Reflections on the Essence of Openness and the Relationship Between Systems and Observation

Traditional System Classification Definitions

According to the interactive relationships between systems and their environments, systems can be divided into the following three categories:

(1) Open system: A system that exchanges both energy and matter with its environment.

(2) Closed system: A system that exchanges only energy but not matter with its environment.

(3) Isolated system: A system that exchanges neither energy nor matter with its environment.

Opposed to open systems are closed systems and isolated systems. In the objective world, the existence of closed systems and isolated systems is relative (that is, absolutely preventing energy exchange or material exchange is impossible; one can only reduce flux to the greatest extent possible within limited degrees, reducing the ratio of exchanged material energy to the system's own material energy), while the existence of open systems is absolute. The human body is a typical open system that can exchange both energy and matter with the external world.

In fact, everything in nature is always interconnected and mutually influential. Strictly speaking, isolated systems are only hypothetical systems that can exist only within limited time and space. Systems with relatively weak connections to their environment are usually treated approximately as isolated systems. In actual research, sometimes closed systems and the environments affected by the system are studied together as isolated systems.

The above is the definition of open systems given by encyclopedias.

Reflection on Traditional Definitions

This definition focuses on the thermodynamic openness issues of real systems occurring in physical spacetime.

But this paper intends to explore the openness issues of systems in an abstract sense. I believe that in terms of sensory imagery, "openness" means "sufficient interaction with the external environment." From a simulation perspective, systems are generally required to be dynamically developing or dynamically operating, with the system's content and boundaries continuously expanding (overall complexity growth). The content of the environment must also change accordingly, because we understand the environment through the system rather than the other way around. We delineate boundaries for the system based on certain purposes (I say "based on purposes" because these models reflecting reality are ultimately designed based on human needs and insights), thus generating the environment.

It can be said that in abstract systems, the environment does not obviously exist—it is not like the environment separated from machines in physical environments (for most massive self-organizing complex systems, this clearly demarcated environmental view is especially unrealistic).

Posing the Core Questions

So what exactly is the environment? What is the essence of openness that describes the relationship between abstract systems and their environment?

Below, I intend to think about this from the perspective of abstract complex systems, thereby providing some insights into this question.

Thinking from the Mathematical Concept of Closure

Closure, also called closed property. In mathematics, given a non-empty set S and a function F: S × S → S, F is called a binary operation on S, or (S,F) is said to have closure. In mathematics, if performing an operation on members of a set generates elements that are still in this set, then the set is said to be closed under this operation.

The above is a simple definition of "closure" found in encyclopedias. So I put forward my viewpoint:

The essence of openness is non-closure—it is the system's emergence of new characteristics beyond existing observations.

Basic Expression of System Operation

We regard S as the system and consider that the system model operates through iterative simulation methods. In this way, we introduce a basic observational variable, namely operating time T, from which we derive the simplest binary expression of system operation: (S, T).

Describing Systems from an Observational Perspective

For systems, we can describe them from an observational perspective. We currently only consider situations with limited observational means—that is, we only have several observational methods and can only use these few, and we must not use combinations of these observational methods, since we can achieve this purpose by adding special new observational methods. Thus, the system is expressed at the observational level as a multi-tuple of observational methods (P1, P2, P3, P4, up to PN), where each observational method represents a way of obtaining information about the system, such as change indicators, distribution differentials, parameter correlations, etc.

Definition of "Constraint" Phenomena

We define a phenomenon as "constraint": statistically detectable observational differences compared to the system's structural starting point.

Constraints can be understood this way: starting from single molecules to construct a system, "life systems" are extremely difficult to emerge, but they still appeared and spontaneously reproduced, maintaining constancy in molecular quantities. Taking the biological structural quantities in the biosphere as the statistical range and comparing them with the "biological structural quantities" of a pile of monotonous stones, obvious behavioral observational differences emerge, especially manifested in different spatial movements, more complex and diverse behaviors, and even high-order intelligence creating more molecular quantities.

This is how, in the process of system self-organization and complexification, emergent new structures organize, constrain, and regulate their "source" to exhibit characteristic differences distinct from completely random situations.

Returning to Understanding the Essence of Openness

Corresponding to "constraints," we must have some kind of observation to achieve awareness of the differences produced by these constraints. This brings us back to understanding "openness":

The essence of openness is observational non-closure.

As long as we can introduce new observational methods (whether they are combinations of existing observations or something entirely new), we can obtain manifestations of the system's characteristic differences.

I'll stop writing here for now.