(Note: In Papiere
zur Linguistik 62/63, 2000, pp 3-14. In case of any discrepancy with the printed version,
the printed version will be the ‘authorized’ version.)
The magical number seven in language
and cognition: empirical evidence and prospects of future research
Gertraud
Fenk-Oczlon and August Fenk,
The first part of this paper is a collection of more or less confirmed occurrences of the magical number 7 in language and of more or less explicit assumptions regarding limits such as the following:
In
crosslinguistic comparison the mean number of syllables per clause seems to be
restricted to a range of 5 to 10 and the
mean length of lexemes to a range of 7
plus minus 2 segments. The upper limit of phonemes per syllable is said to be 9
and languages with more than 9 basic vowels are quite uncommon. 9 or 10 seems
to be the upper limit of gongs per phrase in drum languages and of syllables
per word in whistled speech. Even the mean number of the languages’ cases,
gender and person distinctions is likely to be located in this range.
The second
part offers a theoretical framework for a unified theory of such phenomena. It
is argued that these limits in the range of about 7 plus minus 2 first of all
reflect capacity limits of our working memory (immediate memory span, focus of
attention). Further considerations regard some possible ways in which these
constraints are also manifested in long-term memory materials, i.e. categories
such as case, gender, and person systems.
Introduction
This paper does not
represent the state of the art within an elaborated domain of linguistic
research, nor is it a typical empirical study starting with hypotheses,
operationalizations, and so forth. It is
rather a “collection”:
·
A collection of occurrences of the magical
number 7, plus or minus 2, in linguistic studies.
·
A collection of open questions and ideas for
future research comprising statistical examinations of hypothesized limits in
the region around 7 as well as possible classifications and a more or less unified theory of relevant phenomena.
In the psychology of
information processing the number 7 is a somewhat “magical” invariant:
According to Miller (1956) it manifests itself as a constraint of the span of
absolute judgment, the span of immediate memory, and of the span of attention.
This limit (or these limits?) of about seven, plus or minus two, has (or have)
since figured prominently in information processing theories. Miller (1956: 91)
warned against assuming “that all three spans are different aspects of a single
underlying process”. But “generality” is a relevant dimension of empirical
progress. Thus it is still tempting to search for one “underlying
process” or for one “covering law” for several regularities
corresponding with each other in a certain respect.
Arguments
presented in Fenk-Oczlon & Fenk (2001a,b) point to the behavioral relevance
of the magical number 7 in general - independently of the sense modality of the
input or even independently of whether the respective activity is of rather
afferent/perceptual or efferent/motoric nature, and independently of whether
one analyzes activities of human beings or non-human animals. As suggested by
the experimental findings by Köhler (1952) with birds and by Brannon &
Terrace (2000) with non-human primates, this limit of about 7 is no specific
characteristic of human information processing. A fascinating finding is
reported by Kareev (2000): Small series of about 7 plus minus 2 data pairs
produce stronger correlations between the respective variables than the
population. This would mean that a span of comprehension comprising about 7
elements or chunks of elements does not reflect a rather arbitrary cognitive
limit, but that there must have been a selective advantage and selective
pressure for pushing up the limit to this region where minimal indications and
minimal contingencies can be detected with a minimum of “computational” work.
All these
findings were discussed as indicating some general, extralinguistic or
pre-linguistic cognitive preconditions of language, i.e. some sort of “matrix”
allowing for as well as constraining the evolution of our complex language
system. Is it possible to see some more specific communalities, if one
concentrates on those limits that seem to occur in different fields of linguistic
research?
Linguistic information is a special type of message processed by our cognitive apparatus. If the number seven marks some general limits of this apparatus, it should also show in languages, because language must have developed in adaptation to the general constraints of this apparatus (Fenk-Oczlon & Fenk 2001a).
Relevant
observations and assumptions
The following list of
manifestations comprises cases where the
magical number seven marks the middle of the range of variation (from 5 to 9)
as well as cases where it rather marks
the upper end of variation. And it includes cases where the distribution within
the respective range was already subject to statistical examinations as well as
cases where the limits of variation have the character of as yet uninvestigated
assumptions.
a) In
crosslinguistic comparison (n = 34 languages) the mean number of syllables per
proposition seems to be restricted to a
range of 5 - 10 syllables (Fenk-Oczlon
1983, Fenk-Oczlon & Fenk 1999)
Moreover, we found a
significant crosslinguistic correlation (Fenk-Oczlon & Fenk 1985): the
higher a language’s mean number of phonemes per syllable, the lower the mean
number of syllables per simple declarative sentence. This negative correlation
between number and complexity (duration) of syllables indicates time related
constraints determining this span from 5 - 10 syllables, as does the whole set
of significant crosslinguistic correlations (Fenk & Fenk-Oczlon 1993) found
between the dimensions number of phonemes per syllable, number of syllables per
word, number of syllables per sentence, and number of words per sentence.
Kien et al. (1991) have described comparable action units in humans and
non-human primates, and we have suggested (Fenk-Oczlon & Fenk 2001a) that
intonation units be viewed as a special
case of action units. From this point of view it seems tempting to identify and
measure this segmentation in recordings of, on the one hand, special human
languages not only in the acoustic mode (like drum language and whistled
speech) but also - probably more difficult - of sign languages. On the other
hand it would be interesting to study and analyze the size (in terms of
duration as well as in terms of number
of elements) of the chimpanzees’ tonal patterns or segments of
vocalization.
b) 9
syllables per word is likely to be a maximum in German (Menzerath 1954).
It would be interesting
to study if this is a maximum value in general.
c) The
maximum number of phonemes per syllable
seems to be restricted to the region of about
9 phonemes.
According to Menzerath
(1954) the maximum number of phonemes per syllables is 7 in Rumanian and 8 in English and German. Gil (1986)
studied a list of 170 languages in the
Stanford Phonology Archive and found
that “the most complex syllable structures observed were assigned value
9 - for example, the (C) (C) (C) V (V)
(C) (C) (C) (C) template of English”. (Gil 1986:204)
d) More than
80% of the languages investigated by Crothers have from 3 to 7 vowels, and
languages with more than 9 basic vowel qualities seem to be quite uncommon (Crothers 1978: 104, 113).
Only 6 languages in his
list (Crothers 1978:143) of 209 languages have
more than 9 vowels. Four of these 6 languages have 10 vowels, one has 11
(French), and another one 12 (Pacoh).
e) According to
Miller (1956), referring to Jakobson et al. (1952), there are about 8 or 10
dimensions (distinctive features) that
distinguish one phoneme from another.
f) The
average length of a word is approximately 7 plus minus 2 segments (Nettle
1995).
Nettle found a tradeoff
between word length and inventory size in a sample of ten languages: The bigger
the segmental inventory size in a language, the shorter the average length of a
word. Nettle obtained this finding by determining the word length of isolated lexical
entries in dictionaries, e.g. the infinite form of verbs. It would, however, be
interesting to determine the mean length of words within spoken or written sentences with all their grammatical
affixes.
g) Drum
languages: about 6 to 10 gong-phrase syllables are produced (sent, needed) for
every syllable in a spoken word.
In the
h)Whistled
speech:
The word length seems to be restricted to about nine syllables.
Charalambakis (1994)
studied whistled speech in Antia on the Greek
i) The
average number of cases in languages seems to be restricted to 5.6 terms with
cumulative exponents and to 7.3 terms with separatist
exponents (Plank 1986).
According to Plank
(1986:32) ”cumulative exponents simultaneously express at least two
co-occurring inflexional categories without being formally segmentable into two
or more parts, while separatist exponents express only one inflexional
category of a word form.”
In a later
study, Plank (1999:321f) again separates two (dichotomic) parameters of the
description of case - separation versus cumulation and invariance versus
variance. He assumed that “cumulation and variance are both inherently
uneconomical” and could not see any
cogent
immediate reason why cumulation should go with variance and separation with
invariance in the first place, rather cumulation ought to come with
(economical) invariance and (economical) separation with (uneconomical)
variance. (Plank 1999:322)
We think that frequency
(token frequency) is the key concept
that offers a rather simple explanation: If a language has predominantly
multifunctional cases (one case “accumulates” two or more functions), then this
language will manage with a rather low number of case forms but will need and
use each one of these case forms very often (high token frequency). And signs
with high token frequency tend to both
high variance and short coding for obviously economic reasons (e.g. Zipf
1929, Mandelbrot 1954, Fenk-Oczlon 2001). This explanation should also hold for
“split morphology“ - cumulation/variance and separation/invariance - within
languages: The most frequent cases in a given language will tend to cumulation
and variance. By the way: We assume that
a language‘s speech rhythm interacts with both parameters, cumulation/variance
and separation/invariance, and that there is, on the one hand, a
covariation between stress rhythm, cumulation and variance, and, on the other
hand, between syllable rhythm, separation and invariance.
The highest
number of cases we found so far is 15 (Udmurt). The often reported “giant” number of case categories of
the East Caucasian languages is according to Plank “somewhat misleading, and
quantitatively fairly exaggerated.” (Plank
1986: 44)
j) The number
of crosslinguistic aspectual/temporal gram types seems to be restricted to six (Bybee & Dahl 1989).
k) The number of gender distinctions seems to be
restricted to about 13.
Corbett (1991:55)
reports that Yimas, a Papuan language,
“has eleven noun classes or genders”, and in Arapesh there seem to be
thirteen genders (Corbett & Frazer 2000:316). These are, with the exception of Fula (see below), the
highest values we could found so far.
Bantu languages are said to have extensive gender systems comprising between 10 and 20 noun classes. But actually they have only between 5 and 10, because singular and plural are counted (cf. Corbett 1991:47) as separate classes.
An exception
to this limit of about 11 might be Fula (a West African language) which has,
according to Corbett, about twenty genders in the singular, depending on the
dialect, and five in the plural. “There
are evident semantic principles involved in gender assignment, but many unclear
cases remain” (Corbett 1991:191f). Maybe it is also possible in this case to
identify a factor reducing this extraordinary large repertoire.
l) The
average number of personal pronouns (excluding gender specifications) of 71
languages is about 8.
When analyzing the
person systems of 71 languages from data presented by Forchheimer (1953) and
Ingram (1975) we found a mean number of
8.154 and a median of 7.36.
Among these 71 languages the six-person system was the most frequent, followed by eleven-person system, seven-person system and nine-person system. The maximum was a fifteen-person system.
And it is at least remarkable that in some American Indian languages the pronouns of third person have again a sevenfold classification (Forchheimer 1953).
Discussion
The (hypothesized)
constraints a - h refer to phonological properties and constraints i - l to
grammatical categories. But only few of them can be regarded as a direct
manifestation of immediate memory span (see section A below). Nevertheless an
attempt is made (in section B) to
explain at least some of the remaining universals on the basis of
organisational processes of memory. One of the relevant assumptions: “We will assume that information in semantic
memory is highly organised, and that categorical clustering reflects this
underlying organisation.” (Eysenck 2000:327, referring to Mandler 1967).
(A) The magical
number seven and the immediate memory span
We will at first focus
on considerations regarding the rather direct influence of “focal attention”
and “immediate memory span”. The planning of a whole clause as well the
comprehension of a sentence in its entirety requires a sufficient size of our
immediate memory, or, to put it the
other way round, presupposes that clauses have to be short enough to fit into
this span.
Five very
complex or ten very simple syllables forming a clause (constraint a) or nine
syllables forming an extraordinary long word (constraint b) seem to fit into
such a span. Constraint g (regarding drum languages) and constraint h
(regarding whistled speech) can be explained by such a span as well:
If the
repertoire of the most elementary signs is very small - e.g. only three
elements in the Morsealphabet - , then the equivalence to our graphemes,
syllables, words, sentences (supersigns of different levels) will be
proportionately longer. The segmentation of
an auditorily transmitted message has again to take into account our
immediate memory span: About ten gongs in drum language (constraint g) or
“syllables” of whistled speech (constraint h) seem to mark the upper limit of
such segments or “clauses” in these special languages.
Miller (1956)
postulated a “constant” capacity of short term memory when its capacity is
measured in terms of number of chunks. Baddeley et al. (1975) argued that there
is no valid operationalization of “chunk” and explored in a number of
experiments
the
hypothesis that immediate memory span is not constant, but varies with the
length of the words to be recalled. Results showed: (1) Memory span is
inversely related to word length across a wide range of materials; (2) When
number of syllables and number of phonemes are held constant, words of short
temporal duration are better recalled than words of long duration; (3) Span
could be predicted on the basis of the number of words which the subject can
read in approximately 2 sec (Baddeley et al. 1975: 575)
To cut the arguments of
Baddeley et al. short: constant is nothing but the duration of about 2
sec, not the number of any “chunks” or
any better identifiable units such as words or syllables. If measured in terms
of the number of items (syllables, words), the span of immediate memory (1986:
44) depends on the articulation rate, i.e. the number of syllables or words
that a person can articulate within about 2 sec.
In a later study Baddeley (1994) at first
confirms his theory of a time based span: “The fact that span is strongly
influenced by the spoken duration of the words suggests a system that is time
based rather than chunk based.”(Baddeley 1994:355) But then he admits:
Zhang
and Simon concluded that there is a need to assume effects of both the spoken
duration of the items, as proposed by the Baddeley and Hitch (1974) working
memory model, and also of number of chunks. I accept this and suggest that the
chunking effects may be dependent on the operation of the central executive component
of working memory. (Baddeley 1994:355)
So far Baddeley’s
position regarding the controversy
“constancy of time” versus “constancy of number of units”.
But how about
the “constancy of information” which is in some respects suggested in Miller 1956
and is explicitely postulated in Miller & Selfridge (1950). Baddeley
(1994:354) admits that information theory was rather successful in the area of
language, because it emphasizes the redundancy of language. In this context he
mentions as an example the study by
Miller & Selfridge (1950). Within psychology, however, “the precise
measures of information-processing capacity have proved to be much less
valuable.” (Baddeley 1994: 354).
From our
point of view, this is a rather artificial differentiation, because it was exactly the aim of Miller
& Selfridge to demonstrate, by varying the redundancy of the word strings
to be recalled, that our memory’s capacity in terms of information remains
constant or invariant despite changes of the redundancy of materials.
More
generally we would like to argue that the scepticism regarding the potential of
information theory of e.g. Baddeley (1994) or Shiffrin & Nosofsky (1994)
comes from some misconception of information. Our points in this respect
(Fenk 1986):
·
The sceptics stick to the concept of objective
information.
·
Maybe it is nowhere possible to determine
objective information. Assertions regarding “objective” information would
afford that objective probability values are available, which is not really possible
in empirical science. Anyhow, concerning fixed cpacity limits in
psychology, only subjective information (see next point) can be
relevant.
·
Whatever might have been the original goal of
Shannon‘s (1951) measuring instrument,
the guessing game technique - what it
really and objectively measures is, like “item-
difficulty” in psychology, a relation between certain problem
solvers (guessing persons) and problem (reconstruction of a text): a higher
number of errors in the guessing procedure, does not reflect higher information
per se, but a higher information (higher uncertainty) of the text for
the respective guessing subject or collective of subjects.
Some consequences of
this approach:
a) If Miller & Selfridge had tested the subjective information of their
different word sequences and defined the
y-axis of their famous diagram (1950:181) in terms of bits recalled, the
empirical data would form a straight horizontal line. More central for the
present topic:
b) The controversy
between “constancy of chunks” and “constancy of information”disappears:
From this
point of view, cognitive mechanisms or strategies like chunking and semantic
clustering are methods that enable us - in spite of strict limitations
concerning the subjective information - to expand our capacity as defined in
terms of “objective” information (Fenk 1985:362; for a broader discussion see
Fenk 1986: 212 ff.)
In summary:
There is no theoretical or empirical reason for denying the possibility of
linguistically relevant constraints in all three dimensions - time (in sec),
information (in bits), and number of units (“chunks”, syllables). From this one
may expect “constancy” principles in all three dimensions. Crosslinguistic
computation of already condensed data (mean values per single language) should
show per clause not only a relatively constant number of syllables, but also a
relatively constant duration and informational content.
(B) How does
the magical number seven get from immediate to long term memory?
If it is the immediate
memory span which determines the range of about 7 plus minus 2 (7 plus 8 or
minus 4) units - how can it have any effects on the restrictions for the
repertoires of gender, of case, and of person?
It is at
least remarkable that 15 was not only the maximum in the person, case and
probably also gender systems but is also reported (by Miller 1956) to be the
highest number of categories a subject can simultaneously handle in absolute
judgment experiments: the mean number of categories that a person could simultaneously
handle was 6.5, the range was from 3 to 15 categories. “Seven plus or minus
two” is perhaps only a catchy and simplifying description of this distribution.
Die begrenzte Kapazität des Primär-Gedächtnisses mag eine
entscheidende Rolle bei der Bestimmung der Organisation des mit großer
Kapazität ausgestatteten Sekundär-Gedächtnisses spielen. Wenn das
Primär-Gedächtnis die Funktion eines Arbeitsspeichers hat, in dem neu
angekommene Information so lange aufbehalten wird, bis sie erfolgreich in die
Struktur des Sekundär-Speichers integriert werden kann, dann gehen die
Beschränkungen des ersteren auf das zweite über. Dies würde bedeuten, daß
Material im Dauer-Gedächtnis in Gruppen von nicht mehr als fünf bis sieben
items kategorisiert oder in anderer Form eingeteilt wird, da mehr durch den
Flaschenhals des Primär-Gedächtnisses gleichzeitig nie hindurchgehen.
Wir dürfen auch die Möglichkeit nicht außer acht lassen, daß
die zwei Gedächtnissysteme verschiedene Eigenschaften derselben physischen
Struktur darstellen können.(Norman 1973:230f.)
In some respects similar
is another possible explanation that is “nearer” to linguistic categories in
“secondary memory” and has, moreover, the advantage of being sufficient without
the metaphor of the restricted bottle-neck of consciousness:
Most
apparently, there are two reasons for rapid language acquisition in children:
Some sort of neuronal predisposition or program for the “implementation” of
language, and, more generally, the extremely high efficiency of learning
because of its active hypothesis-testing nature
(Fenk 1986:214). If one is generating and testing rule based hypotheses
about how a sentence might continue or what might be a well formed sentence,
one always has to reactivate or memorize the “repertoire” of possibilities
regarding gender, case, person, etc. Since reactivating and memorizing are
characteristics of the activities of our
working memory, such repertoires should not exceed this working memory’s
capacity. Natural languages could only develop in a way which allows for such
cognitive constraints.
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