Will the world end TOMORROW?

Will the world end tomorrow? That sounds crazy, but ... not so fast. Let's stop and look at it.

In 1960, a team of respected scientists published an article in the journal Science, entitled "Doomsday: Friday, 13 November, A.D. 2026." The article appeared in Volume 132, Issue 3436, dated November 4, 1960, running on pages 1291 through 1295. The authors were Heinz von Foerster, Patricia M. Mora, and Lawrence W. Amiot, and the main topic was a study of the growth of human population. The authors pointed out that any population is governed by its rate of increase (fertility) and its rate of decrease (mortality). They set up the relevant differential equations, analyzed them based on the known historical data, and finally settled on a closed-form equation to calculate N, the human population of the Earth at any given time t.

Note that the denominator of the expression includes the term (t₀ – t), where the current time and date (repesented by t) is subtracted from a reference date t₀. Obviously if we want to take this formula seriously, we have to know when t₀ is, because on that date the denominator of the expression falls to zero and the value of N becomes undefined. What is perhaps more frightening, in the days, hours, and minutes before t₀, the denominator will be very small but still positive. So at that point the value of N will be very large—and growing ever more rapidly—but still (for the moment) defined.

The authors recognized that their article required them to make a determination of the value of t₀, and so they did. After careful consideration of the empirical data regarding current and historic human populations, they determined that t₀ would fall late in 2026, on the 317th day of the year. (Arithmetically, 0.87 x 365 = 317.55.) The 317th day of 2026 is Friday, November 13. Tomorrow! By coincidence, that is also Heinz von Foerster's 115th birthday, or it would be if he were still alive.

So if the von Foerster formula is accurate, we should expect the human population of the Earth to balloon towards infinity today and tomorrow, and then presumably to vanish as the value becomes undefined. If the formula is accurate, tomorrow is Doomsday.*

Heinz von Foerster, 1963, from University
of Illinois publicity department

Logically the next question has to be ... exactly how accurate is that formula? Well, back in 1960 it was pretty accurate, because it was built from the observed data. And in fact for some years thereafter, the predicted population values tracked the actual ones pretty closely. Nearly four decades after publication, the formula predicted that the world's population at the beginning of 1997 would be 5,986,622,074. The actual value was 5,924,787,816, or 98.967% of the predicted value. That's remarkably close.

Then somewhere around the turn of the millenium, the growth of human population began to slow down. Current projections are that human population will stop growing in absolute numbers before the end of the 21st century, and will begin to decline. Many explanations have been offered; I don't know if there is professional agreement on a single one. But in any event, the geometric increase predicted by the von Foerster doomsday formula no longer represents empirical reality.

We can afford to exhale. The world is unlikely to end tomorrow. 

Now, you might ask: This story is fun, but what does it have to do with Quality? Simply this. We use a lot of mathematical models in Quality. Those are valuable, because if we can test products mathematically we don't have to destroy them in real life to find their breaking points. Mathematical testing is a lot less wasteful than destructive testing. But you have to make sure that the mathematical model is valid. Compare it at all the critical points against experimental data. If time is a relevant factor, then check it again after some time has elapsed. It is easy to be misled by a fancy model that no longer checks out. 

We've discussed this topic before, but the point bears repeating.       

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* On the other hand, the formula also predicts that the human population of Earth today—Thursday, November 12—should be 65,335,000,000,000. That's over 65 trillion people. Spoiler alert: it's not.