The length of words reflects their conceptual complexity 1 The length

The length of words reﬂects their conceptual complexity 1

The length of words reﬂects their conceptual complexity

Molly L. Lewis

Department of Psychology, Stanford University

Michael C. Frank

Department of Psychology, Stanford University

We gratefully acknowledge the support of ONR Grant N00014-13-1-0287 and a John Merck

Scholars award to MCF.

Address all correspondence to Molly L. Lewis, Stanford University, Department of Psychology,

Jordan Hall, 450 Serra Mall (Bldg. 420), Stanford, CA, 94305. Phone: 650-721-9270. E-mail:

[email protected].

The length of words reﬂects their conceptual complexity 2

Abstract

Are the forms of words systematically related to their meaning? The arbitrariness of the sign has

long been a foundational part of our understanding of human language. Theories of communication

predict a relationship between length and meaning, however: Longer descriptions should be more

conceptually complex. Here we show that both the lexicons of human languages and individual

speakers encode the relationship between linguistic and conceptual complexity. Experimentally,

participants mapped longer words to more complex objects in comprehension and production tasks

and across a range of stimuli. Explicit judgments of conceptual complexity were also highly

correlated with implicit measures of study time in a memory task, suggesting that complexity is

directly related to basic cognitive processes. Observationally, judgments of conceptual complexity

for a sample of real words correlate highly with their length across 80 languages, even controlling

for frequency, familiarity, imageability, and concreteness. While word lengths are systematically

related to usage—both frequency and contextual predictability—our results reveal a systematic

relationship with meaning as well. They point to a general regularity in the design of lexicons and

suggest that pragmatic pressures may inﬂuence the structure of the lexicon.

Keywords: communication, lexicon, language evolution

The length of words reﬂects their conceptual complexity 3

Introduction

Human languages are systems for encoding information about the world. A deﬁning feature

of a symbolic coding system is that there is no inherent mapping between the form of the code and

what the code denotes (Peirce, 1931)—the color red holds no natural relationship to the meaning

‘stop’, the numeral 3 holds no natural relationship to three units, and in language, the word ‘horse’

looks or sounds nothing like the four-legged mammal it denotes. The arbitrariness of the linguistic

sign has long been observed as a fundamental and universal property of natural language

(Saussure, 1916, 1960; Hockett, 1960). And, despite the growing number of cases suggesting

instances of non-arbitrariness in the lexicon (see Schmidtke, Conrad, & Jacobs, 2014, for review),

there is clear evidence for at least some degree of arbitrariness in language based only on the

observation that different languages use different words to denote the same meaning (e.g., the word

for horse in English is “horse” but is “at” in Turkish).

However, the arbitrary character of language holds only from the perspective of the analyst

observing a language system from the outside; from the perspective of an individual speaker, the

goal of communication provides a strong constraint on arbitrariness. Perhaps this communicative

constraint—roughly, that if my words were any different, I couldn’t use them to talk to you—is

why language doesn’t seem arbitrary to us. Put another way, Saussure (1916, 1960)’s insight was

an insight because the form of language typically feels just right for the use to which we put it,

namely talking to other people.

A rich body of theoretical work has explored communicative regularities in the use of

particular forms to refer to particular types of meanings in context—the study of pragmatics

(Grice, 1975; Horn, 1984; H. H. Clark, 1996). Broadly, this work argues that language users

assume certain regularities in how speakers refer to meanings, and through these shared

assumptions, the symmetry of the otherwise arbitrary character of language is broken. For

example, consider a speaker who intends to refer to a particular apple on a table. Because language

is a priori arbitrary, there are a range of ways the speaker could convey this meaning (e.g., “the

The length of words reﬂects their conceptual complexity 4

apple,” “the banana,” “the green apple,”“the green apple next to the plate,” etc.), but the speaker is

constrained by pragmatic pressures of the communicative context. If the listener also speaks

English, the phrase “the banana” will be an unhelpful way to refer to the apple. Furthermore, if

there is only one apple on the table, the phrase “the green apple” will be unnecessarily verbose

given the referential context. These constraints might lead a speaker to select “the apple” as the

referring expression, because it both allows the listener to correctly identify the intended referent

while also minimizing effort on the part of the speaker.

In the present paper, we examine whether principles of communication inﬂuence the

otherwise arbitrary mappings between words and meanings in the lexicon. This hypothesis is

motivated by a regularity ﬁrst observed by Horn (1984), who noted that pragmatic language users

tend to consider the effort that speakers have exerted to convey a meaning. For example, consider

the utterance “Lee got the car to stop,” which seems to imply an unusual state of affairs. Had the

speaker wished to convey that Lee simply applied the brakes, the shorter and less exceptional “Lee

stopped the car” would be a better description. The use of a longer utterance licenses the inference

that there was some problem in stopping—perhaps the brakes failed—and that the situation is more

complex.

We ask whether speakers reason the same way about the meanings of words, breaking the

symmetry between two unknown meanings by reference to length. Speciﬁcally, we test the

following hypotheses:

Complexity Hypothesis 1: Speakers have a bias to believe that longer linguistic forms

refer to conceptually more complex meanings.

Complexity Hypothesis 2: Languages encode conceptually more complex meanings

with longer linguistic forms.

These two hypotheses are in principle independent from one another, and we test them separately.

We see them as potentially emerging together from the same interactive forces, however, and we

The length of words reﬂects their conceptual complexity 5

return to this relationship in the General Discussion.

An important construct for our hypothesis is the notion of conceptual complexity. One

theoretical framework for understanding this construct is through semantic primitives (e.g., Locke,

1847). Semantic primitives can be thought of as the building blocks of meaning, similar to the

notion of geons in the study of object recognition (Biederman, 1987). The space of possible

meanings could then be described in terms of sets of semantic primitives. In this framework, a

more complex meaning would be one with more primitives in it. (In a probabilistic framework,

having more units would also be correlated with having a lower overall probability). While our

work here does not directly address the character of these underlying semantic primitives, it

assumes that such a unit exists and that meanings can vary in the number of their compositional

primitives.

In the remainder of the Introduction, we ﬁrst review prior work suggesting that

communicative principles are reﬂected in the structure of the lexicon. We then review work related

to accounts of our particular linguistic feature of interest—variability in the length of forms. Then,

in the body of the paper we test the complexity hypotheses above in nine experiments and a corpus

analysis.

Pragmatic equilibria in the lexicon

The present hypotheses are motivated by the possibility that language dynamics take place

over different timescales, and these different dynamics may be causally related to each other

(Christiansen & Chater, in press; McMurray, Horst, & Samuelson, 2012; Blythe, 2015). Our two

hypotheses correspond to two distinct timescales. Hypothesis 1 corresponds to the timescale of

minutes in a single communicative interaction—the pragmatic timescale. Hypothesis 2

corresponds to the timescale of language change, which takes place over many years—the

language evolution timescale. We consider the possibility that communicative pressures at the

pragmatic timescale may, over time, inﬂuence the structure of the lexicon at the language evolution

The length of words reﬂects their conceptual complexity 6

timescale. Although a complexity bias at the language evolution timescale has not been previously

explored, there are a number of other cases in which pragmatic equilibria are reﬂected in the

structure of the lexicon. Here, we describe three such cases: semantic organization, ambiguity, and

one-to-one structure.

Several broad theories of pragmatics include a version of two distinct pressures on

communication: the desire to minimize effort in speaking (speaker pressure) and the desire to be

informative (hearer pressure; Zipf, 1936; Horn, 1984). Importantly, these two pressures trade off

with each other: The optimal solution to the speaker’s pressure is a single utterance that can refer

to all meanings, while the optimal solution to the hearer’s pressure is a longer utterance that

presents no ambiguity. The utterance that emerges is argued to be an equilibrium between these

two tradeoffs.

At the timescale of language evolution, there are a number of cases in which these

pragmatic equilibria are reﬂected in the lexicon. One way these equilibria are reﬂected is in the

size of the semantic space denoted by a particular word. From the hearer’s perspective, Horn

argues there is a pressure to narrow semantic space (Horn, 1984). This reﬂects the idea that the

hearer’s optimal language is one in which every possible meaning receives its own word. One

example of this is the word “rectangle,” which refers to a quadrilateral with four right angles. A

special case of a “rectangle” is a case where the four sides are equal in length, which has its own

special name, “square.” Consequently, the term “rectangle” has been narrowed to mean a

quadrilateral with four right angles, where the four sides are not equal. From the speaker’s

perspective, there is a pressure for semantic broadening. This is because the speaker’s ideal

language is one in which a single word can refer to a wide range of meanings. An example of this

is the broadening of brand names to refer to a kind of product. For example, “kleenex” is a product

name for facial tissues, but has taken on the meaning of facial tissues more generally.

The opposition of these two semantic forces predicts an equilibrium in the organization of

semantic space that satisﬁes the pressures of both speaker and hearer. A growing body of empirical

The length of words reﬂects their conceptual complexity 7

work tests this prediction by examining the organization of particular semantic domains

cross-linguistically (see Regier, Kemp, & Kay, 2015, for review). They ﬁnd that languages show a

large degree of similarity in how they partition semantic space for a particular domain, but also a

large degree of variability. This work demonstrates that the attested systems all approximate an

equilibrium point between speaker and hearer pressures.

Kemp and Regier (2012) demonstrate this systematicity in the semantic domain of kinship.

For each language, they developed a metric of the degree to which Horn’s speaker and hearer

pressures are satisﬁed. A language that better satisﬁes the hearer’s pressure is one that is more

complex, as measured by the description length of the system in their representational language. A

language that better satisﬁes the speaker’s pressure is one that requires less language to describe

the intended referent. To understand this, consider the word “grandmother” in English: This word

is ambiguous in English because it could refer to either the maternal or paternal mother, and so

identifying which mother the speaker is referring to is more costly in English than in a language

that encodes this distinction lexically. They ﬁnd that the set of attested languages is a subset of the

range of possible languages, and this subset partitions the semantic space in a way that near

optimally trades off between pragmatic pressures. This type of analysis has also been done for the

domains of color (Regier, Kay, & Khetarpal, 2007), lightness (Baddeley & Attewell, 2009), and

numerosity (Xu & Regier, 2014).

A second phenomenon that is predicted by these pressures is cases where there are multiple

meanings associated with a word from a context-independent perspective, or cases of lexical

ambiguity. Lexical ambiguity is present in both open-class words like “bat” (a baseball instrument

or a ﬂying mammal) and closed-class quantiﬁers like “some” (“at least one and possibly all” or “at

least one but not all”). Lexical ambiguity is tolerated because the meaning is usually easily

disambiguated by context. When the word “bat” is uttered while watching a baseball game, the

mammal usage of the word is very unlikely. The presence of this type of ambiguity can be viewed

as an equilibrium between the two pragmatic pressures: If the meaning of a word can be

The length of words reﬂects their conceptual complexity 8

disambiguated by the referential context, then it would violate the speaker’s pressure to minimize

effort by keeping track of two distinct words.

Indeed, recent work by Piantadosi, Tily, and Gibson (2011a) reveals systematicity in the

presence of lexical ambiguity in language. They argue that ambiguity results from a speaker based

pressure to broaden the meaning of a word to include multiple possible meanings. In particular,

they suggest that this pressure should lead to a systematic relationship between the presence of

ambiguity and the cost of a word. According to their argument, costly words (in terms of length,

frequency, or any metric of cost) that are easily understood by context violate the speaker’s

principle to say no more than you must. Consequently, there should be a pressure for these

meanings to get mapped on to a different, less costly word. This word may happen to already have

a meaning associated with it, and so the result is multiple meanings being mapped to a single word.

For example, in the case of the word “bat,” a speaker could instead say “baseball bat.” But, because

this referent is easily disambiguated in context from the mammalian meaning, a speaker pressure

should result in the use of the shorter form. This leads to a testable prediction that shorter words

should tend to be more ambiguous. Through corpus analyses, Piantadosi et al. (2011a) ﬁnd this

precise relationship between cost and ambiguity. Across English, Dutch and German, they ﬁnd that

shorter words are more likely to have multiple meanings.

An additional case of this lexical ambiguity is found in words that have very little

context-independent meaning, known as indexicals or deictics (Frawley, 2003). These words get

their meaning from the particular referential context of the utterance, and are therefore highly

ambiguous from a context-independent perspective. There are many types of indexicals that are

present to varying degrees across languages. An example of a temporal indexical form is

“tomorrow.” The context-independent meaning of this word is something like “the day after the

day this word is being uttered in.” Critically, abstracted from any context, this word has little

meaning; it is impossible to interpret without having knowledge about the day the word was

uttered. This phenomenon is also present in person pronouns (e.g. “you” and “I”) and spatial

The length of words reﬂects their conceptual complexity 9

forms, like “here” and “there.” As for lexical ambiguity, this type of ambiguity is a predicted

equilibrium point from Horn’s principles: If the hearer can recover the intended referent from

context, the speaker would be saying more than is necessary by using an overly-speciﬁc referential

term (e.g., “December 18th, 2014” vs.“tomorrow”). Language structure reﬂects this pressure

through lexicalized ambiguity in the form of indexicals.

Finally, the relationship between the meanings of different words can be seen as a

consequence of pragmatic principles. A number of theorists have noted a bias against two words

mapping onto the same meaning — that is, a bias against synonymy (Saussure, 1916, 1960;

Kiparsky, 1983; Horn, 1984; E. Clark, 1987, 1988). This bias is an equilibrium between Horn’s

speaker and hearer principles. Recall that the optimal language for a hearer is one in which each

meaning maps to its own word — exactly a language biased against synonymy. It turns out that the

speaker’s pressure also biases against synonymy. The optimal language for the speaker is a

language where a single word maps to all meanings. But, a case where multiple words map to a

single meaning is also undesirable because the speaker must keep track of two words. So, for both

the speaker and the hearer, there is pressure to avoid synonymy. Thus, when a listener hears a

speaker use a second word for an existing meaning, the hearer infers that this could not be what the

speaker intended because this would violate the speaker’s principle. The result is an assumption

that the second word maps to a different meaning. This pattern is reﬂected in language structure by

a one-to-one pattern in the lexicon — that is, a structure in which each word maps to exactly one

meaning and each meaning maps to exactly one word.

As one kind of evidence for this one-to-one structure in the lexicon, Horn (1984) points to a

phenomenon called blocking. Blocking refers to cases in which an existing lexical form blocks the

presence of a different, derived form with the same root. Consider the following examples:

(a) fury furious *furiosity

(b) *cury curious curiosity

In both (a) and (b), forms that would be expected, given the inﬂectional morphology in English, are

The length of words reﬂects their conceptual complexity 10

not permitted. This is due to the fact that they would have the same meaning as the existing form

because they have the same root. Examples such as this provide some evidence for a one-to-one

structure in language, but a one-to-one structure is a particularly difﬁcult linguistic regularity to

test empirically. Nonetheless, it is an important regularity because it licenses certain inferences in

interpreting the meaning of words. In particular, the cognitive representation of a lexical

one-to-one regularity—mutual exclusivity—has been posited as a powerful bias in children’s word

learning (Markman & Wachtel, 1988; Markman, Wasow, & Hansen, 2003).

Together these phenomena—semantic organization, ambiguity, and one-to-one

structure—provide three cases in which equilibria that are predicted by theories of communication

at the pragmatic timescale are reﬂected in the structure of the lexicon at the language evolution

timescale. While this similarity across timescales does not entail causality, it is suggestive of a

causal relationship between the two timescales. Next, we turn to accounts at both the pragmatic

and language evolution timescale for our linguistic feature of interest: length.

Accounts of the length of linguistic elements

Language forms vary along many dimensions, but a salient dimension is length: words and

entire utterances can have dramatically different phonetic lengths. Researchers have studied this

variability at both the pragmatic timescale (utterances) and the language evolution timescale

(words). Our two hypotheses propose that variability at both timescales is related to the conceptual

complexity of meaning. Here, we review existing work at both timescales that attempts to account

for variability in language length. At the pragmatic timescale, three theories suggest that pragmatic

pressures inﬂuence the length of utterances: Zipf’s theory of communication, Horn’s theory of

communication, and Information Theory. Hypothesis 1 falls directly out of both Horn’s theory of

communication and Information Theory. At the language evolution timescale, two bodies of work

account for word length by appealing to the predictability of the linguistic context and the

conceptual ‘markedness’ of meaning. While distinct from Hypothesis 2, both of these literatures

The length of words reﬂects their conceptual complexity 11

are consistent with the proposal that languages use longer words to encode conceptually more

complex meanings.

Zipf (1936) provided an early account of word length that appealed to a pragmatic pressure

to communicate efﬁciently. He argued that speakers are motivated to minimize their physical effort

and that this constraint could be optimally minimized by using shorter words for meanings that

were used to more frequently. This leads to the prediction that there should be an inverse

relationship between the length of a word and its frequency in usage—and, indeed, the empirical

data suggest a robust correlation between word length and word frequency.

Others, however, have proposed different pressures at the pragmatic timescale that might

inﬂuence the length of linguistic expressions. Both Horn’s theory of communication and

information theory predict that longer expressions should be associated with less predictable or

typical meanings than their shorter counter parts. Under Horn’s theory (1984), a speaker often has

the choice of using two different utterances to refer to the same meaning (in truth functional

terms), and often these utterances differ in length. Horn suggests that the sentences “Lee stopped

the car.” and “Lee got the car to stop” have the same denotational meaning (the successful stopping

of a car), though they differ in length. The claim is that this asymmetry leads to an inference on the

part of the listener that the two differ in meaning.

The logic of this inference is identical to the lexical structure case above. The listener hears

a speaker use a more costly phrase to express a meaning that could have been expressed in a less

costly way. The listener thus infers that this other meaning could not be what the speaker intended

because this would violate the speaker’s principle to say no more than is necessary. Horn adds an

additional layer to this argument. He suggests that not only do these two forms differ in meaning,

but that they map onto meanings in a systematic way: The longer form gets mapped on to the more

unusual meaning, while the shorter form refers to the more usual meaning. Thus, in the above

example, the shorter utterance would refer to a simple, average case of car stopping, while longer

utterance might refer to case where something complex or unusual happened, perhaps because Lee

The length of words reﬂects their conceptual complexity 12

used the emergency brake.

The source of the particular mapping between forms of different lengths and meanings is

unclear. This is because in principle there are multiple equilibrium points in the mapping between

form and meaning. Assuming a one-to-one constraint on the mapping, there are two possible

equilibria: {short–simple, long–complex} or {short–complex, long–simple}. Both satisfy the

constraint that each form gets mapped to a unique meaning. So how do speakers arrive at the

{short–simple, long–complex} equilibrium? This is difﬁcult to derive from models of pragmatic

reasoning. Bergen, Levy, and Goodman (under review) successfully derive this result as a

consequence of the fact that {short–simple, long–complex} is a more optimal mapping for the

speaker. Another possibility relies on iconicity: hearers have a cognitive bias to map more complex

sounding forms to meanings that are similarly complex.

Bergen, Goodman, and Levy (2012) provide a direct test of the length-complexity tradeoff

within a communication game. In their task, partners were told that they were in an alien world

with three objects and three possible utterances. In this experiment, the idea of complexity was

operationalized as frequency, such that participants were instructed that each of the three different

objects had three different base rate frequencies associated with them. The cost of the utterance

was manipulated directly (rather than through utterance length) by assigning different monetary

costs to each object. Participants’ task was to communicate about one of the objects using one of

the available utterances. If they successfully communicated, they received a reward. The results

suggest that both the speaker and hearer expected costlier forms to refer to less frequent meanings,

consistent with Horn’s predicted equilibrium between word length and meaning.

The prediction of a complexity bias at the pragmatic timescale falls more directly out of

information theory. Information theory models communication as the transfer of information

across a noisy channel (Shannon, 1948). Under this theory, speakers optimize information transfer

(in terms of bits) by keeping the amount of information conveyed in a unit of language constant

across the speech stream. A straightforward consequence of this uniform information density

The length of words reﬂects their conceptual complexity 13

assumption is that speakers should try to lengthen unpredictable utterances. There is evidence for

this prediction across multiple levels of communication. At that level of prosody, speakers tend to

increase the duration of a word in cases where the word is unpredictable (highly informative) given

the linguistic context (Aylett & Turk, 2004). There is also evidence for this prediction at the level

of syntactic (Frank & Jaeger, 2008) and discourse predictability (Genzel & Charniak, 2002).

At the timescale of language evolution, there is some indirect evidence that this same bias is

present in the lexicon. These approaches use the linguistic context of a word as a measure of the

complexity of meaning. The idea is that words that are highly predictable, given the linguistic

context, have more complex meanings, while words that are less predictable given the linguistic

context, have less complex meanings. Piantadosi, Tily, and Gibson (2011b) measured the

relationship between the predictability of a word in context and its length. Across 10 languages,

these two measures were highly correlated: words that were longer were less predictable in their

linguistic context on average. This result held true even controlling for the frequency of words.

Additional evidence for this relationship comes from examining pairs of words that have very

similar meaning, but differ in length (e.g. “exam” vs. “examination;” Mahowald, Fedorenko,

Piantadosi, & Gibson, 2012). In corpus analyses, longer forms are found to be used in less

predicable linguistic contexts. They also ﬁnd in a behavioral experiment that speakers are more

likely to select the longer alternative in less predictive contexts. This body of work points to a

systematic relationship between word length and meaning when complexity is operationalized as

predictability in the linguistic context.

A related body of work has examined the relationship between length and meaning under

the rubric of markedness. While many notions of markedness have been discussed in the literature

(Haspelmath, 2006), one version of the hypothesis is that linguistic forms often have binary

morphemic contrasts and these contrasts map onto a broad difference in meaning (Greenberg,

1966). For example, consider the pair “real”–“unreal,” which differ both in valence—positive vs.

negative—and length (the negative form has the extra morpheme “un-”). Greenberg (1966) claims

The length of words reﬂects their conceptual complexity 14

that the difference in length is because negative meanings are conceptually more marked than their

positive counterparts, and that this regularity is a linguistic universal. One explanation of this is

that the set of negated things tends to be larger than the set of positive things (in principle, there are

more unreal things than real things). However, a limitation of this proposal is that there is no a

priori criteria for determining what characterizes conceptual markedness; the accounts are speciﬁc

to each domain. For example, while the negation case appeals to ‘number of things’ as the

determiner of complexity, there is no clear account of why the present form (e.g. “walk”) should

be less marked than the past form (e.g. “walked”) or why state words (e.g. “black”) should be less

marked than change of state words (e.g. “blacken”). Nonetheless, this version of the markedness

hypothesis suggests a relationship between linguistic length and conceptual features, similar to the

complexity hypothesis. The complexity hypothesis differs, however, in positing conceptual

complexity as a general construct that can be applied to a broad class of meanings. In addition, it

differs in the speciﬁcity of the length metric: While markedness predicts a regularity only at the

level of morphemes, the complexity hypothesis predicts a regularity at all levels of linguistic form

(phonemes, syllables, morphemes).

Thus, at the pragmatic timescale, there is a well-motivated prediction that less predictable

meanings should be described with longer utterances. If dynamics at shorter timescales inﬂuence

those at longer timescales, we might expect this same regularity to emerge in the lexicon over the

course of language evolution. At the language evolution timescale, there is some indirect evidence

that longer words refer to more complex meanings, but no work directly and systematically tests

this prediction.

Our studies

The goal of our work here is to test the two complexity hypotheses given above. We present

ten studies that provide support for both hypotheses: a complexity bias in individual speakers

(Hypothesis 1; Experiments 1-8) and a complexity bias in natural language (Hypothesis 2;

The length of words reﬂects their conceptual complexity 15

Experiment Description

Complexity

Hypothesis

Stimulus Type

1 Explicit complexity norms 1 artiﬁcial objects

2 Mapping task 1 artiﬁcial objects

3 Mapping task (control) 1 artiﬁcial objects

4 Explicit complexity norms 1 novel real objects

5 Mapping task 1 novel real objects

6 Mapping task (control) 1 novel real objects

7 Label production 1 novel real objects

8 Memory task to elicit RTs 1 artiﬁcial (a) and novel real (b) objects

9 English complexity norms 2 real words

10 Cross-linguistic corpus analysis 2 real words

Table 1

Summary of studies.

Experiments 9-10; see Table 1 for a summary of our studies). In Experiments 1-7, we test whether

participants are biased to map a relatively long novel word onto a relatively more complex object,

using artiﬁcial objects (Experiments 1-3) and novel, real objects (Experiments 4-7). In Experiment

8, we explore the underlying cognitive construct of complexity in a reaction time task. In

Experiment 9, we elicit complexity norms for English words and then conduct a corpus analysis of

79 additional languages (Study 10). In these studies, we operationalize the notion of conceptual

complexity by manipulating it visually and also measuring it—both directly through explicit norms

and indirectly through reaction time—with the assumption that these metrics serve only as proxies

for an underlying cognitive construct. In the General Discussion, we summarise the support these

studies provide for our hypotheses as well as their limitations and directions for future work.

Experiment 1: Object Complexity Norms (Artiﬁcial Objects)

As a ﬁrst step in exploring a complexity bias, we manipulated the complexity of objects and

asked participants to infer which object a novel word refers to. Object complexity was manipulated

The length of words reﬂects their conceptual complexity 16

by varying the number of primitive parts the objects were composed of. If participants have a

complexity bias, we predicted they should be more likely to map a longer novel word onto an

object composed of more parts, compared to an object with fewer parts. In Experiment 1, we ﬁrst

conducted a norming study to verify our intuitions that the number of object parts correlated with

explicit judgements of complexity. In Experiment 2, we used these normed stimuli in a simple

word mapping task, revealing a complexity bias. Experiment 3 replicated Experiment 2 with

randomly concatenated syllables.

Methods

Participants. In this and all subsequent experiments, participants were recruited on Amazon

Mechanical Turk and received US $0.15-0.30 for their participation, depending on the length of the

task. 60 participants completed this ﬁrst experiment.

Across all experiments, some participants completed more than one experiment. The results

presented here include the data from all participants, but all reported results remain reliable when

excluding participants who completed more than one study. Participants were counted as a repeat

participant if they completed a study using the same stimuli (e.g., completed both Experiment 1

and 2 with artiﬁcial objects).

Stimuli. As object primitives, we used “geon” shapes which are argued to be primitives in

the visual system under one theory of object recognition (Biederman, 1987). We created a set of 40

objects containing 1-5 geon primitives (Figure 1).

Procedure. We presented participants 12 objects from the full stimulus set one at a time. For

each object, we asked “How complicated is this object?,” and participants responded using a slider

scale anchored at “simple” and “complicated.” Each participant saw two objects from each

complexity condition, and the ﬁrst two objects were images of a ball and a motherboard to anchor

All stimuli, experiments, raw data and analysis code can be found at https://github.com/mllewis/RC. Analyses

can be found at: http://rpubs.com/mll/RCSI.

The length of words reﬂects their conceptual complexity 17

Figure 1. Artiﬁcial objects used in Experiment 1. Each row corresponds to a complexity condition.

The complexity condition is determined by the number of “geon” parts the object contains (1-5).

participants on the scale. This and all subsequent experimental paradigms can be viewed directly

here: https://mllewis.github.io/projects/RC/RCindex.html.

Results and Discussion

Number of object parts was highly correlated with explicit complexity judgment (r = .93,

p <.0001; M = .47, SD = .18): Objects with more parts tend to be related as more complex.

Figure 2a shows the mean complexity rating for each of the 40 objects as a function of their

complexity condition. This suggests that we can use manipulations of visual complexity as a proxy

for manipulations of conceptual complexity.

Experiment 2: Mapping Task (Artiﬁcial Objects)

Methods

Participants. 750 participants completed the experiment.

Stimuli. The referent stimuli were the set of 40 objects normed in Experiment 1. The

linguistic stimuli were novel words either 2 or 4 syllables (e.g., “bugorn” and “tupabugorn”) long.

There were 8 items of each syllable length.

The length of words reﬂects their conceptual complexity 18

Figure 2. (a) The relationship between number of geons and complexity rating is plotted below.

Each point corresponds to an object item (8 per condition). The x-coordinates have been jittered

to avoid over-plotting. (b) Effect size (bias to select complex alternative in long vs. short word

condition) as a function of the complexity rating ratio between the two object alternatives. Each

point corresponds to an object condition. Conditions are labeled by the number of geons of the two

alternatives. For example, the “1/5” condition corresponds to the condition in which one alternative

contains 1 geon and the other contains 5 geons. (c) Proportion complex object selections as a

function of the number of syllables in the target label. The dashed line reﬂects chance selection

between the simple and complex alternatives. All errors bars reﬂect 95% conﬁdence intervals,

calculated via non-paramedic bootstrapping in 1a and 1c, and parametrically in 1b.

Procedure. We presented participants with a novel word and two possible objects as

referents, and asked them to select which object the word named (“Imagine you just heard

someone say bugorn. Which object do you think bugorn refers to? Choose an object by clicking

the button below it.”).

Within participants, we manipulated word length and the relative complexity of the referent

alternatives. We tested every unique combination of object complexities (1 vs. 2 geons, 1 vs. 3

geons, 1 vs. 4 geons, etc.), giving rise to 15 conditions in total. Each participant completed 4 short

and 4 long trials in a random order, where each word was randomly associated with one of the

complexity conditions. No participant saw the same complexity condition twice and no word or

object was repeated across trials.

The length of words reﬂects their conceptual complexity 19

Results and Discussion

Across conditions, the more complex object was more likely to be judged the referent of the

longer word. For each object condition (e.g., 1 vs. 2 geons), we calculated the effect size for

participants’ complexity bias—the degree to which the complex object was more likely to be

chosen as the referent of a long word, compared to the short word. Effect sizes were calculated

using the log odds ratio (S

anchez-Meca, Mar

ın-Mart

ınez, & Chac

on-Moscoso, 2003). Effect size

was highly correlated with the ratio of object complexities: The greater the mismatch in object

complexity, the more the longer word was paired with the more complex object (r = .87,

p <.0001).

This experiment provides initial evidence for a complexity bias in the lexicon: Given an

artiﬁcial word and two objects of differing visual complexity, participants are more likely to map a

longer word onto a more complex referent, relative to a shorter word.

Experiment 3: Control Mapping Task (Artiﬁcial Objects)

One limitation of Experiment 2 is that it uses a small set of words as the linguistic stimuli (8

short and 8 long), making it possible that idiosyncratic properties of the words could be driving the

observed complexity bias. In Experiment 3, we sought to test this possibility by using words

composed of randomly concatenated syllables rather than items selected from a small list of words.

The design was identical to Experiment 2, except that we tested only the most extreme complexity

condition, the “1/5” condition.

Methods

Participants. 200 participants completed the experiment.

Stimuli. The referent stimuli were the geon objects composed of either 1 or 5 geons. The

novel words were created by randomly concatenating 2, 4, or 6 consonant-vowel syllables (e.g.,

The length of words reﬂects their conceptual complexity 20

“nur,” “nobimup,” “gugotobanid”). The last syllable of all words ended in a consonant to better

approximate the phonology of English.

Procedure. Participants completed six forced-choice trials identical to Experiment 1b. We

tested only the “1/5” complexity condition (1-geon object vs. 5-geon object). Word length was

manipulated within-participant such that each participant completed 2 trials for each of the three

possible word lengths (2, 4, or 6 syllables).

Results and Discussion

Replicating the “1/5” condition in Experiment 2, we found that participants were more

likely to select a ﬁve geon object compared to a single geon object as the number of syllables in the

word increased (b = .44, p <.0001). This suggests that the complexity bias observed in

Experiment 2 is unlikely to be due to the particular set of words we selected.

Experiment 4: Object Complexity Norms (Novel Objects)

Experiments 1-3 provide evidence for a complexity bias using artiﬁcial objects. The

complexity manipulation in these experiments was highly transparent, however, making it possible

that task demands inﬂuenced the effect. We next asked whether this bias extended to more

naturalistic objects where the variability in complexity might be less obvious to participants. We

conducted the same set of 3 experiments as above using a sample of real objects without canonical

labels. We ﬁnd that the complexity bias observed with artiﬁcial geon objects extends to naturalistic

objects.

Methods

Participants. We recruited two samples of 60 participants to complete Experiment 4.

Stimuli. We collected a set of 60 objects that were real objects but that did not have

canonical labels associated with them (Figure 3).

The length of words reﬂects their conceptual complexity 21

Figure 3. Novel real objects used in Experiments 4-6: Naturalistic objects without canonical labels.

Each row corresponds to a quintile determined by the explicit complexity judgments obtained in

Experiment 4 (top: least complex; bottom: most complex).

Procedure. The procedure was identical to Experiment 1.

Results and Discussion

Complexity judgments were highly reliable across two independent samples

(r = .93, p <.0001; M

= .49, SD

= .18, M

= .44, SD

= .18). Figure 4a shows the relationship

between the complexity judgment for each item across the two samples of participants. Figure 3

shows all 60 objects sorted by their mean complexity rating.

Experiment 5: Mapping Task (Novel Real Objects)

Methods

Participants. 1500 participants completed the experiment.

Stimuli. The linguistic stimuli were identical to Experiment 2. The object stimuli were the

60 naturalistic objects normed in Experiment 2. Five complexity conditions were determined by

dividing the objects into quintiles based on the norms.

The length of words reﬂects their conceptual complexity 22

Figure 4. (a) The correlation between the two samples of complexity norms. Each point corresponds

to an object (n = 60). (b) Effect size (bias to select complex alternative in long vs. short word

condition) as a function of the complexity rating ratio between the two object alternatives. Each

point corresponds to an object condition. Conditions are labeled by the complexity norm quintile

of the two alternatives. (c) The proportion of complex object selections as a function of number of

syllables. The dashed line reﬂects chance selection between the simple and complex alternatives.

All errors bars reﬂect 95% conﬁdence intervals, calculated via non-parametric bootstrapping in 4

and 6, and parametrically in 5.

Procedure. The procedure was identical to Experiment 2, except for the use of naturalistic

rather than artiﬁcial geon objects.

Results and Discussion

As with the artiﬁcial objects, effect size was negatively correlated with the complexity rating

ratio between the referent alternatives (r = .70, p <.005; Fig. 4b). This suggests that the

complexity bias observed with artiﬁcial objects extends to more naturalistic objects, consistent

with the proposal that a complexity bias is a characteristic of natural language more generally.

The effect size in Experiment 5 is smaller than in Experiment 2, however. This may be due

to the fact that some of the effect in Experiment 2 was due to task demands associated with the

transparent complexity manipulation. Nonetheless, Experiment 5 reveals a complexity bias with

naturalistic objects.

The length of words reﬂects their conceptual complexity 23

Experiment 6: Control Mapping Task (Novel Objects)

As with the artiﬁcial objects, we sought to control for the possibility that the results from the

mapping task were due to our particular linguistic items. Thus, we conducted a control experiment

analogous to Experiment 3 using randomly concatenated syllables.

Methods

Participants. 200 participants completed the experiment.

Stimuli. The objects were 12 objects from the ﬁrst and ﬁfth quintile of complexity norms.

The linguistic stimuli were constructed as in Experiment 3.

Procedure. The procedure was identical to Experiment 3, except for the different object

stimuli.

Results and Discussion

Participants were more likely to select an object from the ﬁfth quintile as opposed to the ﬁrst

quintile when the novel word contained more syllables (b = .34, p <.0001; Fig. 4c). This

pattern replicates the complexity bias seen in Experiment 5 with randomly concatenated syllables.

In the present experiment, participants were overall less likely to select the complex object,

compared to the same experiment with artiﬁcial objects (consider the overall higher level of

complex-object judgments in Experiment 5). This may be due to the fact that some of the simple

artiﬁcial objects in Experiment 3 are associated with canonical labels (e.g., the sphere single-geon

object may have evoked the label “ball.”). This may have lead participants to appeal to mutual

exclusivity in their object selections by selecting an object they do not already have a name for—in

this case, the more complex object (Markman & Wachtel, 1988). Alternatively, the novel artiﬁcial

objects may be over all less conceptually complex than the geon objects. Regardless of this shift,

however, the critical ﬁnding is that we replicate the complexity bias with random syllables in both

Experiments 3 and 6.

The length of words reﬂects their conceptual complexity 24

Experiment 7: Label Production Task (Novel Objects)

The previous set of experiments provides evidence for a complexity bias in a comprehension

task with novel words. One limitation of this design, however, is that participants may have been

inﬂuenced by task demands associated with making a forced choice between two contrasting

alternatives. In Experiment 7, we sought to minimize these demands by presenting participants

with an object and asking them to produce a novel label to refer to it. Consistent with a complexity

bias, we ﬁnd that participants produce longer labels for more complex objects.

Methods

Participants. Fifty-nine participants completed the experiment.

Stimuli. The objects were drawn from the set of 60 naturalistic objects used in Experiments

4-6

Procedure. In each trial, we presented a single object and asked participants to generate a

novel single-word label to refer to it. The instructions read:

What do you think this object is called? For example, someone might call it a tupa or

a pakuwugnum. In the box below, please make up your own name for the object. Your

name should only be one word. It should not be a real English word.

Each participant completed 10 trials—ﬁve objects from the bottom and top complexity norm

quantiles each. Order of objects was randomized.

Results and Discussion

There were 26 productions (4%) that included more than one word. These productions were

excluded. Length was measured in terms of log number of characters.

Participants produced novel coinages that varied in length (e.g., “keyo,” “plattle,”

“scrupula,” “frillobite”). Critically, productions tended to be longer for the top quartile of objects

The length of words reﬂects their conceptual complexity 25

(M = 1.94, SD = 0.18) compared to the bottom quartile (M = 1.85, SD = 0.17; t(57)=3.92,

p <.001). We also analyzed length as a function of the complexity norms for each object. Length

of production was correlated with the complexity norms: Longer labels were coined for objects

that were rated as more complex (r = .17, p <.0001). This experiment provides strong evidence

for a productive complexity bias: Even with minimal task demands, participants prefer to use

longer words to refer to more complex objects.

Experiments 8a and 8b: Complexity as a Cognitive Construct

Experiments 1–7 suggest that participants have a productive complexity bias when

complexity is operationalized in terms of explicit norms. In Experiment 8, we try to more directly

examine the cognitive correlates of conceptual complexity. We reasoned that if complexity is

related to a basic cognitive process, we should be able to measure it using an implicit task, not just

via explicit ratings.

To measure complexity implicitly, we adopt a measure from the visual processing literature:

reaction time. In this literature, the amount of information in a stimulus is argued to be

monotonically related to the amount of time needed to respond to that stimulus. Hyman (1953)

demonstrated this using a task in which participants were asked to indicate which light was

illuminated from a set of bulbs. Two factors were manipulated to vary the amount of information

in each bulb: the number of bulb alternatives and the frequency of each bulb illuminating. They

found that the reaction time for responding to an illuminated bulb was linearly related to the

amount of information in that bulb. More recently, Alvarez and Cavanagh (2004) used a reaction

time measure—search rate—to quantify the amount of information in a varied set of visual stimuli.

They found that the search rate of a visual stimulus was monotonically related to the memory

capacity for that stimulus. Together, these results suggest that reaction time is a behavioral

correlate of the amount of information, or complexity, of a visual stimulus.

To collect an implicit measure of complexity for our objects, we measured participants’

The length of words reﬂects their conceptual complexity 26

study time of objects in a memory task. Each participant studied half of the objects in the stimulus

set, one at a time, and then made old/new judgments for the entire set. Critically, the study phase

was self-paced, such that participants were allowed to study each object for as much time as they

wanted. This study time provided an implicit measure of complexity. For both the artiﬁcial

(Experiment 8a) and naturalistic (Experiment 8b) objects, we found that participants tended to

study objects longer when they were rated as more complex.

Methods

Participants. 750 participants completed the task. 250 participants were tested with artiﬁcial

objects (Experiment 8a) and 500 were tested with novel real objects (Experiment 8b).

Stimuli. The study objects were the set of 40 artiﬁcial objects (Experiment 8a) and 60 novel

real objects (Experiment 8b).

Procedure. Participants were told they were going to view some objects and their memory

of those exact objects would later be tested. In the study phase, participants were presented with

half of the full stimulus set one at a time (20 artiﬁcial objects and 30 novel real objects) and

allowed to click a “next” button when they were done studying each object. After the training

phase, we presented participants with each object in the full stimulus set (40 artiﬁcial objects and

60 novel real objects), and asked “Have you seen this object before?.” Participants responded by

clicking a “yes” or “no” button.

Results and Discussion

Experiment 8a: Artiﬁcial objects. We excluded subjects who performed at or below chance

on the memory task (20 or fewer correct out of 40). A response was counted as correct if it was a

correct rejection or a hit. This excluded 9 participants (4%). With these participants excluded, the

mean correct was 72%. Participants were also excluded based on study times. We transformed the

time into log space, and excluded responses that were 2 standard deviations above or below the

The length of words reﬂects their conceptual complexity 27

Figure 5. Effect sizes in Experiments 2 and 4 replotted in terms of study times collected in

Experiment 8. Objects that are studied relatively longer are more likely to be assigned a longer

label, relative to a shorter label. Error bars show 95% conﬁdence intervals.

mean. This excluded 4% of responses (ﬁnal sample: M = 7.40, SD = .66).

Next, we examined study times in this task. Study times were highly correlated with the

number of geons in each object (r = .93, p <.0001): objects that contained more geons tended to

be studied longer. Study times were also highly correlated with the explicit complexity norms

(r = .89, p <.0001): objects that were rated as more complex tended to be studied longer.

However, study times did not predict memory performance. The study times for hits (correct “yes”

responses; M = 7.33, SD = .52) did not differ from misses (correct “no” responses; M = 7.34,

SD = .59; t(223)=.61, p = .54).

The critical question was whether or not mean study times for an object were related to the

bias to assign a long or short word to that object. To explore this question, we reanalyzed the data

from Experiment 2 in terms of study times instead of explicit complexity norms. The ratio of study

times for the two object alternatives was correlated with the bias to choose a longer label (r = .82,

The length of words reﬂects their conceptual complexity 28

p <.001; Fig. 5a): Relatively longer study times predicted longer labels.

Experiment 8b: Novel real objects. We excluded participants who performed at or below

chance on the memory task (30 or fewer correct out of 60). A response was counted as correct if it

was a correct rejection or a hit. This excluded 6 participants (1%). With these participants

excluded, the mean correct was 84%. Participants were also excluded based on study times, using

the same criteria as in Experiment 8a. This led to the exclusion of 4% of responses (ﬁnal sample:

M = 7.36, SD = .72).

Study times were highly correlated with explicit complexity norms for each object. Like for

the geons, objects that were rated as more complex were studied longer (r = .54, p <.0001).

Unlike for the geons, study times predicted memory performance. Study times for hits (correct

“yes” responses; M = 7.24, SD = .60) were greater than for misses (correct “no responses;

M = 7.11, SD = .66; t(393)=9.74, p <.0001).

Critically, by reanalyzing data from Experiment 4 in terms of study times, we ﬁnd that the

ratio of study times for the two objects was correlated with the bias to choose a longer label

(r = .71, p <.005; Fig. 5b).

Together, these ﬁndings suggest that label judgments are supported by basic cognitive

processes related to the complexity or information content of a stimulus. More broadly,

Experiments 1-8 point to a complexity bias in interpreting novel labels: Words that are longer tend

to be associated with meanings that are more complex, as reﬂected in both explicit and implicit

measures.

Experiment 9: Complexity Bias in Natural Language

Experiments 1–8 revealed a productive complexity bias in the case of novel words

(Hypothesis 1). Next we ask whether this bias extends to natural language (Hypothesis 2). In

Experiment 9, we collected explicit complexity judgments on the meaning of 499 English words in

a rating procedure similar to Experiments 1 and 4 above. Consistent with a complexity bias, we

The length of words reﬂects their conceptual complexity 29

ﬁnd that complexity ratings are highly correlated with word length in English: Words with

meanings that are rated as more complex tend to be longer.

To measure conceptual complexity in natural language, we adopt a rating scale approach

similar to that used in previous work to quantify other aspects meaning, like how perceptible a

referent is (concreteness) and how much experience speakers tend to have with a referent

(familiarity; Wilson, 1988). In this work, participants are presented with a 5- or 7- point Likert

scale anchored at both ends of the target dimension and asked to make an explicit judgment about a

word’s meaning. A limitation of this approach is that it requires that all participants conceptualize

the dimension of interest in a similar way. Nonetheless, previous work has shown these measures

to be reliable and easy to handle analytically, and so we adopt them here to quantify conceptual

complexity.

Methods

Participants. 246 participants completed the norming procedure.

Stimuli. We selected 499 English words from the MRC Psycholinguistic Database (Wilson,

1988) that were broadly distributed in their length and were relatively high frequency. This

database includes norms for three other psycholinguistic variables: concreteness, familiarity, and

imageability. This allowed us to compare our complexity norms to previously measured

psycholinguistic variables that are intuitively related to complexity.

Procedure. Participants were ﬁrst presented with instructions describing the norming task:

In this experiment, you will be asked to decide how complex the meaning of a word is.

A word’s meaning is simple if it is easy to understand and has few parts. An example

of a simple meaning is “brick.” A word’s meaning is complex if it is difﬁcult to

understand and has many parts. An example of a more complex meaning is “engine.”

For each word, we then asked “How complex is the meaning of this word?,” and participants

The length of words reﬂects their conceptual complexity 30

indicated their response on a 7-pt Likert scale anchored at “simple” and “complex.” The ﬁrst two

words were always “ball” and “motherboard” to anchor participants on the scale. Each participant

rated a sample of 30 words English words. After the 17th word, participants were asked to

complete a simple math problem to ensure they were engaged in the task.

Results and Discussion

We ﬁrst examined word length in our samples of words, using three different metrics of

word length: phonemes, syllables, and morphemes. Measures of phonemes and syllables were

taken from the MRC corpus (Wilson, 1988) and measures of morphemes were taken from

CELEX2 database (Baayen, Piepenbrock, & Gulikers, 1995). All three metrics were highly

correlated with each other (phonemes and syllables: r = .89; phonemes and morphemes: r = .65;

morphemes and syllables: r = .67). All three metrics were also highly correlated with number of

characters, the unit of length with use in the cross-linguistic corpus analysis below (phonemes:

r = .92; morphemes: r = .69; syllables: r = .87).

Given these measures of word length, we next considered how length related to judgments

of meaning complexity. We excluded participants who missed a simple math problem in the

middle of the task that served as an attentional check. This excluded 6 participants (2%). Critically,

we found that complexity ratings (M = 3.36, SD = 1.14) were positively correlated with word

length, measured in phonemes, syllables, and morphemes (r

phonemes

= .67, r

syllables

= .63,

morphemes

= .43, all ps <.0001, Fig. 6)

. This relationship held for the subset of only open class

words (n = 438; r

phonemes

= .65, r

syllables

= .63, r

morphemes

= .42, all ps <.0001). Word class was

coded by the authors.

This result points to a relationship between conceptual complexity and word length, but to

interpret this relationship, it is important to also control for other known correlates of word length

and complexity. Linguistic predictability is highly correlated with word length, operationalized via

All norms can be found here: https://github.com/mllewis/RC/blob/master/data/norms/.

The length of words reﬂects their conceptual complexity 31

Figure 6. Complexity norms collected in Experiment 9 as a function of word length in terms of

number of phonemes. Words rated as more complex tend to be longer. Error bars show bootstrapped

95% conﬁdence intervals.

simple frequency (Zipf, 1936) or using a language model (Piantadosi et al., 2011a). We estimated

word frequency from a corpus of transcripts of American English movies (Subtlex-us database;

Brysbaert & New, 2009). Importantly, the regularity we describe—a relationship between

conceptual complexity and word length—holds even when controlling for frequency. In English,

the correlation was only slightly reduced when controlling for log frequency (r = .57, p <.0001).

Complexity is reliably correlated with concreteness, familiarity, and imageability

(concreteness: r = .27; familiarity: r = .43; imageability: r = .21). Nonetheless, the

relationship between word length and complexity remained reliable controlling for these factors.

We created an additive linear model predicting word length in terms of phonemes with complexity,

controlling for concreteness, imageability, familiarity, and frequency. Model parameters are

presented in Table 2.This pattern held for the other two metrics of word length (morphemes and

syllables).

The length of words reﬂects their conceptual complexity 32

Estimate Std. Error t value Pr(>|t|)

(Intercept) 7.5020 0.2061 36.40 0.0000

complexity 0.2429 0.0116 20.86 0.0000

concreteness -0.0033 0.0004 -9.16 0.0000

imageability -0.0003 0.0004 -0.81 0.4183

familiarity 0.0024 0.0005 4.80 0.0000

log frequency -1.1556 0.0332 -34.80 0.0000

Table 2

Model parameters for linear regression predicting word length in terms of semantic variables and

word frequency.

This result extends beyond the ﬁndings of previous work on markedness. Although this

difference in the complexity of morphological structure could in principle contribute to conceptual

complexity judgments, it does not explain the pattern in our data. The correlations we observed

hold for words with no obvious derivational morphology (CELEX2 monomorphemes; Baayen et

al., 1995, n = 387; r

phonemes

= .53, r

syllables

= .47, all ps <.0001).

Finally, languages also show phonological iconicity effects, such that semantic features

(Maurer, Pathman, & Mondloch, 2006) and even particular form classes (Farmer, Christiansen, &

Monaghan, 2006) are marked by particular sound patterns. However, the type of iconicity explored

here is broader—a systematic relationship between abstract measures of complexity and amount of

verbal or orthographic effort. Speciﬁc iconic hypotheses that posit a parallel between an object’s

parts and the number of phonemes, morphemes, or syllables in its label do not account for the

patterns in the English lexicon: The length-complexity correlation holds even more strongly for

words below the median in concreteness, those words whose part structure is presumably much

less obvious (r

phonemes

= .73, r

syllables

= .72, r

morphemes

= .47, all ps <.0001).

While correlational nature of this study makes inferences about causality

tentative—complex meanings may be assigned longer words, or words that are longer may be rated

as more complex—this study nonetheless points to a robust relationship between word length and

The length of words reﬂects their conceptual complexity 33

conceptual complexity in English.

Study 10: Cross-Linguistic Corpus Analysis

If the complexity bias relies on a universal cognitive process, it should generalize to lexicons

beyond English. We explored this prediction in 79 additional languages though a corpus analysis,

and found a complexity bias in every language we examined.

Methods and Results

We translated all 499 words from Experiment 9 into 79 languages using Google translate

(retrieved March 2014). The set of languages was the full set available in Google translate. Words

that were translated as English words were removed from the data set. We also removed words that

were translated into a script that was different from the target language (e.g., an English word

listed for Japanese).

Native speakers evaluated the accuracy of these translations for 12 of the 79 languages.

Native speakers were told to look at the translations provided by Google, and in cases where the

translation was bad or not given, provide a “better translation.” Translations were not marked as

inaccurate if the translation was missing. Across the 12 languages, there was .92 native speaker

agreement with the Google translations across all 499 words.

To test for a complex bias, we calculated the length of each word in each of the 79 languages

using number of unicode characters as our unit of length (to allow comparison between languages

for which no phonetic dictionary was available). For each language, we calculated the correlation

between word length in terms of number of characters and mean complexity rating. All 79

languages showed a positive correlation between length and complexity ratings. The grand mean

correlation across languages was .34 (r = .37, for checked languages only).

This relationship also held for the subset of monomorphic words (grand mean r = .23) and

open class words (grand mean r = .30). It also held partialling out frequency (grand mean r = .22).

The length of words reﬂects their conceptual complexity 34

Figure 7. Correlation coefﬁcient (Pearson’s r) between length in unicode characters and conceptual

complexity rating (obtained in Experiment 9). Dark red bars indicate languages for which

translations were checked by native speakers; all other bars show translations obtained via Google

Translate. The dashed line indicates the grand mean correlation across languages. Triangles indicate

the correlation between complexity and length, partialling out log spoken frequency in English.

Circles indicate the correlation between complexity and length for the subset of words that are

monomorphemic in English. Squares indicate the correlation between complexity and length for the

subset of open class words. Error bars show 95% conﬁdence intervals obtained via non-parametric

bootstrap.

Discussion

This corpus analysis suggests that the complexity bias found in natural language

(Experiment 9) generalizes to a broad range of other languages. A notable result from these

analyses is that English appears to have the largest complexity bias of the languages examined.

One possible explanation is that, because our complexity norms were elicited for English words,

our measure of conceptual complexity was most accurate for English words, and thus the

complexity bias was largest for English. If true, then the cross-linguistic estimates of complexity

bias obtained in the present analyses would be conservative estimates of the bias.

The length of words reﬂects their conceptual complexity 35

General Discussion

We began with two observations—the presence of many pragmatic equilibria reﬂected in the

structure of the lexicon, and the fact that several theories of pragmatics predict a tradeoff between

length and complexity. The goal of our work was to explore whether a tradeoff between length and

complexity is present in words—namely, a bias for longer words to refer to more conceptually

more complex meanings. We explored this bias at two timescales. At the pragmatic timescale, we

asked whether participants would be biased to assign a relatively long novel word to a conceptually

more complex referent (Hypothesis 1). At the language evolution timescale, we asked whether

languages tended to encoded conceptually more complex meanings with longer forms (Hypothesis

2). We found support for both hypotheses.

Experiments 1–7 suggest that when conceptual complexity is operationalized via visual

complexity, participants are biased to assign novel words to more complex referents. This pattern

holds true for both artiﬁcial objects where visual complexity was directly manipulated, as well as

for naturalistic objects where we measured visual complexity and analyzed it correlationally. We

also found this pattern across both comprehension and production tasks, suggesting this bias was

not merely the result of task demands. Experiment 8 reveals that visual complexity is highly

correlated with an implicit measure—reaction time—and this measure predicts the bias to assign

an object a long or a short word. Finally, Experiment 9 suggests that explicit measures of

conceptual complexity in English are highly correlated with word length in English, and the corpus

analysis reveals a correlation between English complexity norms and word lengths in a diverse set

of languages.

These studies reveal a regularity in language that appears to be both productive and true

cross-linguistically. The observed bias is highly general, both in terms of the unit of length

(phonemes, morphemes, and syllables) as well as the characterization of semantics. This work

contributes an important extension to the previous work on markedness. Previous work on

markedness described relationships between conceptual features and word length that were

The length of words reﬂects their conceptual complexity 36

post-hoc and domain speciﬁc. Our work suggests that conceptual complexity may be a unifying

framework for thinking about variability in conceptual space across semantic domains. In our work

here, we begin to directly address the cognitive construct underlying conceptual complexity by

revealing a strong relationship between explicit measures of complexity and the implicit measure

of reaction time.

While the broad nature of the regularity we describe is a strength, our work here leaves a

number of open questions. Additional research needs to be done to better understand what

conceptual complexity is and what constructs our measures here describe. Our reaction time

results suggest that, whatever conceptual complexity is, it is related to basic cognitive processes.

But our work does not provide any insight into what the conceptual primitives are such that some

meanings are more conceptually complex than others. In other research, we have explored a

number of hypotheses about factors that may contribute to conceptual complexity (see

Supplemental Information, Experiments 11 and 12). In particular, we hypothesized that the

frequency of objects might contribute to conceptual complexity, such that more frequent objects in

the world were less conceptually complex. Across two experiments using similar methods to those

reported in the main text, we found no evidence that frequency contributed to complexity. Thus,

we leave this difﬁcult topic for future investigations.

A second limitation of our work is that we are not able to provide an account of why word

lengths can change over time for the same meaning (e.g., “television” becomes “TV” or “cellular

phone” becomes “cell”). The answer to this question may be related to the question of conceptual

complexity. One possibility is that the conceptual complexity of a word’s meaning may reduce

over time, and language reﬂects this change by shortening the length of the word. Another

possibility is that this reduction is the result of another pressure on language change: word

frequency. Under this hypothesis, as a word become more frequent, it becomes shorter (Zipf,

1936), and this pressure is independent of the complexity bias. So perhaps such shortenings are

unrelated to the phenomenon we describe here.

The length of words reﬂects their conceptual complexity 37

Finally, our interpretation of this work is limited by the fact that all participants were

speakers of English. A complexity bias could in principle be idiosyncratic to English. The results

from our experiments with novel words would then be the product of speakers merely generalizing

from their native language. Relatedly, the fact that all participants spoke English is also a limitation

for our interpretation of the cross-linguistic corpus analysis. Because our complexity norms were

elicited for English words from English speakers, the ratings are likely imperfect measures of

conceptual complexity for words translated into other languages. Thus, it is difﬁcult to know

whether variability in the magnitude of the complexity bias cross-linguistically is due to true

underlying differences in the bias, or merely a difference in the ﬁdelity of the complexity ratings

cross-linguistically. Speaking against this limitation, however, the presence of a complexity bias

across all 80 languages that we examined suggests that the bias is likely to hold cross-linguistically

in experimental work as well. If anything, the cross-linguistic mean bias is likely larger than our

current estimates in the corpus study, because of the mismatch in complexity judgments between

English speakers and speakers of other languages.

The motivating framework for the present work was the notion of interacting dynamics at

multiple timescales. Our work suggests that a complexity bias is present in both individual

speakers—the pragmatic timescale (Hypothesis 1)—and in the structure of the lexicon—the

language evolution timescale (Hypothesis 2). While the existing data do not speak directly to a

causal relationship between these two hypotheses, a casual interpretation is both parsimonious and

consistent with work in other domains of linguistic structure, reviewed in the Introduction. A

causal account would suggest that the trade off between listener and hearer pressures leads to a

complexity bias at the pragmatic timescale and, over time, these pressures lead to the same

regularity emerging in the lexicon over the language change timescale. Our data are not able to

speak to the processes underlying participants’ judgments—these judgments need not reﬂect

in-the-moment pragmatic inference; they could also be the result of an iconic mapping between

effort and meaning, or a lower-level statistical regularity extracted through extensive experience

The length of words reﬂects their conceptual complexity 38

with a language. Regardless of the cognitive instantiation of this inference, the result is lexicons

that reﬂect Horn’s principle.

The length of words reﬂects their conceptual complexity 39

References

Alvarez, G. A., & Cavanagh, P. (2004). The capacity of visual short-term memory is set both by

visual information load and by number of objects. Psychological Science, 15(2), 106–111.

Aylett, M., & Turk, A. (2004). The smooth signal redundancy hypothesis: A functional

explanation for relationships between redundancy, prosodic prominence, and duration in

spontaneous speech. Language and Speech, 47 (1), 31–56.

Baayen, R., Piepenbrock, R., & Gulikers, L. (1995). Celex2, ldc96l14. Web download, Linguistic

Data Consortium, Philadelpha, PA.

Baddeley, R., & Attewell, D. (2009). The relationship between language and the environment

information theory shows why we have only three lightness terms. Psychological Science,

20(9), 1100–1107.

Bergen, L., Goodman, N. D., & Levy, R. (2012). Thats what she (could have) said: How

alternative utterances affect language use. In Proceedings of the Thirty-Fourth Annual

Conference of the Cognitive Science Society.

Bergen, L., Levy, R., & Goodman, N. D. (under review). Pragmatic reasoning through semantic

inference.

Biederman, I. (1987). Recognition-by-components: a theory of human image understanding.

Psychological Review, 94(2), 115.

Blythe, R. A. (2015). Hierarchy of scales in language dynamics.

Brysbaert, M., & New, B. (2009). Moving beyond Ku

cera and Francis: A critical evaluation of

current word frequency norms and the introduction of a new and improved word frequency

measure for american english. Behavior Research Methods, 41(4), 977–990.

Christiansen, M. H., & Chater, N. (in press). The now-or-never bottleneck: A fundamental

constraint on language. Behavioral and Brain Sciences.

Clark, E. (1987). The principle of contrast: A constraint on language acquisition. Mechanisms of

language acquisition. Hillsdale, NJ: Erlbaum.

The length of words reﬂects their conceptual complexity 40

Clark, E. (1988). On the logic of contrast. Journal of Child Language, 15(02), 317–335.

Clark, H. H. (1996). Using language. Cambridge University Press.

Farmer, T. A., Christiansen, M. H., & Monaghan, P. (2006). Phonological typicality inﬂuences

on-line sentence comprehension. Proceedings of the National Academy of Sciences,

103(32), 12203–12208.

Frank, A., & Jaeger, T. F. (2008). Speaking rationally: Uniform information density as an optimal

strategy for language production. In Proceedings of the Twenty-Ninth Annual Conference of

the Cognitive Science Society.

Frawley, W. (2003). International encyclopedia of linguistics. In (Vol. 2, chap. Deixis.). Oxford

University Press.

Genzel, D., & Charniak, E. (2002). Entropy rate constancy in text. In Proceedings of the 40th

Annual Meeting on Association for Computational Linguistics (pp. 199–206).

Greenberg, J. (1966). Universals of language. Cambridge, MA: MIT Press.

Grice, H. (1975). Logic and conversation. , 41–58.

Haspelmath, M. (2006). Against markedness (and what to replace it with). Journal of Linguistics,

42(01), 25–70.

Hockett, C. (1960). The origin of speech. Scientiﬁc American, 203, 88-96.

Horn, L. (1984). Toward a new taxonomy for pragmatic inference: Q-based and R-based

implicature. Meaning, form, and use in context, 42.

Hyman, R. (1953, March). Stimulus information as a determinant of reaction time. Journal of

Experimental Psychology, 45(3), 188-196.

Kemp, C., & Regier, T. (2012). Kinship categories across languages reﬂect general communicative

principles. Science, 336(6084), 1049–1054.

Kiparsky, P. (1983). Word-formation and the lexicon. In Proceedings of the 1982 Mid-America

Linguistics Conference (Vol. 3, p. 22).

Locke, J. (1847). An essay concerning human understanding. Troutman & Hayes.

The length of words reﬂects their conceptual complexity 41

Mahowald, K., Fedorenko, E., Piantadosi, S., & Gibson, E. (2012). Info/information theory:

speakers actively choose shorter words in predictable contexts. Cognition, 126, 313–318.

Markman, E., & Wachtel, G. (1988). Children’s use of mutual exclusivity to constrain the

meanings of words. Cognitive Psychology, 20(2), 121–157.

Markman, E., Wasow, J., & Hansen, M. (2003). Use of the mutual exclusivity assumption by

young word learners. Cognitive Psychology, 47(3), 241–275.

Maurer, D., Pathman, T., & Mondloch, C. J. (2006). The shape of boubas: Sound–shape

correspondences in toddlers and adults. Developmental Science, 9(3), 316–322.

McMurray, B., Horst, J., & Samuelson, L. (2012). Word learning emerges from the interaction of

online referent selection and slow associative learning. Psychological Review, 119(4), 831.

Peirce, C. (1931). The collected papers of Charles S. Peirce (C. Hartshorne, P. Weiss, & A. Burks,

Eds.). Cambridge: Harvard University Press.

Piantadosi, S., Tily, H., & Gibson, E. (2011a). The communicative function of ambiguity in

language. Cognition, 122(3), 280-291.

Piantadosi, S., Tily, H., & Gibson, E. (2011b). Word lengths are optimized for efﬁcient

communication. Proceedings of the National Academy of Sciences, 108(9), 3526–3529.

Regier, T., Kay, P., & Khetarpal, N. (2007). Color naming reﬂects optimal partitions of color

space. Proceedings of the National Academy of Sciences, 104(4), 1436–1441.

Regier, T., Kemp, C., & Kay, P. (2015). Word meanings across languages support efﬁcient

communication. In W. MacWhinney B O’Grady (Ed.), The handbook of language

emergence (p. 237-263). Wiley-Blackwell.

anchez-Meca, J., Mar

ın-Mart

ınez, F., & Chac

on-Moscoso, S. (2003). Effect-size indices for

dichotomized outcomes in meta-analysis. Psychological Methods, 8(4), 448.

Saussure, F. (1916, 1960). Course in General Linguistics. London: Peter Owen.

Schmidtke, D. S., Conrad, M., & Jacobs, A. M. (2014). Phonological iconicity. Frontiers in

Psychology, 5.

The length of words reﬂects their conceptual complexity 42

Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical

Journal, 27, pp. 379–423.

Wilson, M. (1988). MRC psycholinguistic database: Machine-usable dictionary, version 2.00.

Behavior Research Methods, Instruments, & Computers, 20(1), 6–10.

Xu, Y., & Regier, T. (2014). Numeral systems across languages support efﬁcient communication:

From approximate numerosity to recursion. Proceedings of the 35th Annual Meeting of the

Cognitive Science Society.

Zipf, G. (1936). The psychobiology of language. Routledge, London.