When a drip becomes a flood

I have to start with a small confession - outside of work I dabble in maths for a hobby.

Recently I’ve been looking at exponential functions, which are concerned with modelling growth and decline. They use a special little number called ‘e’, which is like π, turning up in all sorts of places and making the most amazing connections between things. The key idea is that in an exponential pattern, the rate of change is proportional to the size already reached.

All really obscure, you might think, until I tell you that these equations determine things like population growth, compound interest, radioactive decay, the spread of stories on the internet, and how coffee cools in a mug.

A colleague uses a great example to show how exponential patterns can be very surprising. Imagine you are in Wembley Stadium and a water pipe develops a small leak on the pitch. In the first 30 seconds, only a cubic millimetre of water leaks out, but the rate of leakage increases over time, such that the amount of water in the stadium doubles every 30 seconds.

So how long would it be before the stadium was filled with water and everybody drowned? This requires 1.2 million cubic metres of water, which is a million billion times the amount which leaked out in the first 30 seconds. You probably think you’d have days to escape, but the answer is… 25 minutes.

Even more surprising is that three minutes before everyone drowns, there is only three feet of water covering the pitch. Exponential situations can start really small, and look for ages like there’s not much happening. But the bigger it gets, the faster it grows, so they suddenly leap ahead with terrifying speed and consequences.

So how is this relevant to retailing? Well, we have seen a very clear example of exactly this process in the entertainment retail sector. In 1999, when the internet got going, I was just leaving Virgin. We saw then how this new medium could overturn the music and similar markets, and maybe make our stores obsolete.

But for a long time nothing much seemed to happen. The threat looked overstated, and it seemed things wouldn’t change much after all. Then, suddenly, the physical retailers were overwhelmed - Virgin was gone, HMV in trouble and now Game has crashed.

In reality, the internet-based market was growing exponentially all the while, but in the early years it was too small to notice. By the time it was noticeable, things were at the three feet of water stage and it was too late.

I have to tell you that it’s happening again. New technology is here, with mobile at its heart, which will radically reshape the retail landscape. Its usage is tiny, but you can bet it is growing exponentially.

Yet what I am seeing from retailers is inertia, or simple aversion to trying something that looks risky and new. We need to embrace this stuff and make it part of our opportunity, before it threatens to engulf us all.

• Simon Burke is chairman of HobbyCraft.