Imagine you are choosing between two proposed road-improvement plans, but have the budget for only one. Both of the roads mooted for improvement are 20 miles long, and your sole aim is to reduce average journey time by as much as possible. Which would you choose?
Someone travelling slowly to begin with has more time on the road to profit from any gain in speed
1) Improving Road A, which increases the average speed from 20 to 25mph (i.e. 25 per cent faster).
or
2) Improving Road B, which increases the average speed from 40 to 65mph (62.5 per cent faster).
The majority of people, including many experts, instinctively plump for B. Unfortunately they are wrong. They needn’t feel bad about it, however, as a similar version of this conundrum, posed by Max Wertheimer, briefly bamboozled Einstein.
Improving Road A cuts 12 minutes off the journey time, while improving Road B saves only 11 minutes and 32 seconds. Weird, no? Well, only until you remember that someone travelling slowly to begin with has more time on the road to profit from any gain in speed. For instance, increasing the average speed on a 20-mile road from 100mph to the speed of light would save you slightly less than 12 minutes, whereas increasing the speed from 1mph to 5mph would save you the better part of a day. So, to anyone bemoaning the loss of Concorde, I say buy a scooter. Over the course of your life, it will save far more time.
I thank my former colleague Pete Dyson for alerting me to this seeming paradox, which of course isn’t a paradox at all. It is a problem in perception (or perhaps a failure to apply insights from the work of Gerd Gigerenzer to the comparative presentation of statistics).
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