Quote:

Originally Posted by

**PEZenfuego** http:///forum/thread/384994/evolution/140#post_3375977
I wanted to do this. I have no authority on this matter, but it is simple maths and should provide a shadow of what was happening. Here's my source for what it's worth. http://www.infoplease.com/ipa/A0762181.html

I checked these numbers with wolframalpha for what it's worth. This may shed some light on that 4000 number.

Now the model for this is going to be slightly changed by me for ease, but only in an aesthetic sense, not in function.

F=B (e^(rt))

Where F is the final amount, B is the initial amount, e is euler's number (approx 2.718281828459045), r is the growth rate, and t is time.

So I don't know the rate for human growth, but that's fine. I do know enough to find it. Let's rearrange the formula

F=B (e^(rt))

F/B= e^(rt)

ln (F/B)=rt

(ln(F/B)/t)=r

Now we plug in some numbers. I'm going to use 1950 as the beginning amount (2556000053 people) and 2000 (6082966429 people) The difference between 1950 and 2000 is 50 years, so that's my t.

(ln(6082966429/2556000053)/50)=r

r=approx (0.0173409783849915583323504)

I want to use this r to check how well this formula works. Going back to the chart I see 3,039,451,023 as the value for 1960 and value for 1990 is 5,278,639,789. That is a 30 year difference. I am going to use the population values and see if I can hit on that 30 years.

F=B(e^(rt))

F/B=(e^rt)

ln(F/B)=rt

t=(ln(F/B)/r)

t=(ln(5,278,639,789/3,039,451,023)/0.0173409783849915583323504)

t=31.83 years. Not too far off.

1.83*100/30= 6.1% error which isn't too bad.

Okay, so now we want to know how much time it would have taken to go from two human beings (Adam and Eve) to 6 billion human beings. So we solve for T and we use the population in 2000 as our final value. F=6082966429 and B=2

F=B (e^(rt))

F/B (e^(rt))

ln(F/B)= (rt)

t=(ln(F/B)/r)

t=(ln(6082966429/2)/0.0173409783849915583323504)

t=1259.1914 and then let's factor in that percent error. 6% of 1259.1914 is 75.5515 so we have a date between 1184 and 1335 and we subtract it from 2000 to get 665 and 816 as being the years for the dawn of civilization.

Why was my number so far off?

Well that probably has to do with using two pieces of information that were so close together (time-wise) to find my growth rate constant that when attempting find the difference between 6 billion people and 2 people made things behave poorly. More likely however is that a gap formed when we discovered antiseptics and medical treatment bettered. The rate of population growth must have drastically changed. These models are great for making predictions, but their real world applications are slim. Even if we used two dates that were few thousand years apart we would get similar results, however it is likely that they would be closer to the truth. The problem with doing so is that the information we are given is not going to be very precise and would not factor in the big changes throughout the history of man and their effects on population.

I agree with you that the problem with the projection is that the growth rate constant is probably only valid for the relatively narrow range of dates you had available to you. There are projections of earlier growth rates, but I don't know that they are necessarily correct. Nevertheless, I think that it is reasonable to project that in primitive cultures (which we were for most of our species' history), the growth rate was probably quite low due to disease, lack of medical care and predation, etc.