Power law

I will try to make some sense about how to understand life using some recent insights from system dynamics theory, Neo-Darwinism, particle physics and some basic laws of nature. I do not intend to explain what life is, while this would be much to ambitious. I dare to take all posts together as a complex of evidences about life, but this post narrows the perspective to above mentioned starting points.

Like always the main goal is not only to understand, but even more to enable us living this life in a more sustainable way.

Like so often, there is one important clue only that help us understand various aspects of life, power – law. The logic behind is best described in the work of Stuart Kauffman (The origins of Order, 1993; Investigations, 2000; Reinventing the Sacred, 2008). My aim is not to repeat what was already explained, but to implant power law paradigm on most basic facts of life.


The x axis on above graph shows the level of flexibility, where 0 is a highest possible rigidity (the system is frozen) and 10 is highest possible flexibility, where system is in chaos. Output level of information in such a system is shown on y axis. When the system is frozen, it produces almost no information. Information starts to emerge when the system gains flexibility. The information level peaks right on the edge of chaos, right before it drops down from highest value to 0. The edge of chaos is also described as phase transition as the moment of highest criticality according to Kauffman.


The graph also shows the entropy level. On x axis 0 represents maximum entropy and 10 represents the lowest entropy of the system. The line is in fact reverse evolution line of our cosmos running from a big bang moment (10), over the evolutionary peak (around 9 on x axis where information level peaks to 50 on y axis is just vague aproximation) to absolute frozen equilibrium in the cold future of our universe with maximum entropy (0 on x axis). The theory of evolution of our universe, big bang theory, tells us that in the very beginning the entropy of the system was lowest and according to second thermodynamic law the entropy of each system only increases. It seems strange that a system with the highest possible temperature (big bang moment) has lowest possible entropy, while frozen, crystalized system with the lowest possible temperature has the highest one. Both extremes are most unfavourable to life. In the very beginning, there were too many mutations to the system to allow emergence of life – and at the end there are not enough mutations to allow life to reproduce. The peak of blue line represents the zone where the system produces optimal ration of mutations. I guess and hope we are situated in-between 9 and 10 or at least not much lower than 9 on x axis.


X-axis could be also understood as the level of corruption axis. In this case y-axis is societal output level. At lowest numbers, social system is frozen. There is almost no corruption, but no social output either. At the highest corruption, there is no output while the system is in chaos (minimal entropy). The highest output level can be found at the edge of chaos. It is easy to understand the tendency of western societies to formalize democracy (against corruption) as a tendency that is oriented towards 0 on x-axis. It is thus clear that formalization, over-regulation pushes society towards inefficiency. It is less clear which is the moment with the highest output level of society measured on x-axis. We can be sure that deregulation leads to more flexible and more productive society – but we never know when exactly deregulation falls over the edge of highest possible output into the chaos, lowest possible output. Society is the most productive when balancing forth and back on the edge of chaos.


Understanding x-axis as a line of formalization, we could also see it as a line of individualism. Closer to 0, higher the level of collectivism; closer to 10, higher the level of individualism. From this point of view x axis is a religion line as well. Finding rigid collective religions like Catholicism close to 0 and Buddhism as the non-religion based on purely personal development closer to 10 on x-axis. If perceived from power law point of view we can clearly see that Catholicism, started as individual experience (closer to 10) and later developed strongly towards 0, towards objective, rigid belief system that represents fixed background for each individual practising this belief system. That is why institutions like church in fact do not like any intentions to move towards higher numbers on x-axis. This also explains why freemasonry as a strong system based on personal development is in a natural disagreement with Catholic Church, but in close relations to origins of any and thus also Christian religion. What else could be a better explanation of a strong belief system without fixed background as freemasonry? So, y-axis in this case shows the level of fixed background where 0 points the highest value and 50 the lowest level of fixed background content.

There is another development observable in power law graph: distribution and tendency of western vs. eastern civilizations. It is quite clear that western civilization is stuck into a X axis direction towards 0, while all those cultures and civilizations seen as less developed from the point of western view are closer to 10. It is quite clear that western culture is slowly but surely dying and most of those less developed are in fact much more fertile and have much better evolutionary strategy. Might it be that freemasonry as an esoteric close to eastern belief system is occupying highest information output values?


It is not hard to notice that Kauffman power-law differs from “normal” power law. Both laws are the same (one quantity varies as a power of another) up to the moment of criticality when phase transition starts. “Normal” power law does not break in the moment of criticality; it goes forever in both directions. While there may be physical phenomena that follow normal power law distribution, those that are affected by criticality are important for this blog only. Those vastly complex systems that can balance on the edge of criticality are the only that are capable to resist entropy at least while alive, while able to balance on the edge of chaos. That is why “normal” power law is of no interest for our purpose.



Andrej Drapal