Energy and Human Ambitions on a Finite Planet, 2021a

1 Exponential Growth 13
1.4 Upshot: Physics Limits Physical Growth
We saw in this chapter that unabated growth leads to absurd results.
First, we calibrated our intuition in the context of bacteria in jars. The key
point is that the jar is half full one doubling time before it is full. While
this seems obvious, it delays the drama to the very end, acting fast to
impose hard limits <strong>and</strong> catch the inhabitants by surprise. The conditions
that persisted for many generations—thus taken for granted—suddenly
change completely.
Next, we found that continuing a modest growth rate in energy becomes
hopelessly absurd in a matter of centuries. Then we saw another side to
this coin, in the context of thermal consequences on the surface of the
earth if energy growth continues.
In the end, physics puts a timeline on expectations with respect to growth
in energy on Earth. Maybe the ∼300 year scale is not alarming enough.
But it imposes a hard barrier against preserving our historical growth
rate. In reality, other practicalities are likely to assert themselves before
these hard limits are reached. We can therefore expect our growth phase
to end well within a few hundred years. Given that the growth phase has
lasted for far longer than that, we can say that we are closer to the end of
the saga than to the beginning, yet the world is not collectively preparing
for such a new reality. This seems unwise, <strong>and</strong> we will evaluate related
concerns in subsequent chapters.
Many factors will intercede to limit growth in both population <strong>and</strong>
resource use: resource scarcity, pollution, aquifer depletion <strong>and</strong> water
availability, climate change, warfare, fisheries collapse, a limited amount
of arable l<strong>and</strong> (declining due to desertification), deforestation, disease,
to name a few. The point is only reinforced. By some means or another,
we should view the present period of physical growth as a temporary
phase: a brief episode in the longer human saga.
Was the exercise pointless, since the math
leads to absurdity? Is the math wrong? No—
it’s immensely valuable to learn that our
assumption of continued growth (<strong>and</strong> application
of the corresponding correct math)
fails to make sense, ultimately. The logical
conclusion is that growth cannot continue
indefinitely.
Note that a deviation from the assumed
steady 2.3% growth rate changes all the
numbers, <strong>and</strong> therein may lie the solution:
ramp down growth!
A number of these issues will be addressed
in subsequent chapters.
1.5 Problems
Hint: for problems that require solving temperature when it appears as
T 4 , you’ll need to take the fourth root, which is the same as raising to
the 1 4 power. So use the yx button (or equivalent) <strong>and</strong> raise to the 0.25
power. You can check this technique by comparing the square root of a
number to the result of raising that number to the 0.5 power. Another
technique for the fourth root is to take the square root twice in a row.
1. Verify the claim in the text that the town of 100 residents in 1900
reaches approximately 100,000 in the year 2000 if the doubling
time is 10 years.
2. Fill out Table 1.1 for the missing decades between 1940 <strong>and</strong> 2000.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.