TFNR - Complexity
Not to be confused with Entropy is the term "Complexity". There are many definitions and areas of use of this term, which maintains a certain ambiguity also linked to the dichotomy of organized Complexity and disorganized Complexity.
In fact, this term, so important for understanding and evaluating the Evolution of a system, of an object, of Reality, of the entire Universe, is intimately linked to the themes of Organization and of the continuum that leads from chaos to order. And the object of Organization and its Evolution is certainly Information, Relations between Events, the Processes that represent and describe the Dynamics of Reality at all levels. At all levels of Reality, levels of Complexity of Reality, precisely.
Information, Relations, chaos, order, Organization, emergency, systems, Evolution. These, along with many others, are the key terms to understand this elusive concept, Complexity.
Before venturing into the difficult attempt to find a satisfactory definition, let's make a clarification. Complexity is a concept that has assumed particular relevance in and thanks to systems theory. The concept is therefore somewhat tied to the relations between parts in a system. Here, we will try to partially overcome this conceptual constraint. We must try to imagine that elementary objects (not composed of parts) but at the same time complex (which exhibit complex behaviors, as if they were composed of a significant number of parts) can exist.
Let's take for example an object that is commonly considered elementary, a particle, the electron. From observations it is clear that this particle is not composed of parts. But it exhibits bizarre behaviors, balanced between particle and wave, localized and non-localized, solid and impalpable, as if by magic it could reconfigure itself, as an object composed of infinite parts intimately interconnected. Yet no part can be detected or hypothesized.
In this System of Knowledge, in the model that we are trying to build and outline, as we will see better in the next chapter, an electron is a Structure of Information, type Vortex / Particle, sub-type Elementary. Elementary does not mean that it is something monolithic, immutable. But not even a system formed by parts. It is a Structure that represents an organized set of elementary processes (Events organized by Relations, correlations of temporal distributions of elementary spatial fluctuations), a virtually infinite number of processes, as infinite as the event points of the Elementary Field that support its Existence and Essence / Form. "Infinite" as the points of the real axis between two defined extremes are infinite. "Virtually" because the elementary fluctuations resonate around the Planck scale, in fact limiting its infinity to an extremely high number and to spatial and temporal extensions characteristic of that infinitesimal scale.
Why do we assume that a particle that is commonly considered elementary, one of the most elementary particles of the Standard Model, is a complex object? Not as complex as a proton or a neutron, or a meson, but still quite complex? Precisely because its Existence and its Essence / Form, its behavior and its Dynamics are the result of the complex interaction of these dynamic processes that characterize the virtually infinite event points of the portion (volume) of the Field that from time to time support the aforementioned InfoStructure that we call Particle.
After this clarification, with which we wanted to point out that what appears elementary (not composed of parts) and simple from the ontological point of view, if it is complex from the phenomenological and dynamic point of view, perhaps it is also so from the ontological point of view, despite appearances, which often deceive, as is well known, let's try to outline some hypotheses of definitions.
The Information content of a Structure, a Form, a System, the entire Universe is an important quantity that provides us with a "measure" of the Complexity of such an "object". Information can be observed from two different, yet complementary, points of view. The quantity and the quality of Information. These are aspects of Reality that are difficult to deal with, especially in the physical domain.
Information in Physics is a rather "uncomfortable" concept, and so is the concept of Complexity. Qualitative elements are not so easily modeled and calculable, and struggle to enter the equations. But I believe that these two concepts, together with that of emergence, and organization, are fundamental to understanding the evolutionary aspects of Physical Reality at all levels.
Complexity is a measure of the content of Information, the level of organization of the Action, of a Structure, of a Forms. It is a measure of the causal and variational distance of the form from the absolute homogeneity, a measure of the inhomogeneity of a Form. It measures the causal [[action] ] and its variational effect necessary to produce that Form starting from the absolute homogeneity of the distribution of the Elementary Events in / of the Elementary Field, the most fundamental form of Existence.
Complexity represents the extension of the causal process that produced the Form in question, in other words, the quantity and level of organization of the events that produced the above mentioned Structure or Form.
It is the result of the incessant evolution of Information. Evolution of Events, Relations, Processes, Structures of Information and Forms.
In other words, Complexity represents the product of the Process of Formation of Reality, the emergent organization, produced by the incessant evolution, fed by the Force (in the form of the Operator of Reality that we call Relation), which operates to all the levels of the Reality.
In a statistical sense, it represents a measure of the degree of organization of a system or of the Universe as a whole. In the continuous scale that goes from the absolute chaos to the absolute order, evolutionary processes build increasing levels of organization, which correspond to peaks of Complexity that we observe in Reality.
It is in the dynamic equilibrium, or rather, in the imbalance in continuous tension towards an unattainable equilibrium, that the interaction between anabolic processes (constructive - Operator Organization) and catabolic processes (destructive - Operator Transformation produces the Forms of Reality, of which the Operator Selection allows the causal and variational permanence. Negentropy and entropy. The state functions of systems evolve towards locally and / or globally more complex (less probable) states, in an incessant dance on trajectories that now veer towards chaos (for example, the second law of thermodynamics) now towards order (systemic principle of emergent order).
From this definition, it follows that the most complex thing in existence is the Universe itself. Furthermore, if we hypothetically consider human beings as the most complex existing forms and the planet Earth as the only celestial body populated by human beings, Earth should be considered more complex than the rest of the Universe. The definition of Complexity therefore incorporates both quantitative dimensions and qualitative aspects.
All that exists is Information that organizes Fields, Relations between Events. With reference to the Elementary Field, at the most elementary level of Existence, Complexity represents the level of interconnection of the network of organized relations between the processes that animate the event points of the Field itself. And, starting from this elementary level, we gradually find a continuous succession of increasingly complex levels of Existence, connected by a network of Relations that build an infinite hierarchy of emergent Complexity in incessant evolution.
Links to the tables of contents of TFNR Paper
