# Catastrophe Theory (Thom)

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Contributed by: Ed Walters

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 Summary

### What is the Catastrophe Theory? Description

Catastrophe Theory (CT) (René Thom) is a mathematical treatment of continuous action producing a discontinuous result. This theory is related to Chaos Theory. Although it was developed quite separately, it is now seen as a part of Chaos Theory.

Although of a highly mathematical nature, the essence of CT is: to understand change and discontinuity in systems. If a System is ‘at rest’ (ie not undergoing change), then it will tend to occupy a preferred stable state, or at least a defined range of states (Outcome Basin). If a System is subjected to change forces, then the System will initially try to react in such a way that it absorbs the stresses. Furthermore, if it is given the chance, the system will attempt to re-gain its preferred stable state. If, however, the change forces are so strong that they can't be absorbed, then a Catastrophic Change may occur and a new preferred stable state or range of states is established. There is no continuous way back to the 'old' stable state.

An analogy demonstrates the principle. Imagine that a bottle is placed on a desk. It is in a stable state, not changing, what is called Stable Equilibrium. Now imagine pushing the neck of the bottle away from you slowly with your finger, not too far. It is now undergoing change but the bottle is absorbing the change in a continuous manner. It is in Unstable Equilibrium; if you release your pressure, the bottle will revert towards its stable and preferred position. However if you continue to push the neck of the bottle, at some point it will fall. It is now in a new stable equilibrium state. A Catastrophic Change has occurred. A discontinuous change has happened: once the bottle started to fall over, there was no intermediate stable state available until the bottle had hit the desk.

Thom’s ideas mean that Systems may change through a combination of continuous and discontinuous change patterns. This is related to Chaos Theory because the bottle is either standing up or is lying down. These positions describe the possible Outcome Basins (see Chaos Theory). There are positions which it will never be in, because they are positions of intrinsic instability.

There are seven elementary catastrophes: fold, cusp, swallowtail, butterfly, hyperbolic umbilic, elliptic umbilic, and parabolic umbilic. Sub-specializations of Catastrophe Theory include: Bifurcation Theory, Nonequilibrium Thermodynamics, Singularity Theory, Synergetics, and Topological Dynamics.

### Origin of the Catastrophe Theory. History

Now regarded as part of Chaos Theory, Catastrophe Theory was developed in the late 1960s and presented quite independently in 1972 by the mathematician René Thom in his book: "Structural Stability and Morphogenesis". Thom hoped to be able to predict the behavior of complex 'chaotic' systems. It was further developed on a more pragmatic level by E.C. Zeeman in the 70s.

### Usage of the Catastrophe Theory. Applications

The method can be used to understand and to predict the behavior of complex systems. Such as:

• Stock exchanges.
• Locust infestations.
• Biological change.
• Behavior of bridges.
• Attempts to apply Thom's theories to organizations so far had little real success, due to the large number of variables involved.

### Steps in the Catastrophe Theory. Process

CT has many implications for the discipline of Change Management and Organizational Development.

There is a form of change which is smooth, continuous and incremental. This is the general form of change under Business Process Improvement initiatives (BPI) such as Kaizen, Total Quality Management (TQM) and Six Sigma. In CT terms, this is change over a pre-defined existing stable surface.

There is another form of change which is ‘catastrophic’, abrupt, radical, a fundamental departure from what went on before the change. This type of change is quite often the consequence, for example, of Business Process Reengineering (BPR). This type of change is not ‘continuous’ - in CT terms there is a catastrophic change to a new definition of stability.

‘Real’ change is therefore more like BPR. Else there is simply improvement. Which of course may be all that's needed to solve the specific problem! The challenge for change specialists is in deciding when radical change is needed versus an incremental improvement. But the choice is not straightforward since radical change will inevitably result in a period of 'Chaos', while the ‘new’ stability is found and defined. This ties up with the recognized 'unfreezing/freezing' methods of Change Management.

And then of course radical change may be forced upon the organization at times. And there may be no smooth (continuous) way of taking the organization from where it is, towards where it must be, so it is futile to assume that such a path is available.

### Strengths of the Catastrophe Theory. Benefits

• The ideas help to understand the real experience of Change Management and the ideas in Chaos Theory. CT shows why real Change is a hazardous business.
• It does away with the thought that organizations can be varied along 'spectrums' of variable values. There are probably only a few really stable combinations available.
• The theory shows why change cannot be 'managed' as such, but may be influenced.
• The theory deals with the idea of 'form' (Gestalt) and change of form. A novel way perhaps to view organizations.

### Limitations of the Catastrophe Theory. Disadvantages

• The significance of Thom's work to understand organizational behavior is more qualitative than quantitative at the moment.
• Predicting the behavior of even the simplest complex systems still remains a difficult challenge.
• Thom failed in his aspiration to describe complex systems where there are many (more than 5) significant variables. Predicting the behavior of very complex systems (organizations) is likely to remain impossible forever.

Book: Alas all reading materials that go beyond what's written here, quickly become deep in Mathematics!

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