Hot under the collar about 'exponential'

I read an article about how well the Greens did in the local elections recently and got a bit narked. It wasn't about the main thrust of the article (though I'm doubtful how much council election gains for a small party mean in terms of general elections), but rather as a result of a distinctly painful use of the word 'exponential'.

In his article, Peter Franklin says 'the Greens grew exponentially — doubling their council seats from 240 to 481'. There are two problems with this. One is you can't tell if growth is exponential from two data points. And the other is that exponential growth does not mean large growth, as seems to be thought here.

For something to grow exponentially, each data point (often with this kind of data, separated over a time period such as a week, month, year or as here election period) has to be related to the original value by the exponent of the number of data points. That sounds far more complicated than it really is. If you have N data points then the Nth value should be around x^N, where x is bigger than 1.

A classic example is exponential doubling, where x is 2. In that case, after one time period, the result is twice as much as the original value, after two time periods it's four times the initial value and so on. And yes, if Green councillor growth was to continue to double after the next election we could say there was exponential growth - but not from one election.

Note also that x can be, say 1.005. If there were exponential growth like this, the Green councillor count would go from 240 to 241 in the first time period. That could still be exponential, though we wouldn't know until several time periods had passed.

You might think that this is quibbling about word use, rather like moaning that 'decimation' does not refer to a large reduction, but to a one in ten reduction, as it originally did when the Romans were in the habit of killing off one in ten as a punishment. But decimation isn't a scientific term. Exponential is, and it's a very useful term that shouldn't be diluted.

Journalists, please don't mangle it.

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