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The Legend of the Magical Number Seven

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This chapter begins by discussing a simple answer to the question of what primary memory capacity is: that primary memory can hold seven chunks or meaningful units. This answer was shown to have some basis in the facts, but overall it was shown not to be a general rule, and therefore was said to be a legend. However, it should be said that simple answers are not, in principle, bad. One of the goals of science is to find simple rules to explain the available evidence in a comprehensible manner. What makes the simple rules unacceptable is just when they are shown not to match the facts. What is likely to advance people to the next level is a better understanding of the long-term memory processes involved in chunking.
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The Legend of the Magical Number Seven, Page 1
The Legend of the Magical Number Seven
Nelson Cowan, Candice C. Morey, and Zhijian Chen
University of Missouri
Address Correspondence to:
Nelson Cowan
Department of Psychological Sciences
University of Missouri
18 McAlester Hall
Columbia, MO 65211
USA
E-mail: CowanN@missouri.edu
Telephone: 573-882-4232
This is a draft of a chapter for an edited volume. The reference is:
Cowan, N., Morey, C.C., & Chen, Z. (in press). The legend of the magical number seven. In S.
Della Sala (Ed.), Tall tales about the brain: Things we think we know about the mind, but ain't
so. Oxford University Press.
.
The Legend of the Magical Number Seven, Page 2
Origin of the Legend of Seven
Individuals who know very little about experimental psychology are still likely
to have heard or read that people can keep in mind about seven items. Telephone
numbers were developed with some concern for people's ability to remember the
numbers, and local calls in the United States typically require dialing seven digits (or,
in some countries, just six digits). Intelligence test batteries include a test called digit
span in which one is to repeat a list of random digits in the presented order; the digits
in the list change from one trial to the next, and the length of the list keeps increasing
every few trials until the tested individual cannot repeat any lists correctly. Normal
adults typically can repeat lists of about seven digits. This maxim of seven has often
been applied to daily life. For example, some self-help sources proclaim that a good
oral presentation should include up to seven points on the outline. The number seven
appears in dinner-party talk, along with other psychological folk wisdom such as the
best way to raise children or how to bargain with salespeople effectively.
How did this information get established in the public mind? It goes back to a
seminal journal article by George Miller
1
that was published in 1956, in the formative
days of a new field that came to be known as cognitive psychology, the experimental
study of thought processes such as memory, attention, imagery, and language
comprehension and production. Miller's article was written in a very engaging and
entertaining fashion, in part because it began as an hour-long conference presentation
before it was molded into a written article. It begins with the author's humorous
confession that he has been persecuted by the integer seven. He goes on to discuss
three types of psychological task in which this number has emerged.
The first and most obvious task is immediate memory, such as the digit-span
task or similar tasks in which lists are presented and must then be repeated without
The Legend of the Magical Number Seven, Page 3
delay in the presented order. No matter whether the stimuli are words, letters, or
digits, lists of only about seven of them can be recalled. This differs somewhat from
one individual to the next and from one type of memoranda to the next and, indeed,
the title of Miller's article included the phrase, "the magical number seven, plus or
minus two."
In a second type of task that Miller discussed, absolute judgment, a single
stimulus is presented and its correct label has to be recalled. This is tough when the
stimuli are simple and differ in only one dimension, such as a series of lines of
different lengths or a series of tones of different pitches, each with a different label.
It turns out not to matter whether the stimuli differ only slightly or whether they differ
a lot. So long as they differ enough that the research participants can see or hear the
differences between them when they are placed side by side (or, for sounds, in close
succession), the same memory limit applies. The task of identifying an isolated
stimulus can be accomplished adequately only when there are no more than about
seven stimulus choices, again varying depending on the exact context.
A third type of task that Miller discussed is the span of attention. In the
relevant task, a set of haphazardly-arranged objects (or perhaps dots on a computer
screen) must be enumerated as quickly as possible; that is, the participant must
indicate how many objects are present. Now, your own experience probably tells you
that enumerating the objects in a set of, say, two is a very different experience from
enumerating objects in a larger set of, say, eleven. The two objects can be
enumerated very quickly, on the basis of rapid recognition or attention to both at once,
without counting. It is a different matter with eleven objects. One must carefully
keep track of which ones have been counted while one is in the process of counting
the others. Miller said that sets of up to about six or seven objects are enumerated
The Legend of the Magical Number Seven, Page 4
rapidly whereas, with higher numbers, the time to give an answer begins to rise
steeply with each added object in the set.
These three phenomena not only comprised an impressive display of evidence;
they comprised evidence central to the newly developing field of cognitive
psychology. In an earlier era, philosophically-oriented psychologists such as William
James had pointed out that there were several types of memory. James
2
distinguished
between the small amount of information that is or recently was in one's conscious
mind, which he termed primary memory, and the large storehouse of knowledge that
one collects over a lifetime, which he termed secondary memory. If cognitive
psychology was to become scientific, though, there had to be a way to measure and
characterize these types of memory. The estimate that about seven items could be
held in primary memory would be a giant step toward that end. In the era when
Miller wrote, psychologists from the behaviorist tradition, counter to James, were
advising that one should study stimuli and responses only, and should avoid making
statements about unobservable entities inside the human head such as memory or
mental imagery. On the basis of Miller's article and other, converging work published
around the same time, that sentiment was overturned for cognitive psychologists.
Regarding Miller's findings, if people could recall about seven items, there must be
some holding mechanism in the brain, corresponding to James' primary memory, that
could hold about seven items at once but not much more. The well-described findings
were repeated often by psychologists and they eventually reached the general public,
in much the same way that concepts from Sigmund Freud earlier had reached the
public.
The Intent Behind the Legend
There are aspects of Miller's 1956 article
1
that have left the careful reader with
The Legend of the Magical Number Seven, Page 5
a bit of confusion regarding what he intended to say. He does not actually make the
claim that memory span, absolute identification, and enumeration tasks call upon the
same faculty of the mind limited to seven or so items. Instead, he ends with a note on
the mystery of the convergence of many phenomena:
“What about the seven-point rating scale, the seven categories for absolute
judgment, the seven objects in the span of attention, and the seven digits in the
span of immediate memory?...Perhaps there is something deep and profound
behind all of these sevens, something just calling out for us to discover it. But
I suspect that it is only a pernicious, Pythagorean coincidence.” (p. 96)
Often when one ponders a legend and learns more, the supporting evidence
can be seen to have different implications than one might have thought according to
the legend that developed. In this case, it turns out that Miller was not very interested
scientifically in the number seven. Perhaps if he had been, he would not have
attached the adjective "magical" to it. As he explained in an autobiographical essay
3
,
he was asked to give an hour-long presentation at a point in his career when he did not
feel that he had any one research topic developed enough to take up that time period.
He did, however, have some research on immediate memory and on absolute
judgment. He did not want to give two unconnected reports of these research topics
and at first saw no common theme between them. However, he then discovered that
they shared the number seven in terms of research participants' limits in performance.
He decided to make that limitation a theme of the talk to tie them together and, to add
an air of legitimacy, threw in the research on enumeration. However, the reference to
"plus or minus" seven was supposed to convey the humorous notion that a magical
number could have a margin of error. This is an amazing way for a scientific legend
to be born.
The Legend of the Magical Number Seven, Page 6
One concept that was more important to Miller
1
was the concept of chunking.
This means taking multiple items and putting them together to form new groups or
chunks. Before Miller, psychologists tried to measure information in bits, a term
frequently used in computing, meaning a choice between two options. Two bits
equals 2
2
or 4 options, three bits equals 2
3
or 8 options, and so on. For example, how
many yes/no questions would it take you to guess which English letter a friend is
thinking of? With your first question (eliciting one bit of information), you could ask
if the letter comes before N in the alphabet, narrowing the choices down to 13 of 26
letters, or half of the alphabet; with your second question (eliciting a second bit), you
could narrow the choices down to approximately half of that half; and so on, until you
could determine which letter it was. There also is a mathematical definition of bits on
a scale that includes fractions; without going into this definition, it is enough here to
give the example that 2.6 bits is something more than 2 bits but smaller than 3 bits. If
one considers digits from the set 0-9, there are ten choices so each digit conveys
somewhere between 3 and 4 bits of information. If one considers the 26 English
letters, each letter conveys somewhere between 4 bits (2
4
= 16 choices) and 5 bits (2
5
= 32 choices). There are many thousands of English words, so the bit measure for an
English word would be considerably higher.
However, it turned out that bits did not matter for actual research participants.
Memory span is about the same number of items when the items are random digits,
random letters, or random words. It appears that immediate memory should be
measured not in bits, but in units that are psychologically meaningful. Each
meaningful unit is called a chunk. In this regard, human memory appears to operate
in a manner quite different from computer memory, which is composed of many
locations that can be turned on or off, each worth one bit of information.
The Legend of the Magical Number Seven, Page 7
One might have thought that bits would be important for humans, given that
each nerve cell is in a firing or non-firing state at any moment and therefore may
convey only 1 bit of information. Apparently, though, this binary property of
individual nerve cells is not what is important for immediate-memory limits. Perhaps
that is because large portions of the brain's memory system can participate in
immediate memory; not just a relatively small, dedicated portion of the memory
locations as in a computer. What may be important is limitations in the firing patterns
that nerve cells can take on at any moment, such that only a few ideas can be actively
represented concurrently.
Miller and one of his colleagues found that stimuli can be transformed in a
way that makes them easier to remember, by reducing the number of chunks. In the
binary numerical system that is used to encode computer memory locations using only
the digits 0 and 1, the rightmost digit reflects how many ones there are, the next digit
to the left reflects how many twos, and the next digit to the left of that reflects how
many fours; so 001 = 1; 010 = 2; 011 = 3; 100 = 4; 101 = 5; 110 = 6; and 111 = 7. It
would be difficult to remember the binary string 011-111-101-110, yet much easier to
remember the familiar decimal numerical equivalent, 3-7-5-6. If one knows the
binary system, one can recode the binary string into its decimal equivalent. In the
example given here, recoding reduces the load on immediate memory from 12 chunks
(the binary digits shown) down to only 4 chunks (the digits 3, 7, 5, and 6). Another
example that makes the concept clear is memorization of the letter string USAFBICIA.
This looks like 9 chunks (single, unrelated letters) but they can be reduced to three
acronyms: USA (United States of America), FBI (Federal Bureau of Investigation),
and CIA (Central Intelligence Agency). For someone who knows these acronyms by
heart and notices these patterns, there are only 3 chunks to be remembered.
The Legend of the Magical Number Seven, Page 8
In sum, it was not the number seven per se that fascinated Miller, but rather
the processes that were used to encode information and the nature of the units that
were meaningfully encoded. This was intimated in the tone of the closing comments
in his 1956 article
1
and was made clear in his later autobiographical discussion
3
.
People could recall about seven chunks, regardless of the processes that were
involved in deriving those chunks from the stimuli to be recalled.
The formation of chunks in immediate or primary memory often made use not
only of the information present to the research participant, but also of prior knowledge
that was already present in long-term or secondary memory. It is worth noting that
there have been demonstrations that practically anything can be held in immediate
memory, if there is enough knowledge to back it up. Anders Ericsson
4
and colleagues
trained an individual to increase his digit span from the usual seven or so up to 80
digits, in the course of a year. This individual was an athlete who already had
memorized many record running times. This made it easier to transform digits into
multi-digit chunks. For example, 3.98 might be the record time in minutes to run a
mile on a certain type of track. This could be supplemented with new chunks, such as
85.7 as the age of a pretty old man. Grouping sets of three and four digits together to
form new chunks, over a period of months this special individual (or was he just
specially motivated?) learned to repeat lists of about 20 digits, presumably organized
into 5 to 7 larger chunks. Then, somehow he learned to combine several chunks into
even larger super-chunks, so that he eventually could repeat series of about 80 digits.
This skill did not generalize; his memory for letters or words remained at about seven.
Similarly, Jeffrey Rouder and colleagues
5
recently found that, with extended
practice, absolute judgments for line lengths could be extended considerably beyond
the seven or so distinct labels that Miller noted. We do not know just how chunking
The Legend of the Magical Number Seven, Page 9
is involved in absolute judgments but one possibility is that there is a limit in how
many categories can be kept distinctly in mind during the test, which might be
overcome through extended familiarity with the categories.
Problems With The Number Seven
There were findings resulting in seven or so items remembered, and these
findings require some explanation. Still, one might question whether seven actually is
a fundamental number of immediate memory. Consider this. If people are able to
perceive multiple items in terms of chunks that they already know (such as the
acronym IRS) might it not also be possible for them to form new chunks rapidly?
Why is it, for example, that the seven digits in a telephone number are typically
presented in two groups, in the form # # # - # # # #? It seems reasonable to suppose
that some rapid grouping process goes on to ease the process of recall by reducing the
number of independent units that have to be recalled. These questions did not get a
great deal of immediate attention, however. One reason was that, after 1956, George
Miller's career seemed to veer more into the study of language and categorization, as
opposed to primary memory.
Published just four years after Miller's famous article, a 1960 article by
George Sperling
6
became another lasting classic in the field of cognitive psychology
and yielded a different answer about primary memory. The study's main point was
that a large amount of information about how a visual stimulus looks is stored in the
mind for a very short time, but the study also provided information about primary
memory. On each trial, a spatial array of characters (such as letters) was flashed on
the screen briefly. The task was to record all of the characters in the array, or some
part of the array. A large amount of elegant experimental work was included in the
article. It was found that if the row of the array to write down was indicated by a tone
The Legend of the Magical Number Seven, Page 10
presented quickly enough, before sensory memory had faded, it was possible to write
down most of the characters in that row. This showed that sensory memory could
hold visual information from at least 12 characters at once. However, if there was no
tone cue and the entire array had to be written down, there was a more severe limit in
performance so that only about 4 of the items could be written down. The theoretical
model for this task was that information had to be processed, from a visual form in
sensory memory into a more categorized or labeled form in primary memory, before it
could be reported. Either primary memory could hold only about 4 items, or sensory
memory did not last long enough to allow more than 4 items to be processed. One
can imagine an analogy in which a painter must paint objects onto a canvas of limited
size (like primary memory) using an open tray of paint that is plentiful but dries up
extremely rapidly (like a fading sensory memory). The number of objects that can be
painted onto the canvas depends on both the size of the canvas and the time available
before the paint becomes too dry to use. We will return to this issue later.
There also were studies indicating that people could recall roughly 4 clusters
or chunks of objects, though experts could recall chunks comprising more objects.
This research involved people's ability to recall the pieces on a chessboard, as a
function of their expertise in chess.
7
Work continuing along this line
8
has suggested
that even the notion of a chunk is often an oversimplification for what can be a broad
network of associations between items, or template.
There were a few studies by other investigators looking at the issue of
grouping in immediate recall. For example, Tulving and Patkau
9
carried out a study
in which people were asked to remember strings of 24 words that were in jumbled
order, or that resembled coherent English to varying degrees (for example, "The best
grain stamps made in America you beast that see something..."), or that were perfectly
The Legend of the Magical Number Seven, Page 11
coherent English sentences. The task was to recall the words in any order (free
recall). Whenever runs of several words were recalled in the same order in which
they were presented, each such run counted as a single chunk. Many more words
were recalled in the sequences that were better approximations to English, but the
measured number of chunks recalled remained fixed across conditions, at 4 to 6
chunks. It was just that more coherent strings of words led to larger chunks recalled,
not more chunks. Other methods were invented in attempts to identify chunks clearly,
such as making the assumption that the task of recalling lists in order (serial recall)
would proceed relatively smoothly within a chunk but would be more likely to
encounter difficulty between chunks.
10
Overall, though, the magical number seven
was neither seriously questioned nor put to many stringent tests in the early days.
Some investigators lived by it, and others probably were skeptical and ignored it,
perhaps taking their cues from the ending of Miller’s article in which it was said that
the magical number seven was probably just a coincidence.
The year 1975 was, in hindsight, an important one for the study of immediate
memory. By this year, the magical number seven had been recognized as a classic
finding that had withstood the test of time. Yet, two papers were published that also
have had a lasting impact and have cast doubt on the magic of the number seven.
First, Alan Baddeley and colleagues
11
showed that it is not simply the number
of meaningful units that mattered in immediate recall; word length mattered. Lists of
words that took longer to pronounce were not recalled as well as lists of the same
number of words that could be pronounced more quickly. The explanation of that
finding was that people refresh their verbal memories by rehearsing the words (that is,
imagining saying the words to themselves), a process that can be carried out more
efficiently for short words. If the entire list were rehearsed over and over, for
The Legend of the Magical Number Seven, Page 12
example, the time between one rehearsal of a particular word and the next rehearsal of
the same word would be shorter if the words were shorter, leaving less time for
forgetting. It may be that rehearsal takes place in a more complex or piecemeal
manner than that but, in any case, many such methods of rehearsal would lead to the
expectation of the word-length effect that actually was obtained. Baddeley has
amassed a large amount of information about primary memory in subsequent work,
and a time-related limit remains an important part of the theorization that has become
predominant in the field of what is now called working memory, or primary memory
as it is used to help do work such as solving problems and comprehending and
producing language.
Second, rehearsal aside, in a 1975 book chapter
12
one of the founding fathers
of the field of cognitive psychology, Donald Broadbent, began to question how
fundamental the number seven actually was in primary memory. The logic of this
challenge was similar to what has been stated above. It was pointed out that although
people typically could remember up to about seven items, perhaps a more meaningful
number was the number of items that people could remember flawlessly (because
presumably those items are recalled without relying on a mental strategy that can fail).
For sets of only three items, memory was nearly flawless. Adding a fourth or fifth
item resulted in a set that could usually be recalled correctly; adding more made the
situation worse. It therefore appeared that three was a basic capacity limit and that
rehearsal, grouping, or other strategies or mental tricks might be used sometimes to
increase the number recalled beyond that basic capacity. As analogies for these
strategies, a juggler can keep multiple balls off the ground by repeatedly renewing
their upward momentum (like rehearsing), and a person can keep multiple balls off
the ground by putting several of them together on a plate (like chunking). However,
The Legend of the Magical Number Seven, Page 13
jugglers sometimes make mistakes and balls sometimes roll off of plates. Broadbent
pointed out other phenomena to support the notion that the magical number was not
seven, but three. For example, when one attempts to recall items from a category in
secondary memory, one tends to recall in bursts of three items. Try, for example, to
name countries of the world as quickly as possible and you will notice that they tend
to be produced in spurts of just several countries at a time.
Is There a Magical Number After All?
Much more recently, one of the present authors (Nelson Cowan) wrote a
literature review
13
that examined Broadbent's hypothesis more broadly and
systematically. It suggested that, across many types of experiment, something like a
semi-magical number 4 (plus or minus two, varying across individuals and situations)
actually exists. To find this result, one must include only procedures in which the
items are well known and in which it is impossible to form larger chunks from the
items. This can be accomplished, for example, by presenting many items in an array,
like Sperling
6
, with the array presented only briefly so that there is not enough time to
think about all of the items in a way leading to extensive chunking. In a particularly
compelling demonstration of this, called multi-object tracking
14
, there are multiple
objects on the computer screen and then several of them momentarily are marked to
stand out (for example by flashing). When this stops, so that all the items look alike
again, they wander around the screen randomly, in different directions. When they
stop, the research participant is quizzed regarding whether a certain object was one of
the previously-marked objects, or not. People typically can follow or track a
maximum of 4 objects, and sometimes fewer.
Formation of new chunks also can be prevented by presenting lists of spoken
items in a situation in which attention is diverted to another task at the time that these
The Legend of the Magical Number Seven, Page 14
items are presented, making rehearsal impossible. Then the spoken items have to be
recovered from the stream of auditory sensory memory when a cue to recall them is
presented, just after the list in question has ended. If chunking is not possible, it is
assumed that each item remains a single chunk in primary memory. Under such
circumstances, about 4 items (that is, presumably, single-item chunks) can be
recalled. Similar results are obtained if the spoken items are attended but covert
verbal rehearsal is prevented by requiring that the participant at the same time repeats
a meaningless phrase during the testing, a procedure known as articulatory
suppression.
Could it be shown that this capacity limit of about 4 chunks, observed in so
many circumstances when chunks were presumably limited to one item each
13
,
applies also when chunking is possible? If so, then this capacity limit will gain
considerable generality. This does seem to be the case with some of the previous
results
7, 9
. However, the question has so rarely been studied that it cannot be
considered to have been decided.
The reason for the limit of about 4 chunks also has not been determined. One
reason it could occur is that the chunks have to be held in the focus of attention, which
is limited in capacity. Another possibility is that the chunks do not have to be held in
a region of the mind that is limited in capacity, but that the chunks interfere with each
other if they include similar features or concepts.
In the final section of this chapter, we will illustrate the ongoing controversy
and how it might be resolved in the future, by reporting on some recent work on
capacity limits.
Some Recent Studies on Immediate-Memory Capacity Limits
Recently, work has been conducted to help ascertain that there really are
The Legend of the Magical Number Seven, Page 15
capacity limits in immediate memory, and also to determine what the reasons for
capacity limits might be.
One recent study conducted to ascertain the capacity limit
15
went back to the
standard technique to study immediate memory that was discussed by Miller
1
, serial
recall. Instead of preventing chunking (as in Cowan's
13
previous approach), steps
were taken to control chunking. In a training session that preceded serial recall,
words were presented either singly or in pairs. Each word was presented 4 times but a
proportion of those presentations involved consistent pairs of words. For example,
within the training sequence of words, the words brick and hat might each be
presented twice by themselves, and twice in the consistent pair brick-hat. This
mixture was termed the 2-pairing condition. The different training conditions (the 0-,
1-, 2-, and 4-pairing conditions) used with different words are outlined in Figure 1.
The 0-pairing condition involved no training with word pairs per se whereas, at the
other end of the continuum of training conditions, the 4-pairing condition involved
consistent training with words in pairs. The expectation was that more frequent
pairing would increase the likelihood that the pair would be remembered as a single
chunk in serial recall, rather than as two separate words. There also was a cued-recall
test in which, for example, the word brick was presented and the correct response was
hat, if that was a pair that had been presented.
- - - - - Figure 1 here - - - - -
To encourage the recall of learned pairs, items within the 8-word lists to be
recalled were presented in pairs. Each list included words from a single training
condition. Each list that was composed from words in the 1-, 2-, or 4-pairing
condition included only pairs that were already familiar from training. For example,
somewhere within an 8-word list of words from the 2-pairing condition, the pair
The Legend of the Magical Number Seven, Page 16
brick-hat would appear, if it happened to be part of this training condition for a certain
participant (as in the example above). Results of this experiment are depicted in
Figure 2. The blue triangles show that the number of words recalled in the correct list
positions increased markedly as a result of more paired training.
The red circles in Figure 2 show the number of chunks recalled, using one of
several measures of chunking. This reflects the sum of 1-word chunks, or singletons,
and 2-word chunks, or learned pairs. (Several methods were used to ascertain which
pairs had been learned.) The clear finding was that the number of chunks recalled
stayed constant across learning conditions, at an average of about three and a half
chunks, even though the number of words recalled increased with pair training.
- - - - - Figure 2 here - - - - -
Another, very different research procedure
16
will now be introduced, not only
to show the variety of procedures leading to a capacity limit, but also to permit a
discussion of some recent research on the question of why the capacity limit occurs.
In this procedure, a haphazard array of colored squares is briefly presented and is
followed, after a short break of up to a half second, by another array of squares that is
identical to the first one or differs in just the color of one of the squares. The task is
to indicate whether the array has changed or not; half the time, the correct answer is
"yes" and half the time it is "no." To make the decision easier, a circle can appear
surrounding one square, the participant having been instructed that, if anything
changed, it was the color of the circled square. The procedure is illustrated in Figure
3.
- - - - - Figure 3 here - - - - -
This task is easy with up to 4 squares in the array, but it becomes
progressively harder as the number of squares in the array (called the set size)
The Legend of the Magical Number Seven, Page 17
increases beyond 4. There is a way to use the results of the experiment to estimate the
number of squares from the first array that had to be held in primary memory, taking
into account guessing (Cowan
13
, p. 166). For all set sizes, the estimate comes out to
be about three and a half items. If we can assume that the arrays are flashed too
briefly for multi-item chunks to be formed, this means an average of three and a half
chunks.
This array-comparison procedure may be helpful in understanding capacity
limits and what factors cause them, because it is a nonverbal procedure. In a verbal
procedure, the process of rehearsal may get in the way of understanding the
fundamental capacity limit, as discussed above. In a nonverbal procedure, as we will
show, this can be less of an issue.
Recall that one explanation for the capacity limit is that some information in
primary memory must be held in the focus of attention, as William James
2
implied in
his writing long ago. It is clear that the focus of attention is limited; perhaps it is the
focus of attention that has a capacity of three or four chunks of information. To
examine this possibility, one recent study
17
used a dual task in which a spoken list of
digits was to be retained and recited aloud during the reception and retention of the
first array on the trial. Given that spoken digits and visual arrays have very different
features, they need not interfere with one another unless both of them require the
same resource that is severely limited in capacity, such as the focus of attention and
its potential ability to hold information.
There were four different conditions. In one condition, there was no digit
recitation. In two memory load conditions, a random two- or a seven-digit number
had to be recited. The fourth condition was a control to make sure that it was not
recitation per se that hurt recall. In this condition, it was the participant's own seven-
The Legend of the Magical Number Seven, Page 18
digit telephone number that had to be recited during the trial. Because the number
was known, it did not impose a load on primary memory. However, it involved digit
recitation comparable to the seven-digit load condition. Thus, it was only the seven-
random-digit condition that imposed the kind of load that should make demands on
the focus of attention, in addition to articulation.
The results of this study are shown in Figure 4 in terms of the estimated
capacity in each condition (averaged across different array sizes). As expected
according to the theory that the capacity limit is in the focus of attention, performance
was impaired by the seven-digit memory load, but not by the other recitation
conditions. The effect of the memory load was especially great when the load was
recited incorrectly, in which case the valiant attempts to retrieve the verbal
information were probably distracting in and of themselves.
- - - - - Figure 4 here - - - - -
Recent studies differ in their conclusions. In one study
18
, the interference
between visual arrays and digit lists was considerably less than in the study shown in
Figure 4. One possibly important difference between the studies was that only the
study showing more interference
17
required that the digit memory load be recited
aloud during the presentation of visual arrays. Other recent work suggests that the
retention of verbal information can require attention even if it is to be held silently,
provided that two conditions are met. The information must be beyond the amount
that can be conveniently and silently rehearsed, yet it must be unstructured enough
that it cannot be greatly simplified or chunked using information from long-term
memory
19
.
Other recent research has tied the visual array procedure to neural functioning.
Individuals with a larger capacity for the colored squares appear to show electrical
The Legend of the Magical Number Seven, Page 19
signals emanating from the brain that increase more as the number of squares per
array increases from two to four
20
. Images of neural responses to stimulation based
on functional magnetic resonance imaging (fMRI) show select areas of the brain that
respond in a manner similar to the capacity limits observed in behavioral work
21
.
There are many different experimental procedures and each one has to be
analyzed carefully before we will know whether a similar "magical number" truly
applies to all of them, and for the same reason. In one sort of procedure, a visually-
presented list of words is followed by a probe word, which has to be judged to be
present in the list or absent from it. The reaction time to the last word in the list is
shorter than the reaction time to the other words, leading to the possible conclusion
that, actually, only one item is held in the focus of attention in such situations
22
. If
this is the case, then the capacity limit of three to four items might not apply to such
situations. However, further work has shown that the fast reaction time spreads from
one item to four items as the participants become highly practiced
23
. Perhaps,
therefore, when the task is novel or difficult, the focus of attention adjusts and zooms
in to capture less than four chunks, so as to leave more attention free to carry out the
task itself. With practice, the task becomes more automatic and attention can be used
to hold more chunks at once. A slightly different suggestion
24
is that the focus of
attention itself only holds one chunk, but there is a mental region associated with that
focus that holds up to four chunks.
Some procedures are highly controversial. Let us return to the enumeration
procedure discussed by Miller
1
. Subsequent work has set the limit for rapid
enumeration without counting, called subitizing, not at seven but at about four
objects
25
. Some have suggested that subitizing has nothing to do with a limit in
primary memory capacity, but rather with the observation that spatial patterns can be
The Legend of the Magical Number Seven, Page 20
more easily recognized when they consist of fewer objects because, as the number of
objects in the display increases, the number of distinguishable patterns skyrockets
26
.
This might explain why primitive skills of enumeration of small numbers exist even
in infants and non-human animals
27
. However, some research argues against that
interpretation. It has been found that elderly individuals cannot subitize as many
objects as young adults can
28
, yet there is no reason to suspect that the elderly lose the
ability to detect known patterns; a great deal of previous research does suggest,
though, that their primary-memory capacity is diminished relative to young adults.
Has One Legend Been Replaced By Another?
In this chapter, we began by discussing a simple answer to the question of
what primary memory capacity is: that primary memory can hold seven chunks or
meaningful units. This answer was shown to have some basis in the facts, but overall
it was shown not to be a general rule, and therefore was said to be a legend.
However, it should be said that simple answers are not, in principle, bad. One
of the goals of science is to find simple rules to explain the available evidence in a
comprehensible manner. What makes the simple rules unacceptable is just when they
are shown not to match the facts. By analogy, in the realm of physics, it was not a
bad move for Isaac Newton to propose a simple law of gravitational force, because it
helped explain the data of planetary motion collected by Tycho Brahe and the
regularities of planetary motion derived from the data by Johannes Kepler. The laws
of gravity could be clearly observed only in situations in which wind resistance was
eliminated or taken into account; just as, we have suggested, the capacity of primary
memory can be clearly observed only in situations in which rehearsal and chunking
have been eliminated or taken into account.
Just as the more comprehensive understanding of gravity by Albert Einstein
The Legend of the Magical Number Seven, Page 21
eventually displaced the simpler gravitational law of Newton, a more comprehensive
understanding of primary memory capacity is bound to come along and replace the
simple generalization
12, 13
that people can remember on average three or four chunks
of information. Until that time, however, the limit of three or four serves as a useful
guideline for research and theory, as did the gravitational constant for many years.
What is likely to advance us to the next level, beyond a new legend of three or four, is
a better understanding of the long-term memory processes involved in chunking, a
topic emphasized in the seminal work that launched the modern research on primary
memory: the article published by George Miller
1
in 1956, about 50 years before the
present chapter went to print.
The Legend of the Magical Number Seven, Page 22
References
1. Miller, G.A. (1956). The magical number seven, plus or minus two: Some limits
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12. Broadbent, D.E. (1975). The magic number seven after fifteen years. In A.
Kennedy & A. Wilkes (eds.), Studies in long-term memory. Wiley. (pp. 3-
18)
13. Cowan, N. (2001). The magical number 4 in short-term memory: A
reconsideration of mental storage capacity. Behavioral and Brain Sciences,
24, 87-185.
14. Pylyshyn, Z.W., & Storm, R.W. (1988). Tracking multiple independent targets:
Evidence for a parallel tracking mechanism. Spatial Vision, 3, 179-197.
15. Cowan, N., Chen, Z., & Rouder, J.N. (2004). Constant capacity in an immediate
serial-recall task: A logical sequel to Miller (1956). Psychological Science,
15, 634-640.
16. Luck, S.J., & Vogel, E.K. (1997). The capacity of visual working memory for
features and conjunctions. Nature, 390, 279-281.
17. Morey, C.C., & Cowan, N. (2004). When visual and verbal memories compete:
Evidence of cross-domain limits in working memory. Psychonomic Bulletin
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18. Cocchini, G., Logie, R.H., Della Sala, S., MacPherson, S.E., & Baddeley, A.D.
(2002). Concurrent performance of two memory tasks: Evidence for
domain-specific working memory systems. Memory & Cognition, 30,
1086-1095.
19. Jefferies, E., Lambon Ralph, M.A., & Baddeley, A.D. (2004). Automatic and
controlled processing in sentence recall: The role of long-term and working
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memory. Journal of Memory and Language, 51, 623-643.
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The Legend of the Magical Number Seven, Page 25
Figure Captions
Figure 1. Illustration of a procedure used by Cowan, Chen and Rouder
15
to examine
the capacity limit of serial recall expressed in chunks.
Figure 2. Results of a study by Cowan, Chen, and Rouder
15
of the information
produced in the serial recall of 8-word lists. The results are averaged over two
experiments. The blue triangles show that the average number of words
recalled in the correct serial positions increased as a function of the amount of
training with pairs of words. (A similar trend was observed for words recalled
regardless of the serial positions.) The red circles show that the average
number of chunks that were recalled nevertheless remained constant across
these training conditions. Chunks included words recalled as singletons, and
also pairs of words that were presented together within the list and recalled
together with the pair intact.
Figure 3. Illustration of the array-comparison procedure of Luck and Vogel
16
as
adapted by Morey and Cowan
17
.
Figure 4
. Results of a study of the effect of a verbal memory load on the retention of
an array of colored squares to be compared with a second array
17
. A formula
(Cowan
13
, p. 166) was used to estimate visual memory capacity expressed as
the number of squares retained, which was then averaged across arrays with 4,
6, or 8 squares. The key finding is that although repeating 7-digit load had a
strong effect, especially when the load was repeated incorrectly, repeating a
known 7-digit number (the participant's own telephone number) had little
effect. Therefore, it was the demand on attention rather than articulation per
se that disrupted retention of the array of colored squares.
The Legend of the Magical Number Seven, Page 26
Figure 1
Training Conditions (including 4 presentations of each word)
1. Words presented 4 times as singletons, but never paired (0-pairing)
2. Words presented 3 times as singletons, and 1 time paired (1-pairing)
3. Words presented 2 times as singletons, and 2 times paired (2-pairing)
4. Words never presented as singletons, but 4 times paired (4-pairing)
Presentations were randomly mixed as in box, hat, dog-shoe, box, girl, desk, tree-brick, hat, dog-shoe...
Serial Recall Test
For each training condition, a list of 4 pairs of words was presented using known pairs.
Pairs from a condition were randomly arranged in a list, as in tree-brick, dog-shoe, man-tank, rock-coin.
Cued Recall Test (before or after the serial recall test)
The first word in a pair was presented and the correct response was the second word, as in dog - ???
The Legend of the Magical Number Seven, Page 27
Figure 2
0.00
1.00
2.00
3.00
4.00
5.00
0-paired 1-paired 2-paired 4-paired
Training Condition
Number of Units Recalled
Word Recalled
Chunks Recalled
The Legend of the Magical Number Seven, Page 28
Figure 3
Indicate whether this color has
changed between arrays.
Then type digits, if any.
+
1
2
3
4
Ready signal (until speech, if any, starts, then blank for 0.5 second)
Array to remember (0.5 second)
Blank time 0.9 second
The Legend of the Magical Number Seven, Page 29
Figure 4
0.00
1.00
2.00
3.00
4.00
5.00
6.00
No Load 2 Digits Own
Telephone
Number
7 Digits
(Correct)
7 Digits
(Error)
Auditory Load Condition
Estimated Capacity for Squares
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This chapter discusses the role of chunking and organization in the process of recall. There are four concepts associated with the organization of memory: chunk, memory code, decode, and recode. Chunks have been operationally defined as behavior sequences, which tend to occur either adjacently or in an all-or-none manner. Theoretically, they can be defined as item or information sets, which are stored within the same memory code, with the code and the chunk being distinct. Recoding refers to the process of learning the code for a chunk, and decoding is the process of translating the code into the information it represents. Organization plays a major role in the associative relations between an item in a sequence and all the other items in the sequence. When the items are from the same chunk, there appears to be a transferable association, but if they are from different chunks the transfer is small, if it exists at all. Chunks may also represent decision units in recall.
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Immediate serial recall is better for sentences than word lists presumably because of the additional support that meaningful material receives from long-term memory. This may occur automatically, without the involvement of attention, or may require additional attentionally demanding processing. For example, the episodic buffer model (Baddeley, 2000) proposes that the executive component of working memory plays a crucial role in the formation of links between different representational formats and previously unrelated concepts. This controlled integrative encoding may be more important in sentence than word recall. Three experiments examined the effect of an attention-demanding concurrent visual choice reaction time task on the recall of auditorily presented stories, sentences, and lists of unrelated words, in order to investigate the relative importance of automatic and controlled processing for these materials. The concurrent task was found to disrupt the recall of strings of unrelated sentences more than random word lists, suggesting that controlled processing played a greater role in the sentence recall task. On subsequent learning trials, however, recall of the unrelated words was also disrupted by the concurrent task, possibly due to the development of chunking. The large dual task decrement for unrelated sentences did not generalise to the recall of more naturalistic prose, suggesting that the requirement to integrate phonological with long-term linguistic information is not attentionally demanding per se; instead, the integration of unrelated concepts is effortful once recall extends beyond the capacity of the phonological loop. Our results suggest that sentence recall reflects contributions from both automatic linguistic processes and attentionally limited working memory.