Time for your moment of science math quiz.
Ready? Which of the following numbers is larger: 90 or 50? 16 or 14? 9 or 7?
Very good, you get an A. However, this wasn’t really a math quiz at all, but a psychology quiz.
You might have noticed, if you are very perceptive, that it takes a little bit longer to decide which of two numbers is larger the closer they are to each other. Big differences, such as 1 versus 8, are more quickly recognized than small differences, such as 6 and 4. This is called the “distance effect,” and was first documented by two psychologists named Moyer and Landaur back in the sixties.
The effect has since been confirmed many times in laboratory conditions, where peoples’ responses are carefully measured. There is as much as a tenth of a second pause produced by closing in the two test numbers, compared to the speed with which subjects can distinguish them when they are far apart.
What does this tell us?
The standard interpretation for the “distance effect” is that, in some sense, we all have a mental “number line.” That’s the line the teacher drew on the blackboard back in grade school, with zero at one end, then one, two, three, and so on. When asked to judge the difference between numbers, we may actually be judging magnitudes on this line. It’s as if we had to view two physical lengths, like a ruler and a yardstick, and compare them. This, of course, is much easier to do when the sizes are very different.