Real-time processing

Real-time processing: the dynamics of productive and perceptive vocabulary knowledge in L1 and L2

RMA Thesis, University of Amsterdam Eilien Waegemaekers, 5773105 Supervisor: prof. dr. C.L.J. de Bot Co-supervisor: dr. R. Schoonen

“Het is zo gesteld met ons ongelukkig mensengeslacht, dat degenen die de platgetreden paden bewandelen bijna altijd stenen werpen naar hen die nieuwe wegen willen wijzen.” (uit: Voltaire, Filosofisch woordenboek, vertaling J.M. Vermeer – Pardoen)

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Abstract The present study is designed to investigate the dynamics of lexical processing of receptive and productive knowledge in the first and second language in proficient bilinguals. In order to do so, nineteen Dutch second language learners of English performed four lexical processing reaction time tasks that differed with respect to modality (reception vs. production) and language (L1 vs. L2). Within the framework of cognitive dynamics it has been shown that variability patterns in reaction time series do not correspond to random variation but show a specific temporal structure, referred to as pink noise. This phenomenon is suggested to emerge in complex systems that self-organize their behavior and reflects the coordination of the many processes involved in cognitive behavior. The degree to which pink noise is present in the four tasks reveals how late bilinguals are able to coordinate their behavior in the two languages and across the two modalities. The findings reveal more pronounced patterns of pink noise in the receptive tasks than in the productive tasks and somewhat more pronounced pink noise in the L1 tasks than in the L2 tasks. Although the differences in variability patterns in the two modalities can be explained by different task demands the differences between the L1 and the L2 tasks suggest that the participants can better coordinate their behavior in the L1. Furthermore, the presence of pink noise in these lexical tasks is not easily explained by component-dominant models of language suggesting that language processing in general and lexical processing in specific are better explained by interaction dominance.

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Content 1. Introduction………………………………………………………………………………………………………………..... 5 2. Theoretical framework…………………………………………………………………………………………………. 8 2.1 Dynamicity in second language development…………………………………………………… 8 2.2 From static to continuous measures…………………………………………………………………. 10 2.3 The dynamical nature of lexical knowledge………………………………………………………. 11 2.4 Pink noise in cognitive behavior………………………………………………………………………. 14 2.5 Research questions and hypotheses………………………………………………………………….. 19 3. Method…………………………………………………………………………………………………………………………..22 3.1 Cognitive dynamics and pink noise………………………………………………………………….... 22 3.2 Participants……………………………………………………………………………………………………... 23 3.3 Tasks………………………………………………………………………………………………………………..23 3.4 Procedure………………………………………………………………………………………………………... 25 3.5 Analysis…………………………………………………………………………………………………………... 26 4. Results………………………………………………………………………………………………………………………….. 28 4.1 Analysis of response times and errors……………………………………………………………… 28 4.2 Spectral and fractal analysis……………………………………………………………………………... 30 5. Discussion……………………………………………………………………………………………………………………...37 6. Conclusion…………………………………………………………………………………………………………………….. 44 Acknowledgements…………………………………………………………………………………………………………… 45 References………………………………………………………………………………………………………………………... 46 Appendices……………………………………………………………………………………………………………………….. 51

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1. Introduction Learning a second language (henceforward; L2) requires the speaker to learn the vocabulary of that language. And for successful communication the learner needs to be able to both recognize and comprehend the words she hears and be able to access and select the words to form a comprehensible sentence. Despite the fact that these mental processes happen quite unconsciously and might seem rather simple to the language user, they have provided researchers with some serious challenges. One of the puzzling phenomena in research on bilingualism is the functioning of the bilingual lexicon (cf. Kroll & Sunderman, 2003). Early research into the bilingual lexicon focused on the question of whether bilingual speakers have one integrated lexicon or two lexicons for each language. However, answering this question soon turned out to be too complex since firstly, there was disagreement on what exactly is stored in the mental lexicon and secondly, a discussion arose on whether the integration or non-integration of the two languages only applied to certain aspects of lexical representation or to all aspects. The discussion on the bilingual lexicon has led to new research questions in which the focus is on representation, activation during comprehension and selection during production. This way of dealing with scientific problems is a typical strategy used in cognitive psychology; progress can be made by breaking down a complex problem into simpler sub-problems. The argumentation that lies at the basis of this strategy is that the original problem can be solved by combining the solutions to the sub-problems. Although the study of isolated processes can add to the understanding of that particular process, it does not automatically follow that we understand the interaction of that process with other components of cognition. Understanding of human behavior is thus not automatically reflected by understanding the processes of its components but might reside in understanding the interaction and coordination of the individual processes (Wijnants, 2012). This approach to human cognition is called interaction dominance and is related to the thesis of the continuity of mind (Spivey, 2007) which states that the human mind is constantly in motion and does not receive discrete stimuli on which individual interpretations are computed. That is, the world around does not consist of independent stimuli that are spatially and temporally separated from all other stimuli and processing the continuous flow of stimuli happens in a probabilistic fashion. According to Spivey we must get rid of the computer metaphor of mind and start thinking of the mind as a set of possible brain states with fuzzy, overlapping areas that the mind travels through. “We all have the tendency to want to draw a circle around a set of phenomena and label that set with a name like perception and perhaps label another set of phenomena with the name cognition. Even within those circles, we feel the need to draw smaller circles of things like ‘word recognition’, as if it was completely unrelated to ‘object recognition’.” (Spivey, 2007: 28)

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The present research fits into the framework of Dynamic Systems Theory (DST) and is in line with both the interaction-dominant view of human cognition and the continuity of mind thesis. One of the first things that was done by researchers who took a dynamic approach to second language acquisition (Larsen-Freeman, 1997) was altering the more familiar notion of second language acquisition into second language development. The main motivation for this change of terminology is the focus of DST on change over time. When adopting a dynamic approach to multilingualism the focus is on development over time and not on the final stage, a phenomenon that has been the focus of study for many years (see e.g. Birdsong, 1992). Following a DST perspective, there is no final stage in development, and it is impossible to define a language as ‘acquired’, an assertion that also holds for the L1. The term acquisition implies that language development is only about growth whereas development is about growth and decline, two notions that are equally important in language research. Second language development is all about change over time and nonlinearity is an important characteristic of this development; it is not the case that twice as much words are learned when twice as much time is invested and rarely is it the case that growth in e.g. vocabulary follows a straight line. Another important point of focus when taking a DST perspective on second language development is variability. In more traditional approaches variability is seen as a by-product of real data and is considered to be obscuring the underlying development viewed as smooth, linear growth. In a DST perspective variability is considered an intrinsic property of development and patterns of variability can provide insight into the developmental process (Verspoor, de Bot & Lowie, 2011). The variable and nonlinear nature of development also comes to light in vocabulary growth (and decline) in bilinguals. De Bot and Lowie (2010) show that besides variation between learners there is also variation within the performance of a single learner on a simple word naming task over time. Furthermore, Schmitt and Meara (1997) in a longitudinal study of lexical development in Japanese learners of English found that “at least some of the vocabulary is in a state of flux” (p. 25). A DST approach to lexical processing in bilinguals requires continuous measures that reveal the dynamic properties of the process, i.e. its change over time. Analyzing patterns of variability in trial-bytrial fluctuations can reveal these dynamics: “In the vast majority of experiments in cognitive psychology, any information about the order in which empirical observations are obtained is discarded. The implicit assumption of this approach is that performance on successive trials is not correlated and, hence, any variance unaccounted for by the experimental manipulations can be considered random noise.” (Wagenmakers, Farrell & Ratcliff, 2004: 579)

Instead, by keeping the order of the trial series intact task it is possible to treat the overall cognitive performance across many trials as a continuous task. With the appropriate analysis techniques it is then 6

possible to investigate the patterns of variability and reveal long-distance correlations across many trials. Studying the patterns of variability in a lexical processing task can uncover what type of system lies at the basis of this endeavor. Patterns that reveal long-distance correlations are associated with interactiondominant complex systems that self-organize their behavior (Van Orden, Holden & Turvey, 2003) and are not easily accounted for by modular systems. Most of linguistic theories adopt a component-dominant view of the language system and showing that lexical processing comprises characteristics of interdependence would open the way to a paradigm shift in which the language system is no longer viewed as a system defined by its subcomponents but as an interaction-dominant system whereby all subsystems are open systems which “cannot be fully analyzed via encapsulated reductionism, because some of the parameters that drive an open system’s behavior are not internal to the system” (Spivey, 2007: 122). By stepping away from more traditional approaches to the mental lexicon it is possible to shed light on the dynamics of lexical processing in bilinguals and learn more about the nature of lexical knowledge. Vocabulary knowledge can range from reception (i.e. the ability to understand the word’s meaning) to free production (i.e. the ability to use the word in an uncontrolled productive task) and several studies have revealed a discrepancy between receptive and productive vocabulary knowledge in L2 learners (Laufer, 1998; Schmitt & Meara, 1997) where receptive vocabulary knowledge has a greater extent than productive vocabulary knowledge. This asymmetry is also reflected in the development of this knowledge in that free productive vocabulary develops more slowly and less predictably than passive vocabulary (Laufer & Paribakht, 1998). The goal of the present research is to investigate the patterns of variability in the L1 and the L2 for the modality of producing and perceiving. A nonlinear dynamic approach to these four lexical processing tasks (viz. L1 receptive vocabulary, L2 receptive vocabulary, L1 productive vocabulary and L2 productive vocabulary) can reveal information about the degree of consciousness and control (Kloos & Van Orden, 2010) in these processes that would otherwise remain unknown. This thesis starts out with a description of the theoretical framework relevant for the present research. Issues that will be discussed are the fundamentals of dynamic systems, the application of DST to second language development, the need for continuous measures in studies that adopt a DST approach, the dynamical nature of lexical knowledge and some of the complexities related to the bilingual lexicon. Furthermore, the phenomenon of pink noise is introduced and theoretical issues related to pink noise in cognitive behavior are discussed. In the third section the methodology is presented and the fourth section gives the results. In the final two sections the results are discussed and the main conclusions are presented.

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2. Theoretical background 2.1 Dynamicity in second language development The previous section already introduced some of the notions important to Dynamic Systems Theory1. In this section, the application of DST to second language development is described. In de Bot, Lowie and Verspoor (2007) aspects that characterize complex systems are coupled to the language system in the multilingual mind. One of the main characteristics of a complex dynamic system is its change over time and it is the development of the system what is studied in the wide range of fields that have adopted a DST approach. A dynamic system consists of many interacting variables which are completely interconnected and change in one variable will have impact on all other variables in the system. The system itself consists of subsystems and is part of a larger system. Due to the continuous interaction of multiple variables that change over time it is impossible to predict the outcome. As the system develops, it settles into attractor states which are preferred but not necessarily predictable. Attractors can be either strong or weak and depending on the strength of the attractor more or less energy is needed for the system to move on to the next attractor state (de Bot et al., 2007). Other characteristics of dynamic systems are their dependence on initial conditions, their nonlinear development, their emergent properties and the fact that they change through internal reorganization and interaction with the environment. Larsen-Freeman (1997) was one of the first to see the applicability of DST on second language development. In the first place, second language acquisition is characterized by dynamic processes and change over time is a crucial aspect of learning a second language. Moreover, the second language system seems to have the same properties as complex systems, namely it is a self-organizing system, it shows emergence, it develops in a nonlinear fashion and the outcomes are to a certain extent unpredictable. In addition, the system is highly dependent on initial conditions and internal resources of the learner such as the general capacity to learn, problem solving skills, motivational resources and conceptual knowledge all have a huge impact on second language development (Verspoor et al., 2011). By taking a DST perspective on second language development it is possible to explain why the language system is involved with both growth and decline. An assumption in both L1 and L2 acquisition research is that there is a clear end state in acquisition, something that is not supported by a DST perspective. The system is dependent on resources and when no energy is added to the system it will automatically degenerate. In language development, there is no one point in time at which a language is completely acquired, its development is ongoing and the study of attrition or growth is equally important to understanding this development. 1

In many publications the notions Complexity, Chaos, Nonlinear systems and Dynamic Sytems Theory are used interchangeably, I use the term DST to refer to all these notions.

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Although DST seems to be a comprehensive theory that can unify and overarch some more specific theories of language (e.g. cognitive linguistics, emergentism and connectionism (de Bot, Lowie, Thorne & Verspoor, 2013)) there are some problems with respect to its application. Since DST presumes unpredictable outcomes it is a theory that describes and explains but does not predict. In fact, prediction is not what the dynamic approach is after, it focuses on change over time and has as its goal to understand the mechanism of development (van Geert & Steenbeek, 2005). It is possible to point to tendencies, patterns and contingencies but it does not necessarily generate testable hypotheses. In fact, the proposed approach to science is ‘explaining after by before’: “In conventional science, explanation produces prediction in the form of testable hypotheses. In complexity theory, once a system has changed or evolved, the process might be explained by an appeal to such notions as emergence or self-organization, but new predictions are not necessarily a consequence. Of course, we may have expectations of how a process will unfold, […] but essentially, adopting a complexity theory perspective brings about a separation of explanation and prediction.” (Larsen-Freeman & Cameron, 2008: 202)

Furthermore, DST assumes complete interconnectedness, which implies that the study of a single component of language (e.g. syntax) cannot be done without studying all other components (e.g. morphology, phonology, etc.). To give an example, in a study on learning success it is irrelevant to focus on a single factor such as motivation, since motivation is interconnected with other factors such as attitude and these factors influence each other in both ways. By adopting a dynamic view on language development it is informative to look at the causal interconnections of the components and not at the contributions of the individual components. Another possibility is gathering dense data of language learners in natural contexts and interactions and studying variability in their development. Variability is presumed to be a precursor of change, where free and systematic variability will be relatively high when the system is re-organizing and low in a more stable system. Therefore, variability in the data should not be seen as noise or as measurement error, but rather as valuable information that can shed light on the developmental process of the system. Furthermore, research that takes a dynamic approach should not put a boundary between the cognitive system and the human system. Cognition cannot be seen separate from the body and in turn, the body cannot be seen separate from its environment, it is embodied, shared and situated. Embodied cognition implies that “it arises from bodily interactions with the world” (Thelen, Schöner, Scheier & Smith, 2001: 1) whereby it is bound by the perceptual and motor capabilities of the body. It is shared in the sense that it is possible to exchange thoughts with other people in a conversation, e.g. in interaction cognition is constantly changed based on the other person’s response (resulting in shared knowledge). Finally, situated cognition implies that all cognition is directly tight to the here-and9

now, in which there is continuous interaction between the environment and the physical properties of the body. Hence, “the social situation of language use and the psycholinguistic processing can only be artificially separated” (Verspoor et al., 2011: 18), and all language use is tightly connected to the context. DST does not claim to be a theory that is able to completely substitute other approaches in linguistics. However, it wishes to shed light on some aspects of the language system that are often neglected in more traditional approaches. These aspects are bidirectionality of change (growth and attrition), the study of variability and the integration of social and psychological aspects of language.

2.2 From static to continuous measures Since the late 1950s, researchers interested in human cognitive processing have tried to identify principles of cognition by designing models. The earlier models are largely based on the ‘computer metaphor’ of mind. Until the 1980s, many scientists saw the mind as though it functioned in the same way as a computer and language production was characterized as the rule-based manipulation of symbols. Models of that time largely consisted of boxes with a clearly defined interior and exterior (implying that the interior can be differentiated from the exterior) and arrows representing causal sequential connections between boxes (see e.g. Levelt’s speaking model (1989)). A very influential account is that of Fodor (1983) who stated that the mind consists of ‘domain-specific computational mechanism[s]’ (p. 37). Fodor assumes that there are independent modules for each of the sensory modes (e.g. sight, touch, taste) and for language. Within the language module there are processes that are informationally encapsulated and the output of one process serves as the input of the following process. Thus, language processing in this view is seen as a highly linear process. Despite the fact that the ‘computer metaphor’ has led to considerable progress in modeling higher-level cognitive processes, many critics have pointed out discrepancies between computers and brains. For example, in computers processes cannot interact until the outcome of the process is generated whereas brains have many parallel processes going on that can interact (Rumelhart, 1989). Furthermore, computers are assembled according to a blueprint, while brains must assemble themselves (Pinker, 1997). Although the limits of the computer metaphor of mind become more and more acknowledged, present-day science is still stuck with some of its remnants. A DST approach to cognition eliminates these last remnants. Dynamic Systems Theory focuses on complex systems that develop over time both due to internal forces and to energy from outside (de Bot et al., 2013). Research within this framework has as its aim to track change over time and as a direct consequence studies that take a dynamic perspective on the human mind can no longer use static measures, i.e. measures that focus on the response to a certain stimulus at a specific point in time. Instead, development over time is expected to be continuous and nonlinear and in

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order to track this development continuous measures are required. Spivey (2007), in his book, argues for continuous processing, continuous representations and thus for continuous measures: “Mental content does not consist of objects but of events. Individual representations are not temporarily static things in the mind (…). Representations are processes in and of themselves, sparsely distributed patterns of neural activation that change nonlinearly over the course of several hundreds of milliseconds, and then blend right into the next one.” (Spivey, 2007: 139)

According to Spivey, the mind is constantly in motion and stimuli are never presented individually and in isolation, nor is their interpretation computed individually. Cognition should be seen as a “continuously changing pattern of neuronal activity” (Spivey & Dale, 2006: 207). Despite the fact that during the cognitive revolution the theoretical emphasis on stimulus and response was rejected, methodologically the focus has always remained on discrete stimuli and discrete responses. Up until today much psychological and psycholinguistic research adopts a stimulus/response paradigm, without paying attention to the continuous journey that the mind traverses from the moment the stimulus is presented until the final outcome. A problem with this paradigm is not only the assumption that the final outcome reflects the cognitive process that underlies the response to a stimulus but also the neglect of the starting point of the mind. The human mind is continuously subject to a flow of stimuli and the level or ‘state’ of the system depends critically on the previous level. This implies that the focus of research should not only be on the journey from stimulus to response but also on the state of the system when the stimulus is presented. Hence, the use of continuous measures that integrate the temporal dynamics of cognition are preferred over measures that focus on the outcomes of cognitive processes since these measures reveal something about “the time course of processing and the gradual accumulation of partial information” (Spivey, 2007: 53).

2.3 The dynamic nature of lexical knowledge Recent findings in the field of lexical knowledge have led to a change in the way lexical knowledge is viewed. Lexical representations are no longer seen as static but as highly dynamical and contextdependent (Elman, 2011). In Elman’s view on the mental lexicon there is essentially no mental lexicon and words are considered stimuli which operate directly on mental states. Word knowledge is not just the passive storage of meaning but words are stimuli that interact immediately with mental states. It is the interaction between the word and the mental state of that particular moment that reveals the word’s phonological, syntactic, semantic and pragmatic properties. According to Elman “words don’t have meaning as much as they provide clues to meaning” (Elman, 2004: 301). This view corresponds to the DST perspective on knowledge, in which there is no room for passive storage of information. However, 11

this perspective is not shared by all scholars. Jackendoff (2010) argues for a lexicon situated in the longterm memory which stores words from which the grammar constructs phrases. A lexical entry, in his view, contains a small bit of information on its phonological structure, a small bit of information on its syntactic structure and a small bit of information on its conceptual structure (Jackendoff, 2010: 15). An important question for this account is what is listed in the long-term memory. Are lexical entries only units that consist of single words or are idioms and fixed expressions (i.e. units larger than single words) also stored in the lexicon? Jackendoff argues that words, idioms but also rules of grammar and regular affixes are stored in the long-term memory. The fact that both syntactic constructions and words are stored together in the long-term memory goes against the traditional view that grammar and lexicon are neatly separated. However, Jackendoff presumes a multidimensional continuum in which words are in one corner while “maximally general rules are in another corner, and in between are all sorts of other phenomena varying of degrees of regularity” (Jackendoff, 2010: 20). Jackendoff’s view on knowledge corresponds to the representationalist stance whereby thinking can be understood in terms of representational structures in the mind on which computational procedures operate. In this view the passive storage of knowledge as internal entities is needed to explain thinking. DST adopts another view on knowledge, namely the theory of situated action (Gibson, 1979). In this theory the environment plays an important role in shaping cognitive mechanisms and all knowledge is viewed as a reciprocal interaction of the agent and the environment; “an embodied subject acts with the help and under the constraints of a physical world that includes the external environment and the physical properties of the body” (van Geert & Steenbeek, 2005: 421). Elman’s view (2011) of words as stimuli that operate on mental states neatly fits into the dynamic approach to lexical knowledge. An argument in favor of Elman’s proposal comes from the issue that concerns the distinction between rule and word. In early linguistic theory the focus has been on syntactic rules (Chomsky, 1957) and words were seen as inevitable things that had to be learned, but unimportant for linguistic theory. However, in many theories the distinction between word and rule is blurred since specific lexical information plays a role in the interpretation of a grammatical structure. This is exactly what made Jackendoff decide to include syntactic information in the lexicon. However, once you start introducing this kind of information into the lexicon, where do you draw the line of what is stored in the lexicon and what is stored outside? Several studies (i.a. Race, Klein, Hare & Tanenhaus, 2008; Hare, McRae & Elman, 2003; Ferretti, McRae & Hatherell, 2001) have shown that words are highly context-sensitive and listeners make use of detailed knowledge of word properties to come to the correct interpretation. Examples of this detailed information are for e.g. selectional restrictions of verbs, thematic roles associated with verbs and information about the statistical patterns of usage concerning both the syntactic structure and lexical preferences for specific arguments. This already implies that the lexicon should 12

contain very specific information for every lexical item but there are even more difficult challenges for the mental lexicon. Ferretti, Kutas and McRae (2007) have found that the aspect of the verb alters the listener’s expectations about the verb’s arguments. If a sentence with an activity verb was presented in the perfective aspect the associated location was not primed in the participants. On the other hand, when the same sentence was presented in the progressive aspect the associated location was primed. This is because the location is of greater salience for an ongoing event. These findings raise the question whether this type of information is also included in the lexical representation of the verb and if so, whether verbs are stored independently with each inflection or whether there is some general construction stored that primes the associated location for verbs in the progressive aspect. An even bigger challenge to the mental lexicon is the influence of discourse context. Studies have shown that specific agent-verb combinations lead to different predictions of a likely patient but Race et al. (2008) have shown that the overall context preceding the sentence can override such predictions. Since it is obviously impossible to include discourse context in the mental lexicon, a question that needs to be asked is where to draw the line. All this information is relevant to sentence processing and is introduced from the earliest possible stage in processing, so drawing an arbitrary line to what is inside and what outside the mental lexicon would not lead linguistic theory any further. At the same time, if all is included in the mental lexicon “is there then any meaningful distinction between the lexicon and other linguistic knowledge” (Elman, 2011: 12)? Another issue related to the mental lexicon is the quest of how novel uses of known words come into existence. Within the generative framework, at one time the syntax, which acted upon static constituents, was supposed to explain the possibility to form an indefinite number of new sentences (Chomsky, 1957). Constituents were seen as fixed, static parts in which fixed lexical items were inserted. The fact that a word can have a whole range of meanings depending on its context is not explained in this framework. Although this point can be accounted for by adding statistical information to the lexical representation, the problem remains that a word cannot obtain a new meaning. “If novel utterances are to be explained they must, at heart, differ from rules or statistical co-occurrences” (Wallot & Van Orden, 2011a). The bottom line of this argument is that it does not matter how much information you store in the “mental lexicon” it will never explain how new meanings of words come into existence. And this is where a dynamic approach to lexical knowledge can provide an explanation; novelty arises due to the interaction of a word with its environment. What is important to note is that Elman does not claim that language users do not have lexical knowledge; rather, in his view: “[..] representations are not abstract symbols but rather regions of state space. Rules are not operations on symbols but rather embedded in the dynamics of the system, a dynamics which permits movement from certain regions to others while making other transitions difficult.” (Elman, 1995: 2)

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By means of the Simple Recurrent Network (SRN) connectionist model that consists of a multidimensional state space Elman has been able to account for the context sensitivity of lexical knowledge and for the emergence of truly novel meanings. That is, if a word is presented in a context, e.g. run in ‘Jaguars run fast’ this particular instance of run occupies another region in state space than if the word occurred in the context ‘Those children run fast’. However, the two regions in state space overlap and are tightly clustered (Elman, 2004: 303). The uniqueness of the region in state space for each instance of a word allows for context-sensitive interpretations and novel meaning to come into existence. Although Elman’s approach does not extend to the bilingual lexicon it is expected that the same principles hold for bilingual lexical knowledge. In fact, since there is no mental lexicon and words are viewed as operators that interact with mental states there is essentially no difference between L1 and L2 words. However, although not specified in Elman (2004, 2011), L2 knowledge is assumed to be more fragmented. Knowing how to use a word involves knowing how it combines with other words and before that knowledge can be generalized to new contexts a certain amount of input is needed (Elman, 2004). In late bilinguals as those in this study this input is undoubtedly less in the L2. Research has shown that both L1 and L2 lexical knowledge are subject to intra-learner variability in performance (see e.g. de Bot & Stoessel, 2000 for L1 lexical knowledge and de Bot & Lowie, 2010 for L1 and L2 lexical knowledge) but the more fragmented character of L2 knowledge is reflected by the higher intra-learner variation in the L2.

2.4 Pink noise in cognitive behavior A large part of research done in the field of cognitive psychology, including psycholinguistics, relies on response times. Response times are interpreted as a reflection of the time needed for the underlying mechanisms to generate a response to the stimulus and by comparing average response times in specific conditions researchers believe to learn more about these mechanisms. Variability around the mean is in most studies considered as random error or measurement error which is either unstructured or comparable across groups and therefore excluded from the analysis. However, Gilden, Thornton and Mallon (1995) have shown that looking at the fluctuations of reaction times over time can provide information about the underlying system. When the order of responses is kept intact the variability around the mean usually reveals a rich dynamical structure. An example of such structured variability is that of pink or 1/ƒα noise where α is referred to as the scaling exponent and corresponds to the negative slope of the log-log power spectrum (see Figure 2.4.1C and further explanation below). Pink noise is a construct from fractal geometry and reflects the self-similarity of processes on different time scales. This implies that fluctuation around the mean consist of many small changes which are nested in slower but larger changes. This nested pattern is best explained visually: Figure 2.4.1A illustrates an example of a time series that 14

corresponds to pink noise, on the x-axis the successive trials are depicted while the y-axis depicts the participant’s deviation from the overall mean on each trial (z-scores). The time series depicted in Figure 2.4.1A consists of a large number of small changes that are nested in larger, but slower fluctuations. If one would zoom in on the series the same pattern of fluctuations would appear on the smaller timescale. This property of pink noise is called fractal. Fractals are self-similar which entails that the structure of the smaller pieces resembles the whole. An example of a fractal, self-similar object is the romanesco broccoli on the cover of this thesis; the smaller parts are copies of the larger parts which in turn are copies of the biggest part; the whole broccoli. With respect to a response time series “[t]his means that emergent fractal patterns in a data series indicate the presence of system dynamics that extend beyond the time boundaries of single trials or events, and evolve across multiple interdependent timescales of performance” (Wijnants, 2012: 12). This fractal structure extends over the whole trial series implying long-range dependencies in the signal. These serial correlations decay very slowly and are thus persistent. Pink noise can be revealed in a time series by means of spectral analysis2 where the dependencies in the time domain are translated as simple features in the frequency domain (Wijnants, 2012: 138). This is done by a Fourier transform which decomposes the series in waveforms with particular frequencies and amplitudes. In Figure 2.4.1B the results from the spectral analysis are plotted in which frequency is plotted against power, i.e. how often changes of specific sizes occur. What becomes clear from this plot is that there are many changes with small power and few changes with large power. In 2.4.1C the frequency (x) and power (y) are transposed to double-logarithmic axes. Idealized pink noise has a scaling exponent (α) of 1 corresponding to a slope of -1 on a log-log scale. This scaling relation implies that power and frequency are inversely related. If the variability of the response times were completely random one would not find such long term correlations as defined by pink noise. In Figure 2.4.1D, E and F the same time series is depicted but this time presented in random order, hence the fractal, self-similar pattern was destroyed. When spectral analysis is carried out on the randomly shuffled trial series a pattern emerges that corresponds to white noise. White noise implies that there is statistical independence from observation to observation, there is no systematic variation in power as a function of frequency and when plotted on a log-log scale the slope of the regression line is approximately zero. The distinction between white and pink noise is not a binary distinction, in actual data the pattern that shows up generally falls between random variability (i.e. white noise) and self-similar pink noise, having a scaling exponent α (i.e. the positive alternative of the slope of the regression line) somewhere between 0 and 1. When the slope of the regression line is steep (approaching -1) the variability pattern of the trial series corresponds to pink noise, when the slope is shallow (approaching 0) the variability pattern becomes more similar to white noise. 2

For more information on spectral analysis, see Holden (2005).

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The presence of pink noise in trial series runs against conventional statistical intuitions that assume that successive responses are independent. “After all, it is properties of the presented stimulus that are conventionally assumed to be driving a participant’s response, not aspects of the previous response” (Holden, 2005: 272). The structure of the variability in a trial series that exhibits pink noise implies that mean and standard deviation depend on where the sample was taken. As visible in Figure 2.4.2A there are periods in which the deviance from the overall mean is all in positive and calculating the mean in that period would result in a higher mean than the mean of the whole trial series, whereas in other periods the deviance from the overall mean is all in negative and calculating the mean for that period would result in a lower mean. Hence, for pink noise, mean and standard deviation are dependent on the sample size.

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Figure 2.4.1 An example of a 1024 trial series of one participant who estimated fixed time intervals. (A) The x-axis depicts the successive trials, the y-axis the z-scores. (B) Results of the power spectral analysis in linear units (C) The results from B plotted on a log-log scale. (D)-(F) The same succession of plots as (A) through (C) for a randomly shuffled version of the data depicted in (A) (from Holden, 2005; 270).

Up until now the focus has been on the formal description of pink noise, and although important for understanding the phenomenon, the most interesting part lies in the interpretation of the fluctuations found in reaction time series. According to Van Orden et al. (2003) the presence of pink noise in cognitive behavior suggests that processes of the body and mind change eachother’s dynamics. The interdependence among components explains the correlated noise since interdependence allows the behavior of each process to reflect something of the behavior of the whole. In general, complex systems show self-organization, which is expressed by the interaction of components that occur as part of interdependent processes across multiple timescales and results in emergent behavior. One of the assumptions that lie at the basis of interaction-dominant dynamics is that the interactions of the components are more important than the dynamics of the individual components. It is expected that the interactions lead to emergent behavior and only by studying the interactions is it possible to understand more about global phenomena (Wijnants, 2012: 11). Self-organized criticality (SOC) is a specific form of self-organization which is often mentioned in relation to pink noise (van Orden et al., 2003). This kind of self-organization has interesting properties since it makes the system flexible and adaptive. SOC is the attraction of complex systems toward critical states (Bak, 1996). Characteristics of critical states are the reduction of the degrees of freedom for behavior, i.e. they are temporary sources of constraint in which two opposing behaviors are in precise balance and hence, equally likely. The constraints relevant for behavior are best summarized in control parameters (Kloos & Van Orden, 2010). For example, in human behavior infants’ stepping behavior can be summarized in a simplified control parameter. In this case, sources of constraint are, among others, the weight of the leg and the strength of the leg (Thelen & Smith, 1994).

(1) simplified stepping:

In this simplified control parameter the ratio between the weight and the strength can predict infants’ stepping behavior; when the strength of the leg exceeds its weight stepping behavior is possible, when the weight of the leg exceeds its strength stepping behavior disappears. In more general terms the control parameter of human behavior can be visualized as in (2).

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(2) simplified behavior:

The numerator of the control parameter summarizes the constraints that embed the object of behavior in its environment. These embedding constraints determine affordances, which reflect the action potentiality of a material object given the surrounding environment (Kloos & Van Orden, 2010: 24). The denominator of the control parameter concerns the embodied constraints of the object of behavior, i.e. constraints supplied by the body itself. Hence, effectivities are the capacities and capabilities of the body, “the repertoire of what the body can do” (Zukow-Goldring & Arbib, 2007: 2181). When the ratio of the control parameter is 1, the parameter has reached a critical value and the system enters a critical state in which opposing actions are equally available. In the case of infant’s stepping behavior this implies that when the ratio is 1, the opposing behaviors (i.e. stepping and not stepping) are in precise balance. When a system is in a critical state even a tiny change can cause the symmetry to be broken and can enact behavior. Pink noise is claimed to be indicative of a complex system that attracts to critical states (Bak, 1996). In linguistic behavior, such as the lexical processing tasks of the present study, the late bilinguals must have the capacities (i.e. effectivities) to respond to the particular task demands (i.e. affordances). That is, there is a part in the lexical processing tasks that is controllable and a part that is uncontrollable and self-organized criticality is an emergent phenomenon that makes the system stay near critical states in which uncontrollable and controllable degrees of freedom are in the right balance. In L2 processing it is expected that there are less controllable degrees of freedom than in L1 processing, giving way to whiter noise. Hence, a pink-noise scaling relation is a form of balance where the system continuously tries to find the right equilibrium between over-random and over-regular behavior. Over-random behavior would be reflected in white noise, where performance is unconstrained and flexible. On the other hand, overregular behavior would be reflected in Brownian motion (i.e. brown noise with a scaling exponent towards α ≈ 2) in which performance is persistent and rigid, reflected by highly constrained and inflexible components. The scaling relation of pink noise falls exactly in between white noise and brown noise, implying a right balance between unconstrained and flexible behavior and highly constrained and inflexible components. When pink noise is found in cognitive behavior this may be a reflection of an optimal combination of stability and flexibility of the system. By being stable and flexible at the same time the system can accommodate to both familiar and idiosyncratic changes in the environment. This is what is intended by self-organization of cognitive performance in which the processes of the body that occur at different time scales are coordinated (Van Orden et al. 2003).

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Related to the proposal of pink noise as a signature of the tendency to stay near critical states is that of system coordination. This proposal states that pink noise is present in tasks where behavior is optimally coordinated. Evidence for this interpretation of pink noise comes i.a. from Wijnants, Bosman, Hasselman, Cox and Van Orden (2009) who used a precision aiming task that measured the time it required to trace the path from one dot to another dot on a digital tablet. Participants had to perform the task with their non-dominant hand. Across blocks of trials, as participants acquired practice, the whiter noise found in the earlier time series gradually approached pink noise. Wijnants et al. explain the pinker noise in the later blocks as a reduction of degrees of freedom for movement to promote more efficient and coordinated behavior. Similar findings come from Kloos, Kiefer, Gresham, Shockley, Riley and Van Orden (2009) who repeatedly assessed short time-interval estimations in children from 4- to 12-years old. In this study, younger children exhibited white noise while older children were attracted to pink noise. Kloos et al. (2009) explain these findings in younger children by underdeveloped effectivities, i.e. underdeveloped capacities for action. With development children acquire effectivities to better coordinate their bodies in the tasks. Hence, pink noise found in cognitive tasks is explained as an optimal balance of stability and flexibility to adjust to both the customary and idiosyncratic changes in the environment. Wagenmakers, Farrell and Ratcliff (2005) critically evaluate the proposal of pink noise as evidence for self-organized criticality. They argue that the current literature on SOC in human cognition lacks specific models that can generate testable hypotheses. Moreover, the finding of pink noise in cognitive tasks does not guarantee critical behavior (Jensen, 1998). That is, the presence of pink noise can be a result of other factors such as the “aggregation of multiple component processes that separately generate transient correlations” (Wagenmakers et al., 2005: 8). Furthermore, there are some issues with the ubiquitous nature of pink noise. Not all complex systems produce pink noise under all conditions, pink noise is only generated under specific conditions and with specific dependent variables. According to Wagenmakers et al., the literature on 1/ƒ noise has not yet addressed these important questions regarding the experimental tasks and conditions that are expected to lead to the occurrence of pink noise. Finally, even if pink noise is regarded as evidence for SOC it remains unclear how the SOC framework should be applied to human cognition. The overall message from Wagenmakers et al. is that theoretical and empirical development related to pink noise in human cognition is scarce and they emphasize the need for a specific model that can account for, and generate predictions about pink noise in cognitive tasks. The present research wishes to add both empirically and theoretically to these issues.

2.5 Research questions and hypotheses The goal of the present research is to study the dynamics of productive and receptive knowledge in Dutch second language learners of English. This is done by taking a nonlinear approach to reaction times 19

whereby the patterns of variability that arise are investigated for the modality of production and perception in both the L1 and the L2. This approach fits into the framework of DST where lexical knowledge is viewed as highly dynamic and is apposite for answering questions about the change of the language system over time. As described in the previous section, patterns of variability in reaction time series reveal information about the degree of coordination and control of language processing in a specific task. “That is, given that self-organization coordinates the processes of the body across their hierarchy of timescales, and that correlated activity across timescales produces 1/f scaling, one would expect clearer 1/f scaling in coordinated cognitive activities compared with less coordinated activities” (Wijnants, 2012: 18). When adopting these assumptions, it is possible to make some predictions about the patterns of variability on the four tasks. Since the participants all have Dutch as their L1 it is expected that the participants can coordinate their behavior better in the L1 tasks than the L2 tasks. However, recent context of use and task familiarity can change the patterns of variability (de Bot & Lowie, 2010). This is why background information on language usage and self-reports of proficiency are compared with the findings from the spectral analysis. By comparing the two modalities (i.e. production and comprehension) it is possible to investigate whether the receptive-productive gap as found in several studies on L2 lexical knowledge (e.g. Laufer, 1998, Schmitt & Meara, 1997) is also reflected by less coordinated behavior in production. The present research also has a more general aim in that it wishes to investigate whether performance in linguistic tasks show patterns of variability analogue to pink noise. Variability patterns with a scaling exponent α between 0 and 1 have been found in a wide range of cognitive tasks, such as lexical decision, visual search (Gilden, 2001), simple reaction times, word-naming (Van Orden et al., 2003) and movement times in a tracing task (Wijnants et al., 2009). However, the ubiquitous presence of 1/ƒ noise in cognitive behavior remains a topic of debate. Wagenmakers et al. (2004) question the ubiquitous nature of 1/f noise whereas Wallot and Van Orden (2011b) see pink noise as a neural signature of cognitive behavior and therefore expect pink noise in all cognitive tasks. Hence, the research has an explorative character investigating on the one hand whether 1/ƒ noise is present in two linguistic tasks that have not yet been investigated and on the other hand the dynamics of lexical processing in bilinguals by studying changes in patterns of variability as a result of changes in task demands. The research questions are the following: 1. Is 1/ƒ noise ubiquitous in cognitive behavior and can the language system be seen as a selforganizing complex system? 2. How do the patterns of variability in reaction time fluctuations differ for the modality of producing and comprehending? 20

3. How do the patterns of variability differ for performance in the first and the second language?

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3. Method To investigate how productive and receptive word knowledge differ in their fluctuations over time in second language learners a reaction time experiment was developed. This chapter gives a description of the experimental set-up and the methodological framework to which this study is associated. In the first section the nonlinear method of spectral analysis is discussed and it is explained how background noise in reaction time studies can be analyzed in an innovative manner to provide insight into the stability of lexical representations and the degree of control and automaticity of the complex system (of language, in this case). Section 3.2 gives information about the participants of this study and section 3.3 describes the four tasks of the experiment. In section 3.4 the procedure is presented and in the final section it is explained how the data are analyzed.

3.1 Cognitive dynamics and pink noise Recent developments in the field of cognitive dynamics have led to new methods to investigate the degree of intentional behavior and automaticity of cognition (Kloos & Van Orden, 2010). These techniques focus on patterns of variability and use spectral analysis of reaction times which reveal different types of noise (pink, brown and white noise). In conventional reaction time studies background noise gets filtered out before analysis since it is assumed to be a by-product of error in measuring instruments or other external factors. However, background noise is not always uncorrelated noise, i.e. white noise (Van Orden et al. 2003). As described in the previous section, pink noise is a form of correlated noise which reflects the scaling relation between over-random and over-regular behavior. Another type of correlated noise is brown noise, which is found in over-regular behavior, e.g. in stride-interval measurements of young children walking on a treadmill (Hausdorff, Zemany, Peng & Goldberger, 1999). Lowie, de Bot and Plat (to appear) have used spectral analysis of reaction times to investigate the effect of language use on word naming in a bilingual speaker in both the L1 and the L2. The participant had to read 4- and 5-letter words as quickly as possible in two tasks, an L1-task and an L2-task. Reaction times were measured at different time points; after a period of solely using the L1 and after a period of solely using the L2. Spectral analyses show that the variability patterns differ significantly after a 7-day period of exclusively using the L1 than after a 7-day period of exclusively using the L2. On the task of the language used most recently there were more pronounced patterns of pink noise. This shows that language use directly influences both performance in the L1 and the L2 and shows that language use affects the complex system directly.

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The application of this technique in the field of second language development can contribute to the understanding of receptive and productive knowledge in bilingual speakers. Pink noise provides information on the degree of self-organization of the complex system and can therefore give a better understanding of the differences between receptive and productive knowledge in the L1 and the L2 from a continuous perspective. In de Bot and Lowie (2010) lexical representations are described as “inherently unstable and constantly changing due to internal restructuring in the lexical system” (p. 73). Adopting a receptive and a productive task in both the L1 and the L2 helps to answer questions concerning the nature of the four types of knowledge (i.e. L1 perceptive word knowledge, L1 productive word knowledge, L2 perceptive word knowledge and L2 productive word knowledge) with a special focus on change over time. Something that should be taken into account is the fact that within Dynamic Systems Theory all subcomponents are completely interconnected and it is therefore not the case that these four types of knowledge are seen as distinct subsystems that change independently over time. However, the degree of control and self-organization might be different for the different tasks and diverse patterns of variability might come to light. How the language system changes can be different for the L1 and the L2 and for the modality of producing and perceiving, something that spectral analysis of RTs can show.

3.2 Participants Participants for this study are nineteen (n = 19) Dutch second language learners of English enrolled in the third year of the BA English Language and Literature at the University of Amsterdam, i.e. second language learners with a high proficiency in English. All participants are born and raised in the Netherlands and have Dutch as their mother tongue (excluding one participant who was raised bilingually with Turkish and Dutch). The bilingually raised participant is excluded from part of the analyses, but the results from the spectral analysis on the four tasks are reported. Of the nineteen participants six had lived in a foreign country for a period of roughly one year of which three lived in an English-speaking country (the other three lived in France, Austria and Portugal). Most of the participants is female (F=13, M=6) and the age ranged from 20 to 49 years (mean=23,8). All participants fulfilled four different tasks, two productive tasks, one in the L1 and one in the L2 and two perceptive tasks, one in the L1 and one in the L2. In the following section the four experiments are described.

3.3 Tasks Task 1 and 2: Productive word knowledge in the L1/L2 In this task the participants perform a picture naming reaction time experiment which is developed in eprime. The response times are measured both by a voice key and subsequently by a script in PRAAT (Boersma & Weenink, 2013) which automatically measured changes in dB as well as voice onsets (see 23

section 3.6 for a more detailed description of the response time measurements). Participants see a colored drawing of a simple object taken from the picture set produced by Rossion and Pourtois (2004) or an adapted item from the picture set used by Severens, Van Lommel, Ratinckx and Hartsuiker (2005) and are asked to name this object as quickly as possible. In the L1-task participants name the pictures in Dutch and in the L2 task participants name the same pictures in English. The pictures are selected on the basis of several criteria; they cannot have latencies higher than 1100 ms in the study from Severens et al. (2005) and must have a H-statistic that does not exceed 1,5 in the same study and in the corresponding items from the study from Snodgrass and Vanderwart (1980). The H-statistic reflects the percentage agreement score by taking into account the number of names given for a certain item. These criteria were adopted to reduce variability between items and ensure a relatively homogeneous set of items. The picture set consisted of 265 items (see appendix B for all the items) that were randomized twice to form two lists that were presented one after the other (resulting in a trial series of 530 items for each task excluding the 10 trial items). Spectral analysis requires a trial series with a power of 2 (here 2 9=512) and presenting 530 items resulted in a scant buffer of 18 items. Adjacent items that were semantically too closely related (e.g. fishing rod and fish) were manually moved to avoid semantic priming effects as much as possible (McDonough & Trofimovich, 2008). Order of presentation was the same for all participants and was the same for the L1 and the L2 task. As the focus is on the overall performance across many trials and not on the response on individual items there is no need to randomize the items. By keeping the order of presentation the same for all participants on the L1 and L2 task the comparability of the performance on the two tasks is enhanced. On each trial, a fixation signal, visible for 500 ms, is first presented which then is followed by the target picture. The target picture appears in the center of the computer screen and remains on the screen for 200 ms after a response is detected by the voice key. Each response is followed by a fixed 300-ms intertrial interval after which the fixation signal of the subsequent trial becomes visible. Every participant first completed 10 practice trials to get used to the experimental set-up after which the 530 experimental trials start. All responses are recorded using an Edirol R1 Portable Wave/MP3 recorder. Participants are all first tested in the L1 and then in the L2, each of the tasks requiring about 25 minutes.

Task 3 and 4: Perceptive word knowledge in the L1/L2 In this task the participants perform a reaction time experiment which is developed in e-prime. The response times are measured by a response box to make sure the measurement is as accurate as possible. Participants see a fixation signal of 500 ms in the center of the screen after which a written word appears in the same position. After 300 ms two pictures appear, one on the left side of the screen and one on the right side of the screen. One of the pictures corresponds to the written word in the center of the screen. Participants are asked to indicate as soon as possible, by means of pressing the right or the left button on 24

the response box, which picture corresponds to the written word (see figure 3.4.1 for an example of the screen setup).The choice of written over spoken stimuli was based on practical considerations.

Figure 3.4.1 Example item of L2 perceptive word knowledge task

Each response is followed by a fixed 300-ms intertrial interval after which the fixation signal of the subsequent trial becomes visible. Items are the same as in the productive word knowledge task but the two item lists are randomized independently in order to avoid the same order of representation in the productive and perceptive task. Every item is coupled with its target picture and a distractor item, which is randomly chosen from all the other items in the list. Target pictures that were semantically too similar (e.g. chicken and egg) or similar in shape (e.g. pyramid and mountain) were manually altered and coupled with another item. Every participant first completes 10 practice trials to get used to the experimental setup after which the 530 experimental trials start. Participants are all first tested in the L1 and then in the L2, each of the tasks requiring about 25 minutes.

3.4 Procedure The participants are tested individually in a sound proof booth. They are seated in front of a computer screen and were given instructions on the screen (see appendix A for instructions). All participants first performed the perceptive word knowledge task in Dutch followed by the productive word knowledge task in Dutch, this was done to let the participants familiarize with the words and pictures before the productive task. In the perceptive task written words are shown twice in combination with their target picture and all pictures occur two additional times as distractor item. As described above, all tasks started with a short trial session and participants are allowed to ask questions after this session. For the perceptive task, participants are suggested to keep their fingers on the buttons of the response box to assure a quick response. For the productive task, participants are pointed out that they should avoid making other noises

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than the target word with a special note on hesitations such as ‘eh’ and ‘ehm’. Participants are allowed to take a short break in between the two tasks and were offered a small snack and a drink. The English perceptive and productive tasks are performed on a different day with a minimum of one and a maximum of six days between the two parts of the experiment. In addition to the four tasks, each participant was asked to fill in a language history questionnaire (Gullberg & Indefrey, 2003, see appendix C) in which they answered general questions concerning their language background and language usage. Participants received a 15 euro reward for participation.

3.5 Analysis As described briefly in the previous section, in the productive tasks the time between the appearance of the picture and the beginning of the response was measured both with a voice key in E-Prime and subsequently with a script 3 written in PRAAT (Boersma & Weenink, 2013), which automatically measured changes in dB as well as voice onsets. This script automatically determined the unheard beep generated by the E-Prime script as well as the onset of speech in the recordings. Response times were then measured for all correct responses and compared with the RTs that were measured by the voice key in E-Prime. As expected, there were clear inconsistencies between RTs as measured by the script in PRAAT and E-Prime’s RTs. Items that started with /s/ + consonant, /z/ or /v/ often resulted in delays up to 250 ms in the RTs as measured by the voice key. The RTs as measured by the script in PRAAT are used for the analysis. It occurred several times that participants coughed or made other sounds, these absent responses were replaced by missing values and thus excluded from the analysis. Items were marked as incorrect when neither the target name was produced nor a semantic alternative. For example, when table was uttered instead of the target name chair, the item was considered as incorrect. On the other hand, when tap was produced instead of the target name faucet, the item was considered as correct. Incorrect items were included in the analysis since excluding them would interfere too much with the time-ordering of the data (Holden, 2005: 287). The number of incorrect items is compared with the scaling exponents from the spectral analysis. Extreme values were identified after inspection of the data and RTs below the minimum of 200 ms and above 3500 ms were excluded. As a next step, RTs higher than 3 standard deviations above the grand mean were removed4. The remaining data were truncated to 512 trials (by eliminating the first trials), linear trends were removed and z-scores were calculated. Linear trend can be an overall decrease in response times as the task proceeds (e.g. due to fatigue) and are removed since they can bias the estimates of the scaling exponent (Holden, 2005: 288). 3

I am very grateful to Dirk Jan Vet who dedicated much of his time in developing the scripts necessary for analysis. In some of the participants the RTs higher than 3sd could not be removed since it would result in a trial series shorter than 512 items. In these participants the outliers with the highest values were removed until a trial series of 512 items remained. 4

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For the receptive vocabulary task RTs were measured by E-prime, the response times reflect the time between the appearance of the target word on the screen and the response given by means of pressing the right or the left button on the response box. The number of incorrect responses was calculated for each participant for the two tasks. As in the productive vocabulary task the incorrect responses were included in the analysis in order to best preserve the trial order (Holden, 2005: 287). Extreme values were identified after inspection of the data and RTs below the minimum of 200 ms and above 2500ms were excluded. Again, RTs higher than 3 standard deviations above the mean were removed and the data were truncated to 512 trials. Linear trends were removed and the z-scores were calculated. After preparing the data, spectral analysis were performed in PRAAT and MATLAB. The script in PRAAT was written on the basis of Holden (2005) whose guidelines are comparable to the ones used to develop the MATLAB script. The outcomes of the two methods are compared. Besides spectral analysis, a standardized dispersion analysis (SDA) is performed on the same data and results are compared. In a SDA it is calculated “how variability in sample means decreases as progressively larger samples of adjacent data points are aggregated together in a sample mean.” (Holden, 2005: 303). This is done by computing the standard deviation of different bin sizes where bin size corresponds to the number of adjacent data points in each bin for which the standard deviation is calculated. The bin size and the corresponding standard deviation are then transposed on a logarithmic scale and plotted in a graph5. To compare the outcomes of the spectral analysis and the SDA the fractal dimension (FD) is calculated. For the outcomes of the spectral analysis this is FD = 1 + (S + 1)/2, where S is the spectral slope. For the SDA this is FD = 1 – S, where S corresponds to the regression line of the log-log coordinates of the standardized dispersion as a function of bin size. The fractal dimension reflects the changes in variability of a measurement as proportionate to the sample size. Fractal dimensions between 1.2 and 1.5 indicate the presence of pink noise, where lower FDs correspond to more pronounced pink noise. In addition to the nonlinear methods a two-way repeated measures ANOVA is performed to investigate the effect of modality (reception vs. production) and language (L1 vs. L2) on the average response times and the number of errors. Moreover, since all items are presented twice in each task correlations between the response times on the items in the first half of the task and the response time on the corresponding items in the second half of the task are calculated.

5

See Holden (2005) for more detailed information on standardized dispersion analysis.

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4. Results The current section starts out with a description of the results from the analysis of the response times presenting the average response times for the different tasks, the accuracy level and results from the twoway repeated measures ANOVA. In addition, correlations between the response times on the items presented the first time and the corresponding items presented the second time within the same task are presented. In the second paragraph the results from the spectral analysis, the standardized dispersion analysis and the results from the two-way repeated measures analysis of the slopes are presented. Furthermore, the results from the spectral analysis are compared with the participants’ self-reports of proficiency and language usage.

4.1 Analysis of response times and errors Table 4.1.1 shows the average response times and the average number of errors for the four tasks. The average response times are calculated based on truncated and trimmed data where outliers and all values higher than 3SD from the mean are eliminated. The results from the bilingually raised participant are not included in this table. Moreover, the performance of one participant on the two decision tasks was anomalous and was therefore excluded from analysis6. Due to technical problems data is missing for one of the participants on the L1 productive task and for one of the participants on the L2 productive task. This results in four groups of 17 participants for each task. With respect to the average number of errors it is important to note that in the productive task, the absent responses and the semantically erroneous responses are counted as errors but coughs or other involuntary noises are not. Table 4.1.1 Average response times and average number of errors with SD for the four tasks

Task

Number

Average response time (SD)

Average number of errors (SD)

L1 Receptive (Dutch)

17

507,3 (74,1)

8,9 (6,5)

L2 Receptive (English)

17

477,3 (89,4)

9,2 (7,2)

L1 Productive (Dutch)

17

788,1 (118,0)

3,3 (5,9)

L2 Productive (English)

17

833,1 (157,2)

5,7 (5,7)

6

The average response time of this participant was above 3 standard deviations from the grand mean and the individual standard deviation within the two tasks was three times as high as the mean standard deviation, even after removal of the outliers.

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What can be gleaned from this table is that response times were higher for the productive tasks than for the receptive tasks. For the productive task naming latencies were higher in the L2, in the receptive task response times were higher in the L1. For the average response times, a two-way repeated measures ANOVA was conducted that examined the effect of modality (receptive vs. productive) and language (L1 vs. L2) on the response times. There was a statistically significant main effect of modality on the average response times, F (1, 14) = 112,41, p < .001, partial η2 = .89. No significant main effect was found between the L1 and L2 tasks of each kind (F (1, 14) = 0.006, p =.94, partial η2 = .00). However, there was a significant interaction between modality and language on average response times (F (1, 14) = 6,726, p = .021, partial η2 = .325). With respect to errors, the average number of errors was higher on the receptive task than on the productive task. A two way repeated measures ANOVA was conducted to examine the effect of modality and language on the number of errors. No significant main effect was found for neither modality (F (1, 14) = 3.564, p = .08) nor language (F (1, 14) = 1.989, p = .18). Furthermore, there was no interaction between modality and language on the number of errors (F (1, 14) = 0.851, p = .372). In each task every item was presented twice. To investigate the priming effect of the first occurrence on the second occurrence, average response times on the first half of the test are compared with the average response times on the second half of the test. For the L1 receptive task there was an average priming effect of 22 ms, i.e. participants were on average 22 ms faster in the second half of the task. However, a paired sample t-test showed no significant difference between the average times on the first half (M= 529.9, SD= 90.7) and those on the second half (M= 507.6, SD = 67.0) of the test (t (16) = 1.975, p = .07, d = 0.28). For the L2 receptive task there was an average priming effect of 15 ms (first half M= 498.0, SD = 98.4; second half M= 482.8, SD=90,6), again no significant difference was revealed by the paired sample t-test (t (16) = 1.864, p = .08, d = 0.16). For the L1 productive task there was a small average priming effect of 5 ms (first half M= 813.3, SD = 121.8; second half M= 808.0, SD= 130.9), yet, the paired sample t-test showed no significant difference (t (16) =.459, p = .65, d = 0.04). Finally, on the L2 productive task there was an average priming effect of 85 ms. A paired sample t-test showed a significant difference between the average response times on the first half of the test (M=891.7, SD=176.0) and the average response times on the second half of the test (M=806.5, SD=146.0); t (16)= 5,06; p < .001, d = 0.53. In addition to the priming effect it was explored whether response times on the first occurrence of the item correlated with response time on the second occurrence of the same item. In Table 4.1.2 the correlations between the response times on the first and second occurrence of the items are given for the four tasks for every participant. Table 4.1.2 Correlations between response time on items’ first and second occurrence for the four tasks per participants

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Participant

Receptive L1

Receptive L2

0.16** 0.06 0.13* 0.00 -0.05 0.09 0.08 0.10 0.03 -0.06 0.02 -0.01 0.11 0.06 0.03 0.12* -0.02 X

0.08 0.13* 0.08 -0.09 0.01 0.01 0.03 0.09 0.09 0.21** 0.18** -0.08 0.08 0.07 0.05 0.13* 0.18** X

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Productive L1 0.20** 0.09 0.33** 0.18** 0.19** 0.33** 0.07 0.35** 0.21** 0.29** 0.12* X 0.16** 0.10 -0.02 0.17** 0.30** 0.18**

Productive L2 0.16** 0.18** 0.46** 0.25** 0.40** 0.22** 0.06 0.42** 0.18** 0.41** X 0.23** 0.45** 0.23** 0.22** 0.14** 0.39** 0.32**

*. Correlation is significant at the 0.05 level (2-tailed); **. Correlation is significant at the 0.01 level (2-tailed)

Table 4.1.2 reveals that correlations are absent or very weak for the two receptive tasks which implies that participants’ response times did not correspond despite the fact that the items were the same. On the productive tasks correlations between items are stronger and most correlations were significant. The correlations ranged from weak to moderate strength with the strongest correlations on the L2 productive task. The stronger correlations on the L1 and L2 productive task can be explained by the different task demands on the productive and the receptive tasks, these findings will be further discussed in the following section.

4.2 Spectral and fractal analysis The outcomes of the spectral analyses in both PRAAT and MATLAB were plotted power against frequency on a log-log scale and the slopes of the two methods were compared. In Figure 4.2.1 the results from the spectral analysis of one participant on the L1 receptive task are shown for the analysis performed in PRAAT and MATLAB.

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Spectral analysis - PRAAT

Spectral analysis - MATLAB 1,2

-1,4 -1

0

log power

-1,8 -2,2

SLOPE = -.51

log10 power

-2

0,8 0,4

SLOPE = -.47 0

-2,6 -3 log frequency

-3

-2

-1

log10 frequency

0 -0,4

Figure 4.2.1 Power spectrum of the outcomes of the spectral analysis in PRAAT and MATLAB on a log-log scale for a participants’ performance on the L1 receptive task.

What Figure 4.2.1 depicts is that although the calculated frequencies and power did not correspond in the two methods the same scaling relation appears. In fact the slope from the first graph corresponds to α = .51 and is comparable to the slope in the second graph which corresponds to α = .47. On the whole, the scaling exponents that were generated by MATLAB correlated almost perfectly with the scaling exponents from PRAAT producing a correlation coefficient of r > .98 for each of the four tasks. Since the exact step-by-step procedure was familiar for the spectral analysis in PRAAT; the slopes from this analysis will be used for further analysis7. In Table 4.2.1 the slopes of each individual participant on the four tasks are given together with the mean slopes and their SDs. Participant 19 corresponds to the bilingually raised participant and is not included in the calculation of the mean. Due to missing data, the means and SDs are calculated on the basis of the slopes of 17 participants for each task. Table 4.2.1 Slopes on the four tasks for the individual participants, mean slopes and SDs are based on the first 18 participants.

Participant 1 2 3 4 5 6 7 8

Receptive L1 -0.29 -0.21 -0.16 -0.51 -0.41 -0.22 -0.47 -0.20

Receptive L2 -0.12 -0.40 -0.22 -0.37 -0.42 -0.21 -0.29 -0.10

Productive L1 -0.32 -0.32 -0.17 -0.33 -0.17 -0.08 -0.33 -0.19

Productive L2 -0.24 -0.08 0.02 -0.13 -0.21 -0.29 -0.16 -0.21

7

In addition, it is important to note that PRAAT is freeware, and since the spectral analysis yielded the same results, this program provides a good alternative to MATLAB.

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9 10 11 12 13 14 15 16 17 18 19

-0.32 -0.42 -0.17 -0.08 -0.23 -0.24 -0.39 -0.40 -0.50 MISSING -0.20

-0.40 -0.36 -0.26 -0.24 -0.28 -0.32 -0.33 -0.42 -0.41 MISSING -0.34

-0.15 -0.10 -0.26 MISSING -0.17 0.02 -0.29 -0.16 -0.11 -0.25 -0.11

-0.23 -0.24 MISSING -0.24 -0.03 -0.09 -0.15 -0.04 -0.07 -0.09 -0.17

MEAN SD

-.31 .13

-.30 .10

-.20 .10

-.15 .09

What can be gleaned from Table 4.2.1 is that almost all slopes correspond to a scaling exponent that falls within the range of pink noise (0 < α < 18). The slopes were the steepest for the L1 receptive task and the shallowest for the L2 productive task. Table 4.2.2 shows the mean fractal dimension on the four tasks from both the spectral analysis and the standardized dispersion analysis (SDA). At first, the outcomes of the SDA showed fractal dimensions greater than 1.5, corresponding to white noise. However, as suggested in Holden (2005), the inclusion of the largest bin sizes can whiten the scaling relation. When the two largest bin sizes were removed nearly all fractal dimensions (FDs) fell between 1.2 and 1.5, corresponding to pink noise. Table 4.2.2 Mean fractal dimension (FD) and SDs for the spectral analysis and SDA on the four tasks

Spectral analysis

SDA

Mean

Std. Deviation

Mean

Std. Deviation

N

FD L1 Receptive

1.35

0.05

1.36

0.09

15

FD L2 Receptive

1.36

0.05

1.37

0.06

15

FD L1 Productive

1.41

0.05

1.44

0.09

15

FD L2 Productive

1.43

0.06

1.45

0.06

15

Table 4.2.2 illustrates that, although the FDs from the SDA are somewhat higher than those from the spectral analysis, the same pattern appears. The steepest slopes (i.e. the most pronounced pink noise corresponding to the lowest FDs) are found on the L1 receptive task and the shallowest slopes are found 8

The absence of a negative slope in these participants is possibly due to the fact that a relatively large series of consecutive trials had to be eliminated, in one participant due to technical problems, in the other participant because of a coughing attack.

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on the L2 productive task. It is interesting to note that this pattern deviates from Table 4.1.1 in which the average response times were given; the average response times showed the lowest reaction times on the L2 receptive task (see Table 4.1.1). To determine whether the observed patterns of variability are more similar to pink noise or white noise each individual trial series is randomly shuffled five times, computing the spectral slope of each shuffled trial series. In Figure 4.2.2 a reaction time series from the L1 receptive task is depicted together with one of its randomly shuffled surrogate sets. The outcomes of the spectral analysis for both these sets are visualized in the other graphs, both on linear and logarithmic scales.

Normalized Reaction Times

3 2 1 0

-1

D

4 Normalized Reaction Times

A

4

3 2 1 0 -1 -2

-2 0

200 Trial Number

0

400

B

0,03

200 Trial Number

E

0,006 0,005

0,02

0,004

Power

Power

0,025

400

0,003

0,015 0,01

0,002

0,005

0,001

0

0 0

0,5 Frequency

1

0

0,5 Frequency

1

33

-1,1

-0,6

-1,4 -0,1

SLOPE = -0,50 -1,8

-2,2

-2,6

Frequency in Log10 Units

C -1,6 Power in Log10 Units

Power in Log10 Units

-1,6

-1,1

-0,6 SLOPE ≈ 0

-1,6 -0,1

F

-2

-2,4

-2,8

-3 Frequency in Log10 Units

-3,2

Figure 4.2.2 (A) Normalized intact trial series of L1 receptive task. (B) Outcomes of spectral analysis on a linear scale. (C) Same outcomes plotted on double-logarithmic axes. (D)-(F) The same succession of plots but this time for the randomly shuffled set of (A).

The slopes of the spectral analysis from the intact series are compared with their corresponding slopes from the randomized series. There are several ways to establish whether the observed slopes are more similar to pink or to white noise and two of them are reported here, viz. an independent t-test comparing the intact series with the random series and a comparison based on Hausdorff’s criteria9 who stated that if the spectral slope is more than 3SD away from the mean of the surrogate series, then the null hypothesis of white noise can be rejected. An independent sample t-test showed that the mean spectral slopes differ significantly from the randomized series slopes for the L1 receptive tasks (Intact series, M= -0,31, SD = 0.13; Random series, M= -0,02 SD = 0,08; t(36) =-9,121, p < .001, d = 2.6), for the L2 receptive task (Intact series, M= -0,30, SD = 0,10; Random series, M= -0,02 SD = 0,08; t(34) =-11,363, p < .001, d = 2.7), for the L1 productive task (Intact series, M= -0,19, SD = 0,10; Random series, M= -0,03 SD = 0,06; t(34) =-6,773, p < .001, d = 1.9) and for the L2 productive task (Intact series, M= -0,15, SD = 0,09; Random series, M= -0,03 SD = 0,06; t(34) =-5,077, p < .001, d = 1.6). For the two receptive tasks the mean of the spectral slopes was more than 3SD from the mean of the surrogate series, and it can thus be said that the variability pattern on these two tasks is better described by pink noise. For the two productive tasks the mean of the spectral slopes was not more than 3SD from the mean of the randomized series, implying that the null hypothesis cannot be rejected. On the L1 productive task, according to Hausdorff’s criteria (1996), 7 participants showed spectral slopes more similar to pink noise while 11 participants showed spectral slopes more similar to white noise. On the L2 productive task 5 participants

9

Based on Hausdorff, Purdon, Peng, Ladin, Wei and Goldberger (1996).

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showed spectral slopes more similar to pink noise while 13 participants showed spectral slopes more similar to white noise. Both the outcomes of the spectral analyses and the standardized dispersion analyses (SDA) were subjected to a two-way repeated measures ANOVA in which the effect of modality and language on respectively mean spectral slopes and mean FDs was examined. For the spectral slopes, a significant main effect for modality was found (F (1, 14) = 24.271, p < .001, partial η2 = .634) but no effect for language was found (F (1, 14) = 2.132, p = .17, partial η2 = .132). There was no significant interaction effect for modality and language on the average spectral slopes (F (1, 14) = .388, p = .54, partial η2 = .028). Regarding the mean fractal dimension based on the SDA, the two-way repeated measures ANOVA also revealed a significant main effect of modality on the fractal dimension (F(1, 14) = 17.805; p = .001; partial η2 = .56). Again, no significant main effect was found for language (F(1, 14) = .085; p = .77; partial η2 = .006) nor an interaction effect of modality and language on mean FD (F(1, 14) = .003; p = .95; partial η2 = .00). Finally, the individual slopes on the four tasks were compared to the self-reported proficiency and the self-reported frequency of use of the L2. In the language questionnaire all participants rated on a scale from 1 to 5 how well they used English on the skills of speaking, listening, writing, reading, grammar and pronunciation. An overall proficiency score was calculated based on the average rates on these individual skills. However, since all participants have high proficiency in English the overall score had a restricted range from 3,8 to 5 (M=4,5, SD=0,4). A comparison of the self-reported proficiency with the steepness of the slopes on each task showed a correlation of r = -.07 for the L1 receptive task (p = .78), r = .09 for the L2 receptive task (p = .72), r = .02 for the L1 productive task (p = .93) and r = -.04 for the L2 productive task (p = .86). These absent correlations can be explained by the restricted range of the overall proficiency scores. It should be noted that all participants were enrolled in the bachelor program of English and used English on a daily basis during courses and reading activity. Hence, the frequency of use was similar for the participants. However, some participants reported more hours of Dutch in a day while others reported more hours of English. By dividing the hours of Dutch usage by the hours of English usage a ratio was calculated10. The ratios ranged from 0.2 (implying more use of English than Dutch) to 1.33 (implying more use of Dutch) and were compared with the steepness of the slopes on each task. The correlation coefficient was r = .32 for the L1 receptive task (p = .20), r = .29 for the L2 receptive task (p = .24), r = .02 for the L1 productive task (p = .95) and r = -.36 for the L2 productive task (p = .14). The weak but positive correlations on the two receptive tasks imply that more pronounced patterns of pink noise on these two tasks are weakly associated with more usage of English than Dutch. The weak but negative 10

Participants also reported on the usage of other languages, but since the number of hours was very small in these cases; this was not included in the ratio calculation.

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correlation on the L2 productive task implies that more pronounced patterns of pink noise on this task are weakly associated with more usage of Dutch than English. In the next section these findings will be discussed.

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5. Discussion The present study has looked at reaction time fluctuations in lexical processing tasks in proficient DutchEnglish bilinguals to investigate the following three issues. First, it wished to determine what kind of system lies at the basis of lexical processing and whether the language system can be viewed as a selforganizing interaction-dominant system. Second, it wanted to establish how patterns of variability in reaction time fluctuations differ for the modality of producing and comprehending. And third, it wished to observe how patterns of variability differ for the L1 and the L2. In this section, the findings will be discussed and the three questions at issue will be addressed consecutively. Research into fluctuations of response times in trial series has shown that 1/ƒ noise is present in a wide range of cognitive tasks (see e.g. Wagenmakers et al. (2004) for simple response time, Gilden (2001) for interval estimation and lexical decision, and Van Orden et al. (2003) for word naming) and has therefore been argued to be a neural signature of cognitive behavior. The present research has looked at the presence of 1/ƒ noise in yet two other tasks, namely picture naming and word-picture matching reflecting lexical processing for the modality of producing and comprehending. As described in the previous section results from the spectral analysis yielded scaling exponents between 0 < α < 1 corresponding to the domain of pink noise. Moreover, the slopes on all tasks, when compared to the slopes of their randomized surrogate sets were significantly steeper. However, not all participants presented 1/ƒ scaling on all tasks according to Hausdorff’s criterium. Nonetheless, it can be argued that the presence of a single variability pattern that corresponds to pink noise licenses the interpretation of the other variability patterns on the same task as less pronounced examples of pink noise. Idealized pink noise has a slope of -1 but statistical pink noise can show shallower slopes due to external sources of variability (Holden, 2005). Moreover, most studies used data sets of 1024 trials since spectral slopes tend to become more variable when shorter data sets are used (Cannon, Percival, Caccia, Raymond & Bassingthwaighte, 1997), which might have taken place in the present study11. Of course, one must be cautious in identifying long-range dependencies (i.e. pink noise) in a trial series and investigate if the found pattern can be explained by other models (e.g short-range dependencies Wagenmakers et al., 2004). There is much debate about the criteria for defining pink noise and Wagenmakers et al. (2004) argue that a more specific account is needed that can explain how external factors decorrelate the long-range dependencies and how this is related to the self-organized criticality of the system. For this study, the Hausdorff’s criterium is adopted and all slopes that have an exponent lower than 3SD from the slopes of their surrogate sets are considered to correspond to pink noise. 11

Data sets of only 512 trials were used since the duration of the experiment would otherwise be too long.

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There are several accounts that can explain the presence of pink noise in cognitive and motor control tasks. In addition to the interaction-dominant view of cognition that considers 1/ƒ noise as a dynamical signature of the entire system I discuss both the arguments in favor and against of three other component-dominant accounts that explain pink noise (cf. Wijnants, 2012). The first discussed is the multi-scaled randomness account (see e.g. Wagenmakers et al., 2004; Ward, 2002) which claims that the presence of pink noise in time series is only a reflection of the fact that behavior consists of many independent processes that each act on their own time scale. That is, behavior consists of different processes and if one of these processes is quickly changing, another processes is somewhat slower and yet another process is slowly changing, adding up these different processes may yield pink noise (Hausdorff & Peng, 1996). The advantage of this account is that pink noise is quite easily explained, simply adding up processes of different components would be enough to yield 1/ƒ noise. However, a problem with this account is that the independent processes must exactly match the specific characteristics of power and frequency to consistently generate the fractal pattern of pink noise. The widespread occurrence of pink noise in neurology, motor behavior and cognition is not easily explained as in all these cases the individual processes that constitute behavior/performance must by chance correspond to the characteristics necessary to produce pink noise. Another characteristic of pink noise that is not easily explained by this account is its extension over multiple timescales up to the limits of the system. If performance on a simple reaction time task involves in one case 512 trials and in another 1024 trials, pink noise will be found in both instances. In the multi-scaled randomness account this implies that more short-range processes over longer time ranges need to be introduced to account for the pink noise in the longer trial series, a quite inelegant solution. The second model discussed here is that of regime switching. In this account it is assumed that cognitive behavior is governed by shifts in fatigue, strategy or attention (Wagenmakers et al., 2005). During the course of an experiment participants repeatedly change strategies resulting in shifts in variance. Regime-switch models can account for pink noise in human behavior by lining up several short-range dependencies (corresponding to e.g. a specific strategy or a short period of attention drift). However, it is unclear how this account would explain 1/ƒ noise in the beating of a heart and other neurological, physical and motor processes. Moreover, this model cannot easily explain why pink noise is associated with the coordination of a complex system. A third account that can explain pink noise is that of domain-specific modeling (Delignières, Torre & Lemoine, 2008). In this type of modeling a local source of pink noise is introduced into a component of traditional cognitive models. Without going into the technical details of this model, the presence of pink noise represents “complex timekeeping processes that can be statistically localized in components within the system” (Wijnants, 2012: 154). In this account, pink noise is a functional aspect of human performance related to timekeeping that is domain-specific where the source can be localized in a fractal generator. The 38

advantage of this model is that it generates testable hypotheses but problematic is the fact that again it is difficult to imagine domain-specific models with each their independent fractal generator to account for the fact that 1/ƒ noise is found in a wide range of domains. Finally, in the interaction-dominant view pink noise is seen as “the natural outcome of complex, living systems” (Wijnants, 2012: 155). In complex systems components are interdependent and change each other’s dynamics in interaction. Pink noise in this account is explained by the interaction of many processes that change each other’s dynamics over many time scales. That is, the same processes govern behavior in short and in long time frames and all behavior is nested in processes at slower time scales and consists of processes that evolve on faster time scales. This account is able to explain the relation of pink noise to coordination and the fact that external perturbations can decorrelate the 1/ƒ scaling relation. Coordination, as will be discussed further on, is tightly related to the presence of pink noise in all kinds of behavior. The interaction-dominant view explains this relationship as the cooperation and interdependence of processes whereby coordination emerges through the tight coupling of the different processes. That is, the complex system is selforganizing and tends to stay near critical states resulting in optimal coordination. Furthermore, the interaction-dominant account can to a certain extent explain the less pronounced patterns of pink noise when the task involves external perturbations. As the intrinsic dynamics of the system produce the 1/ƒ noise external variation in the experiment will disrupt these dynamics resulting in less pronounced patterns of pink noise. Despite the fact that these four proposals can each explain pink noise in cognitive behavior, the interaction-dominant view seems to be the account that can best explain the findings in this field. Hence, the presence of a 1/ƒ scaling relation in the four tasks, although less visible in the productive tasks, suggests that the interaction-dominant view is the best description of the underlying system (Van Orden et al., 2003) involved in lexical processing. The long-distance correlations in the trial series reflect the self-organization of the system whereby the iterative character is crucial, i.e. the state of the system is informed by the immediately preceding state and external input. Since the immediately preceding state itself is influenced by its own previous state, the system has a potential memory capacity that in the case of the four tasks spans over the entire time course of the task. This type of iterative memory is an inherent characteristic of the complex self-organizing system and should not be confused with the more familiar notions of working memory or long-term memory. The process of iteration is caused by simple iterated rules and thus requires minimal cognitive load but can explain why long range dependencies are found in the trial series (Aks, 2005). Researchers attaining to the interaction-dominant view of cognition argue that critical states are self-assembled in cognitive behavior which allows the subject to flexibly adapt to the continuously changing environment. The fact that pink noise corresponds to a pattern that lies right between completely random behavior and over-regular behavior gives rise to 39

this flexibility. However, self-organized criticality predicts 1/ƒ noise but 1/ƒ noise does not necessarily imply SOC, which is why Farrell, Wagenmakers and Ratcliff. (2006) argue for the use of models that can distinguish between the component-dominant view of human cognition and a model of self-organized criticality. Ihlen and Vereijken (2010) have developed such models and showed that the patterns of variability found in various reaction time experiments could not be replicated by the component-dominant models. I am aware of the fact that the methods used in this study are not exhaustive in establishing the presence of interaction-dominance as opposed to component-dominance. However, recent developments in the field of cognitive dynamics show that new methods involving multifractal structures can statistically reliably establish whether a system is better described by interaction dominance (Ihlen & Vereijken, 2010). Future research into 1/ƒ scaling and interaction dominance in language performance should apply these methods to falsify the component-dominant view. The second research question addressed in this study concerns the differences in patterns of variability for the modality of comprehending and producing. In the previous section it has been shown that the spectral slopes were much steeper on the receptive task than on the productive task. This finding can be explained by several accounts. As suggested by Wijnants (2012), the found patterns of variability for the modality of producing and comprehending can imply that participants are better in coordinating their behavior during perception. However, as suggested by Holden (2005), one must be cautious in interpreting differences in the steepness of the slopes when these are obtained through tasks with different task demands. There were several differences in task demands between the receptive and the productive tasks. In the first place in the receptive tasks the participants responded by means of pressing a button whereas in the productive tasks the participants responded by means of uttering the target word. Moreover, in the receptive task there was a forced choice between the two pictures whereas in the productive task participants no such forced choice was present since they had to simply access the word and produce it. Due to this aspect it occurred in the productive tasks that participants were not able to produce the target word resulting in very long reaction times for that particular item. Such long reaction times, although eliminated from the trial series, distort the time scale (Holden, 2005). In the receptive task no such distortions took place since the forced choice makes it almost impossible to not be able to retrieve the meaning of the target word. Another difference between the productive and the perceptive tasks lies in the modality of spoken versus written words. In the receptive task the words are presented in written form, whereas in the productive task the participants had to respond to the stimulus aurally. This modality difference introduces another variable that might explain the differences in performance on the receptive and productive tasks. Inspection of the correlational data provides another factor of variability that might explain the shallower slopes on the productive task. Correlations between the items on their first and second occurrence were absent or weak in the receptive task, however, in the productive tasks the 40

correlations were stronger. The weak to moderate correlations on the productive task are probably explained by the presence of several items that result in long reaction times on both occurrences. It should be noted that these weak to moderate correlations on the productive task can distort the long range dependencies. In effect, the participant with the strongest correlation between the first and second occurrence of the item happened to be the participant with the shallowest slope on the L2 productive task. In general, the fact that the correlations are somewhat higher on the productive tasks can explain why the pattern of 1/ƒ noise is more decorrelated in these tasks. When looking at average 1/ƒ scaling exponents in different cognitive tasks it seems that the scaling exponent α decreases when more response options are available in the tasks (Wijnants, 2012). That is, most pronounced patterns of pink noise are found on a precision aiming task (i.e. tracing dots as in Wijnants et al., 2009; α ≈ .85) which is a cyclic task and there is therefore no discrete signal that perturbates the task. In a simple reaction time experiment there is a discrete signal coming from the computer where the participants need to respond to and hence, an external source of variation is introduced resulting in less pronounced patterns of pink noise (Van Orden et al., 2003; α ≈ .70). Even less pronounced patterns are found in choice tasks (Kello, Beltz, Holden & Van Orden, 2007; α ≈ .50) which suggest that introducing different response options whitens the pattern even further. Finally, in word naming the 1/ƒ signal is even further whitened (Van Orden et al., 2003; α ≈ .30) explained by the fact that every new trial introduces a unique signal to respond to. In both the receptive and productive tasks in this study every new trial introduces a unique signal to respond to. In addition, where in the receptive task the participants have only two response options in the productive task there is essentially no limit to the number of response options. These external factors that are likely to decorrelate the patterns of 1/ƒ noise and make it difficult to establish whether the degree of coordination is less for the modality of producing or whether the whiter patterns of variability in the productive task are due to particular task demands. The final issue addressed in this study concerns the differences between patterns of variability for the L1 and the L2. In contrast to the comparison between production and perception it is possible to make a proper comparison between the performance on the L1 and the L2 task as task demands were the same. When inspecting the steepness of the slopes and the fractal dimension the slopes are somewhat steeper and the fractal dimensions somewhat lower on the L1 task for both modalities suggesting more pronounced patterns of pink noise in the L1 tasks. However, the slopes did not differ significantly and since in general slopes are more variable with short data sets it is important to be cautious in interpreting the differences. Nonetheless, a more qualitative inspection reveals that the three most pronounced patterns of pink noise were all found in the L1 receptive task while the three most pronounced patterns of pink noise on the L2 receptive task clearly have shallower slopes. For the productive tasks, the highest number of patterns of white noise was found on the L2 productive task. These findings carefully suggest that the 41

participants are better at coordinating their behavior in their L1 than in their L2. Several studies (e.g. Wijnants et al., 2011; Hausdorff, 2009) have shown that 1/ƒ noise is present in healthy well-coordinated performance whereas the variability pattern becomes whiter in less coordinated perfomances (e.g. motor performance in Parkinson patients or reading times in dyslexic participants). As discussed in Wijnants (2012), in an interaction-dominant view of human cognition it is assumed that “more efficient and coordinated systems yield a tighter coupling of mutually constraining timescales of performance, and consequently clearer 1/ƒ scaling, through self-organization […] and emergence” (p. 156). If this view is adopted it is not remarkable that more pronounced patterns of pink noise were found on the L1 tasks since the L1 system is expected to be more entrenched and lexical processing in the L1 is in general more automatized leading to more coordinated behavior. The findings from the present study have some important implications for psycholinguistic models of the bilingual lexicon. The presence of pink noise in lexical processing tentatively suggest that it is in the first place necessary to abandon the component-dominant view of the mental lexicon and adopt an interaction-dominant view. This paradigm shift would imply that all models where there is no complete interconnectedness of the components must be discarded. Models such as BIA+ (Dijkstra & Van Heuven, 2002) and BIMOLA (Grosjean, 1997) have components at different levels that do not interact or that allow for information flow that is unidirectional. These characteristics are not in accordance with the interaction-dominant view of the mental lexicon. Elman’s (2011) view of lexical knowledge does correspond to this view. According to Elman, a word operates as a stimulus on a mental state whereby the meaning is revealed during this interaction. His SRN model, although simplified, is based on a simple iterative rule that can account for context-dependence of words. In this model representations arise in real time through interaction of the word with the current mental state. The fact that behavior is context dependent is also reflected by the weak correlations between the frequency of usage and the spectral slopes. Although these correlations were not significant and did not reveal a consistent pattern it shows that variability patterns are in themselves subject to change and context dependent (leading to multifractal patterns; Ihlen & Vereijken, 2010). In the interaction-dominant view it is the interaction of the different components that gives rise to behavior and focusing on what happens within the components is thus irrelevant. Moreover, a question that needs to be asked is whether it is even meaningful to talk of subcomponents if everything is interconnected and interdependent. Besides the previously discussed theoretical implications, the presence of pink noise in the reaction time series also has some important methodological implications. Many reaction time studies are carried out in the field of psycholinguistics and in the analysis of the results average response times are calculated on the assumption that variance is similar across groups and therefore cancels each other out. Findings from the present study, in addition to evidence previous studies, suggest that this is not the case 42

and averaging over a series of reaction times is statistically unjustified since the average is dependent on sample size. Although the present research embraces the interaction-dominant view of cognition which is in correspondence with a DST approach, I do not argue that this approach is without complications. The interaction-dominant explanation of 1/ƒ noise is often criticized as being underspecified and unable to generate testable hypotheses. Complete interconnectedness and nonlinearity in development imply that outcomes are unpredictable and a question that thus needs to be asked is whether a DST approach to language and cognition will lead to significant progress in understanding these phenomena. However, as argued by Van Orden, Holden & Turvey (2005) the critique of the underspecified character of the account is based on the assumption that a proper model can be reduced to components and causes and effects have a basis in these components. Self-organized criticality is an emergent phenomenon and to model this “[t]here is presently no workable entry level below the level of the emergent phenomena themselves.” (Van Orden et al., 2005: 121). If there were an entry level below global emergence that explained the presence of pink noise in cognitive behavior the interaction-dominant view would make the same ‘mistake’ as other reductionist accounts by stating that the explanation lies in its components. Embracing the interaction-dominant view has both advantages and disadvantages; the advantage is that it brings us closer to understanding the complex and dynamic nature of human behavior, the disadvantage is that in doing so, it runs the risk of being too general.

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6. Conclusion The present study was set out to determine whether variability patterns in four lexical processing tasks corresponded to random variance or whether the patterns had a specific structure that is associated with complex systems that self-organize their behavior in fractal time, that is to say, pink noise. The findings of this study suggest that, in most participants, for the modality of perceiving and producing and in the first and second language, the fluctuations in the time series correspond to pink noise. More pronounced patterns of pink noise were found in the receptive tasks than in the productive tasks which are most likely explained by different task demands. With respect to language, although the differences were small, the patterns of pink noise for both the modality of production and perception were more pronounced in the L1 than in the L2. Moreover, the clearest patterns of pink noise were found on the L1 receptive task suggesting that L1 processing is typically a more efficient and coordinated endeavor. A point that is relevant for all cognitive research that uses a reaction time paradigm is of methodological nature. The presence of pink noise in reaction time series implies that average response times and their respective standard deviations are dependent on sample size and standard analyses that draw upon these constructs are thus statistically unjustified. A question that needs to be asked is whether response times in general can still be compared using linear statistical methods. The findings from the present study have several important consequences for bilingual lexical processing in particular and for language processing in general. The bilingual mental lexicon can no longer be viewed as component-dominant and lexical knowledge can no longer be viewed as fixed but should be viewed as context-dependent and dynamic. The presence of pink noise in the lexical processing tasks in this study cannot easily be accounted for by the bilingual models of the lexicon that draw upon distinct components. Hence, a paradigm shift towards interaction-dominant models is proposed. Lexical processing is nonlinear, continuous and context-dependent just as any other part of language processing and it is about time that it is analyzed as such. There are challenges related to the paradigm shift towards interaction dominance. In fact, as stated by Spivey (2007), interaction-dominant systems are extremely difficult to analyze. However, increasing evidence from a wide range of fields that explores human cognition suggests that the interaction-dominant view is the best way to describe how the mind continuously interacts with the world. In my opinion, the proposed paradigm shift must go along with theoretical and methodological development and the question as to how far the nonlinear dynamic approach will bring us in understanding cognition needs to be approached with a critical mindset.

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Acknowledgements The present thesis would not have been finished without the inspiration, support and commitment from several people that I genuinely want to thank. To start out I want to thank Dirk Jan Vet since without his help the present work would have got stuck at the simple idea to build an experiment. It is partly because of Dirk that I have been able to start this journey into the completely unknown country of Fractals where they speak a language that doesn’t seem to have either a fixed structure, or a fixed lexicon. That is, somewhat like a dynamic system that changes every time you take a look at it. Eventually, with the help of Dirk, I have been able to grasp at least a small part of it, finding out that it is not just complete chaos. Secondly, I want to thank Kees de Bot who has introduced me to the up until eight months ago unfamiliar framework of dynamic systems theory. I really enjoyed brainstorming about the possible ways to go about the research questions and found our sessions in Groningen always very motivating. I furthermore want to express my gratitude to Rika Plat and Wander Lowie who have shown a genuine interest in my work and helped with the analysis and interpretation of the results. I also want to thank Rob Schoonen for being critical at the right moments while giving me the space to carry out my own research project. Finally, I want to thank Doris for our numerous study moments together and Esther for being available for ‘peer review’ whenever I needed it.

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Appendix A | Instructions Productive vocabulary test Welcome to this experiment! You will soon be shown pictures of simple objects, presented one by one. Your task is to name these objects as soon as possible, in English. Before the appearance of the pictures you will see an asterisk (*) in the center of the screen, make sure to pay attention when you see the asterisk because this is a sign that the picture will appear soon. It is important to avoid tapping on the table or making other noises since the microphone will register these noises and these will interfere with the results. On the other hand it is important to pronounce the words clearly, if you notice that the experiment doesn’t continue you should repeat the word. If you press the second button on the responsebox the test will start with a set of trial items. In this way you will get an idea of how the test is build up. After the trial items there is room for questions. Despite fatigue, try to stay focused as much as possible during the experiment. The whole experiment will take more or less 25 minutes. Good luck and thanks for participating! Press the second button to start with the trial items. | Instruction Receptive vocabulary test Welcome to this experiment! You will soon be shown a word in the middle of the screen. Soon after, two pictures will appear, one on the left side of the screen and one on the right side. Your task is to indicate which picture corresponds to the word by means of pressing either the left side button or the right side button on the responsebox. Before the appearance of the word you will see an asterisk (*) in the center of the screen, make sure to pay attention when you see the asterisk because this is a sign that the word will appear soon. If you press a button the test will start with a set of trial items. In this way you will get an idea of how the test is built up. After the trial items there is room for questions. Despite fatigue, try to stay focused as much as possible during the experiment. The whole experiment will take more or less 25 minutes. Good luck and thanks for participating! Press a button to start with the trial session.

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Appendix B | Items in the productive and receptive vocabulary task

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Appendix C | Language History Questionnaire

Name:

Date:

Below are questions about your education, profession, and language use. Please answer these questions as completely as possible. Background: Age: Sex: What is your level of education (high school, university degree): What is your profession (e.g., student, lawyer): Were you born in the Netherlands? Yes

No

If yes: Have you lived in the Netherlands since birth? If no, where else have you lived?

Yes

No

If no: How old were you when you came to the Netherlands? How long have you been living in the Netherlands? Have you returned to the country of your birth for longer than 6 months (if yes, how long)? Yes No Language History: What is your native language? Please list any other languages that you know below. For each, rate how well you can use the language on the following scale: Not Good Language

1

2

Speaking

3 Listening

4

5 Writing

Very Good Reading

Grammar

Pronunciation

1 2 3 4

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For the languages you listed, please indicate below the place and age at which you learned them, and if applicable, whether you learned them by formal lessons (e.g., at school or a course), or by informal learning (e.g., at home, at work, from friends). Language

Country

Age

Lessons (yes/no)

Duration of lessons

Duration of informal learning

1 2 3 4

For the languages you listed, rate how well you agree with the following statements using the scale: Disagree Language

1

2

I like to speak this language

3

4

5

Agree

I feel confident using this language

I think it is important to be good at this language

1 2 3 4

For the languages you listed, which do you use with the following people, for how many hours per day (rough indication) and in which place (home, work, etc): Language

Hours per day

Place

Mother Father Older brother/sister Younger brother/sister Children Other family members Housemates Partner Friends Colleagues

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For the languages you listed, which do you use for the following activities and for how many hours per day? Activity Reading

Language

Hours per day

Watching TV Listening to the radio Email, internet

In general, how well do you like to learn new languages? Dislike

1

2

3

4

5

Like

In general, how easy do you find learning new languages? Difficult

1

2

3

4

5

Easy

If you have any other remarks about your language history that you think may be important for your ability to use these languages, please feel free to write them here: ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------THANK YOU!

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