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Complexity - equilibrium - information: the connection

  Problem: In nature, there is a special category of systems characterized by a continuous (but not necessarily strict) increase in complexi...


In nature, there is a special category of systems characterized by a continuous (but not necessarily strict) increase in complexity. Such continuously increasing complexity systems include evolution, human society, technology, or even the financial system. These systems are characterized by the fact that they are always changing and that change has a direction, an increase in complexity. What are the characteristics of these special systems? What do these systems have in common, what are their common features? 


Evolution is creating increasingly complex biological systems. Evolution is a complex biochemical process in which information is recorded in the DNA helix. 

The complexity of human society is constantly increasing. In human society, the information carrier is speech, the spoken language. Stories are the form of information recording in speech. When the human species began to create stories through speech, the complexity of human society began to increase. 

Technological development is continuous, and humanity is able to create more and more complex technology. Writing is the information recording element of this process. The consequence of writing as a method of recording information is a steady increase in the complexity of technology as a system. 

The complexity of financial systems is also constantly increasing. The information recording element in this process is accounting, the recording of quantities. 


A cryptocurrency system is being born. The cryptocurrency system also uses a special information recording element, the public ledger. The complexity of the cryptocurrency system will continue to grow as long as the system exists. 


It is a feature of any system that increases in complexity over time that information is captured in the process of the system. 

Information capture is not necessarily the core of the process, it can be a side activity. Information capture, and hence information accumulation, may be only a subsidiary property of these systems.

Generalization, theorem:

Generalizing, then, whichever system uses an information capture process, the complexity of that system necessarily increases over time. 

Inversion of the theorem:

So, any system whose complexity is constantly increasing, during the operation of the system there is some information capture process, the system employs an information capture procedure. 

Consequence of the theorem:

It is not normal for these systems to reach an equilibrium state after some time. These systems are in a constant state of change and evolution. 

A corollary of the theorem:

So, if we create a system with information capture process as it is an integral part of the system’s operation, then the system will have an ever-increasing complexity and will never reach an equilibrium state. 

Application of the theorem:

So, if we want to create a system whose complexity is constantly increasing and never reaches an equilibrium state, then we should incorporate an information capture mechanism into the system's operating process.

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