Let’s play with catastrophe theory. I don’t know if you followed the introduction, but we’re going to imagine an organization whose learning happens through an interplay between storytelling and self-organization, where information communication occurs through forms of sociocratic double linking; an organic organization (not rationalized in the industrial, Cartesian sense) that takes multiple forms (like a crystal or a termite mound). This is where I call upon the catastrophe theory of René Thom: how to grasp somewhat the different forms and different movements that this organization will operate to deploy itself (since the initial subject is indeed large-scale organizations). We’ll be able to discuss many other very concrete points later on like remote work, office organization, off-shore, etc but here I want to begin a somewhat theoretical and risky approach..

Risky because catastrophe theory is subject to numerous criticisms; because I’m not at all at all a mathematician so I’ll probably make some big errors; because it seems more like an intellectual game than anything else and – cherry on top – I have strictly to this day no idea of the concrete application of this reflection at my operational level.

If you’re willing to continue despite all this, first of all you need to dive a bit into this theory that caused so much discussion in the seventies only to almost disappear since. I recommend you start with this introduction to the philosophy of catastrophe theory, or this video, ultimately perhaps read this rather short pdf, or quite simply this page web.

Catastrophe theory should rather be understood as the theory of changes in form

To have a few pointers in hand: a catastrophe is an event that emerges, a change in situation: attractions, forces present 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 the soft sciences, we won’t just find formulas (which I’m quite incapable of understanding), but also 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’ll see them below. Zeeman, a follower of Thom, proposes numerous applications of catastrophe theory: to prison revolts, to stock market crashes, etc, etc, to the behavior of an angry or frightened dog. So naturally sociology and psychology seized upon catastrophe theory, changes in form, and we’ll try to use it to think about the movements and changes in form of an organization. However, we often read that the quantitative application of catastrophe theory to human sciences is a dangerous exercise, let’s live dangerously.

What should we look for in it?

What am I going to draw from this theory (I’m sharing my “fresh” thinking with you and perhaps in a few months this path will prove sterile)?

• I’m going to look for a set of forms and movements that allow us to better perceive the organization, and thus propose alternative tooling to the hierarchical, flat and mechanical vision that we’re usually offered.
• I’m going to look for verbs and words, metaphors that we can integrate much more easily as organizational patterns (you’ll see below the “fold” or “the gather”).
• I’m going to look for an impression, a sketch of a Japanese painting, a contemplative side in the broad outlines of organizational forms. I don’t want to fall back into the trap of a rule that says if such a singularity occurs then you’ll necessarily obtain such a 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 primary approach to accomplish in order to reveal its nature. We must reject as illusory this primitive and quasi-cannibalistic conception of knowledge, which wants knowing a thing to require beforehand that we reduce it to pieces”.

Elementary catastrophes and organizations

In the table on the left that comes from this page web you see the seven elementary catastrophes. Each catastrophe, singularity, is triggered by a certain number of parameters and produces certain variables, forms. We say there are seven elementary catastrophes, elementary because we consider few input parameters (from one to two). You’ll also observe– in the table still – that we can attach to each of the catastrophes a spatial and temporal interpretation (through a verb). Thom deliberately seeks – in agreement with the pre-Socratics: Heraclitus and his crew (I dared) – to express his ideas through words and images from life.

“Our models, writes Thom, attribute all morphogenesis to a conflict, to a struggle between two or more attractors; we thus rediscover 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 words of human or social origin like conflict, injustice … to explain the appearances of the physical world. Quite wrongly in our view, because they had this profoundly correct intuition: the dynamic situations governing the evolution of natural phenomena are fundamentally the same as those governing the evolution of man and societies, thus the use of anthropomorphic words in Physics is fundamentally justified”.

(have fun with these applets (so 90’s) on catastrophe theory)

In order of increasing complexity:

The fold

The first of the catastrophes is the “fold”. Imagine a sheet that you fold. There’s an “end”, a “finish”. We associate the verb “to finish”, or “to begin”, with the fold, it ends or begins. There’s a single parameter, we’re 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-Socratic who brought their mathematical analyses back to images that we can naturally grasp. So therefore 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 cases of edge, of end, the organization operates a fold, but a clean fold. A singularity occurs that triggers a result (the fold).

The gather

The gather is the fold of 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’s with the gather 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’m incapable of mastering it. But I can wonder about the forces and attractions that make me evolve on the gather and tip to one side or the other.

For example: the gather 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 on a team, and they are more or less co-located. With these different parameters and their intensity we’ll describe a more or less abrupt gather (one output variable) that will describe the functioning of communication within the team. Will it slowly crumble, will it suddenly break, at what point must we generate a new team.

The key words are capture, break: we cross the summit of the gather, 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 (as I told you you can always play with applets like this one on the swallowtail, they’re really very useful), there’s a sort of superposition, which we can perceive as a tearing or a – on the contrary– a sewing. There are three input parameters and one output variable (I’m writing this for those who understand something about it).

So we evoke problems of superposition, overlap, tension, tearing within the company. Two product lines that overlap, should we merge them, sew them? At what point does this product, this range, tear in two (same for teams, again). I’m not going to dig deeper today 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’m now going to limit myself to the associated verbs, the forms are becoming complicated and I haven’t yet sufficiently integrated the associated model… What’s interesting in the butterfly (four parameters! and still one output variable) is the idea of a hidden surface, covered, a pocket, that flakes, exfoliates, that is peels off in layers. 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’m 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 about the acquisition of subsidiaries, the covering of sectors, but also there the sudden collapse of a wave having reached its crest, catch the notion of vault.
• The hair (elliptic umbilic): Sting, penetrate, plug.
• The mushroom (parabolic umbilic): Break, eject, launch, pierce, cut, bind, open, close.

As for knowing what this can be used for

I still don’t damn well know on the operational level. But I appreciate finding myself equipped with a glossary to describe the movements and changes of companies. From this glossary I can draw lessons, intuitions and a way of understanding the world and the life of organizations. A much more real and effective vision than a table of numbers and/or a hierarchy. Because this is indeed about verbs, actions, movements. If I believe Thom, and if his theory has been seriously shaken, it hasn’t been annihilated and is beginning to enjoy a renewed consideration, this is indeed the basis of all forms of change in nature. Isn’t that mesmerizing?

We talk a lot about holacracy, I haven’t yet tasted its joys, but it’s typically the kind of context where this approach can take on its full meaning: a guide in the form of verbs and images from nature to understand and follow the dynamics of an organization, its changes in form.

Series on organizations

0 - premises: Large-scale Agile: it’s clear as crystal

1 - thinking about your organization: introduction

2 - thinking about your organization: catastrophe theory

3 - thinking about your organization: in the field