The fractal structure of nature was discovered by the French-American mathematician, Benoit Mandelbrot, in 1980. Many of you will be familiar with fractals and so it is not my intention to describe them in detail. Rather, if you are unfamiliar with them, I refer you to the very clear explanation given at https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/07%3A_Mathematics_and_the_Arts/7.04%3A_Fractals
Eliot Kersgaard (2019) defines a fractal as a system with similar properties at all scales. Many readers will be familiar with numerical fractals such as the Mandelbrot set or geometrical fractals such as the Sierpinski triangle. This is where most fractal research has focused. In these cases, Kersgaard’s “scale” is numerical or geometrical. However, these fractals are normally displayed using the two dimensions of a piece of paper or a video screen. So, incorrectly, their scale appears to be spatial. However, “scale” can also apply in a physical sense to features of reality, such as objects, events, or relationships, in which case “scale” is genuinely either spatial or spatio-temporal. The leaf of a fern is, for example, a genuine spatial fractal.
The Viable Systems Model (VSM) was proposed by the British psychologist, Stafford Beer, in his 1972 book “The Brain of the Firm”. This model is used as a framework for understanding human organisations, but it is also thought to apply more broadly to other living things. Again, without going into detail, the model proposes that every organisation has a control component that coordinates the activities of other components, e.g., the brain of a human being or the manager of a team or organisation. For those unfamiliar with the model, I refer you to the explanation at https://www.toolshero.com/management/viable-system-model/.
Beer recognised that his VSM model was recursive, i.e., every model comprised components, one of which was a control component, and every component was a VSM model. However, this was before the fractal structure of nature was discovered by Benoit Mandelbrot. In fact, the VSM model is a fractal generator that applies at all scales of organisation and is comparable therefore to the simple recursive formula used to generate the Mandelbrot Set. Furthermore, control applies to a function, and there are very many functions. This means that the VSM model is likely to apply quite extensively in natural and artificial ecosystems. Choose any “organisation” and function anywhere among living things and you are likely to find that VSM applies. There is never just one “controller” therefore. Rather every living thing both controls and is controlled.
Little work has been done on the fractal nature of human society. However, the following paper raises the concept as a possibility. https://www.academia.edu/47938193/Fractals_in_Social_Sciences_an_introductory_remark
The rule that creates a fractal is known as a generator. For example, a simple recursive mathematical equation acts as the generator of the Mandelbrot set. The generator for human society is, however, more complex. It is the relationships between human holons at various scales that create society. However, these relationships are not always cooperative ones. If that were the case, then all of humanity would comprise just one organisation with a single leader. This is clearly not the case and, as an alternative, I would therefore suggest the following generator.
- A human holon is any person, group of people, or group of groups who cooperate with a common purpose. The cooperation of more than one human holon creates another at greater scale. Thus, human holons form a nested hierarchy.
- Every human holon has a control or management component. This, in conjunction with the principle above, results in a control or management hierarchy. For a holon of greater scale to be formed, it is not necessary that every pair of components cooperate horizontally with one another. However, they must cooperate vertically with the control component.
- A satisfier is an external thing that satisfies a human holon’s needs. For example, it may be food for an individual person, or electricity for a manufacturing organisation. There are many such satisfiers, and they determine the function of their source. The more specialised this function, the less extensive the range of sources, and the more likely it is that two human holons with a common need will share the source of a satisfier.
- The source of a satisfier also depends on the geographical location and culture of the holon. Sources closer to and with a similar culture to the holon tend to be used first. Thus, the closer two holons are geographically and culturally, the more likely they are to share the source of a satisfier.
- The relationship between two human holons is neutral if the source of a common satisfier differs for both. It is also neutral if the source of a common satisfier is shared, but the satisfier is sufficient for the needs of both.
- If the source or sources of a common satisfier are not sufficient for both when they act independently, but are sufficient if they act cooperatively, then two human holons may cooperate. However, a degree of randomness is introduced by holons not considering cooperation in these circumstances.
- If the source or sources of a common satisfier are not sufficient for both, then two human holons will compete to satisfy their needs. Competition, unless externally controlled, can escalate into conflict.
- Leadership roles act as a satisfier and are limited in their availability. So, they will generate competition among any human holons who aspire to them. Thus, there can be horizontal competition between the components of a holon and between discrete holons.
This generator is hypothetical, of course, but I believe it to be a good foundation for a theory of society.
References
Beer, S. 1972. “Brain Of The Firm”. Allen Lane, The Penguin Press, London, Herder and Herder, USA.
Kersgaard, E., 2019. “Life’s Universal Patterns”. Medium. https://medium.com/illumination/lifes-universal-patterns-e534475aabf6
Mandelbrot, B. B., 1982. “The Fractal Geometry of Nature”. W. H. Freeman.
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