Working memory, and the number seven

Almost everyone has heard that short-term memory holds seven items, plus or minus two. It is probably the most widely quoted figure in psychology, and it is a misreading of the paper that produced it.

What Miller actually said

George Miller published The Magical Number Seven, Plus or Minus Two in 1956. The paper is partly a joke about the number seven turning up in unrelated experiments, and its actual argument is more interesting than the figure everyone remembers.

Miller’s point was that the limit is not on the amount of information but on the number of chunks — and that what counts as a chunk is not fixed. He observed that people expand what a single chunk contains through practice, and that this is how the apparent limit gets worked around.

So the paper does not say you can hold seven things. It says you can hold about seven chunks, and that the size of a chunk is up to you.

Why the real number is smaller

Later work, particularly Nelson Cowan’s in 2001, argued that when you strip out chunking, rehearsal and other strategies, the capacity for genuinely unrelated items is closer to four.

That figure holds up across a range of methods designed to prevent people grouping things: showing items too briefly to rehearse, or occupying the voice with an unrelated task. Under those conditions performance falls sharply toward four.

So there are two answers, and both are true:

• About four, if you are prevented from using any strategy.
• Seven to nine, in a typical digit span test where you are free to group.

The gap between them is the strategy, which is why practice raises a digit span score so quickly and then stops.

Chunking, and why it is the whole skill

Consider 1 9 4 5 1 9 6 6 2 0 0 1. Twelve digits, comfortably past anyone’s raw capacity.

Read as 1945, 1966, 2001 it is three items, and most people can hold three items while doing something else. Nothing about your memory changed; the encoding did.

This is what expert memorisers do, and it is why records for digit span run into the hundreds. Those are not people with unusual hardware — they are people with elaborate, practised systems for turning digits into meaningful units.

Three practical versions, in rough order of usefulness:

• Group in twos or threes. The single highest-return change, and the reason our number memory test displays digits in groups.
• Attach meaning. Years, ages, prices, familiar sequences.
• Say it aloud or subvocalise. The phonological loop rehearses sound more reliably than it rehearses shapes, which is also why saying the positions out loud helps on the sequence memory test.

Order is a separate problem

Holding a set of items and holding them in order are different tasks, and most people are noticeably better at one than the other.

The characteristic error in serial recall is not forgetting an item — it is swapping two adjacent ones. Errors also cluster in the middle: the first couple of items and the last couple survive, and positions four to seven of a nine-item sequence are where runs collapse.

This is why our sequence memory and visual memory tests produce different scores for the same person. One asks for order and one does not, and comparing your two results tells you more than either does alone.

What a digit span score does not tell you

It is not a measure of intelligence. Digit span correlates only weakly with working memory measures generally, and barely at all with anything most people mean by intelligence. It is one narrow, highly trainable task.

It is not stable within a person. Tiredness, noise, and having been rehearsing something else a moment earlier all move it. A single result is close to meaningless; a fortnight of results is a trend.

It is not clinical. Digit span does appear in neuropsychological assessment, as one subtest among many, administered under standardised conditions with normative data. A web page has none of that, and a poor score means you had a poor run.

The everyday version of chunking

The clearest demonstration is one you already do without noticing: telephone numbers.

Nobody holds 07700900123 as eleven digits. It is held as 07700 900 123, which is three things. Sort codes, postcodes and card expiry dates all work the same way, and the grouping conventions printed on the objects themselves exist precisely because someone worked out that ungrouped strings are much harder to hold.

The same principle explains why a familiar year is free and an unfamiliar one is not. 1066 costs you nothing because it is already a single stored unit. 1073 is four digits.

Recognition is a different thing again

Our verbal memory test asks whether you have seen a word before, which is recognition rather than recall. That is a much easier task — you are judging familiarity rather than producing anything — which is why scores there run into the dozens while a digit span tops out below fifteen.

It has its own failure mode. Recognition runs on a feeling of familiarity, and that feeling is generated by more than having seen the word in this run: how common the word is, whether it resembles something else you saw, how recently you met it anywhere at all. So the typical error is calling a new word “seen” because it feels vaguely familiar, and common words are much more prone to it than distinctive ones.

Where the limit actually comes from

Two families of explanation compete, and the disagreement is genuinely unresolved.

Decay accounts hold that items fade over time unless refreshed, so capacity is really a race between rehearsal and forgetting. This predicts that anything preventing rehearsal — counting aloud, say — should be devastating, and it broadly is.

Interference accounts hold that items compete with each other, so capacity is limited by how confusable the items are rather than by time. This predicts that similar-sounding items should be harder to hold together than distinct ones, and they reliably are: a list of rhyming words is markedly harder than a list of unrelated ones.

Both effects are real, which is probably why the argument has lasted. For practical purposes the useful implication is shared: make your items distinct. Chunking works partly because 1945 is one distinctive thing where 1, 9, 4, 5 are four confusable ones.

Why this stops mattering above a certain point

Working memory is a bottleneck for things you have to hold right now. Almost nothing you do in a day actually depends on it, because you write things down.

That is not a glib observation. The reason digit span correlates so weakly with real-world performance is that real-world performance is mostly about long-term memory, external aids and knowing where to look things up. Somebody with an unremarkable span and a good notebook outperforms somebody with an excellent span and neither.

So a low score on the number memory test is not a limitation you need to work around; you are almost certainly already working around it without noticing.

The practical summary

Your raw capacity is around four unrelated items and you cannot change it. What you can change is how much each of those four contains, and that is worth doing — it is the difference between remembering a six-digit code and not.

Everything else on this page is a caution against over-reading a number. Take the tests regularly, watch your own trend, and treat the absolute figure as much less interesting than the direction.