I have been reading "Time Reborn" by Lee Smolin and it has been a very informative read. In the book, Lee Smolin mentions that there have been 110 billion humans born over time. I found this number interesting and I thought I could verify it without to much effort. I should note that there is some controversy about these numbers.
This problem is an example of a Fermi problem and my analysis will be approximate because a number of assumptions are required. The approach is similar to that used in this post on estimating the number of babies born in the US every year. The problem's solution is a good example of the use of Mathcad's range variables and array functions.
I started to search for information on how many people have been born over time and I found an excellent reference at the Population Reference Bureau (PRB). I will simply use their data and fill in the computational steps. I repeat their population data in Table 1, with the "births per 1,000" range of 1950 replaced by the average of the range extremes. My goal is to compute the number of births during each period in the table and compare my results with those of the PRB.
|Year||Population||Births Per 1000 people Per Year|
The calculations make a few assumptions:
- Humans began reproducing in 50,000 BCE.
This is the time known as the Upper Paleozoic. 50,000 BCE is reasonable guess for when homo sapiens started showing modern human behavior based on artifacts. Fortunately, there are relatively few humans born during this time, so the uncertainties as to starting date and birth do not introduce large errors.
- I can model the population using a geometric growth formula.
This statement means that I can model population growth at two times (P1 and P0) separated by N years assuming a yearly growth rate of r and the following equation.
- The number of births per year is proportional to the number of people.
This number has varies over time, but the long term trend is down.
Figure 1 shows my calculations for the total number of human births over time. My results are very close to those of the web page author's results.