by David C. Wise
Written 08 June 1991
Originally posted in the Science & Religion Library on CompuServe
One of the ironies of the so-called "creation/evolution debate" is the double standard under which "creation science" often operates, demanding great precision and virtual omniscience of science, while providing none themselves. An example of this is how they will criticize any assumption of constant rates made on the part of science (e.g. radio-isotope decay rates, the speed of light, etc), and yet they do not hesitate to make their own assumptions of constant rates -- especially where such assumptions are unwarrented.
The Institute for Creation Research (ICR) has published a list of "Uniformitarian Estimates -- Age of the Earth" which has been appeared with minor variations in numerous ICR publications. One estimate that appears in each list I have read is that the "Development of total human population" yields an "Indicated Age of Earth" of "4,000 years" or less. This estimate is the result of Dr. Henry Morris' human population model, which has come to be known as the "Bunny Blunder" for reasons that will very soon become apparent.
MORRIS' POPULATION MODEL:
In 1961, Dr. Morris presented his population model in The Genesis Flood , which he co-authored with John Whitcomb. First he observed that population growth can be measured in doubling-times, i.e. the amount of time it takes the population to double in size. Assuming an initial population size of 2, Morris then gives us the following relationships:T is the doubling-time in years n is the number of doublings n * T is the number of years that this doubling has been going on and Pn = 2^n is the size of the population after n*T years.
To calculate how many doublings were required to produce a given value of Pn, we solve for n:n = LOG(Pn) / LOG(2)
Given a world population of 2.5 billion in 1960, Morris found that the human population has doubled slightly more than 31 times.
Now the problem is to find a value for the doubling-time, T. Morris refers to an article by Warren Weaver in which he observed the human population grow from 250 - 350 million in the year 0 CE to 2.4 billion in 1950 CE. Weaver found that from 0 CE to 700 CE there was little change in the world population and that only after another 950 years did the population finally double to 600 million in 1650 CE. The next doubling took 200 years (1650 CE to 1850 CE) and next one after that only 100 years (1850 to 1950). Since then (1950 to 1990), it has doubled again in only 40 years.
Morris discounted the earlier figures as guesses and considered the 1650 figure to be the first valid value. Using the two doublings in the 300 years between 1650 and 1950, he obtained an average value of 150 years for T. Since he felt that the current rate of population growth is atypical because of falling death rates due to medicine and sanitation, he leaned towards the 200-year doubling time between 1650 and 1850 and, splitting the difference, finally set the value of T at a constant 175 years.
Applying this value, we find that the world human population grew from 2 people to 2.5 billion in 5250 years (30 doublings * 175 years / doubling). Subtracting this value from 1950, we obtain a date of -3300, which "leads us back to 3300 B.C. as the time of the birth of Noah's first son!" (Morris, 1961, p.398).
Morris admits that his calculation is not rigorous, but finds it far more reasonable "than to say that the population has been doubling itself since a hypothetical beginning several hundred thousand years ago." To support this, Morris quotes Hauser applying the world population growth rate between 1930 and 1940 (1% per year) to an initial population of 100 individuals over a span of 5000 years and showing that that would produce a ridiculously dense current population of 2.7 billion people per square foot over the entire earth's surface.
The year 1974 saw Morris repeatedly publishing "refinements" of his human population model, culminating in its final form. In Troubled Waters of Evolution, Morris presented it in algebraic form:P = P0 * (1+r)^n, where P is the final population (estimated at 1 billion [10^9] in 1800 CE [AKA AD]), P0 is the initial population (2), r is the rate of population growth, and n is the number of years (solved algebraically as: n = LOG(P / P0) / LOG(1+r) ).
Here, Morris has to find a value for r. At first he applies the then current rate (2% per year in 1974), and finds that the population grew from two people to 3.5 billion in only 1075 years, far too short a time.
So to find a value for r, he solved for r = (P/P0)^(1/n)-1. First he assumed n to be 4000 years and obtained a reasonable value for r of one-half of one percent (.005).
Then returning to his treatment of doubling-times in Genesis Flood, he used the growth of the population from 600 million in 1650 to 1 billion in 1800 to obtain an average annual growth rate of about one-third of one percent (.0034). From this rate, Morris obtained a time of 6100 years which, when subtracted from 1800, yields a date of 4300 BCE for the origin of the human population.
In Scientific Creationism, also published in 1974, Morris briefly offered two population growth models, the one based on the number of offspring per generation (more on this below) and the other as given in Troubled Waters. Of interest here is how he takes the "evolution model ... with its million-year history of man" to task for having 25,000 generations of men result in a world population of only 3.5 billion. Applying his 1/2% or 2.5 children per family to 25,000 generations yields an expected population exceeding 10^2100, a ridiculously enormous number.
Again, Morris openly admits that this method is not rigorous nor completely reliable, but he does strongly endorse it because its results are "reasonable" and do not need to be "modified by various secondary assumptions to fit the known data of population statistics" as the "evolution model" needs to be.
THE BUNNY BLUNDER REVEALED:But now we get to the weird part (no, that isn't what we were just doing). In his article, "Creationists, Population Growth, Bunnies, and the Great Pyramid," David H. Milne points out that since Morris' population model is predictive, then we should be able to use it to determine the world human population at any time in human history. Therefore, it reveals some interesting facts about human history.
According to Morris' model, in 2500 BCE, the world population was 750 people, so there were only about 150 to 200 able-bodied males, all concentrated in Egypt, available to hew and haul the 2.3 million limestone blocks ranging in weight from 2 to 50 tons to build the Great Pyramid of Cheops. During the preceding 200 years, even fewer men built six neighboring pyramids and many other structures. Things were even more hectic back between 3800 BCE and 3600 BCE when the total world population of 10 - 20 people, including women and children, rushed madly back and forth between Crete and the Indus River Valley building and abandoning enough fortified cities and massive irrigation systems to have housed and fed millions. My father was right; we HAVE gotten soft!
One immediately apparent error in Morris' 1974 reasoning is that he forgot the Flood! (how could he, the Father of Modern Flood Geology?) The present human population did not start with some un-named couple recently evicted from an un-named Garden, but rather with the 8 un-named passengers debarking from an un-named Ark at the end of a year-long voyage through an un-named world-wide Flood (isn't this game of "Hide the Bible" fun?). However, working with the ICR's dates for the Creation and Flood (c 8000 BCE and 4600 BCE), and applying Morris' human population model, James S. Monroe discovered some even more interesting "facts" about the antediluvian world. According to the ICR's premises, the world population at the time of the Flood would have been at least 7.2946 E+19 people, or 13,000 people per square foot over the entire earth's surface. And if the flood only happened 4000 years ago as other ICR works suggest, then the mass of people on earth just before the Flood would have exceeded the mass of the earth itself.
Nor does Morris' population model limit us to the human population. If we apply the model to rabbits, whose population doubles every two years, then we find that the world rabbit population (all species of rabbit being due to variation within the basic created bunny kind) had to have come from two bunnies created about 100 years ago. Here we have clear evidence that the earth can be no older than 100 years! The alternative to such a very young earth is to say that creation is on-going and rabbits were created ex nihilo in the last century (please ignore any mention of rabbits in the literature preceeding the time of their creation -- they simply didn't exist). We should see new species being created ex nihilo all the time. But we don't; so why aren't we up to our necks in bunnies? Yes, indeed: Creationism is more fun than science!
This is why Henry Morris' population model is called the "Bunny Blunder" and it is almost as infamous as, though far more hilarious than, Dr. Duane Gish's "Bullfrog Affair". When I heard Fred Edwords tell it, it brought down the house.
ON MODELING POPULATION GROWTH:So where did Dr. Henry Morris go wrong with his Bunny Blunder? He did so because of the standard ICR practice of ignoring the facts (of course, his apparent ignorance of the most basic principles of mathematical modeling also contributed).
First, he falsely assumed constant rates and, second, his model is far too simplistic. In Chapter 3 of his introductory book on the subject, An Introduction to Mathematical Models in the Social and Life Sciences, Michael Olnick presents a similar model of exponential population growth/decay:
from dP/dt = a * P0; where P is the population, P0 is the initial population, t is time, and a is the constant rate of growth/decay [i.e. the difference between the birth rate and the death rate],
Olnick derived the formula: P = P0 * e^(a * t) where e is the natural logrithm base [e = 2.71828 approx.]).
For small values of a, such as 1/3 of 1% (0.00333), this is virtually identical to Morris' formula. For values of a > 0, the model is called a "pure-birth" process and results in exponential growth. For values of a < 0, it is called a "pure-death" process and results in exponential decay. Remember, for both processes the rate, a, is assumed to be constant, as Morris assumed it to be.
In an example, Olnick showed that the pure-birth model accounts rather nicely for the U.S. population growth in the early to mid-19th century, but that extending that growth to the present shows that the population of the U.S. should be over 800 million! By Dr. Morris' logic, this means that the U.S. must be much younger than 200 years old. To Olnick, as to any scientist, this means that something is wrong with the model and that it needs to be refined.
The first and obvious refinement is to not assume the rate of growth/decay to be constant, but to allow it to vary, in other words:
dP/dt = f(P), where f(P) is some function of the population, i.e. the value of the function ,f, varies in response to different values of the population size, P.
Olnick applies this in the Logistic Model, in which the rate of population growth depends on the size of the population and on the ability of the environment to support that population. The Logistic Model postulates a maximum population size that the environment can support, called its "carrying capacity," such that the exponential rate of population growth decreases (i.e. slows down) as the population approaches the carrying capacity of the environment, eventually leveling off to zero-growth at the carrying capacity. This is a much more realistic model and fits the U.S. population curve from 1790 to 1950 quite well.
Obviously, the rate of population growth/decay is not in the least bit constant. The current doubling-time (i.e. the time it takes for a population to double in size) of the human population is close to 35 years. In the first half of this century, it was 87 years. In the last century, it was 120 years, fifty years before that it was 160 years, and in the preceding century it was 240 years. If we extrapolate this trend back (as did E.S. Deevey Jr. in Scientific American, 1960, Vol.203, No.5, pp 194-204) then we will arrive at a far older starting date than Morris' 4000 BCE.
Of course, the real thing is not so simple. The Logistic Model does not take into account disasters such as plagues or wars. At the start of the Plague in Europe (mid-14th century), one quarter of the population died in a single year and the population continued to decline for the next two centuries, drastically so in the epidemic years. Also, the carrying capacity of the environment is variable due to several factors such as drought, good weather, and agricultural technology. In non-human animal populations, predator-prey interactions come into play, resulting in pronounced cycles. All of these factors will affect the rate of population growth/decay.
So the human population, like the rabbit population, can indeed be millions of years old and still be no larger than we find it at present; we need but acknowledge the effects of its environment's low carrying capacity for most of its history. Our population's explosive growth these past few centuries can be attributed to the sudden increase of the carrying capacity due mainly to applied technology, such as agriculture and, more recently, sanitation and medicine.
CONCLUSION:Morris' population model is simplistic even by an introductory textbook's standards and is sadly typical of the ICR's "science." Like their probability arguments, it is based on false premises which are then used to reach false conclusions. Ironically, the Bunny Blunder's assumption of a constant rate of change is exactly what the ICR criticizes radiometric dating for, only here such an assumption is totally unwarranted.
In Troubled Waters, Dr. Morris says: "The burden of proof is altogether on evolutionists if they wish to promote some other population model." Judging from his Bunny Blunder, we need to ask him, "What's up, Doc?"
BIBLIOGRAPHY:E.S. Deevey Jr., "The Human Population," Scientific American, 1960, Vol.203, No.5, pp 194-204.
Philip M. Hauser, "Demographic Dimensions of World Politics," Science, Vol 131, 3 June 1960, p. 1641.
David H. Milne, "Creationists, Population Growth, Bunnies, and the Great Pyramid," Creation/Evolution Issue XVI, pp. 1-5.
James S. Monroe, "More on Population Growth and Creationism," Creation/Evolution Issue XVIII, pp. 44-46.
Henry M. Morris, The Troubled Waters of Evolution, 1974, Creation-Life Publishers, San Diego.
------------- , "The Young Earth," Impact No. 17, September 1974.
------------- , "Evolution and the Population Problem," Impact No. 21, February 1975.
------------- , The Scientific Case for Creation, 1977,Creation-Life Publishers, San Diego.
------------- , Scientific Creationism, 2nd Edition, 1985, Creation-Life Publishers, San Diego.
------------- & John C. Whitcomb, The Genesis Flood, 1961, The Presbyterian and Reformed Publishing Co, Philadelphia.
Michael Olnick, An Introduction to Mathematical Models in the Social and Life Sciences, 1978, Addison-Wesley Publishing Co.
Arthur N. Strahler, Science and Earth History: The Evolution/Creation Controversy, 1989, Prometheus Books, Buffalo, NY.
Warren Weaver, "People, Energy, and Food," Scientific Monthly, Vol 78, June 1954, p. 359.
DOUBLING TIMES AND RATES OF GROWTH:In this article, we have seen the rate of population growth expressed in two different ways: as a rate of exponential growth and as the doubling time of the population. In order to translate from one "unit of measure" to the other, consider the following derivation:
For: T1 = a given point in time T2 = a given point later in time than T1, such that T2 > T1 Delta_T = T2 - T1 A1 = the rate of population growth at time T1 A2 = the rate of population growth at time T2 P0 = the initial population at the reference time, T0 Pn = P0 * EXP(An * Tn), at some time Tn P1 = the population at time, T1 = P0 * EXP(A1 * T1) P2 = the population at time, T2 = P0 * EXP(A2 * T2) By the definition of Doubling Time: 2 = P2 / P1 2 = (P0 * EXP(A2 * T2)) / (P0 * EXP(A1 * T1)) 2 = EXP(A2 * T2) / EXP(A1 * T1) 2 = EXP(A2 * T2 - A1 * T1)Make the simplifying assumption that A1 = A2 = A. This may be justified by assuming that two rates measured relatively close to each other should be similar or by saying that we are analyzing what Dr. Morris has done, so we are repeating one of his basic assumptions. Either way, it makes the math come out much easier and it provides us with the variable, A, for which we are trying to solve:2 = EXP(A * T2 - A * T1) 2 = EXP(A * (T2 - T1)) LN(2) = A * (T2 - T1) LN(2) = A * Delta_TWe can now solve the equation for either A or for Delta_T:A = LN(2) / Delta_T Delta_T = LN(2) / A
Given these two equations, we can convert back and forth between doubling times and exponential growth rates, keeping our simplifying assumption in mind. For example, Morris' rate of 1/3 of 1% gives us a doubling time of 208 years.
Please note also that a constant growth rate requires a constant doubling time; indeed, they are inversely proportional to each other. If the doubling time varies then so also must the growth rate. Morris and Whitcomb's source clearly indicated that the doubling times have NOT remained constant throughout history and yet they chose to ignore their source and to assume a constant rate.
The following is a list of the growth and doubling times of the human population as taken from E.S. Deevey Jr. and reprinted in A. N. Strahler, page 367. I have added a fourth column of calculated growth rates:
Year Population Doubling Time Growth Rate 1,000,000 BCE 125,000 230,000 3.01 E-6 300,000 1,000,000 160,000 4.33 E-6 25,000 3,340,000 22,000 3.15 E-5 8,000 5,320,000 1,000 6.93 E-4 4,000 85,500,000 6,400 1.08 E-4 0 CE 133,000,000 830 8.35 E-4 1650 545,000,000 240 2.89 E-3 1750 728,000,000 160 4.33 E-3 1800 906,000,000 120 5.78 E-3 1900 1,610,000,000 87 7.96 E-3 1950 2,400,000,000 36 1.93 E-2 2000 6,270,000,000 (est.)
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First uploaded on 1997 July 02.
Updated on 2011 August 02.
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