Monday, June 18, 2018

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.

Wednesday, June 6, 2018

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 RenĂ©e 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:

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-
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.

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.

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.

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.