In the 50s William Hick (a British psychologist) examined the speed of perception and information processing. In his experiments he created tasks where the subjects had to select a specific information from a list of information. He measured the change of the time needed for a selection, when the list of information was reduced in size. . The evaluations of the experiments resulted in a logarithmic curve. He approximated the curve with the following formula for the rate of gain of information:
Formula in MathML format (not all browsers support this by now):
Formula in PNG image format:
The entrophy H is derived from the sum of the probabilities (pi) of possible selections multiplied by a logarithmic value (where n is the number of choices). The logarithm of this suggests that human beings do not perform a linear search in lists. We rather try to divide them into categories. This allows us to exclude half the possibilities at each step.
In HCI Hick’s law is used to compare different menu layouts in graphical user interfaces in order to determine which one is most effective.
: William Edmund Hick. On the rate of gain of information. Quarterly Journal of Experimental Psychology, 4(1):1126, 1952.