In the short time since I woke up this morning, the world’s become a few thousand people more crowded. No one is tracking each individual birth or death, of course, but census measurements from around the world have brought us a fairly good means of estimating how many human beings there are, and the minute by minute change of that estimate is shown at the U.S. Census Bureau’s population clock. Right now, that clock shows the world’s population at:

6,758,535,880

Before today, I’d been saying that the world’s population is six billion people, rounding it off to a nice easy number. Now I can see that if I were to round it off, I’d be more accurate to say that there are seven billion of us. It won’t be long until even that’s an understatement.

The world’s population increased by 800 just in the time it took me to write this short article.

And since population grows exponentially, we’re in trouble – too many humans, not enough resources. Of course the skewed distribution of wealth in the world only exacerbates the problem.

Actually, Tom, population is not growing exponentially. In industrialized nations, not counting immigration population is actually shrinking, and as more nations industrialize their population growth rates are leveling off, with more nations’ growth rates heading toward negative territory. It’s a complicated world, and the population trends are correspondingly complicated.

First off, its a global model of human growth, and secondly – even if it’s beginning to “level off” in some countries, the way any life reproduces (including cells in a Petrie dish) is described biologically via an exponential model (the k value in the exponent may become negative, but the data still follows an exponential curve, as opposed to a linear or quadratic one). i’m not being pedantic Jim, it’s just the way it is. (Students often confuse exponential growth or decay – like nuclear waste – as very fast, when it could be measured, like said nuclear waste, in thousands of years, that is, very slowly, or in the case of populations, growing slower or “smaller” in number compared to the amount already around, but adding, often considerably, to the total nonetheless).

Tom,

C’mon, you were being pedantic, as well as incorrect.

Imagine that Arizona’s population growth is truly exponential with a constant k1, and Minnesota’s population growth (or decline) is truly exponential with constant k2. Is the combined population of Minnesota and Arizona truly exponential? i.e. Find the constant k that satisfies

exp(k1*t) + exp(k2*t) = exp(k*t) for arbitrary k1, k2, and t. Good Luck.

Now add in every province of every country in the World. [You would find the same “unexponentiality” with combined populations from multiple Petri dishes, each having a different growth rate.]

In fact some models show world human population cresting sometime this century. According to a Berkeley model (http://math.berkeley.edu/~galen/popclk.html), it took 401 seconds to add 1000 people as the world’s population crossed 5 billion in 1986. In 1999, the world pop. crossed 6 billion at a rate of 1000 people per 407 sec. It is predicted that in 2012, we will cross 7 billion at a rate of 1000 people per 452 sec. That is, we are slowing down, and as Jim indicates heading toward a leveling off. (just shy of 9 bill in 2058 acc. to the Berkeley model). Of course none of the future numbers have much chance of being accurate in any sense, and a lot can happen between now and 2058, but education and birth control do seem to be plausibly behind this trend. There is little reason to despair just yet.