Why do languages tolerate heterography? An experimental investigation into the emergence of informative orthography

It is widely acknowledged that opaque orthographies place additional demands on learning, often requiring many years to fully acquire. It is less widely recognized, however, that such opacity may offer certain benefits in the context of reading. For example, heterographic homophones such as ⟨knight⟩ and ⟨night⟩ (words that sound the same but which are spelled differently) impose additional costs in learning but reduce ambiguity in reading. Here, we consider the possibility that-left to evolve freely-writing systems will sometimes choose to forego some simplicity for the sake of informativeness when there is functional pressure to do so. We investigate this hypothesis by simulating the evolution of orthography as it is transmitted from one generation to the next, both with and without a communicative pressure for ambiguity avoidance. In addition, we consider two mechanisms by which informative heterography might be selected for: differentiation, in which new spellings are created to differentiate meaning (e.g., ⟨lite⟩ vs. ⟨light⟩), and conservation, in which heterography arises as a byproduct of sound change (e.g., ⟨meat⟩ vs. ⟨meet⟩). Under pressure from learning alone, orthographic systems become transparent, but when combined with communicative pressure, they tend to favor some additional informativeness. Nevertheless, our findings also suggest that, in the long term, simpler, transparent spellings may be preferred in the absence of top-down explicit teaching.

Brain responses to a lab-evolved artificial language with space-time metaphors

What is the connection between the cultural evolution of a language and the rapid processing response to that language in the brains of individual learners? In an iterated communication study that was conducted previously, participants were asked to communicate temporal concepts such as "tomorrow," "day after," "year," and "past" using vertical movements recorded on a touch screen. Over time, participants developed simple artificial 'languages' that used space metaphorically to communicate in nuanced ways about time. Some conventions appeared rapidly and universally (e.g., using larger vertical movements to convey greater temporal durations). Other conventions required extensive social interaction and exhibited idiosyncratic variation (e.g., using vertical location to convey past or future). Here we investigate whether the brain's response during acquisition of such a language reflects the process by which the language's conventions originally evolved. We recorded participants' EEG as they learned one of these artificial space-time languages. Overall, the brain response to this artificial communication system was language-like, with, for instance, violations to the system's conventions eliciting an N400-like component. Over the course of learning, participants' brain responses developed in ways that paralleled the process by which the language had originally evolved, with early neural sensitivity to violations of a rapidly-evolving universal convention, and slowly developing neural sensitivity to an idiosyncratic convention that required slow social negotiation to emerge. This study opens up exciting avenues of future work to disentangle how neural biases influence learning and transmission in the emergence of structure in language.

How Network Structure Shapes Languages: Disentangling the Factors Driving Variation in Communicative Agents

Languages show substantial variability between their speakers, but it is currently unclear how the structure of the communicative network contributes to the patterning of this variability. While previous studies have highlighted the role of network structure in language change, the specific aspects of network structure that shape language variability remain largely unknown. To address this gap, we developed a Bayesian agent-based model of language evolution, contrasting between two distinct scenarios: language change and language emergence. By isolating the relative effects of specific global network metrics across thousands of simulations, we show that global characteristics of network structure play a critical role in shaping interindividual variation in language, while intraindividual variation is relatively unaffected. We effectively challenge the long-held belief that size and density are the main network structural factors influencing language variation, and show that path length and clustering coefficient are the main factors driving interindividual variation. In particular, we show that variation is more likely to occur in populations where individuals are not well-connected to each other. Additionally, variation is more likely to emerge in populations that are structured in small communities. Our study provides potentially important insights into the theoretical mechanisms underlying language variation.

The development of rhythmic categories as revealed through an iterative production task

Both humans and non-humans (e.g. birds and primates) preferentially produce and perceive auditory rhythms with simple integer ratios. In addition, these preferences (biases) tend to reflect specific integer-ratio rhythms that are common to one's cultural listening experience. To better understand the developmental trajectory of these biases, we estimated children's rhythm biases across the entire rhythm production space of simple (e.g., ratios of 1, 2, and 3) three-interval rhythms. North American children aged 6-11 years completed an iterative rhythm production task, in which they attempted to tap in synchrony with repeating three-interval rhythms chosen randomly from the space. For each rhythm, the child's produced rhythm was presented back to them as the stimulus, and over the course of 5 such iterations we used their final reproductions to estimate their rhythmic biases or priors. Results suggest that regardless of the initial rhythm, after 5 iterations, children's tapping converged on rhythms with (nearly) simple integer ratios, indicating that, like adults, their rhythmic priors consist of rhythms with simple-integer ratios. Furthermore, the relative weights (or prominence of different rhythmic priors) observed in children were highly correlated with those of adults. However, we also observed some age-related changes, especially for the ratio types that vary most across cultures. In an additional rhythm perception task, children were better at detecting rhythmic disruptions to a culturally familiar rhythm (in 4/4 m with 2:1:1 ratio pattern) than to a culturally unfamiliar rhythm (7/8 m with 3:2:2 ratios), and performance in this task was correlated with tapping variability in the iterative task. Taken together, our findings provide evidence that children as young as 6-years-old exhibit simple integer-ratio categorical rhythm priors in their rhythm production that closely resemble those of adults in the same culture.

From One Bilingual to the Next: An Iterated Learning Study on Language Evolution in Bilingual Societies

Studies of language evolution in the lab have used the iterated learning paradigm to show how linguistic structure emerges through cultural transmission-repeated cycles of learning and use across generations of speakers . However, agent-based simulations suggest that prior biases crucially impact the outcome of cultural transmission. Here, we explored this notion through an iterated learning study of English-French bilingual adults (mostly sequential bilinguals dominant in English). Each participant learned two unstructured artificial languages in a counterbalanced fashion, one resembling English, another resembling French at the phono-orthographic level. The output of each participant was passed down to the next participant, forming diffusion chains of 10 generations per language. We hypothesized that artificial languages would become easier to learn and exhibit greater structure when they were aligned with participants' bilingual experience (i.e., English languages being easier to learn overall), or as a function of practice (i.e., languages learned second being easier to learn overall). Instead, we found that English-like languages became more structured over generations, but only when they were learned first. In contrast, French-like languages became more structured regardless of the order of learning, suggesting the presence of an asymmetric switch cost during artificial language learning. Moreover, individual differences in language usage modulated the amount of structure produced by the participants. Overall, these data suggest that bilingual experience impacts how novel languages are learned at an individual level, which can then scale up to cultural transmission of novel language at a group level.

Iterated learning reveals stereotypes of facial trustworthiness that propagate in the absence of evidence

When we look at someone's face, we rapidly and automatically form robust impressions of how trustworthy they appear. Yet while people's impressions of trustworthiness show a high degree of reliability and agreement with one another, evidence for the accuracy of these impressions is weak. How do such appearance-based biases survive in the face of weak evidence? We explored this question using an iterated learning paradigm, in which memories relating (perceived) facial and behavioral trustworthiness were passed through many generations of participants. Stimuli consisted of pairs of computer-generated people's faces and exact dollar amounts that those fictional people shared with partners in a trust game. Importantly, the faces were designed to vary considerably along a dimension of perceived facial trustworthiness. Each participant learned (and then reproduced from memory) some mapping between the faces and the dollar amounts shared (i.e., between perceived facial and behavioral trustworthiness). Much like in the game of 'telephone', their reproductions then became the training stimuli initially presented to the next participant, and so on for each transmission chain. Critically, the first participant in each chain observed some mapping between perceived facial and behavioral trustworthiness, including positive linear, negative linear, nonlinear, and completely random relationships. Strikingly, participants' reproductions of these relationships showed a pattern of convergence in which more trustworthy looks were associated with more trustworthy behavior - even when there was no relationship between looks and behavior at the start of the chain. These results demonstrate the power of facial stereotypes, and the ease with which they can be propagated to others, even in the absence of any reliable origin of these stereotypes.

Iterated Learning Models of Language Change: A Case Study of Sino-Korean Accent

Iterated learning models of language evolution have typically been used to study the emergence of language, rather than historical language change. We use iterated learning models to investigate historical change in the accent classes of two Korean dialects. Simulations reveal that many of the patterns of historical change can be explained as resulting from successive generations of phonotactic learning. Comparisons between different iterated learning models also suggest that Korean learners' phonotactic generalizations are guided by storage of entire syllable-sized units, and provide evidence that perceptual confusions between different forms substantially impacted historical change. This suggests that in addition to accounting for the evolution of broad general characteristics of language, iterated learning models can also provide insight into more detailed patterns of historical language change.

Monotone Quantifiers Emerge via Iterated Learning

Natural languages exhibit many semantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm with neural networks as agents.

A Systematic Investigation of Gesture Kinematics in Evolving Manual Languages in the Lab

Silent gestures consist of complex multi‐articulatory movements but are now primarily studied through categorical coding of the referential gesture content. The relation of categorical linguistic content with continuous kinematics is therefore poorly understood. Here, we reanalyzed the video data from a gestural evolution experiment (Motamedi, Schouwstra, Smith, Culbertson, & Kirby, 2019), which showed increases in the systematicity of gesture content over time. We applied computer vision techniques to quantify the kinematics of the original data. Our kinematic analyses demonstrated that gestures become more efficient and less complex in their kinematics over generations of learners. We further detect the systematicity of gesture form on the level of thegesture kinematic interrelations, which directly scales with the systematicity obtained on semantic coding of the gestures. Thus, from continuous kinematics alone, we can tap into linguistic aspects that were previously only approachable through categorical coding of meaning. Finally, going beyond issues of systematicity, we show how unique gesture kinematic dialects emerged over generations as isolated chains of participants gradually diverged over iterations from other chains. We, thereby, conclude that gestures can come to embody the linguistic system at the level of interrelationships between communicative tokens, which should calibrate our theories about form and linguistic content.

The emergence of word-internal repetition through iterated learning: Explaining the mismatch between learning biases and language design

The idea that natural language is shaped by biases in learning plays a key role in our understanding of how human language is structured, but its corollary that there should be a correspondence between typological generalisations and ease of acquisition is not always supported. For example, natural languages tend to avoid close repetitions of consonants within a word, but developmental evidence suggests that, if anything, words containing sound repetitions are more, not less, likely to be acquired than those without. In this study, we use word-internal repetition as a test case to provide a cultural evolutionary explanation of when and how learning biases impact on language design. Two artificial language experiments showed that adult speakers possess a bias for both consonant and vowel repetitions when learning novel words, but the effects of this bias were observable in language transmission only when there was a relatively high learning pressure on the lexicon. Based on these results, we argue that whether the design of a language reflects biases in learning depends on the relative strength of pressures from learnability and communication efficiency exerted on the linguistic system during cultural transmission.

Evaluating models of robust word recognition with serial reproduction

Spoken communication occurs in a "noisy channel" characterized by high levels of environmental noise, variability within and between speakers, and lexical and syntactic ambiguity. Given these properties of the received linguistic input, robust spoken word recognition-and language processing more generally-relies heavily on listeners' prior knowledge to evaluate whether candidate interpretations of that input are more or less likely. Here we compare several broad-coverage probabilistic generative language models in their ability to capture human linguistic expectations. Serial reproduction, an experimental paradigm where spoken utterances are reproduced by successive participants similar to the children's game of "Telephone," is used to elicit a sample that reflects the linguistic expectations of English-speaking adults. When we evaluate a suite of probabilistic generative language models against the yielded chains of utterances, we find that those models that make use of abstract representations of preceding linguistic context (i.e., phrase structure) best predict the changes made by people in the course of serial reproduction. A logistic regression model predicting which words in an utterance are most likely to be lost or changed in the course of spoken transmission corroborates this result. We interpret these findings in light of research highlighting the interaction of memory-based constraints and representations in language processing.

Simplicity and informativeness in semantic category systems

Recent research has shown that semantic category systems, such as color and kinship terms, find an optimal balance between simplicity and informativeness. We argue that this situation arises through pressure for simplicity from learning and pressure for informativeness from communicative interaction, two distinct pressures that often (but not always) pull in opposite directions. Another account argues that learning might also act as a pressure for informativeness, that learners might be biased toward inferring informative systems. This results in two competing hypotheses about the human inductive bias. We formalize these competing hypotheses in a Bayesian iterated learning model in order to simulate what kinds of languages are expected to emerge under each. We then test this model experimentally to investigate whether learners' biases, isolated from any communicative task, are better characterized as favoring simplicity or informativeness. We find strong evidence to support the simplicity account. Furthermore, we show how the application of a simplicity principle in learning can give the impression of a bias for informativeness, even when no such bias is present. Our findings suggest that semantic categories are learned through domain-general principles, negating the need to posit a domain-specific mechanism.

How Culture and Biology Interact to Shape Language and the Language Faculty

Recent work suggests that linguistic structure develops through cultural evolution, as a consequence of the repeated cycle of learning and use by which languages persist. This work has important implications for our understanding of the evolution of the cognitive basis for language; in particular, human language and the cognitive capacities underpinning it are likely to have been shaped by co-evolutionary processes, where the cultural evolution of linguistic systems is shaped by and in turn shapes the biological evolution of the capacities underpinning language learning. I review several models of this co-evolutionary process, which suggest that the precise relationship between evolved biases in individuals and the structure of linguistic systems depends on the extent to which cultural evolution masks or unmasks individual-level cognitive biases from selection. I finish by discussing how these co-evolutionary models might be extended to cases where the biases involved in learning are themselves shaped by experience, as is the case for language.

It takes a village: The role of community size in linguistic regularization

Studies of artificial language learning provide insight into how learning biases and iterated learning may shape natural languages. Prior work has looked at how learners deal with unpredictable variation and how a language changes across multiple generations of learners. The present study combines these features, exploring how word order variation is preserved or regularized over generations. We investigate how these processes are affected by (1) learning biases, (2) the size of the language community, and (3) the amount of input provided. Our results show that when the input comes from a single speaker, adult learners frequency match, reproducing the variability in the input across three generations. However, when the same amount of input is distributed across multiple speakers, frequency matching breaks down. When regularization occurs, there is a strong bias for SOV word order (relative to OSV and VSO). Finally, when the amount of input provided by multiple speakers is increased, learners are able to frequency match. These results demonstrate that both population size and the amount of input per speaker each play a role in language convergence.

Evolving artificial sign languages in the lab: From improvised gesture to systematic sign

Recent work on emerging sign languages provides evidence for how key properties of linguistic systems are created. Here we use laboratory experiments to investigate the contribution of two specific mechanisms-interaction and transmission-to the emergence of a manual communication system in silent gesturers. We show that the combined effects of these mechanisms, rather than either alone, maintain communicative efficiency, and lead to a gradual increase of regularity and systematic structure. The gestures initially produced by participants are unsystematic and resemble pantomime, but come to develop key language-like properties similar to those documented in newly emerging sign systems.

When Extremists Win: Cultural Transmission Via Iterated Learning When Populations Are Heterogeneous

How does the process of information transmission affect the cultural or linguistic products that emerge? This question is often studied experimentally and computationally via iterated learning, a procedure in which participants learn from previous participants in a chain. Iterated learning is a powerful tool because, when all participants share the same priors, the stationary distributions of the iterated learning chains reveal those priors. In many situations, however, it is unreasonable to assume that all participants share the same prior beliefs. We present four simulation studies and one experiment demonstrating that when the population of learners is heterogeneous, the behavior of an iterated learning chain can be unpredictable and is often systematically distorted by the learners with the most extreme biases. This results in group-level outcomes that reflect neither the behavior of any individuals within the population nor the overall population average. We discuss implications for the use of iterated learning as a methodological tool as well as for the processes that might have shaped cultural and linguistic evolution in the real world.

Which Melodic Universals Emerge from Repeated Signaling Games? A Note on Lumaca and Baggio (2017) ‡

Music is a peculiar human behavior, yet we still know little as to why and how music emerged. For centuries, the study of music has been the sole prerogative of the humanities. Lately, however, music is being increasingly investigated by psychologists, neuroscientists, biologists, and computer scientists. One approach to studying the origins of music is to empirically test hypotheses about the mechanisms behind this structured behavior. Recent lab experiments show how musical rhythm and melody can emerge via the process of cultural transmission. In particular, Lumaca and Baggio (2017) tested the emergence of a sound system at the boundary between music and language. In this study, participants were given random pairs of signal-meanings; when participants negotiated their meaning and played a "game of telephone" with them, these pairs became more structured and systematic. Over time, the small biases introduced in each artificial transmission step accumulated, displaying quantitative trends, including the emergence, over the course of artificial human generations, of features resembling properties of language and music. In this Note, we highlight the importance of Lumaca and Baggio's experiment, place it in the broader literature on the evolution of language and music, and suggest refinements for future experiments. We conclude that, while psychological evidence for the emergence of proto-musical features is accumulating, complementary work is needed: Mathematical modeling and computer simulations should be used to test the internal consistency of experimentally generated hypotheses and to make new predictions.

Signaling Games and the Evolution of Structure in Language and Music: A Reply to Ravignani and Verhoef (2018) ‡

In their commentary on our work, Ravignani and Verhoef (2018) raise concerns about two methodological aspects of our experimental paradigm (the signaling game): (1) the use of melodic signals of fixed length and duration, and (2) the fact that signals are endowed with meaning. They argue that music is hardly a semantic system and that our methodological choices may limit the capacity of our paradigm to shed light on the emergence and evolution of a number of putative musical universals. We reply that musical systems are semantic systems and that the aim of our research is not to study musical universals as such, but to compare more closely the kinds of principles that organize meaning and structure in linguistic and musical systems.

The Interactive Origin of Iconicity

We investigate the emergence of iconicity, specifically a bouba-kiki effect in miniature artificial languages under different functional constraints: when the languages are reproduced and when they are used communicatively. We ran transmission chains of (a) participant dyads who played an interactive communicative game and (b) individual participants who played a matched learning game. An analysis of the languages over six generations in an iterated learning experiment revealed that in the Communication condition, but not in the Reproduction condition, words for spiky shapes tend to be rated by naive judges as more spiky than the words for round shapes. This suggests that iconicity may not only be the outcome of innovations introduced by individuals, but, crucially, the result of interlocutor negotiation of new communicative conventions. We interpret our results as an illustration of cultural evolution by random mutation and selection (as opposed to by guided variation).

The Cultural Evolution of Structured Languages in an Open-Ended, Continuous World

Language maps signals onto meanings through the use of two distinct types of structure. First, the space of meanings is discretized into categories that are shared by all users of the language. Second, the signals employed by the language are compositional: The meaning of the whole is a function of its parts and the way in which those parts are combined. In three iterated learning experiments using a vast, continuous, open-ended meaning space, we explore the conditions under which both structured categories and structured signals emerge ex nihilo. While previous experiments have been limited to either categorical structure in meanings or compositional structure in signals, these experiments demonstrate that when the meaning space lacks clear preexisting boundaries, more subtle morphological structure that lacks straightforward compositionality-as found in natural languages-may evolve as a solution to joint pressures from learning and communication.

Culture and biology in the origins of linguistic structure

Language is systematically structured at all levels of description, arguably setting it apart from all other instances of communication in nature. In this article, I survey work over the last 20 years that emphasises the contributions of individual learning, cultural transmission, and biological evolution to explaining the structural design features of language. These 3 complex adaptive systems exist in a network of interactions: individual learning biases shape the dynamics of cultural evolution; universal features of linguistic structure arise from this cultural process and form the ultimate linguistic phenotype; the nature of this phenotype affects the fitness landscape for the biological evolution of the language faculty; and in turn this determines individuals' learning bias. Using a combination of computational simulation, laboratory experiments, and comparison with real-world cases of language emergence, I show that linguistic structure emerges as a natural outcome of cultural evolution once certain minimal biological requirements are in place.

Iconicity and the Emergence of Combinatorial Structure in Language

In language, recombination of a discrete set of meaningless building blocks forms an unlimited set of possible utterances. How such combinatorial structure emerged in the evolution of human language is increasingly being studied. It has been shown that it can emerge when languages culturally evolve and adapt to human cognitive biases. How the emergence of combinatorial structure interacts with the existence of holistic iconic form-meaning mappings in a language is still unknown. The experiment presented in this paper studies the role of iconicity and human cognitive learning biases in the emergence of combinatorial structure in artificial whistled languages. Participants learned and reproduced whistled words for novel objects with the use of a slide whistle. Their reproductions were used as input for the next participant, to create transmission chains and simulate cultural transmission. Two conditions were studied: one in which the persistence of iconic form-meaning mappings was possible and one in which this was experimentally made impossible. In both conditions, cultural transmission caused the whistled languages to become more learnable and more structured, but this process was slightly delayed in the first condition. Our findings help to gain insight into when and how words may lose their iconic origins when they become part of an organized linguistic system.

Compression and communication in the cultural evolution of linguistic structure

Language exhibits striking systematic structure. Words are composed of combinations of reusable sounds, and those words in turn are combined to form complex sentences. These properties make language unique among natural communication systems and enable our species to convey an open-ended set of messages. We provide a cultural evolutionary account of the origins of this structure. We show, using simulations of rational learners and laboratory experiments, that structure arises from a trade-off between pressures for compressibility (imposed during learning) and expressivity (imposed during communication). We further demonstrate that the relative strength of these two pressures can be varied in different social contexts, leading to novel predictions about the emergence of structured behaviour in the wild.

Exploring the knowledge behind predictions in everyday cognition: an iterated learning study

Making accurate predictions about events is an important but difficult task. Recent work suggests that people are adept at this task, making predictions that reflect surprisingly accurate knowledge of the distributions of real quantities. Across three experiments, we used an iterated learning procedure to explore the basis of this knowledge: to what extent is domain experience critical to accurate predictions and how accurate are people when faced with unfamiliar domains? In Experiment 1, two groups of participants, one resident in Australia, the other in China, predicted the values of quantities familiar to both (movie run-times), unfamiliar to both (the lengths of Pharaoh reigns), and familiar to one but unfamiliar to the other (cake baking durations and the lengths of Beijing bus routes). While predictions from both groups were reasonably accurate overall, predictions were inaccurate in the selectively unfamiliar domains and, surprisingly, predictions by the China-resident group were also inaccurate for a highly familiar domain: local bus route lengths. Focusing on bus routes, two follow-up experiments with Australia-resident groups clarified the knowledge and strategies that people draw upon, plus important determinants of accurate predictions. For unfamiliar domains, people appear to rely on extrapolating from (not simply directly applying) related knowledge. However, we show that people's predictions are subject to two sources of error: in the estimation of quantities in a familiar domain and extension to plausible values in an unfamiliar domain. We propose that the key to successful predictions is not simply domain experience itself, but explicit experience of relevant quantities.

Culture: copying, compression, and conventionality

Through cultural transmission, repeated learning by new individuals transforms cultural information, which tends to become increasingly compressible (Kirby, Cornish, & Smith, ; Smith, Tamariz, & Kirby, ). Existing diffusion chain studies include in their design two processes that could be responsible for this tendency: learning (storing patterns in memory) and reproducing (producing the patterns again). This paper manipulates the presence of learning in a simple iterated drawing design experiment. We find that learning seems to be the causal factor behind the increase in compressibility observed in the transmitted information, while reproducing is a source of random heritable innovations. Only a theory invoking these two aspects of cultural learning will be able to explain human culture's fundamental balance between stability and innovation.

Greater learnability is not sufficient to produce cultural universals

Looking across human societies reveals regularities in the languages that people speak and the concepts that they use. One explanation that has been proposed for these "cultural universals" is differences in the ease with which people learn particular languages and concepts. A difference in learnability means that languages and concepts possessing a particular property are more likely to be accurately transmitted from one generation of learners to the next. Intuitively, this difference could allow languages and concepts that are more learnable to become more prevalent after multiple generations of cultural transmission. If this is the case, the prevalence of languages and concepts with particular properties can be explained simply by demonstrating empirically that they are more learnable. We evaluate this argument using mathematical analysis and behavioral experiments. Specifically, we provide two counter-examples that show how greater learnability need not result in a property becoming prevalent. First, more learnable languages and concepts can nonetheless be less likely to be produced spontaneously as a result of transmission failures. We simulated cultural transmission in the laboratory to show that this can occur for memory of distinctive items: these items are more likely to be remembered, but not generated spontaneously once they have been forgotten. Second, when there are many languages or concepts that lack the more learnable property, sheer numbers can swamp the benefit produced by greater learnability. We demonstrate this using a second series of experiments involving artificial language learning. Both of these counter-examples show that simply finding a learnability bias experimentally is not sufficient to explain why a particular property is prevalent in the languages or concepts used in human societies: explanations for cultural universals based on cultural transmission need to consider the full set of hypotheses a learner could entertain and all of the kinds of errors that can occur in transmission.