Chapter 3: Dynamics of Forms

“The stable state of a living organism is to be dead” – Schrödinger

From this irruption into the world of nature we will keep two elements in mind: on one hand, the forms taken by nature are often dependent on context and beyond that a macroscopic pattern varies greatly. On the other hand, concerning structures, everything is a question of energy, of energy optimization.

Regarding the question of forms and the lessons for those of our organizations, we will take a detour through René Thom’s catastrophe theory, or rather it will serve as an alibi to break away from Cartesian thinking, and think in verbs (dynamics, energy again).

The aspects of energy optimization seem essential to me. They are everywhere in our organizations: optimization of the communication flow, optimization of the value creation flow, optimization of people’s involvement (energy), etc… Finally, and not the least, optimization of pure energy resources, those of the planet.

Catastrophe Theory

I’m advancing on mined terrain. Catastrophe theory is subject to numerous criticisms; I am not at all (at all) a mathematician. I just wish to take advantage of this theory, and especially the images it conveys to break away from formulas and appeal to verbs. More clearly: it doesn’t matter to truly understand how to apply this theory which doesn’t really apply anyway (hence the heavy fire of criticisms). What matters to me is to start thinking differently about the forms of our organizations: as matter that seizes opportunities, a matter not square, but opportunistic by following principles and not overly precise rules. It is often different while being common. It is not thought of in terms of solving equations or calculations, but in energy and thus in dynamics. The verbs of catastrophe theory call for understanding one’s organization not as an assembly of calculations, but as a magma subject to dynamics.

Theory of Changes in Form

Catastrophe theory should rather be understood as the theory of changes in form. A catastrophe, for René Thom, is an event that emerges, a change in situation: attractions, forces in presence that trigger a change in form. René Thom distinguishes seven types of elementary catastrophes and associated models. A strong criticism against this theory is precisely what I like about it: its openness to soft sciences, we won’t simply find formulas (which I am quite incapable of understanding), but especially verbs to represent these forces and changes in action.

Instead of catastrophes let’s say singularities: when something singular happens the situation changes. According to the number of parameters and variables, as long as we remain in an elementary domain, Thom indicates seven singularities and describes them, we will see them below. Zeeman, a follower of Thom, proposes numerous applications of catastrophe theory: to prison revolts, to stock market crashes, to the behavior of an angry or frightened dog, etc. So naturally sociology and psychology have seized upon catastrophe theory, changes in form, and we will try to use it to think about the movements and changes in form of an organization. However, one often reads that the quantitative application of catastrophe theory to human sciences is a dangerous exercise, I believe we just need to be careful between intuition, inspiration and playing sorcerer’s apprentices.

I will seek in it a set of forms and movements that allow us to better perceive the organization, and thus propose an alternative toolset to the hierarchical, flat and mechanical vision that we are usually offered. I will seek in it verbs and words, metaphors that can be integrated much more easily as organizational patterns (you will see below the “fold” or “the gather”). I will seek in it an impression, a sketch of a Japanese painting, a contemplative side in the broad outlines of the forms of organizations. I don’t want to fall back into the trap of a rule that says if such singularity occurs then we will necessarily obtain such type of organization, just an overall understanding of the dynamics at play. To quote Thom: “This goes against the currently dominant philosophy, which makes the analysis of a system into its ultimate constituents the first step to be accomplished to reveal its nature. We must reject as illusory this primitive and quasi-cannibalistic conception of knowledge, which wants knowing a thing to require first that it be reduced to pieces.” We are in the advent of a holistic approach to the organization. We must see the whole. Hence an approach by silhouette, by dynamics. This is what Thom highlights 40 years ago.

Elementary Catastrophes and Organizations

In the table above, you see the seven elementary catastrophes. Each catastrophe, singularity, is triggered by a certain number of parameters and causes certain variables, forms. We say there are seven elementary catastrophes, elementary, because we consider few input parameters (from one to two). You will also observe – in the table still – that we can adjoin to each of the catastrophes a spatial and temporal interpretation (through a verb). Thom deliberately seeks – in agreement with the pre-Socratics – to express his ideas through words and images of life.

“Our models, writes Thom, attribute all morphogenesis to a conflict, to a struggle between two or more attractors; we thus find the ideas (2,500 years old!) of the first pre-Socratics, Anaximander and Heraclitus. These thinkers have been accused of primitive confusionism, because they used terms of human or social origin like conflict, injustice… to explain the appearances of the physical world. Quite wrongly in our opinion, because they had this profoundly correct intuition: the dynamic situations governing the evolution of natural phenomena are fundamentally the same as those that govern the evolution of man and societies, thus the use of anthropomorphic terms in Physics is fundamentally justified.”

Elementary Catastrophes in Order of Increasing Complexity

The Fold

The first of the catastrophes is the “fold.” Imagine a sheet that you fold. There is an “end,” a “finish.” We associate the verb “to finish,” or “to begin,” with the fold, it finishes or begins. There is a single parameter, we are on one side or the other of the fold, so a single result, a single output variable. If I try to take an image: once again, this is what I like about Thom’s approach, his desire to return to the pre-Socratics who brought their mathematical analyses back to images that one can naturally grasp. So as an image we observe communication within a team. This team grows, grows, grows: that’s the parameter, we regularly add 1 member to the team. Suddenly we reach a point, the catastrophe, the singularity, and communication changes completely: it’s the fold. We’ve passed to the other side. In simple edge cases, the organization operates a fold, but a clean fold. A singularity occurs which triggers a result (the fold).

The Cusp

The cusp is the fold of the fabric in your shower curtain. But this fold is a curve. We imagine a ball that passes from one side or the other of a small hill. Everything depends on the parameters that propel the ball: it will pass quickly or climb up to come back down without crossing the Rubicon. It is with the cusp catastrophe that Zeeman applies the theory to the dog: between fear and aggression: what parameters and according to what forces will the dog go from fear (flight) to aggression (attack). We enter the mathematical aspect of the theory, and I am incapable of mastering it. But I can wonder about the forces and attractions that make me evolve on the cusp and tip from one side to the other. For example: the cusp has two input parameters, we could say again the size of a team, and let’s say its co-location. That is, we have more or fewer people in a team, and they are more or less co-located. With these different parameters and their intensity, we will describe a more or less abrupt cusp (one output variable) which will describe the functioning of communication within the team. Will it slowly crumble, will it suddenly break, at what moment should we create a new team.

The keywords are capture, break: we cross the top of the cusp, passing to the other side: we generate, we become, we unite. I’m talking about teams and communication, you can envision the expansion of subsidiaries across a continent, the different departments of a solution, the life of a company product, etc.

The Swallowtail

Think of a swallow’s tail: at the intersection, there is a kind of superposition, which can be perceived as a tear or a – on the contrary – a seam. There are three input parameters and one output variable (I write this for those who understand something). We therefore evoke problems of superposition, overlap, tension, tearing within the company. Two product lines that overlap, should we merge them, sew them together? At what moment does this product, this line, tear in two (same for teams, again). I won’t dig deeper and I’ll let you find the parameters that will govern this change in form, with the swallowtail there must be three.

The Butterfly

I will now limit myself to the associated verbs, the forms become complicated and I haven’t yet integrated the associated model enough… What is interesting in the butterfly (four parameters! and still one output variable) is the idea of a hidden surface, covered, a pocket, which flakes, exfoliates, that is to say peels off in lamellae. So it empties or fills. Another metaphor, but also therefore a theory allowing us to apprehend the movements of the organization.

The last three elementary catastrophes are a bit more complex because they propose two output variables.

The Wave, the Hair, the Mushroom

Same, for now I have the impression that it becomes vain for me to understand the mathematical aspects and the calculation of these different forms. I am only interested in the verbs that can give me a way to apprehend this theory and project it onto my world.

• The wave (hyperbolic umbilic): Read break, collapse, cover for the wave. Think of the acquisition of a subsidiary, the coverage of a sector, but also there the sudden collapse of a wave having reached its crest, grasp the notion of vault.
• The hair (elliptic umbilic): Prick, penetrate, plug.
• The mushroom (parabolic umbilic): Break, eject, launch, pierce, cut, bind, open, close.

What to Do With All This

Think of your organization as a whole, governed by events that trigger forms and dynamics. If you are more of a mathematician than I am you can use formulas, but I think that tensions are sufficient to understand that we are approaching, perhaps, a singularity, and therefore a change in form.

Keep in mind that the forms most adapted to your organization are probably the most economical in energy. For this, let the natural form emerge. Used thus, the word natural implies the simplest, the most opportune, the one that requires the least energy, and offers the best optimization of context.

In this sense the randomness that prefigures a termite mound underlines the interest of leaving time for emergence. Nothing against the repetition of patterns, which will be good for propagating at low cost your energy (communication, know-how, etc.), but know how to place the cursor in the right place: these are the least fixed, completed pieces of your organization that will be the simplest to evolve.

Think of crystal twinning to think of transverse currents in the organization (surprisingly these twins look a lot like the guilds proposed by an organization like Spotify).