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Second Derivative Stories

At school, if you do A-level maths, you will do calculus. One of the first things that you encounter are derivatives, which are the measure of the rate of change of some variable. Of course a derivative or rate of change may not be constant over time, so the second derivative will be used to show how the rate of change is changing over time.

With me so far? This may sound esoteric, but it turns out that second derivative headlines; such as changes in the rate of inflation (inflation is a first derivative, so changes in it are second derivative, are favorites for headline writers.

I decided to pick up ones that I spotted from the BBC web site, although special mention must go to

Unemployment rate slows but pay rises are lowest on record

Hugo and I originally thought this was two second derivatives in one headline, but the first (unemployment rate slows) looks only to be a first derivative, because 'unemployment rate', is not a 'changing of one thing with respect to another' sort of rate, so not a first derivative.


East European worker influx slows

Influx us a first derivative, so if it changes, such as slows, its a second derivative

Pace of economic slide 'to ease'

which was subsequently changed to

UK economy continues to contract 

Economic slide is a first derivative, so easing is a change in the slide over time: second derivative

The new headline removes the second derivative component, and so removes some of the slighly more positive spin.


Decline in UK car output slowing


First 2009 rise for house prices 

A change in the rate of house price inflation is a second derivative

Swine flu incidence 'is slowing'

100,000 new cases last week, 110,000 new cases this week, so its still rising, buts apparently the amount that it is rising each week is going down. Second derivative.
Indeed, when reported on radio 4, the newsreader said "The rate of increase is slowing down", which is as good a second derivative as you can get

Rate of job cutting 'is slowing'

OK if you interpret job cutting as the first derivative of the number of jobs.

England youth drop-out rate rises

A rate is almost by definition a first derivative, so if it rises, thats a second derivative

Antarctic glacier 'thinning fast'

"One of the largest glaciers in Antarctica is thinning four times faster than it was 10 years ago." Thinning is a rate of change, so if it is faster now than 10 years ago thats a second derivative.


Decline in UK car output slowing

After a bit of a lull, a return to a classic first seen in July

Growth in UK unemployment slows

Couldn't be better


China economic growth accelerates

And another classic

Jobs market decline 'set to slow'

A good example of where you have to go to a second derivative in order to find a hint of good news in what is essentially still bad news. Don't be fooled... The jobs marker is still declining.

Rise in UK unemployment slowing

Much the same as the previous comment. In this case unemployment is still rising

Greenland ice loss 'accelerating'

Unlike the previous Eco-headline, the second derivative is clear in the headline

Decline in car output rate smallest this year

The headline on the front page was "Decline in car output slows". So in four months this is the third time we have had the headline, but still the car output slows..

UK jobless rise continues to slow

Again, using second derivatives to extract a crumb of comfort out of the worsening economic situation

UK inflation rate falls to 3% in February

Changes in inflation rate are always a good source of second derivatives