Economics Could Emerge Out of Boltzmann’s Beauty
We’re all living in a lattice
Understanding the economy as an emergent phenomena is an extension of viewing the value of money as transactional. I proposed a framework, the energy-entropy-information nexus, for understanding multiscale phenomena in complex systems.
The lattice Boltzmann method solves this exact same problem of describing emergent phenomena by starting from describing particles. While it has been adopted by various fields, the method arose for gas simulations, and is most notable for taking the famous Navier-Stokes equations of fluid dynamics heads on.
The method is the successor of the lattice gas automata, part of the larger cellular automata family. Cellular automata describes the dynamics of discrete particles over uniform boxes, called cells. This is akin to your childhood’s hopscotch game.
Automata methods, of which Conway’s “Game of Life” is an example, are part of wider class of approaches that show how complex systems arise from simple rules. The latter is a concept which Stephen Wolfram has been a historic proponent of with his computation on graphs and other projects.
As you might expect, describing complex systems by considering their discrete agents is, well, complex — too complex even for our supercomputers to handle a cup of water, not even. In the case of fluids, it also makes the computation highly prone to statistical errors.
Instead of discrete particles, the lattice Boltzmann method concisely describes a collection of particles by a fictitious particle to which a distribution function, summarizing the statistics of the collection in the cell, is attached. These fictitious particles then interact with each other, collide, within the cell, and then move around to nearby cells as their distribution function dictates. To work, amongst other things, the method assumes that the discrete particles it summarizes are small enough that they interact solely within their vicinity, and that they are unrelated, moving under an assumption of chaos.
Turbulence, describing the “chaotic” behavior of a fluid, is perhaps one of the great unsolved mysteries of physics. More importantly, turbulence is an emergent phenomena. The fact that water could act as a coherent matter, when it is composed of individual atoms, should still surprise at the end of the day.
One of the great mathematicians of the 20th century, von Neumann, presented control and prediction as a dichotomy. He proclaimed that we shall control what we cannot predict, and predict what we cannot control. In his article, “Bitcoin”, Nassim Nicholas Taleb, with whom I share a beloved homeland, called bullshit on (a large part of) our macroeconomics tradition.
I propose adopting the lattice Boltzmann method as a framework for understanding economics. The simplicity of the lattice might be the structure Taleb advocated for, and the complexity of microeconomics is hidden in the interactions, collisions, of the particles. We, the participants in the economy, are the particles, and our collision is how contribute, how we exchange and “add” value.
This gives rise to mesoeconomics.
Similar to Boltzmann’s assumption of chaotic particle behavior, Taleb suggests assuming irrational participants when building the structure for a rational economy. The participants are to be accounted for aggregates, akin to the fictitious particles describing a larger group of particles. This gives rise to mesoeconomics, a field allowing us to describe macroeconomics while being able to structure it by describing microeconomic interactions.
While some might argue that data-driven macroeconomics fill this gap, this is like saying turbulence could be controlled with flow field statistics. As uncertainty propagates, predictions degrade. We are left trying to drive the economy looking back. How has this served us thus far?
Each one of us is unique. Statistically, we are human on average. Describing an average human blinds us to the anomalies of our behavior however. If we have learned anything from the Black Swan, it is working with anomalies rather than ignoring them to simplify our jobs. As such, describing groups of people with full distribution functions, rather than averages, variances, or other statistics, is attractive.
“Living in a lettuce” is the Arabic equivalent for the idiom of living under a rock. Both refer to an individual unaware of the events of the world around him. On the other hand, we have our hyperconnected world. In reality, both conditions push us away from being at peace with ourselves, from our equilibrium.
Following the multiscale approach of this article, we see that isolation, self-sufficiency on the level of a state, has historically led to mass death. Hyperconnectedness stems from superfluous supply or demand seeking to tap large swaths of consumers or producers, respectively, to relax back to equilibrium. Historically, this has resulted in grave colonization or revolution — pushing the system back to equilibrium, away from extremes.
We need just enough connections.
Humans are social beings, and their connectedness lies somewhere in between. We need just enough connections, and the lattice structure gives us exactly that. It allows us to reach our neighbors in nearby cells.
This might seem limiting, but lattice cells correspond to our physical realities. We must exist somewhere. This is also a reminder that our impact must, first and foremost, be local. We could easily imagine cells representing different offices in a corporate headquarters, where different value contributions — collisions — happen.
Groups of cells — offices — share a border describing the interactions across the building’s floors. Cells outside the company describe businesses in its vicinity. As the persons hop from one cell to another, from the office to buy a coffee, we realize that the borders are diffuse. We are able to see the business for what it is outside of itself.
Technology is not a predicament for a hyperconnected world, for technology is cyclical. Further advancement of technology beyond its current state would give rise to vernacular economies again. It is already happening.
Let us not forget the physical realities of our modern ways. A cargo ship docks to load, refuel, unload. An airplane does too. When we do business from thousands of miles away, the collisions, the value contribution is local — or at least it should be , nobody likes leeches — and the value is streamed — advected by the particles hopping from one cell to another, and their energetic collisions.
Even the Internet has a physical reality. There are servers manufactured and set up, cables extended across the ocean floors, energy being consumed to send the data packets through. Bitcoin is about accepting the end of a battle, and moving to innovate up the stack, until the next battle call.
If companies really have diffuse borders, don’t countries do too?
The simplicity of the model calls us to reconsider our nation-states. If companies really have diffuse borders, don’t countries do too? The wars over underwater gas reservoirs agree. Our binary borders defy reality. Their enforcement remains the haunting dilemma of the 20th century. A ghost that haunts presidential elections and diplomatic missions, it forces us to relearn the age of empires.
For those more technically inclined, consider resources as a scalar field of value, or a tensor field if you want more accurate models. The field is advected along with our moves. It is subjugated to our own actions, and pushed around along with our distribution functions. Resources are a given. They are just enough, and we get to reallocate them based on what we do.
By the end of this article, you are getting closer to understanding the “Need” economy. This proposal of a mesoscale economic model is at its heart. Whilst I continue to figure it out, I invite you to contemplate what it could possibly be. By now, you should see that you should focus on your actions, for simple interactions give rise to complex futures. If wealth, value, were attached to resources, you would not be able to control it, but you still could control your contributions.
