True. But having been in the fray so long, they all start to look the same to us. We tend to forget that there is indeed a fairly wide variety of creationism and that not all creationists are YECs. At the same time, though, even many of those non-YEC creationists will still read the YEC literature and try to use YEC claims, such as the Bunny Blunder. So addressing the claim should still be on-topic.
When I posted last night, I couldn't find my reference for population models; I still can't. However, I did reference it in a couple pages that were on my website before my webhost abruptly dropped out of the business. It is:
Michael Olnick, An Introduction to Mathematical Models in the Social and Life Sciences, 1978, Addison-Wesley Publishing Co.
Here is what I wrote on population models on my old page on the Bunny Blunder, which I originally wrote for the library on CompuServe in 1991:
quote:
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.
{ABE: Dawn, are you listening here?}
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.
We know with total certaintude that Buz' model is dead wrong, because he explicitly identifies it as H. Morris' model. We recognize CrazyDiamond's model as pure-birth, which we know to be far too simplistic to be able to model reality and hence is wrong.
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