The global economy, heat engines, and economic collapse

British Petroleum provides some pretty nice tools for visualizing energy consumption like the figure above which drives home effectively the point of just how fast our demand for energy is growing, roughly quadrupling in the past 50 odd years.

In order to understand this growth better, I think it's important to ask why we need energy in the first place. This may seem like a pretty bone-headed question -- of course we need energy. But energy is not an essential ingredient in traditional macro-economic models. In the best case energy is treated as a quantity that can be "substituted" for other ingredients of the global economy as capital and labor.

As a physicist, this seems totally nuts as our individual ability to work rests on the availability of energy. We're not somehow divorced from the laws of the universe. I've never heard of someone being an effective element of the labor force who had completely ceased to eat. And food sure doesn't materialize without work being done.

Instead, I think it's appropriate to treat civilization as a what can be termed a thermodynamic heat engine. The idea of a heat engine was first envisioned by French engineers in the early 1800s. In a car, work is done to propel a car forward by consuming the chemical energy in gasoline at high temperatures and dissipating it as waste heat at low temperatures with the pistons moving up and down in between.

In one way, we're very similar. We consume energy to go through the cyclic motions of going to and from work and the grocery store, sending out internet search requests, and pumping our hearts. All these actions require a temperature gradient where energy is released at high temperatures and dissipate at cold temperatures, whether with our cars, our computers, or the gradient from the inside to exteriors of our bodies. In fact, we can see all of human civilization as a "super-organism" that consumes primary energy to engage in all of its internal circulations, ultimately radiating waste heat to the atmosphere and then to cool of space.

High potential primary energy resources like oil and coal sustain civilization’s circulations against dissipation of waste heat. ‘Useless’ energy ultimately flows to space through the cold planetary blackbody temperature of 255 K. In between lies civilization, including people, their activities, and
all their associated circulations, whether or not they are part of the GDP.

Civilization Growth

A key difference between human civilization and a car is that it can grow. By growing, its thermodynamic engine expands. A larger engine consumes more, dissipates more, and does work ever faster. This positive feedback provides a recipe for exponential growth.

Civilization uses energy consumption mostly to sustain existing circulations. A small fraction is also used to grow civilization through an incorporation of new raw materials (e.g. iron and wood) into its structure. Thermodynamically, this is possible only if civilization consumes a little more energy than it dissipates. A small fraction of the energy that is consumed is available to incorporate raw materials to build civilization.

We’re actually pretty familiar with this. If we eat too much we get fat. I’m told that consuming an extra 3500 calories beyond what we need leads to a pound of weight gain. This is the energy required for the body to turn food into flesh.

A child consumes food today in some proportion to the child’s body mass. The child experiences a production of mass if there is a convergence of energetic flows such that it dissipates less heat than is contained in the food energy eaten. The child’s current size is directly a consequence of an accumulation of prior mass production. Its current rate of food consumption is also a consequence of prior production. As the child grows it eats more. As the child approaches adulthood, the disequilibrium between consumption and dissipation narrows, and (hopefully!) the production of new mass stalls.

So economic production, or the GDP, can be seen as the consequence of this imbalance: production is positive only when primary energy consumption is greater than the rate at which civilization dissipates energy due to all it’s internal circulations. If production is positive, civilization is able to incorporate raw materials into its structure. It grows, and then uses the added population and infrastructure created with the materials to consume even more energy.

Collapse

I think this is what is happening with the BP statistics. Because the GWP exists, we grow, and then use our growth to access more energy which we can then consume with the higher infrastructure demands. The relevant equation is that every 1000 dollars of year 2005 inflation-adjusted gross world product requires 7.1 additional Watts of power capacity to be added, independent of the year that is considered.

Right now, energy consumption is continuing to grow rapidly, sustaining an ever larger GWP. But it is not the rate of energy consumption that supports the GWP, but the rate of growth of energy consumption that supports the GWP.

This important distinction is flat out frightening. The implication is that if we cease to grow energy and raw material consumption globally, then the global economy must collapse. But if don't cease to grow energy consumption and raw material consumption then we still collapse due to climate change and environmental destruction.  Is there no way out?

Is macroeconomics a science?

Macroeconomics can get a pretty bad rap at times, perhaps unfairly. Some of its practitioners are so politically influential on such familiar topics as unemployment and economic growth it's easy for the non-expert with an opinion to get a bit jealous. Few would dispute the merits of the latest winner of the Nobel in physics. But the Higgs boson is pretty inscrutable even to most physicists. It's only natural that economists get more attention -- and criticism -- when Nobel prize winners like Paul Krugman write popular columns for the New York Times.

Yet, even the noted economist Paul Romer has offered the caustic remark that the field is in "...a general failure mode of science that is triggered when respect for highly regarded leaders evolves into a deference to authority that displaces objective fact from its position as the ultimate determinant of scientific truth."

Ouch. So maybe macroeconomists are our modern day equivalent of medieval High Priests. Economists' theoretical models didn't predict the economic crash of 2008. Nonetheless, economists don't seem particularly troubled, certainly not troubled enough to consider that their models might be profoundly off course. From their perch, why should they?

Confirmation bias -- seeing only that which supports existing beliefs -- can be brushed off as the sort of normal human arrogance that we are all susceptible to. But being able to falsify a result lies at the core of the scientific method. It must be possible to set up a test that could lead to a model being discarded. 

For a comparison of professions, imagine if meteorologists predicted sunny days rather than the landfall of a hurricane. And then, because respected NASA scientist James Hansen was himself unconcerned, they put little effort into preventing such a thing from happening again.

That's not what happens. Instead, in meteorology, the validity of forecast models is constantly tested by performing what is known as "hindcasts" -- starting a model sometime in the past to see how well it predicts the present. Aside from the fact that the models are built on basic physics to the greatest extent possible, various model flavors are ranked according to their hindcast accuracy. It's the job of a professional meteorologist to both understand the model workings and know which models do best in which situations to communicate to the public the best forecast possible.

I can find no evidence of the economics profession doing something similar. Traditional macroeconomic models employ equations for the GDP, or “production functions”, that are  “tuned” to match past observations of labor and capital. It is not possible to falsify these moving theoretical targets because they are always made “right” by adding layers of social complexity or by tweaking the production function exponents until a decent fit is obtained. If conditions change and the formula no longer works, economists just tune again and call it a “structural break”.

This is cheating! At least if the goal is understanding how things work. It would be abhorrent to imagine a basic physics equation being adjusted as time progresses for the situation at hand. The speed of light in a vacuum doesn’t get to be different for you than for me or for last year versus this year.

Let's take for example the basic Cobb-Douglas production function used by economists as a starting point for relating economic production Y to labor L and capital K. The quantity A is a “total factor productivity” that has been thought -- largely due to efforts by Paul Romer -- to be related to innovation.

Y = A L^α Κ^1-α

Here the parameter α is tuned to past data in order to reproduce values of Y. In economic studies, when the inelegant Cobb-Douglas function (or whatever is used as a replacement) doesn’t work well, for whatever reason, the approach is not to ask whether or not something might be fundamentally wrong about the premise behind the fit, but rather to add ever more bells and whistles until once again a sufficient fit is obtained, totally independent of any consideration of dimensional self-consistency.

For example, maybe a constant exponent α doesn’t provide a good fit unless A is allowed to change too according some equally complex function. Paul Romer introduced government stimulus of R&D to obtain this sort of example of complexity:

So many free parameters! With such a complex function one could replace labor with the historical population of rodents in Calcutta and tune A, α and β in such a manner that the Cobb-Douglas function would still reproduce beautiful timelines for Y. As John Von Neumann quipped With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

This is not what sophistication should look like! Making things ever more mathematically complex does not make things more true, if anything less so. It feels akin to astrology, a highly complex, self-consistent model based on un-physical nonsense. Totally convincing to those who are looking to believe that the world has order and explanation, and that they alone have the years of training required to understand it, but completely lacking in any means for falsifiability.

It gets worse. The production functions lack the simple element of dimensional self-consistency. Take a basic physics equation, Newton's F=ma, or Force equals mass times acceleration. Mass has units of mass, obviously, and acceleration has units of distance per time squared. So the units of force are mass times distance per time squared. The equation would be totally bogus if force were declared to have any other sorts of units.

Now compare Newton's F = ma with the Cobb-Douglas function. There is nothing fundamental about the free parameter α since it is just a number. In fact, it can have any value depending on the statistical fit, the country, or the period considered. Suppose for the moment that α = 0.3. If A is just a number, labor has units of worker hours, and capital units of dollars, then Y would necessarily have the absurd units of worker hours to the 0.3 power and dollars to the 0.7 power. This has nothing to do with the real units of economic output which are dollars per time!

A couple years ago I had the opportunity to discuss economic growth models with well-known environmental economist Robert Ayres on a visit to Paris where he lives. He was quite adamant that I was wrong about everything. I don't think he had actually bothered to read anything I had done, which was too bad given the condition for the meeting (his idea) was that I buy and read his latest book. I tried to be patient, but eventually raised this units issue with him. His response was "only a physicist would care about units"!

Perhaps, I have been too harsh -- everybody is trying their best -- but it looks like fluency in Latin in the Catholic Church, where established macro-economists need something sufficiently opaque in order to maintain their high-priesthood. More generously, economics is complicated and economists just don’t yet know yet how to describe it without such detailed dimensionally inconsistent fits; even in physics, similar fits are occasionally used to describe interactions of particles with turbulence, for example, simply because the underlying physics can be rather challenging.

And maybe my rant is just another one of those pot-shots from non-economists, I have however tried to do better, by creating an economic growth model with no bells and whistles that can be easily tested and discarded. It is founded on a proposed constant relationship between energy consumption rates and a very general representation of total inflation-adjusted wealth (analogous to capital K) and is borne out by observations. Further evaluation of the model has been done by performing hindcasts, asking whether we predict the present with a deterministic model that is initialized at some point in the past. Again, in this case it appears we can: current global rates of energy consumption growth and GWP growth can be accurately predicted based on conditions observed in the 1950s, without appealing to any observations in the interim, with skill scores >90%.

For myself, there's adequate contentment in simply understanding some of the power of thermodynamics. But that is balanced by some abhorrence with certain aspects of macroeconomics.

George Orwell on the metabolism of the industrial world

When discussing biophysical economics -- the idea that the human economy can be treated like any other biological organism that grows subject to resource constraints -- well-known names include Charlie Hall, Cutler Cleveland, and Robert Costanza. My personal favorite for the level of insight, using prose rather than math, is the work of Geerat Vermeij.

Recently, I've been reading George Orwell's 1937 book "Road to Wigham Pier", a testimony of the plight of the British working class. He captures similar themes, more eloquently, I think, than anything else I've read:

Our civilization...is founded on coal more completely than one realizes until one stops to think about it. The machines that keep us alive, and the machines that make machines, are all directly or indirectly dependent upon coal. In the metabolism of the Western world the coal-miner is second in importance only to the man who ploughs the soil. He is a sort of caryatid upon whose shoulders nearly everything that is not grimy is supported.

....

Watching coal-miners at work, you realize momentarily what different universes people inhabit. Down there where coal is dug is a sort of world apart which one can quite easily go through life without ever hearing about. Probably majority of people would even prefer not to hear about it. Yet it is the absolutely necessary counterpart of our world above. Practically everything we do, from eating an ice to crossing the Atlantic,and from baking a loaf to writing a novel, involves the use of coal, directly or indirectly. For all the arts of peace coal is needed; if war breaks out it is needed all the more. In time of revolution the miner must go on working or the revolution must stop, for revolution as much as reaction needs coal. Whatever may be happening on the surface, the hacking and shovelling have got to continue without a pause, or at any rate without pausing for more than a few weeks at the most. In order that Hitler may march the goose-step, that the Pope may denounce Bolshevism, that the cricket crowds may assemble at Lords, that the poets may scratch one another's backs, coal has got to be forthcoming. But on the whole we are not aware of it; we all know that we 'must have coal', but we seldom or never remember what coal-getting involves. Here am I sitting writing in front of my comfortable coal fire. It is April but I still need a fire. Once a fortnight the coal cart drives up to the door and men in leather jerkins carry the coal indoors in stout sacks smelling of tar and shoot it clanking into the coal-hole under the stairs. It is only very rarely, when I make a definite mental-effort, that I connect this coal with that far-off labour in the mines. It is just 'coal'--something that I have got to have; black stuff that arrives mysteriously from nowhere in particular, like manna except that you have to pay for it. You could quite easily drive a car right across the north of England and never once remember that hundreds of feet below the road you are on the miners are hacking at the coal. Yet in a sense it is the miners who are driving your car forward. Their lamp-lit world down there is as necessary to the daylight world above as the root is to the flower. 

The full chapter, truly remarkable for its description of the work life of the miners, is here. 

When I am digging trenches in my garden, if I shift two tons of earth during the afternoon, I feel that I have earned my tea. But earth is tractable stuff compared with coal, and I don't have to work kneeling down, a thousand feet underground, in suffocating heat and swallowing coal dust with every breath I take; nor do I have to walk a mile bent double before I begin. The miner's job would be as much beyond my power as it would be to perform on a flying trapeze or to win the Grand National. I am not a manual labourer and please God I never shall be one, but there are some kinds of manual work that I could do if I had to. At a pitch I could be a tolerable road-sweeper or an inefficient gardener or even a tenth-rate farm hand. But by no conceivable amount of effort or training could I become a coal-miner, the work would kill me in a few weeks. 

Are renewables our salvation?

A past article in the New York Times by climate and energy writer Brad Plumer cast a ray of hope on the shadow that was cast by Donald Trump's decision that the United States should exit the Paris Climate Accord. Independent of government mandates, private companies are spontaneously moving into the renewables business. "Last year in the United States, 19 large corporations announced deals with energy providers to build 2.78 gigawatts worth of wind and solar generating capacity, equal to one-sixth of all of the renewable capacity added nationwide in 2017"

Hurray for capitalism! Climate's curse may be yet be it's salvation! Solar and wind may have the issue of being either expensive or intermittent. But production prices keep falling, and with a continental sized electrical grid, it’s probably sufficiently windy or sunny somewhere. Remarkably, solar and wind seem to be succeeding. 

There a couple of considerations in this discussion that I don't see frequently addressed and I think may be really important. First, new sources of energy have historically added to past sources rather than replaced them. Second, any source of energy, whatever its source, enables civilization to further destroy its environment through the extraction of matter.

Consider the figure above, which provides a broad brush view of energy consumption in the United States over the past couple of hundred years. Overall, total energy consumption has risen dramatically. With the establishment of European settlers, society was first powered off wood, adding coal to the mix around 1880, with non-solid fossil sources taking off around 1950. Nuclear and renewables have (so far) been smaller players. 

There’s a couple of interesting things to notice about these curves. First is their shape: following an initial period of exponential growth, each source tends to plateau. Then, when new sources are added,  they are additive: previously dominant sources do not decline, or at least not by much -- they simply become part of a larger mix. The curve for coal is particularly interesting. While there was marginal decline between 1910 and 1950, since then consumption of coal appears to have been resuscitated by oil and natural gas. Fluid fuels didn’t replace coal. In fact it was quite the opposite!

Why would this be? I think a case could be made that what is going on is that new energy sources grow civilization, thereby increasing all of its aspects, including population, vehicles, and homes, as well as their corresponding demand for all types of energy, irrespective of source. Energy supports the technological advances that make previously inaccessible sources of energy more accessible.  With the introduction of oil, mechanized digging of coal gets easier; with an explosion of human population aided by the fertilizer produced with oil, demand for electricity produced by coal increases too.

There are many physical analogs for this sort of behavior. To use the language of physics, we could think of an energy type as a “degree of freedom”. In low energy systems, certain possible degrees of freedom may be “frozen out”, and be inactive. With increasing energy added to the system, these degrees of freedom become active, but not at the sacrifice of those degrees of freedom that were previously active at lower energies. 

So renewables are great as a substitute fuel for the purposes of slowing climate change, provided they actually replace rather than add to existing sources of energy. Unfortunately, it is not clear that there is any precedent for this sort of thing happening.

A second issue is that civilization is made of matter not energy. As civilization grows, it accelerates its rate of pollution as it goes. Acting as an open thermodynamic system, we use energy to extract raw materials from our environment in order to feed and grow our children, construct the stuff of civilization, and offset ever present decay. As we do so, resource extraction depletes the oceans of fish, the forests of trees, and the ground of minerals, leaving behind material waste products such as plastic, nitrogen, and exotic chemicals that pollute our land, water and air. 

How can it be that renewables are any sort of environmental panacea if they simply add to the energy mix that we use to extract raw materials from our environment and leave behind an ever growing pile of waste? 

Whether the energy source is oil or solar doesn’t really matter. Energy of whatever stripe is used to acquire the raw materials from our environment, the components of all the stuff of humanity, building more of us while leaving less of the environment in its wake. Sure, maybe renewables do not leave behind carbon dioxide in quite the same way as fossil fuels, but the energy they do provide helps contribute to our seemingly unstoppable conversion of matter from the environment into the matter that composes civilization. 

So, even if sunlight and wind is seemingly infinite, our planet Earth is not. Any short-term material gain of ours is a loss for the world around us. Renewables only accelerate this process.

Is brain thermodynamics the link between economics and physics?

I've argued that the accumulated wealth of civilization is fundamentally linked to its total rate of energy consumption through a constant. The total historically accumulated value of humanity's inflation-adjusted production -- not just the annual accumulation called the GDP -- rises every year by a percentage that matches the increase in humanity's energetic needs.

But how could this be? The value of stuff is determined by our brains. How do our brains somehow "know" collectively how fast we consume energy? How do we comprehend how a psychological construct like money can be tied to a thermodynamic construct like energetic power? Doesn't economic value go only so far as human judgement?

As a clue, even with no one home and all the utilities turned off, a house still maintains some worth for as long as it can be perceived as being potentially useful by other active members of the global economy. Real estate agents talk about "Comps" for determining the value of a home. Comps are based on the recent sale value of other homes in the neighborhood. Comps were determined by people with brains (though arguably less so in a real-estate bubble) who in turn are connected through social and work connections to other people with brains, and with several degrees of separation, everyone on this planet with a brain. 

Individual brains process a wealth of information from the rest of civilization using extraordinarily dense networks of axons and dendrites. Patterns of oscillatory neuronal activity lead to the emergence of behavior and cognition. Powering this brain activity requires approximately 20 % of the daily caloric input to the body as a whole. Arguably this number is 100% since neither the body nor the brain could survive without the other.  

And we are connected not just to each other but, by definition, all other elements of civilization, including our transport and communications networks. We and civilization also couldn't survive without each other.  Dissipative neuronal circulations along brain networks may implicitly scale with dissipative circulations along civilization networks. Our collective perceptions must reflect global economic wealth. 

Individually, our brains may seem very personal, and a small part of the whole. But they are also connected to each other. They are part of a much larger "super-organism" that includes not just our bodies but our stuff. Our brains collectively march to broader economic circulations along global civilization networks that are sustained by a dissipation of oil, coal, and other primary energy supplies. 

Summing wealth over all the world’s nations, 7.1 Watts is required to maintain every one thousand inflation-adjusted 2005 dollars of historically accumulated economic production. This relationship may seem unorthodox by traditional economic standards, but it may also be seen as a type of psychological constant that ties the physics of human perception to the thermodynamic dissipative flows of energy that drive the global economy.

On the exponential growth, decay and collapse of civilization

Last week I had the fortune of seeing Rogers and Hammerstein's Carousel during a short trip with my wife to New York City. It's a 1940s classic set in a fishing town in New England. Some of the themes are a bit dated to be sure, but then I still love Italian opera which can be totally absurd. This particular Broadway production fittingly introduced Renée Fleming in the role of Nettie - a real treat to hear this world-famous soprano sing.

The plot of the musical contrasts a happy couple with one that is more challenged. For the happier, fisherman Enoch woos his bride-to-be Carrie in a song showing off his good-husband-material ambition:

Enoch

When I make enough money outa one of my boat,

I'll put all of my money in another little boat.

I'll make twice as much outa two little boats,

An' the first thing you know, I'll have four little boats;

Then eight little boats, then a plenty little boats,

Then a great big fleet of great big boats.

All catchin' herring, bringin' into shore;

Sailin' out again, an' bringin' more.

An' more, an' more, an' more!

The first year we're married,

We'll have one little kid.

The second year we're goin'

Have another little kid.

You'll soon be donnin' socks

For eight little feet-

Carrie

I am not enough for another fleet!

Utterly hokey, but presumably this was Rogers and Hammerstein's intention. At least it's clear that Enoch picked up somewhere a basic mathematical mastery of powers of two and the ingredients for exponential growth.

Exponential growth is curious, particularly in the economics literature where it is often presented as a God-given truth without questioning where it actually comes from. In fact, whether we look at boats, fish, or kids, or anything else, exponential growth is subject to fundamental thermodynamic constraints. The rate of exponential growth constantly changes over time as a function of past growth and current conditions, and that rate can evolve from being positive (growth) to negative (decay).

There's a couple of important themes: 

System growth
This is the most basic ingredient of exponential growth. As a system grows, it grows into the resources that enabled its growth in the first place, increasing its interface with its supply. A larger interface permits higher flow rates of the resources thereby allowing the system to grow faster. A bigger fleet catches more fish. As long as fish are profitable, this leads to a bigger fleet yet.

Diminishing returns

Even if a system grows into new resources, growth rates have a natural tendency to slow with time. The reason is that systems compete with their growing selves for available resources so that growth of the interface succumbs to diminishing returns. The more Enoch's fleet grows, the more his own boats compete with with the rest of the fleet for the remaining fish that are there; the bigger the fleet, the more competition. The consequence is that the interface of boats with fish does not grow as fast as the fleet itself so consumption stabilizes.

Discovery

As former U.S. Secretary of Defense Donald Rumsfeld famously put it, there are the "unknown, unknowns... There are things we do not know we don't know.". A system grows exponentially by growing its interface with known resources. Normally, diminishing returns takes over, but by way of this growth, there can also be discovery of previously unknown resources. Early Portuguese fisherman could not easily have anticipated the extraordinary riches of cod to be found in the New World that would propel fish catches skyward.

Depletion

Resources can be depleted if they are not replenished as fast as the ever increasing rate of consumption. In turn, growth of the interface between the system and its supply grows more slowly than it would otherwise.  Enoch catches fish to grow his fleet. But New England fish stocks decline - there are limits to growth.

Decay
Poor Enoch will eventually grow old and his boats and nets constantly need repair. What can't be fixed also slows growth. Exponential growth is still possible if decay is slow enough. But an unpredicted hurricane could wipe out Enoch's entire fleet of boats beyond his knowledge or control, in which case gradual decay can easily tip towards collapse.

Putting it together
Putting all these things together we end up with a mathematical curve for growth known as the logistic function characterized by increasing rates of explosive growth followed by decreasing rates of exponential growth. Growth then stagnates and tips into either slow or rapid decline.

An example of the timeline is shown above, illustrated for the special case where resources are in fixed supply and simply drained like a battery. Resources are consumed by the system; the system thrives on resources but is always consumed by decay. While growth is initially exponential, diminishing returns takes over. Then, during a period of overshoot, the system keeps growing for a time, even as resources and consumption decline, but eventually decay takes over and tips the system into decay and collapse. Critically, there is no equilibrium of steady-state to be had, not at any point.

But, the situation is rarely as simple as a depleted battery. This is because resources can be discovered.  The figure above shows how this works. All the same phenomena are present as in the drained battery scenario except just as the system enters overshoot and plateaus, a new resource is discovered, and the system enters a second period of exponential growth. Eventually decay still takes over, but it does not forbid the system from potentially entering some new phase of growth in the future, perhaps repeating the original cycle.

It's easy to see some of these dynamics at play in our civilization. At least in the U.S., energy has consumption has seen multiple waves of exponential growth, diminishing returns, competition and discovery. Since the mid-1700s, we have progressed from biomass, to coal, to petroleum, each discovery rescuing the U.S. so that it can continue expansion outward of its interface with primary energy supplies. Currently, natural gas and renewables appear to be entering a new exponential growth phase, with coal sliding into decline. 

Similar things can be seen in world population growth going back even further in time: always successive pulses of exponential growth, followed by stagnation, then discovery, and renewed expansion. We are now growing faster than ever.

So what does this mean for us and our future? The thermodynamics and mathematics of how a system grows can be described and predicted provided we know the size of resources and the magnitude of decay.  The problem is that we don't because there are always the "unknown unknowns". That said, we can say with some confidence that there are two main forces that will shape this century, resource depletion and environmental decline: it seems like one of the two will get us.  

So far resource discovery has more than adequately kept civilization afloat. But this cannot continue forever. When will it stop? This depends on this balance between discovery and decay. Discovery of new energy resources seems to be fairly unpredictable. Still, we've been remarkably good at it considering doomsday forecasts of Peak Oil have been overcome by the introduction of shale oil, natural gas, and renewables. Nonetheless, we currently double our energy demands every 30 years or so. Can new discoveries keep pace?  If they can, won't that lead to environmental disaster as atmospheric CO2 concentrations climb past 1000 ppm and we lay waste to the forests, oceans, and ground? 

Unlike diamonds, exponential growth cannot be forever. It just can't. Eventually, something has to give.

  

What's your Carbon Footprint?

Much has been made of the question of how we can reduce our individual impact on climate change. We all of us want to make a difference. If we individually consume less, surely we're doing our part to save the planet.

But I really think the premise is wrong, because in an interconnected world, none of us can be meaningfully separated from the whole. 

Consider the number of degrees of separation between you and anyone else on the planet. This might seem like a pretty hard thing to assess given how many of us there are and in some pretty far-flung places. I don’t know personally anyone in the Papua New Guinea Highlands (to mention some arbitrarily remote location), but I can be pretty sure that it’s not too much of a stretch to suppose my Australian friend has a friend who has been to the PNG capital Port Moresby where he ran across a guy whose cousin occasionally makes trips to the capital to work for “luxury” items to take back to his remote mountain jungle dwelling where he presents them to his wife. 

That would be just five degrees of separation. Certainly, the relationships are pretty far-flung, but it’s like the line from the TV series Breaking Bad,  “I know a guy who knows a guy.” None of us is truly independent of anyone else.

The same principle can apply to all of history. Suppose that an estimated 100 billion people have walked the earth in the last 50,000 years. With each successive generation, each of us is related to two others to the power of the number of generations. Exponentials lead to big numbers quickly: 100 billion people equates to just 37 successive generations. So, it shouldn’t take too great a number of generations before the number of your number ancestors is similar to the number of people living at that time. As evidence, all humans look and act pretty much the same. One way or another, there was sufficient intermingling for us all to have ancestors in common.

So, as a first approximation, we are linked through our social and economic connections to everyone currently alive, and moreover we can be linked by blood and tradition to everyone who has ever been alive.

It seems then that the question should be not what is your carbon footprint but what instead is our carbon footprint, that for humanity as a whole. We are a collective “super-organism” that has evolved over time by burning carbon based fuels to sustain ourselves and to grow. Individually, we may profoundly feel that we can behave as isolated entities; our personal economic choices, in however limited a way, can reduce the collective rate of CO2 exhalation. 

The evidence is against this argument, however.  If we term our collective wealth as the accumulation of all past economic production, summing over all of humanity over all of history, then the data reveal a remarkable fact: independent of the year that is considered, collective wealth has had a fixed relationship to added atmospheric CO2 concentrations. Expressed quantitatively,  2.42 +/- 0.02 ppmv CO2 is added every year for every one thousand trillion inflation-adjusted 1990 US dollars of current global wealth.   

A useful analogy here is to a growing child, who consumes food and oxygen and exhales carbon dioxide. The rate of CO2 exhalation by the child is determined by the sum of all cellular activity in the child. All the child’s current living cells require energy, and all produce CO2 as a waste product. But there are two key things: first, no set of cells can be magically dissociated from any set of others, e.g. the heart from the brain, as they are all interdependent; and second, the total number of current cells in the child is not determined by what the child does today, but rather by child’s past. Over time, the child grew from infancy to its current size, accumulating cells such that prior growth determined the child's current capacity to exhale CO2.

For humanity, it is the same. We currently “exhale” CO2 as a total civilization, but our current rate of exhalation is a collective enterprise by its intertwined parts as they have emerged from past civilization growth. 

So, if emissions are so tightly linked to the collective whole, and all past growth of civilization’s consumptive needs has already happened, entirely beyond our current control, what individually can we do right now?

To further illustrate the problem, let’s look at CO2 concentrations in the atmosphere. To calculate the actual increase in atmospheric CO2 concentrations, one has to consider that the land and oceans absorb a fraction of what is emitted. Estimating carbon sinks is possible but can get pretty tricky. Nonetheless, we can look at the observed relationship between economic activity and atmospheric chemistry to get a sense of what is going on. 

Looking above at the past 2000 years of atmospheric carbon dioxide concentrations, obtained from Mauna Loa in Hawaii and from ice cores in Antarctica, and measured as a perturbation from a baseline “pre-industrial” concentration of 275 ppmv, there is a surprisingly tight power-law relationship with global GDP. For the entire dataset :

log[CO2(ppmv perturbation)] ~ 0.6 x log[GDP(2005 USD)]

Amazingly, for over 2000 years, the relationship between CO2 and economic activity has been pretty much a mathematical constant.

In fact, if we look just at the past 60 years in the above, the relationship is linear and even tighter: since 1950, for every trillion inflation-adjusted year 2005 USD of global economy, the atmospheric concentration of CO2 has been 1.7 ppmv higher.

And, we could turn this around. With an extremely high degree of accuracy, we could estimate the global GDP simply with a CO2 probe at Mauna Loa. In units of trillion year 2005 USD and ppmv CO2:

   

GDP  = 0.58 x CO2 - 174

An atmospheric chemist could easily obtain the size of the global economy within a 95% uncertainty bound of just 1.5%! No need for economists!

Of course, we have to be careful with correlation and causation. And even if the above relationship has worked extraordinarily well for the past 65 years, the underlying basis for a relationship between GDP and CO2 concentrations is in fact rather more complicated. Nonetheless, these data clearly support an argument that what matters for determining the concentrations of this key greenhouse gas are collective human activities. 

The relationship between CO2 and world economic activity has been extremely tight and invariant over a very long time period during which the configuration of humanity has changed extraordinarily. There have been periodic wars,  famines, and global economic crises. We do not consume the same raw materials with the same efficiencies to the same extent now as we did in the past. The mix of wind, solar, nuclear and fossil fuels has been consumed in widely varying mixtures using an extraordinary range of different technologies. 

Yet this tie remains. What is going on? Speculating, perhaps one way to look at it is to consider individually the impact of buying that fuel efficient Prius, or turning down the thermostat. A car or house that consumes less fuel allows for an instantaneously incremental reduction in the demand for fuel. Sounds great. Except, the resources for producing the fuel are still available. If demand drops incrementally, then oil producers reduce prices to increase demand. Cheaper gas is more desirable, and so the collective response of all consumers is to consume more. Ultimately, the net effect on the collective rate of fossil fuel consumption of buying a fuel efficient Prius is zero (or even an increase). 

“No man is an island entire of itself...” We have no individual carbon footprint. We are only “... a part of the main”. We'd like to think our individual actions matter but it is only collectively will they reduce our impact on climate. And this will be very, very hard. As unpalatable as it may be, the only successful climate action will be to dramatically and collectively deflate the global economy.  Unfortunately, this may be a bit like asking that growing child, once it has reached a healthy adulthood, to voluntarily suffocate or shrink back to infancy. 

Is there an alternative perspective that allows for change but is still consistent with the observations? It would be nice to think that our individual or collective actions can meaningfully decouple the economy from changes in atmospheric composition. But how?