“If we attempt to strip anything down to its purely logical representation, such as if we attempt to define the “ultimate meaning” of concepts such as truth, existence or life, or attempt to reduce subjects such as philosophy, mathematics or quantitative economics into a set of formulas, then this effort will most certainly fail.”
-Brian Arthur
A Primer
What is called the Extended Order by Hayek or Ponzi structures in our previous articals exists not only in economics or finance, similar structures can be observed in abundance in physics, biology, behavioral studies, and more. The most apparent is the unfolding of a human’s life, whose potential growth seems to fit an ever extending order of capacity. Would there be a more general pattern behind these phenomena? We found that there is such a type of research that is very close to the heart of what we want to understand — complex adaptive system.
An Introduction to Complex Systems
The study on complex systems focus on how individuals, through their interplays, co-create their aggregate system, and how the system forms relationships with its external environment through the formation of feedbacks. Complex system analysis treats the behavior of the entire system or the aggregate as the essential subject for research. As a cross-discipline field of research, complex system studies have taken numerous contributions from other fields, such as self-organization in physics, spontaneous order in social sciences, chaos theory in mathematics, evolution in biology, etc. Therefore, complex system is usually used as a broad terminology that includes research methodologies for a number of diverse scientific questions. Complex system theory originated from system theory in the 1930s. It has been in existence for just 40 to 50 years.
In order to give physical forms to the abstract concept of complexity science, below are some familiar phenomena that can help with the understanding of certain features of complex systems:
Ant colony is the most famous complex system in biology. Every ant obeys a set of simple rules about how to interact with other ants as well as with the external environment. On their own, the ants are clueless about the behaviours of the ant colony . However, if we elevate our view to that of the aggregate, then we will be able to observe the many complex behaviours of the aggregate ant colony. It would be able to carry weights that are tens and hundreds of times heavier than individual ant, create bridges of ants across water and even form flotilla of ants on rivers. The ant colony is an intelligent being.
In economics, Matthew Effect is also a result of complex systems converging to equilibrium. In other words, it describes a phenomenon where resources aggregate in a specific direction and continuously resources accumulate to a path where the strong gets stronger. In economics, the phenomenon is described by Brian Arthur as the rule of increasing return.
There is also the well known butterfly effect. As another embodiment of complex system theory, small changes in initial conditions will cause dramatic differences in the eventual results. Complex system is distinctively nonlinear. It doesn’t follow the linear relationships of cause and effect of a linear system. In other words, reduction from effects to causes is not viable. Many social systems that we are a part of are complex systems. In order to understand the complex systems of our society, we need to examine and understand its ecology through the lenses of network systems.
From Complex System to Complex Adaptive System
There are two layers of meaning for the “complex” in complex system:
At the first layer, by establishing a set of simple rules, an order will certainly emerge after enough individuals inhabit the system governed by the rules. Moreover, because there are many inhabitants, there must be coincidences or accidents happening and population changes due to the interplay process of the inhabitants. This creates the effect where order on the aggregate level cannot be foresaw by any individuals.
At the second layer, the set of rules made initially will spontaneously give rise to Darwinian mechanisms as the environment changes due to population increase. The rules become more complex and leads to changes in the environment. The changes in the environment further causes the rules to evolve as individuals adapt their responses to the changing environments and to each other’s changing strategies and behaviours. This is the essence of a complex adaptive system, the individual continuously changes one’s strategy and behaviours in order to better adapt to the impact from the historical path taken and thus new rules were formed as individuals adopt different strategies and thus behaviours.
Simply put, individuals in complex systems obey a set of fixed rules. They are more akin to cells in an immune system, or ions in a spin glass, or logic paths in programs. They do not possess “memory”. On the other hand, individuals in a complex adaptive system(CAS) are adaptive. They are intelligent and possess “memory”, they are able to adjust their internal models or their models of how to forecasts can be reached by learning from past experience. Rainstorms, dunes, atmospheres are all complex systems, but they are not CAS. Typical CAS include human brain, ant colony and economic bodies.
The Relationship Between Complex Adaptive Systems and Economics
The Extended Order envisioned by Hayek is a self-organizing and naturally growth inclined complex structure that stands between the primal instincts and rationality of human. In this structure, individuals are constantly adapting to an ever changing aggregate order, and in the meantime changes the order through their own adaptive behaviours. To a certain extent, complex adaptive system theory reveals the principal patterns of the progression of individual behaviours and the behaviours of the aggregate economy. The Extended Order play a critical role in the cyclic but naturally growth inclined nature of the economy.
Classical economics, neo-classical economics and Chicago school of economics are more concerned with equilibrium theories. While a shift from general equilibrium to partial equilibrium is happening in theoretical work in economics, the core of its studies is still on equilibrium. The attitude towards out-of-equilibrium is that it can only exist as a temporary, fleeting state of instability, and thus the economy will eventually recover to its old equilibrium or reach a new state of equilibrium.
However, according to Hayek’s Extended Order and Brian Arthur’s Complex Economics, real world is always in a natural state of ebb and flow, of out-of-equilibriums. Therefore, the real world presents a picture of fundamental uncertainty and continuously evolving technologies.
This would imply that there is no perfect strategy for individual, thus the behaviours of an individual cannot be seen in the light of perfect rationality as we have commonly defined, neither can the economy deviating from a proposed state of equilibrium be seen reasonable in the light of perfect rationality. Rationality itself is an imperfect assumption. Thus seeing the economy this way will exacerbate the deviation from equilibrium even further. If we look at the birth of blockchain technology and Bitcoin, the technology was not born out of nowhere, it was an organic combination of cryptography, P2P network protocols, consensus algorithms, game theory and other mature technologies. It is an engineering feat. It is from the coupling of existing technologies that new technologies arise. In the meantime, hidden demand makes themselves appear as new technologies come to scene and undergo exponential expansion and evolution, which will also drive the evolution of new technologies. Without Bitcoin’s blockchain structure, there cannot be Ethereum’s smart contract. Technological innovation itself is continuously creating new demand and fulfilling new demand. The evolution of technology is destructive to the state of equilibrium in economics.
According to Dingding Wang of Peking University, economic research methodologies can be generalized as “from principle to phenomenon”, yet they can be better said as “from internal to external”. Internal model is created from the understanding of the essence of observed phenomena.
By observing these phenomena economists can derive a set of definitions in order to explain the prerequisites for economic activities (preferences and restraints). Because such definitions are derived from the essence of phenomena, economists would be able to logically deduce propositions that can be proven in reality. Contrary to this method is that of biology, which can be generalized into “from phenomenon to principle”, or “from external to internal”. Biologists cannot give an inherent definition to the essence of “life”, thus a biologist can only observe the surface phenomena and build her understandings — forming a tentative thesis on the evolution of life that she observes, and continue to collect and analyze data in order to build a deeper understanding and evolve a thesis that might better explain the essence of life. This process will repeat itself as the biologist peels the onion and goes deeper into the layers of phenomena through observations — This is an endless process, as Arthur pointed out. This understanding itself is a part of the emergent order.
As the more generalized pattern behind the Extended Order, complex adaptive system is closely connected to economics. If we can understand complex adaptive system, then we will have a much deeper understanding of not just how the entire economy functions, but how society functions as well.
A Little Side Episode — Deconstructing Palindrome
This is a small game that can demonstrate how processes in complex adaptive system develops:
Here is a typical palindrome (Thanks to Douglas Hofstadter): A man, a plan, a canal: Panama.
If you arrange the palindrome backwards you would get the same order of letters and it would mean the same thing backwards. Let us attempt to use a simple complex adaptive system to deduce the reverse：
1. the initial goal is to write a palindrome about Panama.
2. Since it is a palindrome, then there must be a respective reverse: Amanap | panama
3. It should fit grammar rules, dismantle it： A man a p | panama
4. P needs to become a full word, we could have plan： A man a plan | panama
5. palindrome — the respective reverse: A man a plan | nal panama
6. nal needs to be completed, canal seems quite appropriate: A man a plan | canal panama
7. some more palindrome: A man a plan a c | canal panama
8. Add in the punctuations, it is complete: A man, a plan, a canal: Panama
In this episode we discovered that this process only followed two basic rules, palindrome and word logic. Panama can be seen as a random starting point. By following these two rules and undergoing a series of evolution, we eventually reached a steady state. This essentially shows how complex adaptive system evolves. Every individual in the system interacts with the environment and each other by adhering to a set of simple rules, which leads to changes in the environment and that leads to changes in the behaviours of the individuals — mutually become the causes of changes in each other, a dance of intertwined evolution.
References:
1. “Complexity and the Economy”, Brian Arthur
2. “Complexity: The Emerging Science at the Edge of Order and Chaos”, Mitchell Waldrop
3. “The Engine of Complexity”, John E. Mayfield
4. “The Fatal Deceit”, Hayek
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