Essay by Eric Worrall
While critics were initially less than impressed, by the 1970s the paper’s apparently on track predictions had grown its fan base.
Doomsday: Friday, 13 November, A.D. 2026
At this date human population will approach infinity
if it grows as it has grown in the last two millenia.Heinz von Foerster, Patricia M. Mora, Lawrence W. Amiot
Among the many different aspects which may be of interest in the study of biological populations (1) is the one in which attempts are made to estimate the past and the future of such a population in terms of the number of its elements, if the behavior of this population is observable over a reasonable period of time.
All such attempts make use of two fundamental facts concerning an individual element of a closed biological population — namely, (i) that each element comes into existence by a sexual or asexual process performed by another element of this population (“birth”), and (ii) that after a finite time each element will cease to be a distinguishable member of this population and has to be excluded from the population count (“death”).
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Human Population
In order to check whether or not the hypothesis expressed in Eq. 3 has any merit at all, we took the human world population as a test case, since it was felt that the most reliable long-range data on the development of a population comprised of communicating elements may be found in the history of men. The use of estimates of the world population rather than of populations of certain geographical regions eliminates to a certain extent the influence of local fluctuations and migration. A bibliographical search produced 24 estimates (see 9–11) of the world population, ranging over approximately 100 generations from the time of Christ (t = 0) almost to the present (t = 1958). These estimates were carefully checked with respect to their independence, and those which were suspected of being merely cross references in the literature were eliminated from the statistics in order to avoid improper weighting.
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The method of least squares was employed in order to extract from the data the three values t₀, K, and k; the following values were obtained:
t₀ = A.D. 2026.87 ± 5.50 years (10a)
K = (1.79 ± 0.14) × 10¹¹ (10b)
k = 0.990 ± 0.009 (10c)The root mean square deviation for all points considered is approximately 7 percent.
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It requires only simple calculations to show that if Charlemagne had had Eq. 6, with the evidence he could have had with respect to the world’s population, he could have predicted doomsday accurately within 300 years. Elizabeth I of England could have predicted the critical date within 110 years, and Napoleon within 30 years. Today, however, we are in a much better position, since we are required to extrapolate our evidence only 4 percent beyond our last point of observation: we can predict doomsday within approximately 10 years.
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Optimists versus Pessimists?
It is hoped that the preceding exposé will add some fuel to the heated controversy about whether or not the time has come when something has to be done about population growth control. This controversy has divided those elements of the population under consideration who profess to show some interest in human affairs into two strictly opposed camps (14): the optimists, who see in the population explosion a welcome expansion of their clientele, be it consumers of baby goods (15), voters, or devoted souls (16), and, on the other hand, the pessimists, who worry about the rapid depletion of the natural resources and the irreversible poisoning of our biosphere (14, 17). While the optimists adhere to the thesis that no matter how fast the population is growing, food technology and the industrial sciences will easily keep pace with the development and thus will maintain the elements of the human population — at least for some generations to come — in a perfect state of economic and individual health, the pessimists prefer to paint the future of mankind in not quite the same rosy colors by pointing to the increasing growth rate of the population while assuming that industrial and scientific development will proceed at a much slower pace. Hence, the pessimists anticipate that further rapid increase in the population density will be accompanied by a deterioration in human dignity, and they see the ultimate fate of the human race as a mere vegetation of the individual on the edge of existence, if no measures are introduced to keep the world population under control (18).
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Since the tendencies today do not point in the direction of observable efforts to reduce the mean life span, tₘ, of human individuals — on the contrary, we see a steady increase in this value — it is clear that our people-stat has to control the fertility γ*, and has to maintain it at the level 1/tₘ. Today, this means cutting the birth rate to about half its present value or, in other words, cutting the size of an average family to just a little above two children. Tomorrow, of course, it will be more difficult, since — as we have seen — the gap between birth rate and death rate is widening every minute.
Among the suggestions that have been advanced for meeting this problem — legislation, heavy taxation of families that have more than two children, cancellation of tax deductions, and so on — space travel has been proposed recently as an alternative (19). It is only unfortunate that no re-entry permit to earth can be given these space-trotters.
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Read more: https://www.science.org/doi/epdf/10.1126/science.132.3436.1291
I asked Claude to read the paper and figure out the final form of the doomsday equation:
N(t) = 1.79 x 10^11 / (2026.87 – t)^0.99
As t approaches 2026.87 (November 13 2026), the population estimate N(t) approaches infinity.
Here’s a video by Anton Petrov, which discusses this paper;
Those 1960s doomsayers predicted a hyperbolic population growth curve, then recommended draconian government intervention – more tax, Chinese Communist style child limits, or even sending people on a one way trip to space.
At the time the paper was published apparently the reception was skeptical (see below).
But by the 1970s the paper gained wider acceptance.
By the 1990s it was all over. It became obvious the predictions of the paper were diverging from reality.
The lesson is pretty plain I think, and has application to the alleged climate crisis. Extrapolation is a dangerous game – especially when there is and always has been robust evidence human populations do not irrationally increase without limit. Or in the case of the fake climate crisis, robust evidence that the world was entirely habitable during much warmer past regimes such as the PETM, a brief period of extreme warmth which coincided with our monkey ancestors first appearance in the fossil record.
I’d love to know your thoughts on why the authors got it wrong. Their math, their approach to developing their doomsday equation starts with simple and defensible assumptions. At face value the math looks straightforward and elegant. But as Thomas Henry Huxley said in 1870, “The great tragedy of Science — the slaying of a beautiful hypothesis by an ugly fact.“
To be fair the paper did claim a 10 year margin of error, so maybe we just haven’t given doomsday enough time to manifest.
If you want to know more about population doomsday, Stuart Umpleby’s site is worth a visit. This article referenced the Pogo cartoon and the 1975 Serrin paper from that site.
