Scientific confirmation of this principle began in 1916, when Arthur Gates, a psychologist at Columbia University, created an ingenious study to further Bacon’s insight. If someone is trying to learn a piece of text from memory, Gates wondered, what would be the ideal ratio of study to recitation (without looking)? To interrogate this question, he had more than 100 schoolchildren try to memorize text from Who’s Who entries. He broke them into groups and gave each child nine minutes to prepare, along with specific instructions on how to use that time. One group spent 1 minute 48 seconds memorizing and the remaining time rehearsing (reciting); another split its time roughly in half, equal parts memorizing and rehearsing; a third studied for a third and recited for two-thirds; and so on.
After a sufficient break, Gates sat through sputtered details of the lives of great Americans and found his ratio. “In general,” he concluded, “best results are obtained by introducing recitation after devoting about 40 percent of the time to reading. Introducing recitation too early or too late leads to poorer results.” The quickest way to master that Shakespearean sonnet, in other words, is to spend the first third of your time memorizing it and the remaining two-thirds of the time trying to recite it from memory.
--Benedict Carey, NYT Magazine, on the golden ratio