Exponential Economist Meets Finite Physicist
Some while back, I found myself sitting next to an
accomplished economics professor at a dinner event. Shortly after
pleasantries, I said to him, “economic growth cannot continue
indefinitely,” just to see where things would go. It was a lively and
informative conversation. I was somewhat alarmed by the disconnect
between economic theory and physical constraints—not for the first time,
but here it was up-close and personal. Though my memory is not keen
enough to recount our conversation verbatim, I thought I would at least
try to capture the key points and convey the essence of the tennis
match—with some entertainment value thrown in.
Cast of characters:
Physicist, played by me;
Economist,
played by an established economics professor from a prestigious
institution. Scene: banquet dinner, played in four acts (courses).
Note:
because I have a better retention of my own thoughts than those of my
conversational companion, this recreation is lopsided to represent my
own points/words. So while it may look like a physicist-dominated
conversation, this is more an artifact of my own recall capabilities. I
also should say that the other people at our table were not paying
attention to our conversation, so I don’t know what makes me think this
will be interesting to readers if it wasn’t even interesting enough to
others at the table! But here goes…
Act One: Bread and Butter
Physicist: Hi, I’m Tom. I’m a physicist.
Economist: Hi Tom, I’m [ahem..cough]. I’m an economist.
Physicist: Hey, that’s great. I’ve been thinking a bit about growth and want to run an idea by you. I claim that
economic growth cannot continue indefinitely.
Economist: [chokes on bread crumb] Did I hear you right? Did you say that growth can
not continue forever?
Physicist: That’s right. I think physical limits assert themselves.
Economist: Well sure, nothing truly lasts
forever. The sun, for instance, will not burn forever. On the billions-of-years timescale, things come to an end.
Physicist:
Granted, but I’m talking about a more immediate timescale, here on
Earth. Earth’s physical resources—particularly energy—are limited and
may prohibit continued growth within centuries, or possibly much shorter
depending on the choices we make. There are thermodynamic issues as
well.
Economist: I don’t think energy will ever
be a limiting factor to economic growth. Sure, conventional fossil fuels
are finite. But we can substitute non-conventional resources like tar
sands, oil shale, shale gas, etc. By the time these run out, we’ll
likely have built up a renewable infrastructure of wind, solar, and
geothermal energy—plus next-generation nuclear fission and potentially
nuclear fusion. And there are likely energy technologies we cannot yet
fathom in the farther future.
Physicist: Sure,
those things could happen, and I hope they do at some non-trivial scale.
But let’s look at the physical implications of the energy scale
expanding into the future. So what’s a typical rate of annual energy growth over the last few centuries?
Economist: I would guess a few percent. Less than 5%, but at least 2%, I should think.
Total
U.S. Energy consumption in all forms since 1650. The vertical scale is
logarithmic, so that an exponential curve resulting from a constant
growth rate appears as a straight line. The red line corresponds to an
annual growth rate of 2.9%. Source: EIA.
Physicist: Right, if you plot the U.S. energy consumption
in all forms
from 1650 until now, you see a phenomenally faithful exponential at
about 3% per year over that whole span. The situation for the whole
world is similar. So how long do you think we might be able to continue
this trend?
Economist: Well, let’s see. A 3%
growth rate means a doubling time of something like 23 years. So each
century might see something like a 15–20× increase. I see where you’re
going. A few more centuries like that would perhaps be absurd. But don’t
forget that population was increasing during centuries past—the period
on which you base your growth rate. Population will stop growing before
more centuries roll by.
Physicist: True enough.
So we would likely agree that energy growth will not continue
indefinitely. But two points before we continue: First, I’ll just
mention that energy growth has far outstripped population growth, so
that
per-capita energy use has surged dramatically over
time—our energy lives today are far richer than those of our
great-great-grandparents a century ago [economist nods]. So even if
population stabilizes, we are accustomed to per-capita energy growth:
total energy would have to continue growing to maintain such a trend
[another nod].
Second, thermodynamic limits impose a cap to energy growth lest we cook ourselves. I’m not talking about global warming, CO
2
build-up, etc. I’m talking about radiating the spent energy into space.
I assume you’re happy to confine our conversation to Earth, foregoing
the spectre of an
exodus to space, colonizing planets, living the Star Trek life, etc.
Economist: More than happy to keep our discussion grounded to Earth.
Physicist:
[sigh of relief: not a space cadet] Alright, the Earth has only one
mechanism for releasing heat to space, and that’s via (infrared)
radiation. We understand the phenomenon perfectly well, and can predict
the surface temperature of the planet as a function of how much energy
the human race produces. The upshot is that at a 2.3% growth rate
(conveniently chosen to represent a 10× increase every century), we
would reach boiling temperature in about 400 years. [Pained expression
from economist.] And this statement is
independent of technology. Even if we don’t have a
name for the energy source yet, as long as it obeys thermodynamics, we
cook ourselves with perpetual energy increase.
Economist: That’s a striking result. Could not technology pipe or beam the heat elsewhere, rather than relying on thermal radiation?
Physicist: Well, we
could
(and do, somewhat) beam non-thermal radiation into space, like light,
lasers, radio waves, etc. But the problem is that these “sources” are
forms of high-grade, low-entropy energy. Instead, we’re talking about
getting rid of the
waste heat from all the processes by which we use energy. This energy
is thermal in nature. We might be able to scoop up
some
of this to do useful “work,” but at very low thermodynamic efficiency.
If you want to use high-grade energy in the first place, having
high-entropy waste heat is pretty inescapable.
Economist: [furrowed brow] Okay, but I still think our path can easily accommodate at least a
steady energy profile. We’ll use it more efficiently and for new pursuits that continue to support growth.
Physicist:
Before we tackle that, we’re too close to an astounding point for me to
leave it unspoken. At that 2.3% growth rate, we would be using energy
at a rate corresponding to the total solar input striking Earth in a
little over 400 years. We would consume something comparable to the
entire sun in 1400 years from now. By 2500 years, we would use energy at the rate of the
entire Milky Way galaxy—100 billion stars! I think you can see the absurdity of continued energy growth. 2500 years is not
that long, from a historical perspective. We
know what we were doing 2500 years ago. I think I
know what we’re
not going to be doing 2500 years hence.
Economist: That’s really remarkable—I appreciate the detour. You said about 1400 years to reach parity with solar output?
Physicist:
Right. And you can see the thermodynamic point in this scenario as
well. If we tried to generate energy at a rate commensurate with that of
the Sun in 1400 years, and did this on Earth, physics demands that the
surface of the Earth must be
hotter than the (much larger)
surface of the Sun. Just like 100 W from a light bulb results in a much
hotter surface than the same 100 W you and I generate via metabolism,
spread out across a much larger surface area.
Economist: I see. That does make sense.
Act Two: Salad
Economist:
So I’m as convinced as I need to be that growth in raw energy use is a
limited proposition—that we must one day at the very least stabilize to a
roughly constant yearly expenditure. At least I’m willing to accept
that as a starting point for discussing the long term prospects for
economic growth. But coming back to your first statement, I don’t see
that this threatens the indefinite continuance of
economic growth.
For
one thing, we can keep energy use fixed and still do more with it in
each passing year via efficiency improvements. Innovations bring new
ideas to the market, spurring investment, market demand, etc. These are
things that will not run dry. We have plenty of examples of
fundamentally important resources in decline, only to be substituted or
rendered obsolete by innovations in another direction.
Physicist: Yes, all these things happen, and will continue at some level. But I am not convinced that they represent limitless resources.
Economist:
Do you think ingenuity has a limit—that the human mind itself is only
so capable? That could be true, but we can’t credibly predict how close
we might be to such a limit.
Physicist: That’s
not really what I have in mind. Let’s take efficiency first. It is true
that, over time, cars get better mileage, refrigerators use less energy,
buildings are built more smartly to conserve energy, etc. The best
examples tend to see factor-of-two improvements on a 35 year timeframe,
translating to 2% per year. But many things are already as efficient as
we can expect them to be. Electric motors are a good example, at 90%
efficiency. It will always take 4184 Joules to heat a liter of water one
degree Celsius. In the middle range, we have giant consumers of
energy—like power plants—improving much more slowly, at 1% per year or
less. And these middling things tend to be something like 30% efficient.
How many more “doublings” are possible? If many of our devices were
0.01% efficient, I would be more enthusiastic about centuries of
efficiency-based growth ahead of us. But we may only have
one more doubling in us, taking less than a century to realize.
Economist:
Okay, point taken. But there is more to efficiency than incremental
improvement. There are also game-changers. Tele-conferencing instead of
air travel. Laptop replaces desktop; iPhone replaces laptop, etc.—each
far more energy frugal than the last. The internet is an example of an
enabling innovation that changes the way we use energy.
Physicist:
These are important examples, and I do expect some continuation along
this line, but we still need to eat, and no activity can get away from
energy use entirely. [semi-reluctant nod/bobble] Sure, there are
lower-intensity activities, but nothing of economic value is completely
free of energy.
Economist: Some things can get
awfully close. Consider virtualization. Imagine that in the future, we
could all own virtual mansions and have our every need satisfied: all by
stimulative neurological trickery. We would stil need nutrition, but
the energy required to
experience a high-energy lifestyle would
be relatively minor. This is an example of enabling technology that
obviates the need to engage in energy-intensive activities. Want to
spend the weekend in Paris? You can do it without getting out of your
chair. [More like an IV-drip-equipped toilet than a chair, the physicist
thinks.]
Physicist: I see. But this is still a
finite expenditure of energy per person. Not only does it take energy to
feed the person (today at a rate of 10
kilocalories
of energy input per kilocalorie eaten, no less), but the virtual
environment probably also requires a supercomputer—by today’s
standards—for every virtual voyager. The supercomputer at UCSD consumes
something like 5 MW of power. Granted, we can expect improvement on this
end, but today’s supercomputer eats 50,000 times as much as a person
does, so there is a big gulf to cross. I’ll take some convincing. Plus,
not everyone will want to live this virtual existence.
Economist:
Really? Who could refuse it? All your needs met and an extravagant
lifestyle—what’s not to like? I hope I can live like that myself
someday.
Physicist: Not me. I suspect many would
prefer the smell of real flowers—complete with aphids and sneezing; the
feel of real wind messing up their hair; even real rain, real
bee-stings, and all the rest. You might be able to simulate all these
things, but not everyone will want to live an artificial life. And as
long as there are
any holdouts, the plan of squeezing energy
requirements to some arbitrarily low level fails. Not to mention meeting
fixed bio-energy needs.
Act Three: Main Course
Physicist:
But let’s leave the Matrix, and cut to the chase. Let’s imagine a world
of steady population and steady energy use. I think we’ve both agreed
on these physically-imposed parameters. If the flow of energy is fixed,
but we posit continued economic growth, then GDP continues to grow while
energy remains at a fixed scale. This means that energy—a
physically-constrained resource, mind—must become arbitrarily cheap as
GDP continues to grow and leave energy in the dust.
Economist: Yes, I think energy plays a diminishing role in the economy and becomes too cheap to worry about.
Physicist:
Wow. Do you really believe that? A physically limited resource (read
scarcity) that is fundamental to every economic activity becomes
arbitrarily cheap? [turns attention to food on the plate, somewhat
stunned]
Economist: [after pause to consider] Yes, I do believe that.
Physicist:
Okay, so let’s be clear that we’re talking about the same thing. Energy
today is roughly 10% of GDP. Let’s say we cap the physical amount
available each year at some level, but allow GDP to keep growing. We
need to ignore inflation as a nuisance in this case: if my 10 units of
energy this year costs $10,000 out of my $100,000 income; then next year
that same amount of energy costs $11,000 and I make $110,000—I want to
ignore such an effect as “meaningless” inflation: the GDP “growth” in
this sense is not
real growth, but just a re-scaling of the value of money.
Economist: Agreed.
Physicist: Then in order to have
real GDP growth on top of flat energy, the fractional cost of energy goes down relative to the GDP as a whole.
Economist: Correct.
Physicist: How far do you imagine this can go? Will energy get to 1% of GDP? 0.1%? Is there a limit?
Economist:
There does not need to be. Energy may become of secondary importance in
the economy of the future—like in the virtual world I illustrated.
Physicist: But if energy became arbitrarily cheap, someone could buy
all of it,
and suddenly the activities that comprise the economy would grind to a
halt. Food would stop arriving at the plate without energy for purchase,
so people would pay attention to this. Someone would be willing to pay
more for it. Everyone would. There will be a floor to how low energy
prices can go as a fraction of GDP.
Economist: That floor may be very low: much lower than the 5–10% we pay today.
Physicist: But is there a floor? How low are you willing to take it? 5%? 2%? 1%?
Economist: Let’s say 1%.
Physicist:
So once our fixed annual energy costs 1% of GDP, the 99% remaining will
find itself stuck. If it tries to grow, energy prices must grow in
proportion and we have monetary inflation, but no real growth.
Economist: Well, I wouldn’t go that far. You can still have growth without increasing GDP.
Physicist: But it seems that you are now sold on the notion that the cost of energy would not naturally sink to arbitrarily low levels.
Economist:
Yes, I have to retract that statement. If energy is indeed capped at a
steady annual amount, then it is important enough to other economic
activities that it would not be allowed to slip into economic obscurity.
Physicist:
Even early economists like Adam Smith foresaw economic growth as a
temporary phase lasting maybe a few hundred years, ultimately limited by
land (which is where energy was obtained in that day). If humans are
successful in the long term, it is clear that a steady-state economic
theory will
far outlive the transient growth-based
economic frameworks of today. Forget Smith, Keynes, Friedman, and that
lot. The economists who devise a functioning steady-state economic
system stand to be remembered for a longer eternity than the growth
dudes. [Economist stares into the distance as he contemplates this
alluring thought.]
Act Four: Dessert
Economist:
But I have to object to the statement that growth must stop once energy
amount/price saturates. There will always be innovations that people
are willing to purchase that do not require additional energy.
Physicist:
Things will certainly change. By “steady-state,” I don’t mean static.
Fads and fashions will always be part of what we do—we’re not about to
stop being human. But I’m thinking more of a zero-sum game here. Fads
come and go. Some fraction of GDP will always go toward the
fad/innovation/gizmo of the day, but while one fad grows, another fades
and withers. Innovation therefore will maintain a certain flow in the
economy, but not necessarily
growth.
Economist:
Ah, but the key question is whether life 400 years from now is
undeniably of higher quality than life today. Even if energy is fixed,
and GDP is fixed once the cost of energy saturates at the lower bound,
will quality of life continue to improve in objectively agreed-upon
ways?
Physicist: I don’t know how objective such
an assessment can be. Many today yearn for days past. Maybe this is
borne of ignorance or romanticism over the past (1950′s often comes up).
It may be really exciting to imagine living in Renaissance Europe,
until a bucket of nightsoil hurled from a window splatters off the
cobblestone and onto your breeches. In any case, what kind of universal,
objective improvements might you imagine?
Economist: Well, for instance, look at this dessert, with its decorative syrup swirls on the plate. It is marvelous to behold.
Physicist: And tasty.
Economist:
We value such desserts more than plain, unadorned varieties. In fact,
we can imagine an equivalent dessert with equivalent ingredients, but
the decorative syrup unceremoniously pooled off to one side. We value
the decorated version more. And the chefs will continue to innovate.
Imagine a preparation/presentation 400 years from now that would blow
your mind—you never thought dessert could be made to look so amazing and
taste so delectably good. People would line the streets to get hold of
such a creation. No more energy, no more ingredients, yet of increased
value to society. That’s a form of quality of life improvement,
requiring no additional resources, and perhaps costing the same fraction
of GDP, or income.
Physicist: I’m smiling
because this reminds me of a related story. I was observing at Palomar
Observatory with an amazing instrumentation guru named Keith who taught
me much. Keith’s night lunch—prepared in the evening by the observatory
kitchen and placed in a brown bag—was a tuna-fish sandwich in two parts:
bread slices in a plastic baggie, and the tuna salad in a small plastic
container (so the tuna would not make the bread soggy after hours in
the bag). Keith plopped the tuna onto the bread in an inverted
container-shaped lump, then put the other piece of bread on top without
first spreading the tuna. It looked like a snake had just eaten a rat.
Perplexed, I asked if he intended to spread the tuna before eating it.
He looked at me quizzically (like Morpheus in the Matrix: “You think
that’s air you’re breathing? Hmm.”), and said—memorably, “It all goes in
the same place.”
My point is that the stunning presentation of
desserts will not have universal value to society. It all goes in the
same place, after all. [I'll share a little-known secret. It's hard to
beat a Hostess Ding Dong for dessert. At 5% the cost of fancy desserts,
it's not clear how much value the fancy things add.]
After-Dinner Contemplations
The
evening’s after-dinner keynote speech began, so we had to shelve the
conversation. Reflecting on it, I kept thinking, “This should not have
happened. A prominent economist should not have to walk back statements
about the fundamental nature of growth when talking to a scientist with
no formal economics training.” But as the evening progressed, the
original space in which the economist roamed got painted smaller and
smaller.
First, he had to acknowledge that energy may see physical limits. I don’t think that was part of his initial virtual mansion.
Next,
the efficiency argument had to shift away from straight-up improvements
to transformational technologies. Virtual reality played a prominent
role in this line of argument.
Finally, even having accepted the
limits to energy growth, he initially believed this would prove to be of
little consequence to the greater economy. But he had to ultimately
admit to a floor on energy price and therefore an end to traditional
growth in GDP—against a backdrop fixed energy.
I got the sense
that this economist’s view on growth met some serious challenges during
the course of the meal. Maybe he was not putting forth the most coherent
arguments that he could have made. But he was very sharp and by all
measures seemed to be at the top of his game. I choose to interpret the
episode as illuminating a blind spot in traditional economic thinking.
There is too little acknowledgement of physical limits, and even the
non-compliant nature of humans, who may make choices we might think to
be irrational—just to remain independent and unencumbered.
I recently was motivated to read a
real economics textbook: one written by people who understand and respect physical limitations. The book, called
Ecological Economics, by Herman Daly and Joshua Farley, states in its Note to Instructors:
…we
do not share the view of many of our economics colleagues that growth
will solve the economic problem, that narrow self-interest is the only
dependable human motive, that technology will always find a substitute
for any depleted resource, that the market can efficiently allocate all
types of goods, that free markets always lead to an equilibrium
balancing supply and demand, or that the laws of thermodynamics are
irrelevant to economics.
This is a book for me!
Epilogue
The
conversation recreated here did challenge my own understanding as well.
I spent the rest of the evening pondering the question: “Under a model
in which GDP is fixed—under conditions of stable energy, stable
population, steady-state economy: if we accumulate knowledge, improve
the quality of life, and thus create an unambiguously more desirable
world within which to live, doesn’t
this constitute a form of economic growth?”
I
had to concede that yes—it does. This often falls under the title of
“development” rather than “growth.” I ran into the economist the next
day and we continued the conversation, wrapping up loose ends that were
cut short by the keynote speech. I related to him my still-forming
position that yes, we can continue tweaking quality of life under a
steady regime. I don’t think I ever would have explicitly thought
otherwise, but I did not consider this to be a form of economic growth.
One way to frame it is by asking if future people living in a
steady-state economy—yet separated by 400 years—would always make the
same, obvious trades? Would the future life be objectively better, even
for the same energy, same GDP, same income, etc.? If the answer is yes,
then the far-future person gets more for their money: more for their
energy outlay. Can this continue indefinitely (thousands of years)?
Perhaps. Will it be at the 2% per year level (factor of ten better every
100 years)? I doubt that.
So I can twist my head into thinking
of quality of life development in an otherwise steady-state as being a
form of indefinite growth. But it’s not your father’s growth. It’s not
growing GDP, growing energy use, interest on bank accounts, loans,
fractional reserve money, investment. It’s a whole different ballgame,
folks. Of that, I am convinced. Big changes await us. An unrecognizable
economy. The main lesson for me is that growth is not a “good quantum
number,” as physicists will say: it’s not an invariant of our world.
Cling to it at your own peril.
http://www.resilience.org/stories/2012-04-11/exponential-economist-meets-finite-physicist
