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You can repeat back a phone number after hearing it once, but not a string of twenty random letters. That limit is one of the most famous findings in psychology, and it is often summed up as "seven, plus or minus two". The number is the part everyone remembers. The more useful idea, for anyone learning chemistry or physics, is what George Miller called chunking. This post explains both, with an example you can try on yourself.
Who was George Miller?
George A. Miller (1920–2012) was an American psychologist. In an obituary in American Psychologist, Steven Pinker ranks him among the most important psychologists of the 20th century, credits him with helping to drive the cognitive revolution and with founding psycholinguistics, and notes that he received the National Medal of Science in 1991. He is most widely known for one paper.
What did "The magical number seven" actually say?
The paper is The magical number seven, plus or minus two: Some limits on our capacity for processing information, published in *Psychological Review* in 1956. It begins with a memorable opening line: "My problem is that I have been persecuted by an integer." The full text is free to read.
Miller looked at two kinds of experiment that both seemed to give a limit of about seven. In *absolute judgment*, people label a single stimulus, such as a tone's pitch, from a set of possible values; accuracy breaks down when there are more than about seven categories. In *immediate memory span*, people repeat back a list just heard; most manage around seven items.
Then he made his key move. He argued that the two limits are different in kind, and that the shared seven may be a coincidence: "Absolute judgment is limited by the amount of information. Immediate memory is limited by the number of items." To make the point he introduced a distinction between bits of information and "chunks of information". Memory span, he wrote, is "a fixed number of chunks", almost independent of how many bits each chunk contains.
What is recoding?
Miller called the process of building bigger chunks recoding. His example is a learner of radiotelegraph (Morse) code. At first each dit and dah is a separate chunk. Soon the learner hears letters as chunks, then words, then whole phrases, and "the amount of message that the operator can remember increases correspondingly".
He also reported a demonstration by Sidney Smith. People can repeat back about nine binary digits. But if you learn to recode binary into a larger base, you can hold far longer strings.
Try it. Read this once, cover it and write it down: 101101001110. That is twelve items, too many for most people.
Now group it in threes and rename each group as its octal digit: 101 = 5, 101 = 5, 001 = 1, 110 = 6. The string becomes 5516: four chunks, easy to hold. To recall it, write 5516 and expand each digit back into three bits. You have not stretched your memory; you have changed the units.
Is the number really seven?
Probably not. Miller himself ended his paper unwilling to read anything deep into all the sevens, suspecting "a pernicious, Pythagorean coincidence". Later, Nelson Cowan reviewed a wide range of data in The magical number 4 in short-term memory (2001). He argued that Miller's seven was "a rough estimate and a rhetorical device", and that when people are stopped from rehearsing or chunking, the limit averages about four chunks.
Four is not much. That is why chunking matters so much in study: it is the main way experts get around the limit. In a well-known case, Ericsson, Chase and Faloon (1980) reported that after more than 230 hours of practice one volunteer increased his digit span from 7 to 79, using a mnemonic system.
How can a student use chunking?
Learn formulas as single units, then link them. v² = u² + 2as should be one chunk, not seven symbols. Once it is, you can hold it alongside the problem's data.
Group facts by a rule. In inorganic chemistry, learn a trend once ("ionisation energy rises across a period, with these exceptions") instead of a list of values. Our post on remembering inorganic chemistry has more examples.
Write down what you cannot chunk yet. If a problem has more than three or four new quantities, put them on paper so your working memory can focus on the method.
Practise until steps merge. Solving many problems of one type turns a five-step procedure into one move. That is recoding in Miller's sense.
For how short-term storage works in more detail, read our post on Alan Baddeley and the working memory model, and for what this means for how lessons should be designed, see John Sweller's cognitive load theory.
What can a student take from Miller's way of working?
Miller noticed a pattern across very different experiments, then refused to accept the easy explanation. He asked what exactly was being limited, and that question produced the idea of chunks. When you see the same number or pattern in several chapters, ask the same thing: is this one rule, or a coincidence?
Chunking depends on knowing how concepts link to each other. The Fermi Concept Library places every concept in physics, chemistry, biology and mathematics in a map, so you can see which ideas belong together as one chunk.
Your next step: take one chapter's formulas, group them into three or four families, and write each family on a single card.
