Memorising Numbers

Short-term memories are those that we hold in our mind’s eye through active rehearsal. If I tell you a telephone number to call on your cell phone which is in the next room, you will probably store it in your mind through active rehearsal. In order to retrieve the number as you move into the next room, you will find yourself repeating it over and over to yourself. If anything interrupts you on your journey—maybe even the ringing of the telephone you are coming to retrieve—the number is likely to be either mistakenly recalled with the numbers out of order or forgotten completely. When you were told the number, it took the form of a short-term declarative memory: a clear conscious piece of information conveyed to you.In this instance, the telephone number was only intended to be remembered for a short period of time—until you get to the phone and dial it. But if you want to include the number within the list of people you wish to stay in touch with, that episodic memory will have to be transferred into semantic memory: general knowledge learned through repetition. If you dial the number frequently enough it will be transferred into semantic memory. This transition may happen slowly—requiring multiple repetitions—unless the number is very important to you and/or is accompanied by some emotion.349370527222750045468020871345655370067819216523445680 75614503594923400960676590Look at the above string of digits for one minute. Turn away and write down as many as you can remember, starting from the left. How many were you able to come up with? According to the Montreal Cognitive Assessment (MOCA), the Gold Standard among neuropsychological screening tests, your performance was acceptable if you remembered 5 or more. But what is the upper limit of numbers that can be remembered by a group of people randomly chosen?In the 1940s, a Harvard psychologist named George Miller discovered the numerical limit (seven) while designing a jamming signal for the armed forces aimed at disrupting German radio communications. In the process, he measured how people judge the magnitude of various physical stimuli. How loud is it? How bright? Miller found that people’s ability to make judgements across a range of stimuli is limited to about seven alternative states. When Miller measured the capacity of people’s short-term memory for digits, he discovered that it was also seven. He read a string of numbers and asked his subjects to repeat the numbers. He found that most people could repeat strings of five to nine numbers with the rare exception capable of learning strings of ten or more digits (in a few pages, I’ll show you how to repeat more than ten digits on your first try!).Noting that the number seven appeared both in the sensory magnitude rating (how loud?) and the digit span, Miller wrote in 1956 one of the most whimsically titled and famous papers in psychology, “The Magical Number Seven, Plus or Minus Two.” (Interestingly, Miller was not the first to observe this. The nineteenth-century philosopher Sir William Hamilton pointed out that most people experience difficulty with numbers containing more than seven digits: “If you throw a handful of marbles on the floor, you will find it difficult to view at once more than six or seven without confusion.”)Later, research by Miller’s students and colleagues showed that the “magic number seven” applied to digits, words, pictures, and even complex ideas. The take-home message from Miller’s work? The brain works within certain limitations, and these limitations hold true over a wide range of human endeavors.