13 Oct 2015 17:09 IST

All about the butterfly effect

This Chaos theory concept has important ramifications in business and manufacturing world

If your boss ever asks you to keep in mind the ‘butterfly effect’, chances are, he has just returned from a business conference. Someone might have made a presentation about a sudden loss of market share, arguing that a change in packaging led to a ‘butterfly effect’, causing the loss. So your boss must have been intrigued and decided to use the term at the next opportunity.

Say, at a meeting, you are explaining a minor error or some trivial matter. He doesn't like it. He wants to say ‘Small things matter, so pay good attention to them. Be more careful’. Perhaps he wants to say ‘Don’t be sloppy’. Instead, he asks: “Haven’t you heard of the butterfly effect?” He is bored of plain-speak. Alternatively, he thinks he can criticise you sophisticatedly. Impressing his superiors simultaneously is just the icing on the cake.

Small variations, big changes

The butterfly effect is an important concept in Chaos theory, in mathematics. It refers to ‘sensitive dependence on initial or starting conditions’. According to this theory, certain kinds of systems show large changes in their outputs due to small variations in their inputs, or the conditions, at the start.

The effect was noticed during a weather model simulation run by American mathematician, Edward Norton Lorenz. When systems have non-linear (effect disproportional to its cause and nature of the cause) or time-dependent (relationship between cause and effect changing with time) character, they may display the butterfly effect.

The butterfly effect is named after the oft-heard phenomenon — the formation of a severe hurricane being dependent on whether a single butterfly had fluttered its wings days or weeks earlier. Whether this has actually happened or not is unknown. But that is another story.

We see such events in nature. A rock rolling down a slope can cause a landslide or do no harm — small changes in its initial direction can make a big difference. Small changes in temperature or the dwindling of some predator species can affect life forms, depending on where they occur.

The rumour mill

We see such effects in social situations too. If a rumour is heard initially by someone who believes in it and is influential, it can spread and can cause major events, like riots. If the same rumour is heard by more diligent, balanced people in its formative stage, it may get squashed early enough to avoid trouble.

The butterfly effect is unpredictable because the underlying cause and effect relationships are too many and too fast-changing to allow any real-time calculation. Algorithmic trading of securities is banned in some places for this reason. It can stress out the automated markets in unpredictable ways. Weather systems, too, are hugely complex, full of a large number of interdependent variables that are changing rapidly over time.

Three conditions

For the butterfly effect to take hold, the following conditions are necessary:

1. There are a large number of independent and interdependent variables and they have ‘many to many’ relationships

2. The cause and effect relationships depend on the value of variables and also on time

3. It is not possible to confine ‘unwanted’ variations; neither is it possible to design processes which are tolerant to small changes in inputs

Our modern lives depend on systems that fulfil the first two conditions. The manufacture and use of automobiles, the aviation industry, the Internet and the financial sector have a very large number of variables and are characterised by complex and changing relationships. Yet they operate mostly without any butterfly effect. This is a testimony to human ingenuity in ensuring that the third condition does not occur.

When your boss, or his boss, asks you to keep in mind a likely Butterfly Effect, pay heed. You might be able to contribute to the avoidance of the third condition, whether he had this in mind or not.