Energy and Human Ambitions on a Finite Planet, 2021a

2
1 Exponential Growth
<strong>Human</strong>s have amazing strengths, but also significant weaknesses. Chief
among them, perhaps, is our collective difficulty in grasping the mathematical
consequences of exponential growth. 1 This is an ironic state,
given that our economic <strong>and</strong> political goals are often geared explicitly
to support continued growth. The degree to which an expectation <strong>and</strong>
desire for continued growth is woven into our society makes it important
to examine the phenomenon carefully, so that we might avoid building
upon a shaky foundation. In this chapter, we explore the general nature
of exponential growth, in order to underst<strong>and</strong> the impossibility of its
long-term continuance by way of exposing various absurd consequences
that uninterrupted growth prescribes. The upshot 2 is that our societal
framework eventually must face a m<strong>and</strong>atory departure from the current
model—a piece of knowledge we should all lodge into the backs of our
minds. Subsequent chapters will address applications to economic <strong>and</strong>
population growth—including more realistic logistic growth curves,
then pivot toward nailing down limits imposed by our finite planet.
1.1 Bacteria in a Jar ..........2
Exponential Math ........4
1.2 <strong>Energy</strong> Extrapolation ......7
1.3 Thermodynamic Absurdity . 10
1.4 Upshot: Limits to Growth .. 13
1.5 Problems ............. 13
1: ...anodtoAlBartlett, who worked to
raise awareness about exponential growth
2: The word “upshot” means final result or
bottom-line. Each chapter has an Upshot at
the end.
1.1 Bacteria in a Jar
One hallmark of exponential growth is that the time it takes to double
in size, or the doubling time, is constant. An important <strong>and</strong> convenient
concept we will repeatedly use in this chapter is the rule of 70:
Definition 1.1.1 Rule of 70: The doubling time associated with a percentage
growth rate is just 70 divided by the percentage rate. A 1% growth rate
doubles in 70 years, while a 2% rate doubles in 35 years, <strong>and</strong> a 10% rate
doubles in 7 years. It also works for other timescales: if p<strong>and</strong>emic cases are
increasing at a rate of 3.5% per day, the doubling time is 20 days.
Note that any growth, however slow, can be
characterized by a doubling time, even if
the process does not involve discrete steps
of doubling.
NGC 253 photo credit: Dylan O’Donnell.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.