## Posts Tagged ‘**Nonlinearity**’

## On the nonlinearity of organisational phenomena

### Introduction

Some time ago I wrote a post entitled, Models and Messes – from best practices to appropriate practices, in which I described the deep connection between the natural sciences and 20^{th} century management. In particular, I discussed how early management theorists took inspiration from physics. Quoting from that post:

Given the spectacular success of mathematical modeling in the physical and natural sciences, it is perhaps unsurprising that early management theorists attempted to follow the same approach. Fredrick Taylor stated this point of view quite clearly in the introduction to his classic monograph, The Principles of Scientific Management…Taylor’s intent was to prove that management could be reduced to a set of principles that govern all aspects of work in organizations.

In Taylor’s own words, his goal was to “*prove that the best management is a true science, resting upon clearly defined laws, rules and principles, as a foundation. And further to show that the fundamental principles of scientific management are applicable to all human activities…*”

In the earlier post I discussed how organisational problems elude so-called scientific solutions because they are ambiguous and have a human dimension. Now I continue the thread, introducing a concept from physics that has permeated much of management thinking, much to the detriment of managerial research and practice. The concept is that of *linearity*. Simply put,* linearity is a* *mathematical expression of the idea that complex systems can be analysed in terms of their (simpler) components. *I explain this notion in more detail in the following sections.

The post is organised as follows: I begin with a brief introduction to linearity in physics and then describe its social science equivalent. Following this, I discuss a paper that points out some pitfalls of linear thinking in organisational research and (by extrapolation) to management practice.

### Linearity in physics and mathematics

A simplifying assumption underlying much of classical physics is that of *equilibrium *or* stability*. A characteristic of a system in equilibrium is that it tends to *resist change*. Specifically, if such a system is disturbed, it tends to return to its original state. Of course, physics also deals with systems that are not in equilibrium – the weather, or a spacecraft on its way to Mars are examples of such systems. In general, non-equilibrium systems are described by more complex mathematical models than equilibrium systems.

Now, complex mathematical models – such as those describing the dynamics of weather or even the turbulent flow of water- can only be solved numerically using computers. The key complicating factor in such models is that they consist of many interdependent variables that are combined in complex ways. 19^{th} and early 20th century physicists who had no access to computers had to resort to some tricks in order to make the mathematics of such systems tractable. One of the most common simplifying tricks was to treat the system as being linear. Linear systems have mathematical properties that roughly translate to the following in physical terms:

- Cause is proportional effect (or output is proportional to input). This property is called
*homogeneity*. - Any complex effect can be expressed as a sum of a well defined number of simpler effects. This property is often referred to as
*additivity*, but I prefer the term*decomposability*. This notion of decomposability is also called the*principle of superposition*.

In contrast, real-life systems (such as the weather) tend to be described by mathematical equations that do not satisfy the above conditions. Such systems are called *nonlinear*.

Linear systems are well-understood, predictable and frankly, a bit boring – they hold no surprises and cannot display novel behaviour. The evolution of linear systems is constrained by the equations and initial conditions (where they start from). Once these are known, their future state is *completely* determined. Linear systems cannot display the range of behaviours that are typical of complex systems. Consequently, when a complex system is converted into a linear one by simplifying the mathematical model, much of the interesting behaviour of the system is lost.

### Linearity in organisational theories

It turns out that many organizational theories are based on assumptions of equilibrium (i.e. that organisations are stable) and linearity (i.e. that the socio-economic forces on the organisation are small) . Much like the case of physical systems, such models will predict only small changes about the stable state – i.e. that “business as usual” will continue indefinitely. In a paper published in 1988, Andrew Abbott coined the term *General Linear Reality* (GLR) to describe this view of reality. GLR is based on the following assumptions:

- The world consists of unchanging entities which have variable attributes (eg: a fixed organisation with a varying number of employees)
- Small changes to attributes can have only small effects, and effects are manifested as changes to existing attributes.
- A given attribute can have only one causal effect – i.e. a single cause has a single effect.
- The sequence of events has no effect on the outcome.
- Entities and attributes are independent of each other (i.e. no correlation)

The connection between GLR and linearity in physics is quite evident in these assumptions.

### The world isn’t linear

But reality isn’t linear – it is very non-linear as many managers learn the hard way. The problem is that the tools they are taught in management schools do not equip them to deal with situations that have changing entities due to feedback effects and disproportionately large effects from small causes (to mention just a couple of common non-linear effects).

Nevertheless, management research is catching up with reality. For example, in a paper entitled Organizing Far From Equilibriium: Nonlinear changes in organizational fields, Allan Meyer, Vibha Gaba and Kenneth Collwell highlight limitations of the GLR paradigm. The paper describes three research projects that were aimed at studying how large organisations adapt to change. Typically when researchers plan such studies, they tacitly make GLR assumptions regarding cause-effect, independence etc. In the words of Meyer, Gaba and Collwell:

In accord with the canons of general linear reality, as graduate students each of us learned to partition the research process into sequential stages: conceptualizing, designing, observing, analyzing, and reporting. During the conceptual and design stages, researchers are enjoined to make choices that will remain in effect throughout the inquiry. They are directed, for instance, to identify theoretical models, select units and levels of analysis, specify dependent and independent variables, choose sampling frames, and so forth. During the subsequent stages of observation, analysis, and reporting, these parameters are immutable. To change them on the fly could contaminate data or be interpreted as scientific fraud. Stigma attached to “post hoc theorizing,” “data mining” and “dust-bowl empiricism” are handed down from one generation of GLR researchers to the next.

Whilst the studies were in progress, however, each of the organisations that they were studying underwent large, *unanticipated* changes: in one case employees went on mass strike; in another, the government changed regulations regarding competition; and in the third boom-bust cycles caused massive changes in the business environment. The important point is that these changes invalidated GLR assumptions completely. When such “game-changing” forces are in play, it is all but impossible to define a sensible equilibrium state to which organisations can adapt.

In the last two decades, there is a growing body of research which shows that organizations are complex systems that display emergent behaviour. Mainstream management practice is yet to catch up with these new developments, but the signs are good: in the last few years there have been articles dealing with some of these issues in management journals which often grace the bookshelves of CEOs and senior executives.

### To conclude

Mainstream management principles are based on a linear view of reality, a view that is inspired by scientific management and 19^{th} century physics. In reality, however, organisations evolve in ways that are substantially different from those implied by simplistic cause-effect relationships embodied in linear models. The sciences have moved on, recognizing that most real-world phenomena are nonlinear, but much of organisational research and management practice remains mired in a linear world. In view of this it isn’t surprising that many management “best” practices taught in business schools don’t work in the real world.

**Related posts:**

Models and messes – from best practices to appropriate practices