Table Of ContentGabriel Altmann, Reinhard Köhler
Forms and Degrees of Repetition in Texts
Quantitative Linguistics
Editors
Reinhard Köhler
Gabriel Altmann
Peter Grzybek
Volume 68
Gabriel Altmann, Reinhard Köhler
Forms and Degrees
of Repetition in Texts
Detection and Analysis
DE GRUYTER
MOUTON
ISBN978-3-11-041179-9
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Foreword
The present volume is not a textbook of general quantitative text analysis; it
focuses only a single yet important aspect of textual phenomena: repetition. The
main purpose of the book is, obviously, the introduction of quantitative models
and methods for the analysis of repetition types and their individual character-
istics. Another significant aim is to show that the creation of a text is only to a
certain extent controlled by rules. It goes without saying, of course, that an
author is free to shape his/her text within the boundaries set by grammatical
and other linguistic rules and that these rules can even be violated. What is
known to a much lesser extent and what may become clearer to the reader of the
following chapters is that there are text laws, which govern the properties of
every text beyond conscious control by the author and beyond any grammatical
description. The lawfulness of textual phenomena on the one hand and the
freedom of the author on the other hand are only seemingly contradictions.
Only on the background of universal laws is it possible to recognise the individ-
ual characteristic of an author or a text. Individuality can be considered as a
specific set of values of the parameters of universal laws.
Repetition is just one of the textual phenomena which abide by laws. By
now, we know only a few corresponding hypotheses. The existence of these
laws must be postulated not only a priori as required for any kind of research
but is also a consequence of the fact that texts are made within a linguistic
community and have to meet certain needs. Some of these needs co-operate
with each other, some others compete. The dynamic system consisting of co-
operating and competing processes produces linguistic mechanisms which are
observable only by their consequences in form of laws. A text is the product of
self-regulating and self-organising cognitive and social mechanisms.
New hypotheses must be set up to investigate these mechanisms and a mul-
titude of texts and their properties must be studied. The empirical results are at
the same time the data by means of which the hypotheses are tested and pro-
vide heuristic stimulation for other hypotheses.
Text linguistics as a discipline has brought valuable conceptual achieve-
ments and progress in the description of text structure. Currently, however, the
epistemological status of this discipline does not surmount the domain of defi-
nitions and empirical generalisations and is, thus, still far from an explanatory
state. Maybe the time has not yet come to pursue a higher research goal, i.e. the
formulation of a text theory. Nevertheless, this book wants to give correspond-
ing impulses and show some methodological approaches on the basis of not
more mathematics than is absolutely needed. It combines the categorical analy-
VI | Foreword
sis of repetition into nine forms as described by Altmann (1988) and his meth-
odological approach with recent research results.
G.A. and R.K.
Contents
1 Introduction | 1
1.1 The universe of discourse | 1
1.2 Forms of repetitions | 4
1.3 Prolegomena for a future text theory | 6
2 Shapeless Repetition | 11
2.1 Phonic effects | 12
2.2 Two variables | 17
2.2.1 The activity index | 17
2.2.2 Excursus | 21
2.2.3 Comparing activity indices | 25
2.3 Global indicators | 31
2.3.1 Entropy | 33
2.3.2 Comparison of two entropy values | 37
2.3.3 The repeat rate | 38
2.3.4 Moments of distributions | 40
2.4 Modelling using probability distributions | 49
2.5 Some text laws | 63
2.5.1 The Zipf-Mandelbrot Law | 63
2.5.2 The Simon-Herdan Model | 73
2.5.3 Hřebíček’s Reference Law | 77
2.5.4 Type-Token Models | 80
2.5.5 Perspectives | 89
3 Positional repetition | 91
3.1 The rhyme in “Erlkönig” | 91
3.2 Open rhymes | 94
3.3 The gradual climax | 97
3.3.1 The linear climax | 97
3.3.2 Reduced climax | 99
3.3.3 The exponential climax | 101
3.4 Other positional repetitions | 106
4 Associative repetition | 111
4.1 Associative repetition of two words | 113
4.1.1 Short texts | 114
4.1.2 Long texts | 117
VIII | Contents
4.2 Presentation | 120
4.3 The minimal (acyclic) graph | 121
4.4 Vistas | 123
5 Iterative repetition | 127
5.1 Binary sequences | 128
5.2 Large samples | 133
5.3 Comparison of runs in two texts | 133
5.4 Runs of more than two kinds of elements | 135
6 Aggregative repetition | 137
6.1 Random distances: binary data | 137
6.2 Models of aggregation trends | 141
6.3 Brainerd’s Markov-chain model | 146
6.4 Non-binary data | 155
6.5 Similarity aggregation | 158
6.6 Vistas | 161
7 Repetition in blocks | 163
7.1 The Frumkina law | 164
7.2 Testing the Frumkina law | 166
7.3 Vistas | 174
8 Parallel repetitions | 177
8.1 Cochran’s Q-test | 178
8.2 Analysis of variance | 179
8.3 The chi-square test | 182
9 Cyclic repetition | 187
9.1 Fourier analysis | 189
10 Summary | 193
References | 195
Index | 203
1 (cid:31)Introduction
1.1 (cid:31)The universe of discourse
Repetition of textual elements is more than a superficial phenomenon. Repeti-
tion may even be considered as constitutive for units and relations in a text: on
a primary level when no other way exists to establish a unit – as in a musical
composition (a motif can be recognised as such only after at least one repeti-
tion) – and on a secondary, artistic level, where repetition is a consequence of
the transfer of the equivalence principle from the paradigmatic axis to the syn-
tagmatic one (cf. e.g., Jakobson 1971).
For our purposes, we do not presuppose any specific definition of the term
text. Any meaningful spoken or written sequence of linguistic units in a natural
language can be analysed by the methods presented in this volume. We do not
even presuppose fundamental properties such as cohesion and coherence; on
the contrary: there are objective methods which can be used to find such prop-
erties. In our examples, we will analyse only written texts, which makes the
procedures easy to follow and to reproduce by the reader.
We will use the term textual unit to denote any phenomenon in a text which
can be defined in an operational way, i.e. a phenomenon which can be identi-
fied unambiguously on a set of criteria and whose properties can be measured.
Here is a list of some commonly considered textual units:
Character Phrase Metrical foot
Grapheme Bar Lemma
Phoneme Clause Lexeme
Syllable Sentence Syntactic construction
Morph, Morpheme Paragraph Hreb
Word-form Sememe Motif
Numerous textual units can be found in works on text-linguistics such as Koch
(1969, 1971), Daneš / Viehweger (1977), Gottman / Parkhurst (1980), Dressler /
de Beaugrand (1981), Hřebíček (1997, 2000). All such units possess (or better:
can be ascribed) an unlimited number of properties, with respect to which the
researcher can classify the units. Some examples of properties of the word
HOUSE are the following ones:
2 | Introduction
Property Value
Length in characters 5
Length in syllables 1
Length in morph(eme)s 1
Part-of-speech Noun
Number of meanings (polysemy) n
Number of metaphorical meanings k
Polytextuality (no. of texts in a t
corpus in which the unit occurs)
Number of compounds (productivity) m
Number of derivations (productivity) d
Inflectional paradigm regular
Relative frequency p
Origin Germanic
Number of contexts (polytextuality) r
Number of synonyms x
Number of variants in a dialect atlas y
Every unit can also be considered from the point of view of its function in the
discourse and with respect to other relations. Here, some of them are listed:
Grammatical function Reference Co-reference
Anaphora Cataphora Poetic figure
Speech Act Metaphor Argumentation
Each of them can be subdivided into individual kinds or categories, such as the
argumentation relations for instance into {background, circumstance, non-
volitional cause, volitional cause, contrast, condition, concession, evaluation,
elaboration, …} or speech acts e.g., (after Searle 1969) into {assertives, direc-
tives, commissives, expressives, declarations}. Thus, not only the units can be
studied but also their properties, i.e. classes of units sharing one or more prop-
erties, and their functions. Generally, the term repetition will be used in the
sense of occurring several times in a text. There are various reasons why a tex-
tual unit may occur repeatedly in a text:
(cid:31)(cid:31) Limitation of inventory. If an inventory is small, the corresponding units
must occur with a frequency greater than one. In an English sentence with,
say 50 characters, some characters will occur repeatedly since the character
inventory is smaller than 50. On the other hand, sentences need not be re-
peated for reasons of inventory size because there is no limited number of
sentences in a natural language. The repetition of units from a finite but not
too small inventory such as the morpheme inventory of a language may be
used as an indicator of creativeness.
