Energy and Human Ambitions on a Finite Planet, 2021a

1 Exponential Growth 9
solar energy hitting the planet at 100% efficiency. But our planet is a
tiny speck in space. Why not capture all the light put out by the sun,
in a sphere surrounding the sun (called a Dyson sphere; see Box 1.3)?
Now we’re talking some real power! The sun puts out 4 × 10 26 W. If it
were a light bulb, this would be its label (putting the 100 W st<strong>and</strong>ard
inc<strong>and</strong>escent bulb to shame). So the number is enormous. But the math
is actually pretty easy to grasp. 11 Every century gets another factor of
ten. To go from where we are now (18 × 10 12 W) to the solar regime
is about 14 orders-of-magnitude. So in 1,400 years, 12 we would be at
18 × 10 26 W, which is about 4.5 times the solar output. Therefore we
would use the entire sun’s output in a time shorter than the 2,000-year
run of our current calendar.
11: Math becomes easier if you blur your
vision a bit <strong>and</strong> do not dem<strong>and</strong> lots of precision.
In this case, we essentially ignore
everything but the exponent, recognizing
that each century will increment it by 1, at
our chosen 2.3% rate.
12: In this case, the “real” answer would
be 1,335 years, but why fret over the details
for little gain or qualitative difference in the
outcome?
Box 1.3: Dyson Sphere Construction
If we took the material comprising the entire Earth (or Venus) <strong>and</strong>
created a sphere around the sun at the current Earth-Sun distance, it
would be a shell less than 4 mm thick! And it’s not necessarily ideal
material stock for building a high-tech sphere <strong>and</strong> solar panels. The
earth’s atmosphere distributed over this area would be 0.015 m thick.
Don’t hold your breath waiting for this to happen.
Bypassing boring realism, we recognize that our sun is not the only
star in the Milky Way galaxy. In fact, we estimate our galaxy to contain
roughly 100 billion stars! This seems infinite. A billion seconds is just
over 30 years, so no one could count to 100 billion in a lifetime. But
let’s see: 100 billion is 10 11 . Immediately, we see that we buy another 11
centuries at our 2.3% rate. So it takes 1,100 years to go from consuming
our entire sun to all the stars in our galaxy! That’s 2,500 years from
now, adding the two timescales, <strong>and</strong> still a civilization-relevant time
period. Leave aside the pesky fact that the scale of our galaxy is 100,000
light years, so that we can’t possibly get to all the stars within a 2,500
year timeframe. So even as a mathematical exercise, physics places yet
another limit on how long we could conceivably expect to maintain our
current energy growth trajectory.
The unhinged game can continue, pretending we could capture all the
light put out by all the stars in all the galaxies in the visible universe.
Because the visible universe contains about 100 billion galaxies, we
buy another 1,100 years. We can go even further, imagining converting
all matter (stars, gas, dust) into pure energy (E mc 2 ), not limiting
ourselves to only the light output from stars as we have so far. Even
playing these unhinged games, we would exhaust all the matter in the
visible universe within 5,000 years at a 2.3% rate. The exponential is a
cruel beast. Table 1.3 summarizes the results.
Table 1.3: <strong>Energy</strong> limit timescales.
Utilizing
years until
Solar, l<strong>and</strong>, 20% 250
Solar, earth, 100% 390
Entire Sun 1,400
Entire Galaxy 2,500
Light in Universe 3,600
Mass in Universe 5,000
By coincidence, the visible universe has
about as many galaxies as our galaxy has
stars. By “visible” universe, we mean everything
within 13.8 billion light years, which
is as far as light has been able to travel since
the Big Bang (see Sec. D.1; p. 392).
The point is not to take seriously the timescales for conquering the sun
or the galaxy. But the very absurdity of the exercise serves to emphasize
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.