## Introduction

So I got pointed to the http://www.icr.org, which if you haven’t poked around on the site, you really should. It is quite interesting (not really in a good way). However, I want to look at a particular article on the young earth, arguing from population growth rates. The relevant sentences are:

Using census records from the last 400 years and a bit of algebra, and assuming a natural logarithmic growth, eight Flood survivors 4,500 years ago produce 7 billion people almost exactly. This is powerful evidence that biblical history is accurate, and man-made evolutionary history is not.

Then they footnote the following:

The formula for logarithmic human world population growth is $P = Po e^{rt}$, where P = the current population, Po = the initial population, e = the base of natural logarithms (2.718), r = the average annual population growth rate (0.456% or 0.00456 in the calculator), and t = the time interval from Po to P.

Finally, in the middle of the article, they are incredulous of the low net birth rate in pre-agricultural human populations:

Thus, the first human couple that supposedly evolved from ape-like ancestors would have had only 6 million descendants after 2.4 million years. This requires a population growth rate of about 0.000000009-essentially zero. Virtually no growth for 2.4 million years?

So, how do we respond to this sort of analysis? One could try to simply write it off as the rantings of a person blinded, by their religious bias, to a true understanding of science.  However I prefer an alternative approach. It may be tilting at windmills, but I prefer to take a claim at face value, and see why it fails, and to ask followup questions. Since the math here is so simple, it is easy to demonstrate any errors, assumptions, etc.. and get to the bottom of it. So, someone has made a claim, I don’t agree, how do I proceed?

## Did they do their arithmetic right? Yes!

The first thing I like to do is, assuming they are right in all of their numbers, do they do the calculation correctly. This eliminates a pretty obvious error that could have caused the problem. I suspected they got it right, but I wanted to make sure. The math is

$P=P_o e^{rt}$

The code is:

r=0.00456
t=4500.0
Po=8.0

print Po*exp(r*t)/1e9,"billion"


Yielding

6.52849018681 billion


The other direction is, how long ago were there only 8 people?

$\begin{array}{rcl} P(t)&=&P_o \times e^{r\cdot t} \\ \log P(t) &=& \log(P_o) + r\cdot t\\ t&=& \frac{\log(P(t))-\log(P_o)}{r} \end{array}$

or


Po=6.5e9  # current population
r=0.00456
P=8       # target population

t=(log(P)-log(Po))/r print t, “years”

resulting in


-4499.04089302 years.


## Is their growth rate correct?

Here I am using data from http://www.census.gov/population/international/data/worldpop/table_population.php. It is possible (in fact likely) that the original post used a slightly different data set, but they didn’t cite it so I can’t confirm that. The conclusions will not be qualitatively different, but that would be one of the questions I’d have for the author (see below).

It is instructive to look at the data set both on a normal scale and a log scale. The key thing here is that a constant growth rate translates to a straight line on the log scale. Let’s see if this is the case (see the lower of the two plots, especially):

Linear? Not so much.

I then chose a time-frame over which to calculate the average which gave (for my data set) as close to their growth rate above – this is essentially the growth rate consistent with the Biblical chronology. In my data set that average is from 1300 to 2010, or 700 years (theirs, they claim, it was 400 years so there is clearly a difference in data sets here – however, they don’t reference their actual data, and regardless, this same analysis would work in their case too).

You can see from here that this average yields the Biblical number of 4500 years ago, but that it is clearly not a good assumption to think that the growth rate, even over this time-frame, is constant. Because of this, depending on how far back you do the averaging, you get a different time of the Flood. For example, the following show cases for 1600-2010, and 1950-2010. The last one is the closest to a constant growth rate, but gives a ridiculous -1200 years back to 8 people!

(As an aside, Richard Dawkins does the same calculation with rats, and comes up with an astonishing 1900 or so for the beginning of the Earth.)

## Bottom Line

The biggest problem with this calculation is assuming a constant growth rate. Once it isn’t constant, then the time-frame over which you calculate the average makes a big difference. Only one possible time-frame will result in something consistent with the Biblical account, so one would have to justify:

1. Why you can possibly assume constant growth rate in the distant past knowing it wasn’t constant in the time-frame we know about.
2. Even given a solid justification (which I don’t believe actually exists…but I’m open to suggestions), you have to further justify why the particular time average you take, that is consistent with the Biblical account, is the one you should take.

You can’t use as a reason “because it’s consistent with the Biblical account”, because the entire point is to justify the Biblical account, or to demonstrate that the data is consistent with it. It’s not, if you have to postulate that the Biblical account is correct, and choose the specifics of the calculations to meet that.

## Questions for Brian Thomas, M.S. at the ICR.

Here are the questions I’d like answered. I’m not expecting any, but I’d be thrilled to get one!

1. What data set did you use? I’m sure it won’t make any difference, but it is good to make sure that we all agree on the numbers.  I’d be happy to run my analysis through any data set that you provide.
2. Using your data set, and your analysis, do you confirm my observation that your result is sensitive to the time-frame (i.e. the 400 years in your case, 700 years in mine) over which you are obtaining your “average” growth rate?
3. If it is, do you have a justification for using that, and only that, time-frame?
4. Do you have a justification for using an average growth rate model in the face of data that clearly shows that the growth rate is not constant?

## Comment about Growth Rates before Agriculture

The original article was astounded that the growth rate, prior to agriculture, could be so low.  Essentially, they seem to believe that exponential growth should have started once you had people, and gone at a constant rate the entire time.  However, before agriculture, there would have been a fairly low carrying capacity, and human population would follow logistic growth, not exponential.  Near the carrying capacity, the growth rate is essentially zero, exactly as observed.  A little bit of reading on how populations actually change might be helpful to these people.

I am a professor of Science and Technology at Bryant University in Smithfield, RI, and a research professor in the Institute for Brain and Neural Systems, Brown University. My research is in computational neuroscience and statistics. I teach physics, meteorology, astonomy, theoretical neuroscience, systems dynamics, artificial intelligence and robotics. My book, "Theory of Cortical Plasticity" (World Scientific, 2004), details a theory of learning and memory in the cortex, and presents the consequences and predictions of the theory. I am an avid python enthusiast, and a Bayesian (a la E. T. Jaynes), and love music.
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### 5 Responses to Creationist Math

1. John Smith says:

Henry Morris, the “father of scientific creationism” and co-founder of the ICR calls extrapolations based on the human population growth rate one of the strongest arguments supporting a young age for Earth. Other creationists have a different opinion. ID-supporter, philosopher Alvin Plantinga calls it “stupid” and advises YECs that making such stupid arguments causes people to reject not only creationism but also the Bible. Why do even other creationists think that population growth rate arguments are stupid? Let’s take a look.

Morris proposes a “very conservative” estimate of the human population growth rate of about 1/2% per year. Using that growth rate, it is very simple to show mathematically that a starting population of two humans would produce Earth’s current population in about 6,000 years. Presto! Adam and Eve plus 6,000 years equals conclusive proof of YEC, right? Samuel Birley Rowbotham’s mathematical calculations conquered the spherical-Earth theory. Now Henry Morris’s mathematical calculations have conquered evolutionary biology.

Well, as the saying goes: “Figures don’t lie; but creationists can figure.” Or something like that. Anyway, as you point out, Morris is wrong here, but there’s a funnier way to show that than the technical argument you used.

Morris gives only the starting and ending points of his extrapolation, because those figures fit in with his preconceived theory, but if a mid-point of the calculation is considered, it is clear just how ridiculous Morris’ argument is. For example, using the date of Noah’s Flood as the starting point, Morris’s extrapolation would produce a world population of about *85,000 by the time Jesus was born, and that creates a bit of a problem for Morris. If that 85,000 is divided among the six habitable continents, that would put only about 13,000 people in all of Africa. Israel is far from being the most populous nation in Africa, but even if they were allotted a full 30% of that 13,000, there would still be only about 4,200 people in Israel around the time of Jesus. And that raises an interesting question: How Jesus could have fed a multitude of 5,000 men as reported in the New Testament, if the total population — men, women, and children — was only 4,200?

Creationists are such bunglers, that in their attempt to confirm the validity of the Old Testament, they have come up with a formula that undermines the validity of the New Testament.

*I didn’t actually crunch the numbers. Hopefully they’re not too far off.

• brianblais says:

I think Dawkins does it a different way, using rats population growth and showing that the world can’t be older than around the 1900’s. :)

I deliberately did not speak about data much before the data claimed in the original post, to avoid any wiggle room. Even with your calculation, they could simply deny any population on other continents, or some such evasion. Although I agree with your example (I havent worked the numbers, but it’s probably close), and also agree that it makes the point quite well, I wanted to demonstrate the problem here using only the data that *they themselves trust*. BTW I did email the ICR on this, just to point out that I had author questions. I didn’t expect an answer…

2. John Smith says:

And that was supposedly one of creationism’s *strongest* arguments. Hee, hee, hee. I just get a kick out of that.

3. conmpasion says:

Hello. I believe we all chose to have faith in one book or another. Who knows what part of our “scientific knowledge” people are going to make fun of a few generations from now as we do from generations that came before?

You say that we can’t assume a constant growth rate – which makes sense – but how about an average one? And if so, which is it? Lets crunch the numbers and see if it makes sense. You argue that the growth rate doesnt work, but you don’t propose an alternative.

One article (found at http://creation.com/where-are-all-the-people) argues: “Evolutionists also claim there was a ‘Stone Age’ of about 100,000 years11 when between one million and 10 million people lived on Earth. Fossil evidence shows that people buried their dead, often with artefacts—cremation was not practised until relatively recent times (in evolutionary thinking). If there were just one million people alive during that time, with an average generation time of 25 years, they should have buried 4 billion bodies, and many artefacts. If there were 10 million people, it would mean 40 billion bodies buried in the earth. If the evolutionary timescale were correct, then we would expect the skeletons of the buried bodies to be largely still present after 100,000 years, because many ordinary bones claimed to be much older have been found.12 However, even if the bodies had disintegrated, lots of artefacts should still be found.” –

I’m sure there’s a way to explain this issue logically, and as you say – us religious have a biased perspective and we make up our numbers… I agree… I also believe that ironically you do the same thing. Why don’t we just agree that we both have faith in our perspectives?