Miller: Magical Number 7 +/- 2

From: Baden, Denise (
Date: Fri Nov 10 1995 - 16:12:38 GMT

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George Miller:
 undertook experiments to test how accurately people can
assign numbers to the magnitudes of various aspects of a stimulus
i.e. experiments in absolute judgement. Also referred to as the
capacity of people to transmit information. He introduces the
concept of variance, saying that an increase in variance leads to an
increase in information . If there is a high variance we don't know
what will happen so an observation will yield a large amount of
information. conversely, a low variance means we know what will
happen, so an observation will not yield much information.

In experiments on absolute judgement the subject is thought of as a
communication channel. The amount of overlap/concensus between the
inputted stimuli (the information given to the subject) and the
output (subjects responses/answers) = the amount of transmitted
information. A 1:1 relationship = no errors. If the output
information is less than the input information, errors have
occurred. The normal profile of the 'channel capacity' of a subject
is that as the input information is increased, the transmitted info
increases at first, then levels off as more errors are made.

Terminology: Miller uses 'bits of information' i.e. every time the
number of alternatives is increased by a factor of 2. 1 bit of
information is added. Thus 2 bits of info corresponds to 4
alternatives, 4 bits of info to 16 options etc.

Unidimensional stimuli: Listeners were asked to identify tones
varying from 100-8000 cps, by assigning each frequency with a
number. At up to 3 tones, responses were all correct. at 4 different
tones, occasional confusions occurred. 5+ tones led to frequent
confusion. It was found that the amount of transmiited info
increased linearly up to about 2 bits (4 tones) and plateaued at
around 2.5 bits (6 tones). This means that, exceptional musical
ability aside, we cannot pick more than 6 different pitches that the
listener will never confuse. N.B. I was interested to hear how
little this varied according to the gaps between the stimuli i.e.
whether a narrow or a wide range of frequencies were used.
Judgements on loudness gave a channel capacity (cc) of 2.3 bits (5
alternatives). Judgements on taste intensity gave a cc of 1.9 bits
(4 taste options). Visual judgements gave 3.5 bits. This was the
largest cc measured and accords with the view that visual perception
is our primary sense.

Miller speculates that this narrow range may be built into us either
by learning or the design of our nervous systems: "we possess a
finite and rather small capacity for making such unidimensional
judgements and this capacity does not vary a great deal from one
simple sensory attribute to another". However, we can identify
thousands of faces, objects, words etc. but this may be because
these stimuli vary in many dimensions.

2-dimensional judgements: the cc for determining the position of a
dot in a square was 4.6 bits (24 positions). Saltiness + sweetness
judgements gave 2.3 bits. The cc for saltiness only was 1.9 bits.
loudness + pitch yielded 3.1 bits (2.5 and 2.3 bits were obtained
for pitch and loudness respectively). So the extra dimension
increases the cc, but not by a factor of 2.

6-dimensional judgements: the cc for absolute judgement on stimuli
varying along 6 accoustic variables was 7.2 bits (150 categories).

Miller concludes that the addition of varying attributes to the
stimulus increases the channel capacity, but at a decreasing rate.
So as we add more variables we increase the total capacity, but
decrease accuracy for any particular variable. This is probably
adaptive, as in a changing world it is better to have a liitle info
about a lot of things than have a lot of info about a small segment
of our enviroment.

When it comes to immediate memory, an experiment by Pollack showed
that the amount of info transmitted increases almost linearly as the
amount of info per item is increased.

To return to my point in the seminar about 'The Mind of a
Mnenomist', if one considers that the amount of info S recieved in
each stimulus was high (eg words/ numbers also conjured up shapes,
colours, texture, sounds, smells, tastes etc) then it follows from
Millers paper that he should have an exceptional memory. S, for
example sees '8' as naive, milky blue and 'red' as a man in red
shirt coming towards him. If one broke down his experience of a
stimulus into the number of dimensions it had for him, the number
would be phenomenally high. Pollacks experiment showed that 1 bit of
info per item led to about 8 items being retained; 5 bits of info
led to 35 items being retained. Therefore if the stimulus contained
50 bits of information, the linear scale suggests he should be able
to record 350 items. I don't suggest that S's synaesthesia can explain
all of his abilities, such as his long-term recall and difficulty in
forgetting, but I believe his synaesthesia is related to a great extent
to his phenomenal memory.

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