April 21, 2026 | 10:30am - 12:30pm
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04/21/2026 10:30
04/21/2026 12:30
Biology Seminar
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Topic: The Mathematics of Human Population Growth and CO2 Emissions
Speakers: Victor M. Yakovenko, University of Maryland
More: https://www.ias.edu/sns/events/biology-seminar
As a postdoc at Rutgers University, I attended a physics colloquium
presented by Sergei Kapitza in the fall of 1992. His talk argued
that human population growth is hyperbolic with a singularity in the
year 2026. Actually, this claim was first published by Heinz von
Foerster et al. in 1960 in Science. Using current empirical data
from 10,000 BCE to 2023 CE, we re-examine this claim. We find that
human population initially grew exponentially in time as N(t)~exp(t/T)
with T~3000 years. This growth then gradually evolved to be
super-exponential with a form similar to the Bose function in
statistical physics. Population growth further accelerated around
1700, entering the hyperbolic regime N(t)=C/(t_s-t) with the
extrapolated singularity year t_s=2030, which essentially confirms the
claim by Kapitza and von Foerster et al. We attribute the onset of
the hyperbolic regime to the transition to massive use of fossil fuels
upon the Industrial Revolution, as evidenced by a linear relation that
we find between world population and the increase in CO2 level from
1700 to 2000. But in the 21st century, the inverse population curve
1/N(t) deviates from a straight line and follows a pattern of "avoided
crossing". As a result, the singularity transforms into a
square-root Lorentzian peak at t_s=2030 of the width \tau=32 years.
Our predicted year 2030 of the peak in human population is much
earlier than in other demographic forecasts. We also find that the
increase in the CO2 level since 1700 is well fitted by
arccot[(t_s-t)/\tau_F] with \tau_F=40 years. It implies a Lorentzian
peak in the annual emissions d(CO2)/dt at the same year t_s=2030.
Bloomberg Hall Biology Conference Room (1st Floor, Room 113)
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