## The Total Number of Humans Ever (religious "pseudo-science")

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mathmannix
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### The Total Number of Humans Ever (religious "pseudo-science")

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=N0ekt), 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?

Now, it must be apparent that all the numbers of world population on this table are estimates, and are presumably more accurate the closer we come to the present. This is evident in the converging of the various numbers, which are all between 1.2 and 1.3 billion in 1850. I'm willing to stipulate that the UN number for half a billion people in the year 1500 is more or less accurate. Before that, the world was largely unexplored, and without written records, the numbers could be way off. (Which, obviously, they must be, given our original hypothesis, for probably any year BC).

So, how can we get a total?
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

Sorry, are you asking what the total number of humans was in 2348 if you assume there were 8 humans total, and then... uh... populations got back to reality and we went from there?

I guess my question is how you want an answer, given that you're defining the conditions up to an indeterminate period of time.

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mathmannix
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### Re: The Total Number of Humans Ever

Well, if I assume that the growth is purely exponential, and I set the current population is roughly 7.2 billion (at t=4361), and N0=8, then I get k=0.00473, more or less. But this gives me a population of only 4701 in 1000 BC (surely much too low) and a population of over 2.6 billion in 1800 and 5.3 billion in 1950 (both clearly too high). So, the growth is not strictly exponential. I wondered if there was another model out there that made more sense and fit the estimated data better...

EDIT: furthermore, if I assume exponential data with two known data points, say N2014=7,200,000 and N1950=2,555,982,611, then I get k=.0161819421 or so, which gives me a date for the flood (N=8) at roughly the year AD 740.
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

I guess I don't understand what you're asking then... You have a current point and a start point that you want to work with. Just go from there then?
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

It seems to me you are asking for the estimated growth in the period from 2348 BC to 1500 AD (8 to .5 billion), from there you can assume the real-world estimates hold.

So, a straight exponential figure could be found that would cover that time, but then you could argue that it doesn't makes sense for there to be such a huge growth during a time where we at least have a modest sampling of populations, and that the population at 1 AD must've been between X and Y and so we need two growth figures, 2348 BC to 1 AD and 1AD to 1500 AD. But then you'd possibly need to segment it again and again to match up real world estimates with a proposed population of 8 in 2348 BC. Essentially you're trying to find what that growth rate would have been from 2348 BC to meet up with our earliest estimates of population, right? Whatever it was, it must've been a bit rough on the womenfolk...

speising
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

I think it's clear that the human population didn't develop according to some simple formula. There were some innovations throughout history that had a huge impact, like agriculture, industrialization, medicine, and warfare. I'd guess that our numbers stayed quite level for large stretches while we were in homeostasis with our ecosystem until we found some way to overcome a bottleneck.

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### Re: The Total Number of Humans Ever (religious "pseudo-scien

Thanks a lot Haber!
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

speising wrote:I think it's clear that the human population didn't develop according to some simple formula. There were some innovations throughout history that had a huge impact, like agriculture, industrialization, medicine, and warfare. I'd guess that our numbers stayed quite level for large stretches while we were in homeostasis with our ecosystem until we found some way to overcome a bottleneck.

True. It may seem awkward to have an inflection point with a precipitous drop - and those first 2000 years are going to need a very silly growth rate no matter how you plot it - but by 1 AD, you're going to have most populations roughly at or near their respective technologically-exapanded carrying capacities, right?
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

8*1.01^2348=112118073983 The growth rate really doesn't have to be all that big. 2000 are a long time for exponential growth if you don't run into natural limitations.

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### Re: The Total Number of Humans Ever (religious "pseudo-scien

One thing that sticks out is that there would be a transition from hunter-gather to farming. Gathering is very labor efficient (twenty hour work weeks) but requires large amounts of land per person. Agriculture is very land efficient, but requires a lot of work (both ongoing and investment).

As a first order approximation I would take the highest documentation population growth rate and apply it immediately post flood. Then I would take the earliest well documented growth rate and use it backward from that time. The point where those two cross would be assumed to be the inflection point.
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lorb
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### Re: The Total Number of Humans Ever

mathmannix wrote:Well, if I assume that the growth is purely exponential, and I set the current population is roughly 7.2 billion (at t=4361), and N0=8, then I get k=0.00473, more or less. But this gives me a population of only 4701 in 1000 BC (surely much too low) and a population of over 2.6 billion in 1800 and 5.3 billion in 1950 (both clearly too high). So, the growth is not strictly exponential. I wondered if there was another model out there that made more sense and fit the estimated data better...

EDIT: furthermore, if I assume exponential data with two known data points, say N2014=7,200,000 and N1950=2,555,982,611, then I get k=.0161819421 or so, which gives me a date for the flood (N=8) at roughly the year AD 740.

Let's define a function p(t) of yet unknown characteristics that is earth population t years after the flood.
It seems to me you are starting with two fixed points and a simple exponential curve, but later realize that you want more points to (approximately) fit onto your curve. If you say p(2348)=4701 is much too low, what kind of population numbers do you think are realistic for that point? Once you have more points this becomes just curve fitting which has a number of mathematical tools to achieve different fits.
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sevenperforce
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### Re: The Total Number of Humans Ever (religious "pseudo-scien

It's really really difficult to convincingly argue that the human population was significantly less than it was even in 1000 BCE. The religious pseudoscientists have to propose hyper-exponential growth between 2348 BCE and 1348 BCE. Which, incidentally, is roughly the period of time when they also believe there was The One True Ice Age. Go figure.

PsiCubed
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### Re: The Total Number of Humans Ever (religious "pseudo-science")

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=N0ekt), 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)

gmalivuk
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### Re: The Total Number of Humans Ever (religious "pseudo-science")

Why are you multiplying total population by number of generations?

If a population is stable at 100M people that doesn't mean 100M people are born every generation, it means as many people are born every generation as die, which is considerably less because people lived longer than 20-25 years.
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