American in bad maths shocker

On the way into work this morning I heard an interview with an American diplomat attending the Bali climate change conference. He was being pushed on why the US wasn’t committing to reducing its emissions. Whatever your thoughts on this — I think it’s very important — the thing that struck me was the diplomat’s seeming lack of understanding of maths.

During the interview the interviewer asked, “Will you commit to slowing the rate of increase of emissions?”, or something very much like that. The diplomat then said no, but said they were planning on doing so. During his reply he likened reducing the rate of increase to zero as “stopping at an intersection” — an inaccurate and misleading statement.

Having a zero rate of increase of emissions still means you’re emitting huge amounts of carbon. By definition you’ll be emitting the most carbon ever at that point, and next year you’ll still increase your emissions by the largest amount ever.

In maths terms the increase in emissions is a first derivative and the rate of increase of emissions a second derivative. The best everyday analogue to this is speed and acceleration — themselves first and second derivatives of position.

If you imagine emissions as your distance along a motorway, the increase of emissions is your speed. The rate of increase of your emissions is then your acceleration. In this context, the US is currently accelerating faster and faster.

If they reduce their rate of increase to zero. this is like them stopping accelerating. They won’t have “stopped” as the diplomat would have us believe, but will be hurtling down the motorway at a constant speed — the highest speed they attained during their acceleration.

So, was the diplomat aware of his blunder here? Probably not, though it’s well within the remit of his job to make something unimpressive sound much better than it is.