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”).
…
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.
…
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.
…
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.
…
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).
…
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.
…
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.
Depending on how people react to the midterms, could be right.
Bad luck, that.
If I have read this correctly, we are looking at yet more circular logic: using a N(t) = a x b / (t0 – t)^c formula is to assume a doomsday. Not only that, but it actually puts in the precise doomsday date.
The paper makes a very entertaining read, they start from easily explained assumptions, then try to use historical estimates to fit parameters to their formula.
There’s a paragraph which claims their doomsday calculation could have been performed in the time of emperor Charlamagne or Elizabeth the first (from memory) using available data.
The funny part is their maths is broadly right. Where I think they went wrong is they didn’t look closely enough for historical examples where economic pressure caused people to have fewer children. If they’d factored that into their calculation the doomsday hyperbolic discontinuity would have disappeared.
No. Their maths is completely wrong right from the start. They deliberately chose to fit the population using a function with a singularlity in it just so that they could predict the end of the world at some finite time in the future. Had they chosen to fit a logistic model or even an exponential curve to the data then that would not have the singularity and hence nothing to write about.
Economic pressure usually causes people to have more children – that’s why poor countries have the highest birth rates and countries that had massive economic success(Japan, South Korea) have the lowest reproduction rates.
China does no longer need a forced one-child policy since the economy is thriving.
Its birthrate is dropping like a stone and reached a record low this year.
Well, yes and no. Yes, one can apply an exponential curve fit to a data set of three of more data points . . . but doing such to any natural process reflects complete ignorance that very, very few natural processes proceed on an exponential increasing trend to infinity without encountering negative feedback factors.
The paper was clearly not meant to be taken seriously except perhaps as a lesson in how not to extrapolate. Nobody would really believe that the end of humanity would come as a result of being squeezed to death in 2026. Note also their claim that “although it is always fascinating to imagine one’s future fate, the possibility of deriving some fun by extrapolating our function into the past should not be overlooked….thus, if one desires to calculate the date of the emergence of a hypothetical “Adam”-that is, N =1 one finds it about 200 billion years
ago. Even astronomers in their wildest speculations have not yet come up with
an age of the universe which would approximate this figure”
So they clearly didn’t believe that their equation worked in predicting the past and there is no reason to believe that they or anyone believed that the equation would work in predicting the future. It is just an example of mathematicans have a joke and Science publishing it for a laugh.
Ah I see – we should interpret this paper as a mathematical joke, despite serious reports around the same time such as Club of Rome “The Limits to Growth” (1972) making similar forecasts, while extrapolated climate disaster forecasts are deadly serious guides to our likely future annihilation. Got it.
Of course it is a joke. Nobody ever thought that the population would become infinite within a finite time period. The clue is in the extrapolation to the past — they knew that the prediction that humanity had existed for close to 200 billion years was nonsense and similarly extrapolation into the future would produce similarly nonsense. They are also clear that they are predicting what would happen if we were living in “paradise” and again the use of such a phrase should be a clear signal that they are not being serious.
And the “limits to growth” was making the opposite forcast, i.e. that there are limits to growth while this paper assumes that there are none.
The paper was a warning. Nobody expected human population to approach infinity. They expected other factors to intervene, such as higher taxes discouraging children.
The only thing the paper was warning about was the danger of using the wrong function to fit your data. Nobody would ever expect a function with a singularity in it to be a good way to fit a population curve.
It depends on how the paper was received in the official realm.
If it gained some serious attention than the joke(which the infinite approach suggests) completely missfired – or the “joke” was
of the AOC-kind of joke, who claimed that the world will end in 5 years (or so) and then later paddled back, saying only a spongeIQ person would think it was literal.
Problem is that millions heard her initial claim, but no one read the retraction.
And keep in mind – the 60ies were the decade when hiding under the school desk could save you from a nuclear explosion(while nowadays nothing can save humanity from 0.01% co2, not even schooldesks).
Therefore the line between jokes and not-jokes may be blurry as Paul Ehrlichs doom prediction(Population Bomb) already complemented such jokes in the 60ies in a serious way and in 1960 the global population reached 3 billion and population centers popped up everywhere –
and before this “joke” above was published TIME released an article(The Numbers Game) about the same topic.
Is a joke a joke when 99% don’t get the joke or is it a psyop?
Actually, an exponential curve with a exponent less than infinity does not end with, let alone contain, a singularity.
they were fake then and they are fake now
Ah, So Science didn’t do Science back then either? 😉
Or at least they assumed that people liked a good joke and were intelligent enough to recognise one when they published it.
Kinda like climate change. Except there are a lot of scientists who didn’t get the joke.
Do they often publish jokes in Science, which purportedly is the most sophisticated science publication? So, any time a paper bombs, it can be explained as a joke?
Mr. Walton: The joke here is your lame attempt to backfill an explanation for this scientific malpractice from the 60s. Can you find any reference from the past that this paper was a joke? Or is it your exclusive invention? I submit that you are the first person in over 60 years to posit this notion. You can show I’m wrong with one reference.
You are quite right, of course, but the problem is that they never realised that General Circulation Models were the exact same kind of joke. No-one could seriously believe that an inaccurate model with 20-minute iterations could predict a century ahead. In other words, they were obviously a joke. These jokes simply don’t work and should not be used anywhere anyone could take them seriously, which is everywhere in green land.
there is no such a thing as “Science” – it is as mythical as a dragon.
And, of course, all the weeping and gnashing of teeth over the climate crisis is another of their jokes.
By my calculations which are rather train of thought and at the x86 FORTH level before being raised to CoSy for output ,
2026.87 | fractional date given
.87 365.25 f* _f |>| 317.77 | Number of days after New Year
`i 20260100 317 _i Days+ ,/ |>| 20261113 | Date 11 13
.77 24. f* _f |>| 18.48 | hour
.48 60. f* _f |>| 28.80 | Minute .
I know I have some words around to do it more elegantly , but , whatha hay ?
The people at Our World in Data propose a different model that recognizes the demographic effects of relatively recent and ongoing improvements in infant and early childhood survival rates as well as the emancipation of women; that human beings exercise agency and are not rabbits.
https://ourworldindata.org/cdn-cgi/imagedelivery/qLq-8BTgXU8yG0N6HnOy8g/bfcc4286-5dfe-4c81-61e8-220943c77d00/w=2364
In 1978, as a freshman biology student, I pulled the numbers for 1975 out and proceeded to blow this bullshit out of the water.
If I, as an 18 year old freshman with access to a college library, could demolish this, and the idiotic psuedo Malthusian starve to death crap that was around at the same time, how did this come to be accepted?
If you have time send your refutation of doomsday to WUWT submit news tip, mention my name in your message :-).
It was accepted because it was humorous enough to be worth publishing and was clearly never meant to be taken seriously. Later interviews with the authors revealed that they tweaked the numbers so that the world would end on Friday the 13th, again a clear signal that they were not serious.
Why didn’t they publish it in a humor magazine rather than the prestigious science publication, Science? I think you’re rationalizing.
Because it wouldn’t be funny:
https://pubmed.ncbi.nlm.nih.gov/30545967/
Not being able to detect inside baseball humor is one way for an in-group to protect itself from impostors.
A bit like here, minus the abuse.
Mr. Z: I call this “backfilling”, nobody thought this paper was a joke until Mr. Walton suggested it here, he’s trying to fill in an explanation for something presented as serious science. Why can’t he accept what actually happened?
Messing about with mathematical models is not behaving as a scientist – it is behaving as a mathematical statistician
Having read the publication at the time (early ’60’s), there was no attempt at humor. It was a serious attempt to use the newest tools available (monster computers) to handle complex social issues using (what were then) complex differential equations based mostly on assumptions. I was a “skeptic” then, and it prepared me for skepticism three decades later when CAGW was proposed as “serious science”. And for skepticism three decades further on when the “doomsday flu” bug arrived, courtesy of “Dr. Science” himself!
No need to ask Claude to read the paper to notice:
Good ol’ engineers.
Three engineers were in a rental car, and headed to a conference. The engine in the car began to cut out and run rough. The mechanical engineer said “I think the fuel injection pump is going bad”. The electrical engineer said “I think it’s probably the engine control unit”. The software engineer said “Just shut the car down and restart it and everything should be fine”.
An engineer and a scientist (both male) are placed at either end of a long hallway, with a beautiful woman exactly half way between them.
The engineer and the scientist were instructed that each time the bell rang, they could move exactly half the distance to the woman.
The bell rang, the engineer moved, the scientist didn’t.
The bell rang again, the engineer moved and the scientist didn’t.
The bell rang a third time, with the same results.
Finally the engineer asked the scientist why he wasn’t moving.
The scientist answered that since they could only go half way each turn, they could never reach the woman, so why bother.
The engineer responded, that while the scientists math was correct, it was also true that eventually they would get so close, that the remaining distance didn’t matter.
One of the risks of writing something that is clearly tongue in cheek, is one day the people reading the joke won’t accept it was a joke. The Climate alarmists sadly fall into that category of gullible anxious souls. No doubt they all have good intentions but unfortunately lack the education to understand interconnected chaos. (who does)?
I can speak so, because in this example we are certain infinite humans won’t suddenly turn up on November 12th this year in time to lend credibility to the prediction based on pseudo mathematical logic.
When future certainty is presented as an unavoidable truth, I am reminded of Harold Macmillan’s famous response, when asked, about what will most likely blow government of course?
His answer “events dear boy, events”, was the most complete indication of what will impact every future.
Anyway, I have a dental appointment on the 12th, I must get that in before the close down of humanity…..
“One of the risks of writing something that is clearly tongue in cheek, is one day the people reading the joke won’t accept it was a joke.”
Especially when published in Science.
Was it a joke when the Chinese implemented their one child policy?
I seem to recall the Chinese government had ways of punishing people for more than 1 child but don’t recall what it was. Now they’re begging people to have more children but they’re not interested.
Wouldn’t be the last time Science published a “joke”. Their articles on climate change prompted me to cancel my subscription 10 years or so ago.
Science published a paper back in October, 2009. Volume 326. The title was “Fixing a Critical Climate Error”. It was highly destructive to forestry- which was my “tipping point” against the climatistas. The idea was that cutting trees in forestry work results in carbon emissions- especially if the wood goes to a biomass burner. The argument is that if a tree is cut and burned (even in a well managed forest- managed for the long term)- the CO2 emission must be counted as such. Until then, forestry claimed that as long as the total amount of carbon in the forests doesn’t drop, there is no NET EMISSIONS. The authors’ claim is that- get this- say you cut a tree- well, that’s a negative and it won’t be balanced by growth until, essentially, THAT spot where that tree was regrows a tree of the same size. Totally ignoring the obvious fact that the forest as a whole is still growing. And, with good forestry you DON’T BURN ALL THE TREES, despite what some fools here keep saying. The best wood goes into sawlogs or veneer, other wood goes to pulp and the dregs go into the local firewood market or converted to chips for biomass burners. So, most isn’t burned. But lets say you’re managing a big company forestry operation with 100K acres. Maybe you cut 5K acres each year- thinning some and clear cutting others. But, the 95K acres is still growing and will sequester more carbon than whatever CO2 went up a chimney in your home or a biomass burner. So, the forest AS A WHOLE isn’t contributing CO2 to the atmosphere, it’s actually increasing sequestered carbon.
This Science paper was the foundation of the argument here in Wokeachusetts to not allow any biomass burners in the state. Of course many people here have chip burning stoves- but the chips have to come in from thousands of miles away. And, if we had such biomass burneing power plants, the market for the “junk wood” would be fantastic- allowing many stands to receive some silvicultural work- even though the value of those trees is low, every penny counts in forestry since it’s hardly ever very profitable. Without this market, by now, forestry has dwindled every year since I started as a forester in 1973.
Instead of forestry, the enviros want to lock up all the forest land- calling them “reserves”- where nature will do its own thing- forgetting that 99.99% of all the forests in the state had been clearcut by 1830 and most of it had been high graded (cut the best and left the rest) several times in the 20th century- so it’s not virgin landscape- but those enviros just HATE forestry- while preaching that it’s to save the planet from burning up. At one state forest- the state had a contract on 100 acres- for a thinning of an oak stand- leaving the best trees. The enviros said it was going to be clearcut- so they showed up and chained themselves to the logging machinery.
Their hatred of forestry- pretending it has to do with the climate- is what turned me against the climatistas- because in this case I know they were dead wrong- so I concluded they’re probably dead wrong on many other so called climate issues. Then another forester here suggested this site and I’ve been reading it ever since.
So, my dislike of Science is pretty intense.
appreciate your reply No one benefits when “science” becomes “political”
If there is a global energy shortage in 20 years, there will be problems with the food supply.
Some oil-producing countries will run out of their oil reserves within 20 years.
If there is a global energy shortage in 20 years, will it lead to World War III?
Years left of Oil by Country.
https://www.worldometers.info/oil/
Or is there enough oil left for another 200 years?
https://www.aogr.com/web-exclusives/exclusive-story/north-america-holds-vast-oil-and-gas-reserves
227 years at today’s prices, using today’s technology.
As prices rise, more oil becomes recoverable.
As technology improves, more oil becomes recoverable.
If prices rise, more oil becomes recoverable.
This means that the remaining recoverable oil is more expensive to extract, and the price of oil becomes higher.
Among frustrated SF writers, some become mysterious and charismatic government agents who scheme with aliens, like the Cigarette Smoking Man in The X-Files, while others fulfill their literary ambitions by publishing in peer-reviewed scientific journals instead of pulp magazines that cost a few cents.
It always amazes me how supposedly intelligent people are so stupid. Apparently they have no common sense. As a Chemical Engineer, we were taught to think about the answers to our problems and consider if they made sense.
My physics teacher in high school called it “The Principle of Least Astonishment”.
If your calculations of the speed of a dropped hammer from 300 ft exceeds the speed of sound, go back and try again.
Thank you, Brother “Physics is Relevant!” Clark.
It’s called homework, due process, in biology a juvenile characteristic as also curiosity. What we need now are equations to predict what is going to happen from these “skills” that I received within a supposed science link that actually had a little science.
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Strange. James Serrin is a fully established member of the Clifford Truesdell school of continuum mechanics. Mathematically beyond reproach.
He did not quite make it to his 100th Birthday.
More appropriate if you had said “He did not continue so as to reach his 100th birthday.” 🙂
Yogi Berra
Gosh . . . I thought that most people had heard—more importantly, understood—the meaning of this well-publicized phrase by the time of graduation from high school:
“Past performance is no guarantee of future results.”
Good grief (and shades of “Club of Rome” sophomoric thinking)!
The authors use a function which exhibits a singularity at a particular time. Just common sense should have told them that such would be physically impossible and thus that that function was nonsense.
The fundamental premise of “they were wrong about that, so they must be wrong about this” does not follow. Climate change may or may not be catastrophic, but the failure to predict one thing about population does not prove anything about other predictions unless they use the same methodology.
Just more lies, damned lies and statistics. Nothing to see here worth the time or the trouble
I am certain that there will be another pandemic, and another. I have no idea which one, or the third … or the next, will decimate part of the population of people in the world.
Numbers will change significantly, there will be wars and dark ages on some continents or parts thereof – and humans will probably survive to go on and stuff up in some other way in their future.
I am not sure why anyone ever took this seriously. Simple exponential functions do not model population growth. An actuary named Benjamin Gompertz published a model that produced an S shaped curve called the Gompertz function in 1825, 135 years before the Foerster paper.
https://en.wikipedia.org/wiki/Gompertz_function
The logistic function that also produces an S shaped curve and was published a few years after Gompertz.
https://en.wikipedia.org/wiki/Logistic_function
Of course Malthus described the end of an exponential growth regime in 1798, when he proposed that there was an upper bound to population growth limited by resource growth. Malthus was wrong about his prediction of disaster because resources can grow at a more than linear rate (every mouth is accompanied by two hands), but he also allowed that population could be limited by vice. I guess he would say that what we are actually seeing — delayed marriages and fewer children per woman — is vice.