Re: George Miller [Magical Number 7 +/-2] Part 5

From: Stevan Harnad (
Date: Mon Mar 02 1998 - 19:43:47 GMT

> From: catriona barrett <>
> > "There is a clear and definite limit to the accuracy with which we
> > can identify absolutely the magnitude of a unidimensional stimulus
> > variable. I would propose to call this limit the span of absolute
> > judgment, and I maintain that for unidimensional judgments this
> > span is usually somewhere in the neighborhood of seven."

English translation: If you are identifying sounds of different
loudness as very loud, moderately loud, etc., there is a limit to how
many categories you can chop it up into. Around 7 seems to be the most.

> In this section Miller is stating that there is a limit to the
> number of ways in which we can accurately measure or define one
> single object,

No. We can measure or define an object in countless ways. There is a
limit on how many subdvisions we can make along one dimension.

> i.e. the amount of information we can hold about any
> one object is limited,

True, but that isn't the Miller limit, which has to do with dimensions
rather than objects.

> and Miller suggests that this limit is
> approximately seven. This is what he means by 'The Span of Absolute
> Judgement'.

Suppose I read off a list of random words and ask you to say them back
to me. Up to about 7-9, you will be accurate. More than that and you
just produce more errors.

> > "We are not completely at the mercy of this limited span, however,
> > because we have a variety of techniques for getting around it and
> > increasing the accuracy of our judgments. The three most important of
> > these devices are (a) to make relative rather than absolute
> > judgments;

This means that instead of trying to say which loudness this sound is,
on a 10-point scale (which is too big), just say whether this sound or
that sound is louder. That's a relative judgment, comparing two sounds,
instead of an absolute judgment, based on one sound all by itself.

> or, if that is not possible, (b) to increase the number
> > of dimensions along which the stimulus can differ;

That means don't just have the sounds vary in loudness; have them also
vary in pitch, and in tone-colour (i.e., which instrument they sound
like); then you will be able to subdivide them into more than 7

> or, (c) to arrange
> > the task in such a way that we make a sequence of several absolute
> > judgments in a row."

That's cheating, because each absolute judgment follows another,
allowing relative judgments to be made. (If there are 12 loudnesses,
then I may not be able to say whether this one is a 9 or a 10, but if
I hear it right after a 9, I will be able to do it, helped by the
comparison from the preceding relative judgment.)

Very rarely do things that need to be identified conveniently come in
series so you can compare each identification with the one that came
before it. (Also, ordering does not help if the loudness that follows is
very differnt -- say a 10 followed by a 3. It only helps if they are
adjacent loudnesses: a 10 followed by an 11.)

However, we CAN remember longer strings or things by grouping them.
So if I remember objects in 4 groups of three, I can remember them
better than as 12 objects in a row. Memory for a series of 12 tones is
improved by thinking of them as 3 groups of 4 notes; rhythm helps
separate them too. We can say them as 4 quadruplets.

> Miller suggests ways in which we can increase our span of absolute
> judgment:
> (a)"Relative rather than absolute judgments" - Instead of looking at
> objects as completely non-related, we could, and we do in fact link
> objects together by similar characteristics in order to be able to
> remember more. An example is looking at an apple, an orange, a
> banana and a pear in a bowl. Instead of remembering these as four
> different objects out of the approximate seven we are supposedly
> limited to, we would usually group all these objects into one group,
> fruit. Grouping these four objects together would still enable us to
> remember that there was an apple, banana, orange and pear in the bowl
> by remembering that they were all pieces of fruit but we would only
> be using up one of the seven possible pieces of information that we
> are limited to, thus making room for other pieces of information!

True, but it only works if we have the category "fruit" (i.e., we know
they are all fruit). This is an example of recoding ( = re-naming )
things rather than an example of relative judgment. We can remember
about 7 "chunks" of information. If you show me 15 objects, I will have
trouble remembering them by rote, but if they consist of 4 fruits,
3 sports, 5 birds and and 4 cars, I might well remember them all,
remembering them first as 4 categories, and then the less than 7 members
of each.

> (b)"Increasing the number of dimensions along which stimuli can
> differ" - Miller suggests that we can make more accurate judgments
> about and between objects if we make several observations about them.
> An example is looking at a mug and seeing it just as for what it is,
> a mug. On the other hand we could define it in more ways. We could
> say that the object is a mug, that it is blue, that it is made of
> china, that it has a handle, and so on. Miller goes on to say that by
> making "yes-no judgements" about each piece of information about an
> object we can actually increase our span of absolute judgment to
> approximately 150. However, he then also goes on to say that this
> limit is probably more in the region of thousands if there is a limit
> at all. This makes sense as in our everyday life we can remember what
> seems like an endless amount of information, not just 7 or 150 pieces.

This is pretty straight-forward: From seeing just one object, I can
probably say what value it has on many more than 7 dimensions.

> (c)"Making a sequence of several absolute judgments in row" - An
> example of this would be remembering a telephone number. When we look
> at a telephone number what we see is approximately six absolute
> digits. When we need to remember a telephone number we do not learn
> each digit as an absolute but rather we remember all the digits
> together as if they were only one number. A way of testing whether or
> not this is true is to ask somebody what the fourth digit in their
> telephone number is. Although it will not take them long to tell you,
> the chances are that they had to recite the number starting from the
> beginning until they got to the fourth digit, which means that to
> remember the digit they grouped all the digits into one number or one
> piece of information.

This is an effect of grouping and rhythm. We do it a lot.

> Miller then suggests that there is a 'Span of Perceptual
> Dimensionality', i.e. that a stimulus e.g. a mug can only be defined
> in a limited number of ways and he believes that it is approximately
> 10.

This is a bit vaguer than the other Miller limits and has not stood the
test of time.

> Miller explains (c) in more detail and describes experiments where
> instead of just presenting subjects with a stimulus and immediately
> asking them to name it, subjects are presented with several stimuli
> and are then told to say what they were presented with. Miller
> believes that in this way subjects are using their 'immediate memory'
> rather than their 'absolute judgement'. Kid-sib probably doesn't
> understand this, sorry,

Hearing/seeing several things in a row allows you both to group and to
make relative judgments to make the task of remembering easier.

It's hard to recognise a loudness of level 4 as 4 all alone, but if
it is in a series such as 2 6 - 4 5 - 3 1 your chances of recovering the
right levels are improved by being able to group them and supplement the
absolute judgments with relative comparisons.

> but even Miller himself starts to get
> confused. He goes on to say that there is a 'Span of Attention' that
> will allow us to immediately remember approximately six objects that
> are in our field of vision i.e. if the setting was unfamiliar to me,
> while sitting at this computer, if I shut my eyes I would only be
> able to remember the screen, the keyboard, the mouse, sheets of
> paper, my pencil and my purse. Miller says that it may be natural to
> consider the span of immediate memory, span of absolute judgment and
> span of attention to all be different parts of the same thing i.e.
> that they all work together. Miller states that to do this is a grave
> mistake, and he actually made it.

There are similarities and maybe some causal connections, but the
7-part dimension limit and the 7 item recall limit are probably not the
same thing (though related by how dimensions may be used in re-coding
things into bigger "chunks"), and the 7-feature limit is probably not

> Miller originally claimed that the span of immediate memory was
> limited to seven pieces of information but managed to raise doubt
> about his theory by using the following example. He suggested that if
> the span of immediate memory were to remain at a fixed level then it
> should automatically follow that the span should be short when items
> contain a large amount of information and long when the items contain
> a small amount of information. However, this is not necessarily true.
> If decimal digits are worth 3.3 bits of information each then
> remembering 7 of them would result in 23 pieces of information. The
> average English word is worth approximately 10 pieces of information
> each and if the amount of information we can recall is to be
> regulated then it should follow that we should only be able to
> remember 23 pieces of information about English words, as with
> decimal digits which would subsequently mean that we could only
> recall two or three words at any one time. If that was true we would
> be in big trouble when it came to revising for and sitting exams!

I think Miller realised that recoding items into bigger chunks
effectively allowed any amount of information -- in the sense of the
number of bits that answer yes/no questions such as "is it a level 5
loudness" -- to be packed into a chunk.

> Miller refers to experiments carried out by Hayes and Pollack which
> reveal that the amount of information that is transmitted to memory
> does not remain exactly the same at all times but that the amount of
> information increases as the amount of information about each
> separate items increases. The limit for binary items was found to be
> approximately nine and for monosyllabic English words was found to be
> approximately five, hence "The Magic Number Seven Plus Or Minus Two".

This number is still being researched. I might give you some up to date
work on it once you have all understand the classical paper.

> In conclusion Miller states that our absolute judgment of a stimulus
> is limited by the amount of information attributed to that stimulus
> and that our immediate memory is limited by the number of items.
> Miller distinguishes between bits and chunks of information but
> states that the span of immediate memory does not necessarily depend
> on the number of bits in a chunk i.e. digits in a telephone number.
> He also states that this area still needs a lot of research.

I will explain bits vs. chunks next time.

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