The Imminent Peaks of World Population and CO2 Emissions
Research by Victor Yakovenko

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[1] "The End of Hyperbolic Growth in Human Population and CO2 Emissions" by V. M. Yakovenko

Published:  Physica A, 661, 130412 (2025); 16 pages, open access,  PDF,  arXiv:2508.11038
Abstract:  Using current empirical data from 10,000 BCE to 2023 CE, we re-examine a hyperbolic pattern of human population growth, which was identified by von Foerster et al. in 1960 with a predicted singularity in 2026. We find that human population initially grew exponentially in time as N(t)~et/T with T=2080 years. This growth then gradually evolved to be super-exponential with a form similar to the Bose function in statistical physics. Around 1700, population growth further accelerated, entering the hyperbolic regime as N(t)~(ts-t)-1 with the extrapolated singularity year ts=2030, which is close to the prediction by von Foerster et al. We attribute the switch from the super-exponential to the hyperbolic regime to the onset of the Industrial Revolution and the transition to massive use of fossil fuels. This claim is supported by a linear relation that we find between the increase in the atmospheric CO2 level and population from 1700 to 2000. In the 21st century, we observe that the inverse population curve 1/N(t) deviates from a straight line and follows a pattern of "avoided crossing" described by the square root of the Lorentzian function. Thus, instead of a singularity, we predict a peak in human population at ts=2030 of the time width \tau=32 years. We also find that the increase in CO2 level since 1700 is well fitted by arccot[(ts-t)/\tauF] with \tauF=40 years, which implies a peak in the annual CO2 emissions at the same year ts=2030.

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