years, this gives us a total of:

100 million people/generation x 1000 years / (20 years/generation) = 5 billion people (as an upper bound)

So adding the flood bottleneck can reduce the total number of people who ever lived by

at most 5 billion (the actual reduction would be smaller, since 1000 years was a generous overestimate)

Now, let us try to find a quick estimate for the number of people who lived in modern times since 1500 AD. Let's assume a generation length of 25 years:

1990-2015: 6 billion x 25 / 75 = 2 billion

1965-1990: 4 billion x 50 / 67 = 3 billion (total 5 billion)

1940-1965: 3 billion (total 8 billion)

1890-1940: 1.5 billion x 2 = 3 billion (total 11 billion)

1790-1890: 1.25 billion x 4 = 5 billion (total 16 billion)

1690-1790: 0.75 billion x 4 = 3 billion (total 19 billion)

1500-1690: 0.5 billion x 8 = 4 billion (total 23 billion)

That's already over 4 times the maximum possible effect of a flood bottleneck. Continuing backwards using reasonable numbers we have:

1000-1500: 0.35 billion x 20 = 7 billion (total 30 billion)

1 - 1000: 0.25 billion x 40 = 10 billion (total 40 billion)

1348 BC - 1: 0.15 billion x 54 ~ 8 billion (total 48 billion)

By now we are already over 9 times the maximum possible "flood" effect. And these last three rows are really nothing more than rough educated guesses anyway. So basically, the answer to "how many people lived from 2348 BC to present day" is:

very roughly 50 billion (for the time range of 2348 BC - 2016 AD).

With the the proposed bottleneck having negligible effects on the result.

BUT WAIT. As long as we are assuming a creationist scenario, what about evolution and the age of the earth? In the proposed scenario, how long did humans exist

before 2348 BC?

This time it matters a great deal whether you pluck "about 2000 years" or "hundreds of thousands of years" into the equation:

2000 years might add another 5 billion to the total (and if you want to take the preflood Biblical generation lengths literally - it would be even less). So in this case the rough total would still be around 50-60 billion.

The "hundreds of thousands of years" option is harder to calculate, but fortunately it has been done for us: Since the bottleneck doesn't alter the calculation by much, we can simply take the Haub's estimate of 100 billion.

So to summarize, the answer to the OP question is:

(1) About 50-60 billion if you assume man was created around 4000 BC.

(2) About 100 billion if you assume the usual scientific timeline.

(and the flood bottleneck effect in both of these scenarios is negligible)