The time it takes a population to double in size is a dramatic way to picture rates of population growth, one that most of us can understand more readily than percentage growth rates. Human populations have often grown in a pattern described as "exponential." Exponential growth occurs in bank accounts when interest is left to accumulate and itself earns interest. Exponential growth occurs in populations because children, the analogue of interest, remain in the population and themselves have children.
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Exponential growth occurs when the increase in population size in a given period is a constant percentage of the size at the beginning of the period. Thus a population growing at 2 percent annually or a bank account growing at 6 percent annually will be growing exponentially. Exponential growth does not have to be fast; it can go on at very low rates or, if the rate is negative, can be exponential shrinkage.
Saying a population is "growing exponentially" has almost come to mean "growing very fast," but that interpretation is erroneous. True exponential growth is rarely seen in human populations today, since the percentage rate of growth has been changing. In most cases, the growth rate has been gradually declining since the late 1960s. Nevertheless, it is useful to be aware of the exponential model, since it is implied every time we project a population size into the future with qualifying statements such as "if that rate continues."
For mathematical details on exponential growth, see P. R. Ehrlich, A. H. Ehrlich, and J. P. Holdren, Ecoscience: Population, Resources, Environment (Freeman, San Francisco, 1977), pp. 100-104. The term "exponential" comes from the presence in the equation for growth of a constant, e, the base of natural logarithms, raised to a power (exponent) that is a variable (the growth rate multiplied by the time that rate will be in effect).
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A key feature of exponential growth is that it often seems to start slowly and finish fast. A classic example used to illustrate this is the pond weed that doubles each day the amount of pond surface covered and is projected to cover the entire pond in thirty days. The question is, how much of the pond will be covered in twenty-nine days? The answer, of course, is that just half of the pond will be covered in twenty-nine days. The weed will then double once more and cover the entire pond the next day. As this example indicates, exponential growth contains the potential for big surprises.
The potential for surprise in repeated doublings can be underlined with another example. Suppose you set up an aquarium with appropriate life-support systems to maintain 1.000 guppies, but no more. If that number is exceeded, crowding will make the fishes susceptible to "ich," a parasitic disease that will kill most of the guppies. You then begin the population with a pair of sex-crazed guppies. Suppose that the fishes reproduce fast enough to double their population size every month. For eight months everything is fine, as the population grows 2→4→8→16→32→64→128→256→>512. Then within the ninth month the guppy population surges through the fatal 1,000 barrier, the aquarium becomes overcrowded, and most of the fishes perish. In fact, the last 100 guppies appear in less than five days -- about 2 percent of the population's history.
One problem with this analogy is that it is very highly theoretical. It is purely based in maths.
I do not know any pond which has been covered with pond weed in one day, after having only half as many the day before.
I don't know any Aquarium of guppies where in nine months the guppy population is caught by ich and mostly perishes.
Besides, a key word if it would occur is "sex crazed".
Men have some of that after fall, but also a capacity for self control, like in punishing rapists as for collective capacity, or like in going to monasteries as for individual one.
Now, let us have a look at the concept of exponential growth of population.
Can a population double in a generation? Theoretically that is not a problem. Two people get four children (but Adam and Eve got more). Or the six people in the generation after Noah get twelve children (each two getting four, but actualy they got more than that) - no problem. Suppose you do not believe in Adam or Noah? Well, the mathematical capacity for doubling is the same. So, Evolutionists say we have been around for 100.000's of years (just counting Homo Sapiens and presuming, probably wrongly, that Heidelberg man and Neanderthal man were no men, plus assigning the usual ages to these creatures presumed to be ancestry intermediate between apes and us, and probably just dead old uncles - or ancestors - between Noah and us). We Christians say humanity had one round before the Flood and has had another since then, basically 5000 years (ok, 4972, actually). Since Noah. How many generations are that? How much would we have doubled to, if exponential growth had been uniformally 2:1 per generation?
I made a calculation on that one, assuming 5000 years, so it goes likely nearly twice as many as we should get in pure mathematics for just 4972 years. Here are my results:
|5,708,990,770,823,839,524,233,143,877,797,980,545,530,986,496 = 2152 = doubling each generation for 152 generations.
5000 years : 33 years per generation = 151.5151515 ... generations.
Obviously there are other factors to population growth than exponentiality, but it is one main such - the other main being limited resources and our perception of them, while disasters augmenting temporarily mortality are a subsidiary strong third.
This is from back 24-II-2015. I saved it in my guestbook.
Perhaps the population in pure exponential mathematics would just have been:
Let's divide this by 7 billion:
So, the calculation is that much off between the theory of exponential growth at set rate of doubling each 33 years and the actual population we have.
Is that because there has been another set rate, which is lower and which has been uniform? No, it is because human behaviour is adaptable. Even if a couple easily can get four children, many don't get into couples and many don't get four children.
This much the Ehrlichs agree on. It's just that they think this can be done easier by contraception.
Well, it can also be done easier by wars. And these might not always be as bad as contraception.
Nevertheless, in same chapter, they slurred the Catholic Church:
Even though the media occasionally give coverage to population issues, some people never get the word. In November 1988, Pope John Paul II reaffirmed the Catholic Church's ban on contraception. The occasion was the twentieth anniversary of Pope Paul's anti-birth-control encyclical, Humanae Vitae.
Fortunately, the majority of Catholics in the industrial world pay little attention to the encyclical or the Church's official ban on all practical means of birth control. One need only note that Catholic Italy at present has the smallest average completed family size (1.3 children per couple) of any nation. Until contraception and then abortion were legalized there in the 1970s, the Italian birth rate was kept low by an appalling rate of illegal abortion.
The bishops who assembled to celebrate the anniversary defended the encyclical by announcing that "the world's food resources theoretically could feed 40 billion people." [Washington Post, Nov. 19, 1988, p. C-15.] In one sense they were right. It's "theoretically possible" to feed 40 billion people - in the same sense that it's theoretically possible for your favorite major-league baseball team to win every single game for fifty straight seasons, or for you to play Russian roulette ten thousand times in a row with five out of six chambers loaded without blowing your brains out.
One might also ask whether feeding 40 billion people is a worthwhile goal for humanity, even if it could be reached. Is any purpose served in turning Earth, in essence, into a gigantic human feedlot? Putting aside the near-certainty that such a miracle couldn't be sustained, what would happen to the quality of life?
First of all, I don't think feeding 40 billion people would take a miracle. But second, I also do not think that it would mean a quality of life being lowered. Using the kind of resourcefulness and reruralisation I think feeding them would imply is probably rather healthy for the overweight and overstressed.
And thirdly, I think that Catholicism has two sides when it comes to population: banning contraception and extolling monasticism.
Now, not that I'd want to become a monk myself, as per where my life has brought me, I might have done better at age twenty, but it uses far less resources and has a far better quality of life and extends this better quality of life to non-monastic Catholic or even not actively anti-Catholic non-Catholic neighbours.
So, I trust the tradition of the Church as well as the common sense that God created our genitals to be used for procreation, and consider the recommendation of the Ehrlichs as being as stinking as my pants are right now, since two shorts and one pair of pants were stolen or lost and with too few people giving money for my laundry.
And that stinks!
Hans Georg Lundahl
St Austin of Canterbury
To honour today's saint, here is "And His Word Went Marching On"
Not linking to Ehrlich book, but title is Paul R. Ehrlich & Anne H. Ehrlich, The Population Explosion, 1990. And chapter cited is 1 Why Isn't Everyone as Scared as We Are? - The title could be answered "because we are not New England Puritans or otherwise into Responsabilistic Heresies". Not being Atheist, we believe God takes His responsibility for making observance of His law work out.