Doomsday: Friday, 13 November, A.D. 2026

Foerster, Heinz von; Mora, Patricia Montero; Amiot, Lawrence W.

doi:10.1126/science.132.3436.1291

Cited by 266 publications

(145 citation statements)

References 6 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…Note that here we are talking about a mathematical singularity (division by zero) of the kind described for example in von Foerster, Mora, and Amiot (1960); Meyer and Vallee (1975); Kremer (1993); Johansen and Sornette (2001);Bettencourt, Lobo, Helbing, Kühnert, and West (2007). This is different from the "technological singularity" discussed by various authors (Vinge 1993;Kurzweil 2005;Yudkowsky 2007) 5 .…”

Section: Generalized Nonlinear Regression Resultsmentioning

confidence: 97%

Superexponential long-term trends in information technology

Nagy¹,

Farmer²,

Trancik³

et al. 2011

Technological Forecasting and Social Change

View full text Add to dashboard Cite

Moore's Law has created a popular perception of exponential progress in information technology. But is the progress of IT really exponential? In this paper we examine long time series of data documenting progress in information technology gathered by Koh and Magee (2006). We analyze six different historical trends of progress for several technologies grouped into the following three functional tasks: information storage, information transportation (bandwidth), and information transformation (speed of computation). Five of the six datasets extend back to the nineteenth century. We perform statistical analyses and show that in all six cases one can reject the exponential hypothesis at statistically significant levels. In contrast, one cannot reject the hypothesis of superexponential growth with decreasing doubling times. This raises questions about whether past trends in the improvement of information technology are sustainable.

show abstract

Section: Generalized Nonlinear Regression Resultsmentioning

confidence: 97%

Superexponential long-term trends in information technology

Nagy¹,

Farmer²,

Trancik³

et al. 2011

Technological Forecasting and Social Change

View full text Add to dashboard Cite

show abstract

“…Noting that equation (2) It has long been recognized that population dynamics can exhibit growth like equation (2) [5]. Exponential growth is more common, but if per capita growth rates increase with population size (due, e.g., to improved technology) and resources are effectively unlimited, superexponential growth ensues.…”

mentioning

confidence: 99%

Mathematical Expression of a Global Environmental Catastrophe

Rothman¹

2017

Notices Amer. Math. Soc.

View full text Add to dashboard Cite

“…A point of departure from this assumption is provided by two dynamic-K models allowing for innovative solutions. The one assumes K changes instantaneously with N(t) (4,5), whereas the other considers large-scale social changes introduced with delays in the dependence between N and K (8, 11).…”

mentioning

confidence: 99%

“…We ask to what extent models that are premised on a constant global K as in Suweis et al (3) agree with an alternative class of carrying capacity models on predicting the timing for unsustainable global population growth. In particular, factors that symbolize innovation and adaptation lead to K representations that are not constant (4,5) but may depend on a dynamic population size.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Fifty years to prove Malthus right

Kaack

Katul

2013

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

A major question confronting sustainability research today is to what extent our planet, with a finite environmental resource base, can accommodate the faster than exponentially growing human population. Although these concerns are generally attributed to Malthus (1766Malthus ( -1834, early attempts to estimate the maximum sustainable population (ergo, the carrying capacity K) were reported by van Leeuwenhoek (1632Leeuwenhoek ( -1723 to be at 13 billion people (1). Since then, the concept of carrying capacity has evolved to accommodate many resource limitations originating from available water, energy, and other ecosystem goods and services (1, 2). In PNAS, Suweis et al. (3) apply the concept of carrying capacity using fresh water availability on a national scale as the limiting resource to infer the global K. They estimate a decline in global human population by the middle of this century. We ask to what extent models that are premised on a constant global K as in Suweis et al. (3) agree with an alternative class of carrying capacity models on predicting the timing for unsustainable global population growth. In particular, factors that symbolize innovation and adaptation lead to K representations that are not constant (4, 5) but may depend on a dynamic population size.The workhorse model for describing population growth remains the logistic equation (6-8). Attributed to Pierre-François Verhulst (9) and popularized by Pearl and Reed (10), the logistic equation is dN(t)/dt = rN(t)(1 − N(t)/K), where N(t) is the population, t is time, and r is the growth rate. For a constant K and r, the solution is an S-shaped function saturating to a constant population size N(∞) = K. Suweis et al. (3) determine the r and K for each country, using a population time series from 1970 to 2010, water availability, and water use per capita. If a country has a water surplus, it can export water to water-poor countries as virtual water (VW) in the form of food. The momentary K of a nation is based on a combination of local and traded VW that provides water-poor countries the possibility to extend their population size above the local carrying capacity. The global K was assumed to be constant in time, reflecting the finite fresh water supply of the planet. A point of departure from this assumption is provided by two dynamic-K models allowing for innovative solutions. The one assumes K changes instantaneously with N(t) (4, 5), whereas the other considers large-scale social changes introduced with delays in the dependence between N and K (8, 11).In 1960, von Foerster et al. (5) humorously developed the first model type to predict a doomsday associated with a mathematical singularity in population dynamics on November 13, A.D. 2026. They concluded that "[. . .] our great-great-grandchildren will not starve to death. They will be squeezed to death" (5, 12). To illustrate occurrences of singularities in finite times, the logistic equation can be recasted as dN(t)/ dt = r′N(t)(K − N(t)). Von Foerster et al. (5) made the assumption that K(t)...

show abstract

Doomsday: Friday, 13 November, A.D. 2026

Cited by 266 publications

References 6 publications

Superexponential long-term trends in information technology

Superexponential long-term trends in information technology

Mathematical Expression of a Global Environmental Catastrophe

Fifty years to prove Malthus right

Contact Info

Product

Resources

About