Fractal organization as a response to complexity

Useful fractals

The solutions proposed by fractal mathematics have led various branches of human endeavor to incorporate them into their workings. People have begun to see the world in fractals, non-integer dimensional spaces, and ineluctable probabilities. Fractal models allow a management of phenomena that is no longer hierarchical, linear or directly causal. The cause must be sought at another level, that of the balance of constraints. The fractal theory was developed by the mathematician Benoit Mandelbrot and was developed in response to practical problems in telecommunications, linguistics and telecommunications, linguistics, and finance.

Applied theories always end up matching the changes they induce. The world of education teaches and develops both theories and, subsequently, their applications. When these applications affect the organization, it is also called upon to rethink its operations.

From the moment we are able to intentionally influence something, our responsibility is engaged. Our knowledge penetrates more and more deeply into the laws of life, of nature and of the relationships it establishes; what appeared to us to be simple to us is clearly not. The complexity now revealed can overwhelm us. complexity can overwhelm us... unless we manage it with the modern tools modern tools that accompany our discoveries and proper organization.

A transforming school management

At the time of the industrial revolution, the formerly artisanal organization shifted to a management style that corresponded to the new spirit driven by the scientific discoveries of electricity, thermodynamics, chemistry, and the atom.

A scientific organization of work followed, and the schools gradually organized themselves in a logic corresponding to the social evolution that followed from this reorganization of relationships. Since then the school has been run from a ministry, departments and a principal, in a line corresponding to an industrial hierarchical organization. The preceptor became a teacher as the craftsman became a worker.

The arrival of communication technologies destabilizes this structure. Within a few years, our management models have all been disrupted by these technologies. Educational management is under stress because the profession is no longer so attractive. The deterioration of working conditions and the resulting shortage of teachers, as well as the new realities of students, call for a review of operations to recreate truly attractive educational environments for both staff and students. This is something that many institutions are in the process of achieving.

Fractal?

Mandelbrot was fascinated by the fact that nature actually produced relatively few geometric shapes but many patterns that we intuitively recognize.

• The "random" arrangement of stars in the sky is not the same as the arrangement of raindrops on the pavement.
• The shapes of clouds or the skylines of cities make a similar pattern for all of them and yet all are different.
• The curves of stock market activity are all different but take on a different specific appearance than earthquakes.

His genius was to find the way nature produced these types of shapes whose principle was both reproducible and seemingly random. Since these are the completed forms that have to undergo every possible randomness, they necessarily correspond to the optimal response obtained when their characteristics have faced almost every situation.

The theory of fractals does not apply so much to individuals but rather to groups composed of large numbers of individuals. The diversity of characteristics and behaviors of individuals and their responses to their environment is taken as a whole. Since educational systems are composed of thousands of schools and individuals in a diversity of contexts and characteristics, they represent a good field of application.

Applied to organizations, the fractal theory of organizations proposes three principles:

• Sense
  
  The purpose of the whole is shared by all. The importance of everyone's role, from the humblest role to the most prominent, is understood, regardless of the level of the organization. For example, the idea of "making a profit" will not make sense to workers who do not see any benefit in it, but the idea that profits must be made in order to invest in a clear mandate, environment, culture or other, can be shared by the whole organization. A fractal structure can thus be reproduced at all scales. Consent is an implicit condition for sharing meaning. It cannot be imposed.
  
  
• Autonomy
  
  "Autonomy is not the freedom to do what one wants but to do what one must in the way one wants."
  
  If the purpose is known, everyone can contribute in the way that best suits the situation. A firefighter remains in his firehouse except when there is an emergency. Unpredictable situations will be answered to the extent of the autonomy of the performers who are able to adapt to each context.
  
  
• Reciprocity
  
  Reciprocity is a recognized interdependence. In a closed system, planet earth is one, all flows must cycle. If one organism consumes oxygen, another must produce it. If a company makes a profit, it must return profits to its environment. No organism can constantly take without seeing the source dry up unless it is part of a cycle.
  - We cannot constantly ask for trust without returning information about the results from the effort. -
  - Worker burnout indicates a lack of reciprocity while motivated workers are more a sign that they see meaning, enjoyment and interest.
  - A school produces graduates who find utility in the society that supports the school, etc.
  

Fractal organization in response to an unpredictable environment

Fractal organization applies at different scales both material and temporal. Establishing a fractal organization for an insufficient number of elements or for a short period of time will offer little benefit since the set of possibilities will boil down to almost nothing and will be encountered quickly or insufficiently. There will be a lack of resources to respond and an unexpected event will eventually be fatal. A simpler organization will be a better response.

The school system is as resilient as any large organization. It already has a partly fractal organization, the same organization replicates itself at many levels and scales: small, medium, or large schools are quite similar in their operation. It remains to establish the best models and optimal sizes. In social groups, the need to recreate a new division often appears around 150 members (Dunbar). The school does fit the social group, but what are its constraints and capabilities? How does it best respond to them? Fractal organization can help deal with both complexities and constraints.

References

Michel Henric-Coll - Fractal Organization
https://books.google.ca/books?id=6bwMBAAAQBAJ&printsec=frontcover&hl=fr&source=gbs_ge_summary_r

Benoit Mandelbrot - Fractal objects. Form, Chance and Dimension
https://www.decitre.fr/livres/les-objets-fractals-9782081246171.html

Mandelbrot - Wikipedia
https://fr.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot

Fractal - Wikipedia
https://fr.wikipedia.org/wiki/Fractale

Fractals and the Art of Roughness - Benoit Mandelbrot's Ted Lecture