Structure of Systems  Introduction
Introduction
In this series of documents, we are concerned with the organisational structure, of systems, and with the way that such structures evolve. In the past, the representation of such structures has been too simplistic and hard to change, e.g. organisation charts or wiring diagrams. We need to do better.
We view any system, as being a component, in many larger composite systems, as well as being, itself, a composition, of smaller component systems. Clearly, composite systems can share components. Thus, systems exist in a huge, directed graph, with the system, represented by the bottom node, of each line, in the graph, being a component, of the system, represented by the top node. At the extremes, the top node, of the whole directed graph, represents the universe, and the bottom nodes represent microscopic systems (many, of which are, at present, beyond human decomposition, or even comprehension).
We see systems evolving, by means of movements, of component systems, between composite systems. The movements are driven, by interactions, between composite systems, and these interactions are supported, by systems, that connect the interacting composite systems. All, of the movements, are reflected, by changes to the directed graph.
The above is obviously taking an extremely broad view of systems. It is assuming, that any set, of systems, can form a composite system, even if these component systems are remote from each other, and never likely to interact. Thus, all systems, and all past and all future states or component structures, of systems, exist in the directed graph, described above.
In the real world, we must restrict our attention, to a subgraph of the full directed graph. We could think of this subgraph, as being illuminated, by a notional spotlight, with the spotlightbeam moving gradually, across the total graph. Alternatively, we could just think of this subgraph, as a graph, representing the systems, that are of interest to us. In a later document, we will describe our notation, for representing this graph and its gradual evolution.
We have produced a series, of documents, as listed below. The second document, describes our notation, supporting the view outlined above. The third and later documents give examples, of the use, of the notation, with the examples ranging, over systems, in various disciplines.
LongLived Systems
The systems that we represent, in our examples, are all reasonably longlived. These systems seem to defy, the Second Law of Thermodynamics. That law says that the universe is evolving, towards a state, of maximum disorder or chaos. However, the organisation of the systems that we describe remain ordered, though changing, over lengthy periods. Physicists, and more recently business theorists, have explored this apparent contradiction. This exploration started in the mid nineteenth century:

Second Law of Thermodynamics  starting in 1824, this law was expressed in many ways. Initially, its expression involved macroscopic quantities, like volume, pressure, and temperature.

Entropy  Rudolph Clausius introduced the concept of entropy, or disorder. He expressed the Second Law, as saying that order decreases (entropy increases), or remains constant, in a closed system (and for our purposes, the universe is a closed system).

Statistical Entropy  Ludwig Boltzman introduced the microscopic view, of thermodynamics and its laws. He recognised that the closed system, being considered, is made up of a very large collection, of particles  e.g., atoms. He defined entropy, as the number of possible states, of this collection of particles. He recognised, that these microscopic states cannot be described, or measured. However, he did provide a statistical formula, for entropy, founding the subject of statistical mechanics. This was refined, by Willard Gibbs, and is now referred to, as Gibbs Entropy.

Dissipative Systems  given the Second Law (with any of its definitions), one would expect the universe to break up, into small particles, and, ultimately, just energy. However, although the majority, of the universe, is increasing in entropy, there are islands of decreasing, or static, entropy (suns, planets, plants, animals, humans, etc). Ilya Prigogine realised, that these islands achieved this, by maintaining order internally, and by exporting increased disorder (entropy), to their surroundings. They exported increased entropy, by consuming reasonably complex organised systems (as food) and emitting less organised systems (as waste). Ilya Prigogine believed that it was essential, to concentrate on indeterministic systems, rather the deterministic ones. In fact, he looked upon the latter as a waste of time. He was interested in bridging the gap, between General Systems Theory and Thermodynamics. He had worked with Turing.

Free Energy  The renowned physicist, Erwin Schrodinger, became involved, with this subject, as an explanation for living things. He introduced the term negentropy, for the export of entropy by living things. He was persuaded that Free Energy was a better way, of explaining entropy.

Information Entropy  Claude Shannon is referred to, as the father of information theory, although his impact went beyond this field. He extended the idea of entropy, by saying that entropy should be a measure, of how "surprising" the average outcome of a variable is. He applied this definition, to communications theory, taking entropy as the measure, of information content of a message. He used the techniques, of statistical mechanics, and his formula, for information entropy, is closely related to that produced, by Boltzman and Gibbs.

Viable System Model  clearly VSM, developed by Stafford Beer, has a close relationship to Dissipative Systems (see above). Dissipative Systems are viablesystems, within the meaning that Beer gave to this phrase, and most dissipative systems could be described in terms, of VSM concepts. Ross Ashby related his Law of Requisite Variety, to Shannon‘s information theory. Stafford Beer seems to be connected, with Claude Shannon, via Ross Ashby, Norbet Wiener and Warren Mc Culloch, but we cannot yet identify precise technical links. Eric Schwarz was later than Beer, and seems to be seen, as developing Stafford Beer‘s ideas. He did draw on the dissipative systems ideas. Another definite influence, on Stafford Beer, was Humberto Maturana, but we do not think that he connects with the above (or that was a major influence on Stafford Beer).
Documents
Our background is in IT, so our main interest is in representing the structure, of IT systems and their interactions with human systems, business systems, and other systems. However, we thought it would be useful to explore the problem, of structural representation, across a range of disciplines. We hope that we have acquired adequate knowledge, of these disciplines, to make the examples, taken from them, useful, but we certainly do not claim any deep knowledge of the disciplines. The following is the list, of documents, that we have produced:

Introduction  this document

Notation  introducing the notation, that is used, in the other documents

KissingHands  describing the evolution of government in England

Mitochondrion  describing one, mitochondrion, component, of a human cell – needs updating

VSM Model  describing Stafford Beer’s Viable System Model – this is a static model, as Stafford Beer does not formally describe the dynamics, of his model  needs updating
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