More Living or Dead?

Date: 08/14/97 at 14:49:33
From: J. Zifkin
Subject: Living vs dead - more of which?

I am puzzled. Are there more people living on earth now than have ever 
lived - i.e. are there more people living now than have ever died? 

Thanks.
JZ

Date: 08/19/97 at 13:15:49
From: Doctor Rob
Subject: Re: Living vs dead - more of which?

This is a very complicated question, and it is actually better 
directed at a demographer than a mathematician. I can't give you a 
really definitive answer.

The population of the Earth is said to be growing at a rate of about
1.7 percent per year.  The formula for the number of people living at 
any given time is then

  P = P0*e^(0.017*(t-t0))

where the population level was P0 at time t0.  

Say t0 = 2000 and p0 = 6250000000, which isn't too far off.  Then

  P = 6250000000*e^(0.017*t-34)

This can't have been true in the past, however, since when t = 0, we 
would get P = .000011, which is ridiculous.  

This over-simple model does not take into account the ravages of war, 
famine, and pestilence, which reduced the average rate of growth over 
the last 10,000 years, and the fact that infant mortality has greatly 
decreased since the Industrial Revolution, therefore increasing the 
number of potential parents.

Further complicating matters are that the rates of birth are 
declining, but the rates of death are also declining, so that the 
average life expectancy is increasing (it has roughly doubled in the 
last 500 years, and probably doubled in the preceding 1000 years, 
too).

I am arguing that this is not a question that can be resolved
mathematically, but we have to resort to historical data.

The estimated world population is:
  Year   Pop (Millions)  Ratio
  1650         550
                         1.12
  1700         615
                         1.18
  1750         725  
                         1.24
  1800         885
                         1.31
  1850       1,175
                         1.36
  1900       1,600
                         1.60
  1950       2,564
                         2.44
  2000       6,250

I think from this chart it can be argued that there are fewer people
living today than have ever died, but the numbers must be fairly 
close, i.e., of the same order of magnitude.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/