Discourse Processes

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Expectations on Hierarchical Scales of Discourse: Multifractality Predicts Both Short- and LongRange Effects of Violating Gender Expectations in Text Reading Chase R. Booth, Hannah L. Brown, Elizabeth G. Eason, Sebastian Wallot & Damian G. Kelty-Stephen To cite this article: Chase R. Booth, Hannah L. Brown, Elizabeth G. Eason, Sebastian Wallot & Damian G. Kelty-Stephen (2016): Expectations on Hierarchical Scales of Discourse: Multifractality Predicts Both Short- and Long-Range Effects of Violating Gender Expectations in Text Reading, Discourse Processes, DOI: 10.1080/0163853X.2016.1197811 To link to this article: http://dx.doi.org/10.1080/0163853X.2016.1197811

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Date: 17 October 2016, At: 08:05

DISCOURSE PROCESSES http://dx.doi.org/10.1080/0163853X.2016.1197811

Expectations on Hierarchical Scales of Discourse: Multifractality Predicts Both Short- and Long-Range Effects of Violating Gender Expectations in Text Reading Chase R. Bootha, Hannah L. Brownb, Elizabeth G. Easonc, Sebastian Wallotd,e, and Damian G. Kelty-Stephenf a

Classics Department, Grinnell College; bGender, Women’s, & Sexuality Studies, Grinnell College; cMathematics and Statistics Department, Grinnell College; dMax Planck Institute for Empirical Aesthetics, Frankfurt, Germany; eInteracting Minds Centre, Department of Culture and Society, Aarhus University, Aarhus, Denmark; fPsychology Department, Grinnell College ABSTRACT

Reader expectations form across hierarchical scales of discourse (e.g., from coarse to fine: genre, narrative, syntax). Cross-scale interactivity produces word reading times (RTs) with multifractal structure. After introducing multifractals, we test two hypotheses regarding their relevance to reader expectations: (1) multifractal evidence of cross-scale interactions from RTs preceding violation of expectations would interact with mean reading speed to predict RTs immediately after the expectation violation and (2) postsurprise RTs would exhibit stronger cross-scale interactions. Thirty-four adult participants read one of two 2,000-word stories that used gender stereotypes to suggest that an ambiguously named protagonist was male. However, the stories postponed gender information until word 1,000: male in one story and female in the other. For slower readers, cross-scale interactions accentuated postreveal slowing but also minimized subsequent pausing over 15 postreveal RTs. Surprise strengthened cross-scale interactions over all postsurprise RTs. These results suggest that multifractality may index anticipation across multiple scales of discourse.

Introduction Expectation plays a major role in reading and especially in how we approach narrative. Even deep in their most fundamental neural particulars, cognitive systems are “striving for coherence” (Tylén et al., 2015, p. 106). As readers settle into a text, such as the current article, they expect to see many words that structure a specific discourse, such as “hypothesis” and “theory,” “results” and “model,” “approach” and “challenge” in a scientific article. Readers begin reading each sentence anticipating the next words that they have not seen yet (e.g., Schotter, Lee, Reiderman, & Rayner, 2015). Indeed, some of the best writing will come from authors who themselves can anticipate their readers’ expectations and lay out a comfortable terrain that will reach out and make contact with what the reader expects to see. The sooner a reader finds a foothold for his or her expectations in the words ahead, the more comfortably he or she can settle into a narrative and strive a bit less to find coherence. Certainly, the letters, the words, and the phrases follow sequence that will denote the intended meaning, but no reader builds comprehension like a bridge extending outward into nothing. Rather, they cast out expectations, the struts and girders at first, spreading between themselves and the to-be discovered CONTACT Damian G. Kelty-Stephen IA 50112, USA. q 2016 Taylor & Francis

[email protected]

Psychology Department, Grinnell College, 1115 8th Ave., Grinnell,

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coherence, answering those vast questions like “What type of story is this one?” and “(Why) should I be paying attention?” More invested readers cast out ever finer threads into the future directions of the text, trying to fill in the steps ahead with the bricks and wires they expect will get them through a chapter or a passage, a sentence or a word. Of course, text sequence matters, but the striving reader is often looking ahead and gradually ignoring some details and filling in other details that may not arise strictly from the sequence on the page. As our bridge metaphor suggests, expectations lighting the way of the reader through a text unfold at many scales at once (Graesser & McNamara, 2011). At the broadest scales, a reader brings their knowledge of the content and the literature to know what sort of information to expect and where in the form of a document to expect it (Wilkinson, Reader, & Payne, 2012). At the finest scales, the reader brings their knowledge of phonemes and phonotactic legality to the table (Rossi et al., 2011). For instance, as the reader scans an individual word from left to right, a single letter “r” beginning the word should, he or she will know, precede either a vowel or the consonant “h” but, so long as previous words signal that the language is English, nothing else. Expectations can change the set of rules that will matter. The same reader can safely ignore traditional “r”-beginning rules if previous words encourage an expectation that the “r”-beginning string should be understood as an acronym or proper noun (e.g., RNA or RZA) and not a common word. Two aims: Tutorial on multifractality and empirical demonstration of gender-expectation violation This article has two major aims. The first aim is to present multifractal methods for modeling nonlinear interactions across scales that support expectations for discourse processing. Narrative might violate expectations at any level of discourse, and the notoriety of many an author and film director depends on the surprise value, for an average audience, of plot twists. However, some audience members are better able to foresee the crucial plot twist long before others can. Multifractality may quantify individualreader anticipation even for relatively brief narratives. The second aim is to demonstrate that multifractal structure in individual participants’ reading performance can predict individual-readers’ differences in response to finding their expectations about violated by new gender information. Expectations about gender serve only as an example, a known platform upon which we can engineer the plot twist or the surprise. That is, we are no longer aiming at the average reader but to account for all those different abilities of various individual readers to anticipate twists and turns in the narrative’s discourse. In this way, multifractal modeling may allow psycholinguistic research to ratchet up the precision of its predictions for various individual readers. Evidence of interactions across different scales of reading We need to ratchet up our models of reading because reader expectations at different scales can interact in ways that linear modeling is alone unable to anticipate (Van Orden & Kloos, 2005). For cleanliness of experimental design, we can simply ignore this fact and examine word perception separately from examining long-term coherence of discourse (McNamara & Magliano, 2009). Typically-developing readers can recognize a letter string as a word or as a nonword without much context to couch the letter string. However, readers striving for coherence thrive on the fact that expectations at one level support another. The purpose of this section is to suggest that, when our experiments leave these interactions across scale room to exert themselves, the interactions across scales might quickly foster a complexity in reading beyond what linear models can express. Effects of expectations during reading span at least from the scales down from sublexical features (Smith & Levy, 2013) up to the scales of several words (Kliegl, Nuthmann, & Engbert, 2006). On a single-word level, phonological expectations can help us decide whether the entire printed string of letters is a word. In case of typographical spelling errors, homophony of the misspelled word speeds our recognition of the intended target word (Berent & Van Orden, 2000). However, this support from

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phonological expectations can be as much a hindrance as a help: The more different ways there are to spell a pronounceable sound, the longer it will take participants to recognize a printed word (Stone, Vanhoy, & Van Orden, 1997). So, even the (silent) reading of words depends on those extended bodily postures (beyond the word itself), those articulators poised to act some ways but not others that would allow the reader to convert the spelled word into a speech stream. Should the letters appear out of pronounceable order, phonological or articulatory expectations fall by the wayside, and the reader’s ability to ignore or to correct for this distortion and carry on is language dependent. That is, languages carry their own expectations, bearing different tolerances for moving the smaller parts out of order while preserving intended meaning (Velan, & Frost, 2007). Past the deceptive simplicity of single-word processing, interactions across scales in language processing only become more complex when the words compose a coherent stream of discourse. The meanings of the individual words have sprawling contingencies reaching up to even the highest and longest scales of discourse, with whole logical turns of an argument resting on the reader being able to find a steady footing in the definition of a single word or a few words. For example, in the very next section of our own discourse here, we take pains to clarify what exactly we mean by the single word “nonlinear” so that our audience is clear that we do not intend a variety of meanings unrelated to subsequent deliberations. Just like in the previous sentence warning the reader of what lies ahead, new layers of expectations appear in coherent discourse above the word level, such as expectations that are carried over from sentence to sentence (Zwaan, Magliano, & Graesser, 1995) or, as in our article’s case, from section to section. If we upgrade from the challenge of typographical transposition of letters in single word to the challenge of potentially surprising word orders, the fact of cross-scale interactions remains the same: Discourse at longer scales can help just as well to resolve reader uncertainty stemming from variable and sometimes confusing word order (Kaiser & Trueswell, 2004). Furthermore, narrative coherence can wipe out the effects of single-word features on single-word processing (Teng, Wallot, & Kelty-Stephen, 2016). The surprise we experience during plot twists evokes the hierarchical organization of reading. The discourse of a narrative prompts long-range expectations that, in turn, prompt some but not all shorterrange expectations. As we read further into a text, we grow into readers that seek at smallest grains of words and phrases what the larger grains of discourse have prompted us to expect. Longer-range sensitivity to whole-narrative-level coherence nests word processing, leading sometimes to “misfires” when readers encounter words not primed by previous long-range narrative structure and requiring greater processing effort resulting in increased word reading times (RTs), reflecting a reassessment of the text and of reader expectations (Blanchard & Iran-Nejad, 1987; Graesser & McNamara, 2011; Hoeken & van Vliet, 2000). Thus, an important feature of reading’s hierarchical organization is the spreading of effects from one processing scale to another, from long-range to short-range and back to long-range again. Such cross-scale interactions depart from the notion that cognitive hierarchies respect a near-decomposability of scales (e.g., Simon, 1969), and they incline our theories of reading toward models differing from a relatively constant sum of relatively similar parts (e.g., Ihlen & Vereijken, 2010). Prevailing state of the art: Hierarchical linear models of reading performance We suspect that the challenge of modeling these cross-scale interactions in discourse reflects a limitation of linear modeling. Make no mistake: We find the recent developments in psycholinguistic treatments of nested time scales through hierarchical linear modeling to be encouraging. Before proceeding further, we hope to state clearly that hierarchical linear modeling is so elegant that we ourselves chose to use it here to demonstrate the significant effects of multifractality on reading performance. Linear modeling is extremely useful in teasing out independent effects not exhaustible by simpler models containing fewer and more intuitive predictors. Despite any superficial appearance of hypocrisy, ungratefulness, or logical inconsistency, we present multifractal modeling as an important signature of nonlinearity that carries specific information about reading performance and use

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hierarchical linear modeling to submit multifractal content to all the same rigors that any other novel predictor must survive to enter into serious theoretical discourse. In the specific domain of discourse, the only limitation of linearity that concerns us is linear modeling’s incapacity to express a particular relationship across time scales such as in the successively differentiating branching structures (noted below in more detail). This limitation should not be surprising at all: The earliest mathematical expressions of this successive differentiation described the process as “nonlinear” (e.g., Turing, 1952). Our hope is that by capturing the strength of nonlinear interactions across scales in a compact numerical quantity that contributes significantly to linear modeling of RTs, multifractal modeling might extend the reach of the current hierarchical linear models of reading. Essentially, the difference between multifractal modeling and current modeling in psycholinguistic research boils down to the linearity of the latter and what linear modeling presumes to do with the measurement we take of reading performance. However, the assumption of linearity is not the price of doing statistics. It is an empirical hypothesis that can be tested, and it can fail or hold. Failures of linearity are by no means a reason to stop doing science or even to stop linear modeling altogether, but multifractality may offer statistical traction more amenable to data that fails to be consistent with linearity. If the preconditions for linearity are met, linear modeling provides robust and versatile tools for almost any phenomenon. However, in case linearity fails, nonlinear metrics, such as multifractality, can be used to enhance linear modeling. Hence, we suggest incorporating measures of nonlinearity in our linearly modeled hypotheses. For the purposes of this article, we use the term “nonlinearity” to refer not just to nonadditivity but to the capacity of systems to grow through the iterative, progressive differentiation of finer-grained structure from the foundations of originally coarse-scale structure (e.g., Molenaar, 2008; Turing, 1952). Such interactions across scales can change the form and the function of component materials that began mostly—though not completely—homogeneous. For instance, a tree might sprout “the same” leaves across all of its branches. However, the pattern of foliage will depend on early branchings of the young sapling: Branches thrusting upward towards the sun will boast the greenest leaves, and the branches growing closest to the trunk and lowest to the ground might be bare from poorer lighting and continual infestation by insects. Greener leaves will attract a different set of pests whose behavior will leave newer marks on the foliage patternings. Ultimately, the complex outcome of foliage patterns depends on the species of tree and on the directions of early branchings. We hope to test exactly the same sort of branching development in the reader’s developing perception of discourse when reading a narrative. Of course, each word in a text prompts similar stimulation of the retina and the same cortical processes for reading to unfold in support of visual word recognition. However, a reader’s understanding also develops early on from diffuse, uncommitted interests and expectations, and rather than making tangible branches as in a tree, reader understanding differentiates itself into a more complex set of choices and expectations about the next phrases or words that should follow. There is a place for linear and for nonlinear modeling alike. However, on the occasions when we study such phenomena that depend on the differentiation of originally coarse-, large-scale structure into progressively finer and finer detail and when we suspect that fine details never quite shake off traces of the older long-range structures—on these occasions, linear modeling will benefit from measures of nonlinearity that speak to these successive iterations of long-range structure into fine details. Linear modeling: Main effects and interactions Linearity is the premise that any measurement should be treated as a sum of variously independent predictors, and it delivers exactly that: Linear regression approximates dependent measurements as a weighted sum in which the weights have signs and sizes indicating the direction and magnitude of each predictor. The error term e remains time symmetric. All components of this model remain independent given the understanding that the effects, their interactions, and the noise term remain constant across time. Under the assumption of independence across time, linear models have no history and no capacity to evolve a new predictor to improve reading performance or to expel old predictors that no

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longer serve their purpose for successful reading. Even when hierarchical linear models for modeling repeated-measures data include interactions with time, the effect of time is itself time invariant and requires identically and independently distributed residuals (Singer & Willett, 2003). Effects of time being time invariant may sound strange, but the alternative of time-varying statistical estimates would be nonstationary. Multifractal analysis for modeling the nonlinear interactions across scale in discourse processing Multifractal analysis may not reveal and inventory by name all proper predictors of reading performance, but it can diagnose the strength of nonlinear interactions across scales precisely in that Turing-style case of differentiation that proceeds through successive branching of coarse-scale structure into fine-grained structure (Ihlen & Vereijken, 2010; Mandelbrot, 1983). Multifractality—and not fractality—is the proper diagnosis of nonlinear interactions across scale Fractal structure (i.e., power-law structure in series of measurements) has been a popular symptom of nonlinear interactions across scale (e.g., Jensen, 1998), but positive evidence of fractal structure from “monofractal” analysis is only consistent with—and not conclusive evidence of—nonlinear interactions across scales (Ihlen & Vereijken, 2010). Monofractal analysis only tests for a single fractal pattern, indicated by a single power law. Multifractal analysis becomes necessary to distinguish those cases of fractal scaling that are symptomatic of nonlinear interactions across scales. It is always possible to model a single observation of strictly monofractal data linearly—following a form of linear structure called “autoregression.” So, when we do multifractal analysis and find multifractal results, it is also necessary to test that the multifractality is not spuriously due to linear autocorrelation. Fractal structure might just be linear autoregression Here, we consider linearity itself and face up to the perhaps strange-sounding proposal that fractality might just be a property of linear systems and linear models. The strangeness has largely to do with the fact that nonlinear interactions provide an intriguing explanation for the observation of fractal structure in measurements (e.g., Jensen, 1998). If the phenomenon under scrutiny in composed of nonlinear interactions across time scales, then a sensible prediction is one should observe at least one (mono-)fractal pattern. The converse, however, is false: Evidence of one single fractal pattern over time does not entail nonlinearity. Additionally, from the premise of nonlinear interactions across scales, the more generic predictions are (1) multiple fractal patterns and (2) irreducibility of these multiple fractal patterns to linear structure (Ihlen & Vereijken, 2010). Autocorrelation is part of the definition of linearity. Linearity is a mathematical property depending on three stable properties. The first two, that is, mean and variance (or standard deviation), warrant little introduction. The third is the autocorrelation function—less popularly known but, coincidentally, most important for the point that fractal structure can be linear (Mandic, Chen, Gautama, Van Hulle, & Constantinides, 2008). The autocorrelation function is a set of coefficients indicating independent contributions of past values of our measure to current values of the same measure. As its name suggests, the autocorrelation specifies how much a random variable covaries (i.e., “correlates”) with itself (“auto-”). Nonzero correlation produces a linear process called “autoregressive,” entailing that we can statistically regress current values on past values. Because most introductory statistics training begins and ends with additive white Gaussian noise as the classic random process, it may help to describe additive white Gaussian noise as a case of zero autoregression (i.e., no memory). One of the most ornate descriptions of the autocorrelation for discrete time series came from Granger and Joyeux (1980) with the concept of fractional integration (FI). At first read, this phrase might not seem to make any sense. After all, integrations and differencings typically occur in whole

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numbers. However, this mathematical innovation aimed to solve a problem that was no less troubling: Some series of repeated measures were stationary but had residuals that failed to be independent despite short-lag autoregressive components. The exact math for FI is beyond the scope of the present article. The outcome is considerably easier to articulate: FI gives a weight to all past values of y leading up to each current value y(t). That is, FI deploys the entire (measured) past history of y to predict each current value of y. The model would resemble the following: y^ ðtÞ ¼ FI 1 yðt 2 1Þ þ FI 2 yðt 2 2Þ þ . . . þ FI t21 yð2Þ þ FI t yð1Þ þ 1ðtÞ;

ð10Þ

where FIi denotes the diminishing weights with increasing i, entailing both a stronger effect for more recent values but also a never-quite-vanishing effect of values all the way back in the history of the time series. The autocorrelation diverged, that is, diminished without converging to zero. Problems with plausibility. FI time series effectively demand infinite predictors, limited only by the length of the series of repeated measurements. That means, for psycholinguists finding symptoms of FI in their measures, that psycholinguistic dependent variables (e.g., word RT) depend unparsimoniously on everything in the measured past. So, the cognitive system under examination would remember literally everything of its past behavior but remember each part independently, for example, individual words but not words together in sequence. FI might remain a noise term providing the background variability for a sequence-memory predictor as in hierarchical linear models. However, this memory for words-in-sequence would be entirely separate from memory for individual words—a strange state of affairs. Given how much sequences prompt memory for single details as readers strive for coherence, this type of memory warrants skepticism. “Jack and Jill went up a ____” would prompt a nursery-rhyme reader’s memory for “hill.” Hence, no matter a reader’s ability to remember that the third word was “Jill” and that the fifth word was “up,” a human reader’s memory relies on sequence too. For FI series, however, it should only matter that “Jack,” “and,” “Jill,” “went,” “up,” and “a” are the first, second, third, and so on words in the sequence. Also, typographical errors would hamstring reading: It should be meaningless to say “Jack and Jill want up a hill.” Without sequence effects, there would be no way for the FI reader to infer from context that, really, the intended word would have been “went” and not “want” to satisfy the known sequence. Models of reading must address the fact that sequence memory can influence individual-word memory. Conversely, the word “pail” (meaning “bucket” but sounding like “whiteness”) may occur few other times in an English reader’s experience than in the phrase “to fetch a pail of water.” So, we have also to address the capacity of memory for a word to invoke memory for words in sequence. This example offers a case in which interactions across scale can be nonlinear, when readers leverage the same information at multiple grains and at the same time and potentially changing the very identity/semantics of the item to be perceived/processed. Thankfully, multifractal analysis allows a rigorous way to test whether the interweaving of word processing with sequence-of-word processing is actually more seamless than linear models would allow. Schematic descriptions of linear autoregression versus nonlinear interactions across scales. As we said at the outset, we have a choice between two options: first, treating with discourse processing as though reading enlisted a hierarchy of processes who levels are nearly decomposable in theory and actually decomposed by linear modeling or, second, treating with discourse processing as though reading enlisted nonlinear interactions across scale. Nearly decomposable hierarchical models of reading would predict linear-autoregressive regimes, that is, they would predict reading behavior as composed of independent and non-overlapping processes situated at separate time lags (e.g., average word RT nested in average clause RT, nested in average sentence RT, nested in average RTs of subtopics of the discourse). Each time-lagged process might represent, on average, the contribution of past experiences on current reading behaviors, and we might assign previous words at different time lags to different components of the reading behavior. That is, words at sufficiently long time lag from the present word might belong to a “sentence” or “topical” discourse process, and words at short time lags from the present word might belong to a “syntactical” or “semantic” process. For instance,

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Figure 1. Two perspectives on individual word RTs: a) the autoregressive perspective that each word RT reflects the cumulative summing of subsequent and independent processes regarding lexical aspects of preceding words (top) and b) the multifractal perspective that each word RT reflects the interactions unfolding among processes at different scales of reading (bottom).

an autogressive model of individual word RTs would entail that individual words contribute independent accumulating effects to RTs for subsequent words (Figure 1a). Of course, processes unfolding as the sum of many independent components (e.g., sublexical features, words, clauses, sentences, topics, etc.) would be at odds with the widespread evidence that all these features interact with each other (Van Orden & Kloos, 2005) and blend across time scales (Wallot, Hollis, & van Rooij, 2013; Wallot, O’Brien, Haussmann, Kloos, & Lyby, 2014). Not surprisingly, then, we can identify the mathematical model that would capture this different view point, distinct from the linear autoregressive model described above (Figure 1b). (Mono)fractal means “single power law” but multifractal means “many power laws.” Between linear (i.e., autoregressive) models and hierarchical models incorporating nonlinear interactions across scales (Figure 1b), an important distinction is that the resulting behavior will exhibit what has become known as multifractal fluctuations (Ihlen & Vereijken, 2010). The nonlinearity of successive branching across time scale produces variability in a power-law form. Power-law forms are the proper mathematical form expressing the diverging relationships that we noted appear in autocorrelation for FI series. The fractional nature of integration in linear modeling has given power-laws the shortened descriptor “fractal.” We burden this term “fractal” with the prefix “mono” to distinguish patterns with a single power law from patterns with multiple power-law forms: The former case thus becomes known as “monofractality,” and the latter is mostly only ever known as “multifractality.” Power laws have been commonplace features of psychology in the Fourier-transform power spectra of response times in cognitive tasks (Gilden, Thornton, & Mallon, 1995) and in the form of forgetting curves and prospective memory (Anderson & Schooler, 1991; Chater & Brown, 2008). A key feature of power laws is self-similarity: Over any arbitrary interval of scales, the trajectory of growth (or when the power law is inverse, decay) has the same form as the trajectory over the entire range of scales. Such conditions of self-similarity entail that rather than simply characterizing the power-law distribution in terms of average long-scale structure or simply averaging short-scale behavior, we might describe the correlation and interaction among these scales in terms of a power-law exponent that governs the distribution over all intervals alike (Mandelbrot, 1983). FI linear autoregression entails “1/f b” fractality. The autocorrelation function has a one-to-one relationship with Fourier-based power spectra. Whereas the former unfolds across the domain of lags, the latter unfolds across the domain of frequencies f. So, it is no coincidence that FI series exhibit power spectra with “1/f b” trajectories in power decreasing across increasing frequency, the gradual

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diminution of spectral power across frequencies that never converges to zero (i.e., that diverges). As long as the divergence remains the same (within 2 standard errors) across repeated measures, then single fractal patterning remains within the purview of explicit features of linear modeling. Multifractality is predictive of cognitive/perceptual interactions with the key factors in a task environment Indeed, it might have been easier to ignore multifractality if the variability in power-law exponents across time were not so persistently predictive of rather interesting cognitive and perceptual performance (e.g., Kelty-Stephen & Dixon, 2014): The variability in power-law scaling over successive time intervals predicts psychologically relevant responses that led us to explore the relatively alien literature on multifractality. As it turns out, multifractal modeling depends on statistical physicists’ attempts to describe the full variability of power-law exponents, and rather than express this variability of power-law exponents in terms of a standard error or confidence interval as in linear modeling, this multifractal modeling seeks to specify the span of power-law exponents as a multifractal spectrum. For instance, the spectrum width indicating the degree of multifractality for word RT series appears to complement word reading speed as a positive predictor of reading comprehension (Wallot et al., 2014; see also Wallot, O’Brien, Coey, & Kelty-Stephen, 2015). For statistical physics, this width serves as more diagnostic measure of nonlinear interactions across time scales than a single power-law exponent. Hence, this width might inform how nonlinear interactions across time scales operate to shape discourse processing. Statistical test for nonlinear interactions across time scale: Comparison of multifractality between original series and linear-surrogate series The final step in multifractal investigations of nonlinear interactions across scales often involves what are known as surrogate series. This last step actually helps us to determine when the multifractalspectrum width provides significantly different information than a simpler standard error for the linear-modeling FI, that is, it will help us determine the degree to which the multifractal-spectrum width WMF actually reflects nonlinear interactions across scales. Alternately, this determination could also let us know when the data are indistinguishable from linear processes and so when we might as well limit modeling to the linear case. What surrogate series stand in for is the null-hypothesis case for the data being purely linear (Schreiber & Schmitz, 1996). They are series mimicking the linear properties (i.e., mean, variance, and autocorrelation) of the original series. The diagnosed nonlinearity of interactions across scales depends on how much multifractality (i.e., the multifractal-spectrum width, henceforth WMF) of the original series differs from the WMF for the best approximations of linear versions of the data? Hence, we compute a standardized measure of difference from the multifractal-spectrum width between original and surrogate, that is, a one-sample t statistic subtracting original WMF from the average WMF of the surrogate series and dividing that difference by the standard error of WMF of the surrogate series. We denote this t statistic as tMF.1 We plan to use tMF indicator to address our second aim of showing how multifractality might model individual-reader differences in discourse processing. Applying multifractal evidence of nonlinear interactions across scales to postsurprise reading Before proceeding to our second major aim, we first emphasize that it is well known that violating expectations about referent gender startles the average reader (Duffy & Keir, 2004). We aim not to 1

To further guard against sample size bias, we also computed bootstrap t statistics based on repeated resamplings of the surrogate WMF values. The one-sample t statistics were statistically indistinguishable from the bootstrap t statistics, indicating that the onesample t statistics sufficed.

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rehash this fact. Rather, the fact serves as the completely unsurprising backdrop against which the foregoing work of statistical physicists might show a perhaps surprising relevance to the psycholinguistic issue of discourse processing. Our focus runs orthogonal to previous work on what average readers do. Although linear modeling has informed us about the average reader’s response to surprise about gender, we aim here to capture what nonlinear modeling can show regarding the interindividual differences across readers. The second aim of this article is to demonstrate that multifractal modeling of RTs allows prediction of what individual readers might do. That is, we measured word RTs over the entire span of their reading of a story and for each of many individual readers. Using socially prevalent gender stereotypes, the first half of the story set up a specific expectation about an unnamed protagonist’s gender. Any single individual reader’s ability to assume the gender expectation would depend on that individual reader’s proficient navigation of narrative text at many different scales at once (i.e., word, phrase, sentence, social situation in narrative). We wanted to test whether the multifractal structure of this first half-story word RT series would quantify the nonlinear interactions across scales involved in taking up the gender expectation from the narrative for each individual reader. We specifically expected that the multifractal structure of the presurprise RTs would predict individual reader’s responses after the violation of the gender expectation. Hence, rather than rehashing an average main effect of genderreferent surprise, our second aim was to show that multifractal modeling might provide a much more sensitive prediction of individual differences in how readers navigate the same “objective” information so as to construct idiosyncratic expectations about narrative. Knowing the multifractal structure might allow us to predict how well the reader stumbles through subsequent text when new information shows the expectation to be false. The question for present work was whether multifractal evidence of interactions across time scales provides an apt measure of discourse processing both in surprise after a plot twist and in recovery from surprise. Participants read one of two 2,000-word stories, both eliciting expectations about protagonist gender but revealing protagonist gender only on word 1,000. One story fulfilled the stereotyped expectation, but the other did not. We used the latter story’s 1,000th word as a “misfire” to surprise the reader by changing referent gender (e.g., Duffy & Keir, 2004). We only used gender expectations as an example of narrative-level processes at longer time scales that might interact with word-processing at shorter time scales. We blend the insights from linear modeling of reading behavior with current theorizing that suggests multifractality as a statistical signature of interactions across scales. Multifractality might predict effects of discourse-word interactions under genderreferent ambiguity. Role of multifractal signatures: Main effects and interactions The present work embeds multifractal evidence of nonlinear interactions across scale tMF as a predictor in a mixed-effect linear regression model. The starring roles in these linear models are largely interaction terms. The use of regression interactions for testing our predictions about the relevance of multifractality is a key aspect of the approach for a few reasons. First, we hope to show how multifractal measures might moderate both the effects of quantities like average single-word RT and the effects of single-word lexical features (e.g., Wallot et al., 2014, 2015). The second reason for interactions is that effects of multifractal measures and standard deviation may moderate one another (Kelty-Stephen & Dixon, 2014). If multifractality can help to incorporate nonlinear interactions across scales into psychological theorizing, interactions strike us as theoretically more interesting than main effects. These nonlinear interactions across time scales are most interesting insofar as they allow the organism to manipulate, explore, and interpret the known parameters of a task environment. There are already plenty of known single-word features that can increase or decrease average reading speed in the guise of main effects. Hence, multifractal evidence appears in interaction terms, allowing us to quantify and test how readers make use of features that psycholinguists have been hard at work to unearth.

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Hypotheses First, at short range, we predicted that multifractal evidence of interactions across time scales tMF would itself interact with reading speed to predict the boost and gradual decay in word RTs indicating surprise and/or increased processing effort immediately after the revealing of protagonist gender (Hypothesis 1). Second, we expected that participants who had experienced the surprise in the stereotype-unfulfilled condition would, over the longer range of the remaining story (words 1,001 –2,000), exhibit an increase in tMF above and beyond standard deviation (Hypothesis 2).

Methods Participants Thirty-four undergraduate students (22 women) aged 18 to 23 years provided informed consent according to Grinnell College’s Institutional Review Board. Experimenters randomly assigned half of them to the stereotype-fulfilled group and another half to the stereotype-unfulfilled group. Materials Dell desktop PCs (Dell, Inc., Round Rock, TX) presented instructions and text stimuli on 17-inch monitors in 14-point Courier New approximately 1.5 feet away from seated participants’ eyes. “F” or “J” keys on QWERTY keyboards allowed participant response depending on hand dominance. A Matlab (Mathworks, Natick, MA) script allowed self-paced presentation of single words at a time with each new keypress. Words appeared in sequence from one of two 2,000-word stories that experimenters composed. Both stories described an interview between a first-person narrator and the protagonist. Words 1 to 999 were identical across stories, failing to indicate the protagonist’s gender but giving the protagonist stereotypically male professions (i.e., a soldier) and mannerisms (i.e., an aggressive temperament). The 1,000th word revealed the protagonist’s gender as male or female in the “stereotype-fulfilled” or “stereotype-unfulfilled” story, respectively. The next 1,000 words only differed by gendered pronouns. Procedure Experimenters instructed participants on using “F” or “J” keys to progress to the next word. After completing the story, participants answered seven questions probing reading comprehension. Data analysis Multifractal analysis Chhabra and Jensen’s (1989) method estimated multifractal spectra twice for each participant’s word RT series: once for the prereveal portion (words 1 –999) and once for the postreveal portion (words 1,001 – 2,000). Average proportion changed with sample size according to what physicists have called “singularity strengths” a. The multifractal spectrum width WMF reflects the differences between singularity strength for the largest and the smallest fluctuations. A schematic guide to the multifractal algorithm. Multifractal analysis requires repeated measurements (Figure 2). Its major concern is the homogeneity or heterogeneity of these repeated measures, and so the next step after collecting the repeated measurements is to partition (or “bin”) the series according to a wide range of bin sizes, usually from four points to a fourth of series length. Multifractal analysis continues by calculating statistics on the binned quantities and examining how these statistics change with bin size (i.e., with time scale). The third step of the multifractal procedure estimates the exponent a defining how average bin proportion grows with bin size. The fourth step

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Figure 2. Schematized first steps in the multifractal algorithm. The first step is to take repeated measures (top left). The second step is to partition the series into non-overlapping bins of different sizes (bottom left). The third step is to calculate the average proportion of the area under the series’ curve for each bin size and fit the exponent relating average proportion to bin size—an exponent called the singularity strength a (top right). The fourth step is to calculate the Shannon entropy across the binned proportions for each bin size and fit the exponent relating Shannon entropy to bin size—an exponent called the Hausdorff dimension f (bottom right).

quantifies this variability across bin proportion as Shannon entropy and estimates the f exponent relating bin size to Shannon entropy. The fifth step repeats the third and fourth steps with different settings of a parameter q. Proportions raised to exponent q provides “mass” m. In this algorithm, mass serves to weight proportions (Figure 3, left). Mass weighting proportions provides a conservative way to resolve heterogeneity in repeated measures. One response to heterogeneity is to exclude outliers beyond a chosen cutoff. Some measurements have expectable extremes (e.g., eye movements contain enormous, ballistic “saccade” movements and small, tremor-like “fixation” movements), and it is practical to analyze saccades separate from fixations (Rhodes, Kello, & Kerster, 2011). The multifractal approach uses mass to continuously ratchet up larger or smaller values according to the exponent q that can reveal structure that those dichotomous splits omit (e.g., in eye-movement measures) (Kelty-Stephen & Mirman, 2013). q-Based variability in mass m(q) generalizes single a and f estimates from earlier steps into continua a (q) and f(q). Multifractal analysis distinguishes temporally heterogeneous series from homogenous series by the amount of variety in a(q) and f(q).

Figure 3. Schematized concluding steps in the multifractal algorithm as described in the main text, using q to convert bin proportions into mass (top left). Mass allows generalizing a and f in steps three and four into a continuously varying a(q) and f(q) (bottom right). Corresponding pairs of a and f for each value of q compose the multifractal spectrum (top right).

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Figure 4. Schematic of contrast between multifractal properties between original series and IAAFT surrogate mimicking linear properties of the original series. The IAAFT surrogate involves reshuffling the values while also preserving the original series’ amplitude spectrum or autocorrelation function, hence preserving linearity (left) but destroys any nonlinear interactions across time scale in the original series (top right). Comparing multifractal-spectrum width between original series and a small sample of surrogates can test the null hypothesis that original series’ multifractal-spectrum width is predictable from or reducible to linear features.

The sixth step of the multifractal procedure involves plotting a(q) and f(q) as ordered pairs composing the multifractal spectrum, an often-asymmetric and inverted U-shaped curve (Figure 3, right). We included a(q) and f(q) whenever log-scaled linear fits correlated at r of .995 for the log-scaled linear fit. We excluded values of q either (1) for which mass-weighted proportion and for which Shannon entropy were undefined (e.g., due to masses rounding to zero) or (2) power-law fits for which r , .995.2 Surrogate comparison Diagnosing nonlinear interactions cross-scales requires comparison with a sample of surrogate series (50 samples in the present analysis) preserving linear autocorrelation and destroying the original sequence (i.e., iterative amplitude-adjusted Fourier transform [IAAFT]; Ihlen & Vereijken, 2010; Schreiber & Schmitz, 1996). Figure 4 schematizes IAAFT generation as reordering portions of the series to produce new series with comparable average temporal structure. Generating IAAFT surrogates involves a Fourier transform and then repeatedly scrambling the phase spectrum and preserving the amplitude spectrum. tMF indicates multifractal interactions across time scales. Linear Mixed-Effect (LME) modeling LME is a regression technique for repeated measures. It hierarchically nests random effects for individual participants within sample-general models that can include time-varying predictors as fixed effects (Singer & Willett, 2003). LME maximum-likelihood estimation evaluates new effects as a change in deviance defined as 2 2 times log-likelihood (i.e., 2 2LL). For m new predictors, reduction in 2 2LL is chi-square distributed with m degrees of freedom. One LME model tested effects of stereotype fulfilment (postsurprise coded as 1 or 0 for “stereotypeunfulfilled” or “stereotype-fulfilled” groups, respectively), prereveal tMF (calculated from RTs for words 1 –999), and prereveal mean reading speed (MeanRT; mean of word RTs for words 1 – 999) on orthogonal polynomial terms for words 1,001 to 1,015. Because the nonlinear, nonmonotonic profile of word RTs might bias a simple linear slope estimate, we fit orthogonal linear, quadratic, cubic, and 2 See a brief step-by-step example using an extremely small 32-measurement series that outlines the calculation of each bin proportion and mass (http://sites.google.com/site/foovian/DPD-15-00105Supp.pdf).

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Figure 5. Example series of word RTs in narrative sequence just preceding the revelation of the protagonist’s gender on word 1,000.

quartic polynomial components to the word RT profiles over 15 words immediately after the 1,000th word. A second model testing effects of stereotype fulfillment (postsurprise) on postreveal tMF (calculated from RTs for words 1,001 – 2,000), above and beyond standard deviation SD and multifractal-spectrum width WMF of the same postreveal RT series. For both models, random-effect structure included only an intercept for individual participants. More elaborate random-effects structures failed to improve model fit or failed to converge.

Results Comprehension check Groups did not exhibit different reading comprehension scores, t(32) ¼ 1.54, p ¼ .13 (Ms ¼ 5.56 and 5.06 questions correct, SEs ¼ .32 and .34, in stereotype-fulfilled and stereotype-unfulfilled groups, respectively). Prereveal RTs (Words 1 – 999) exhibit multifractal evidence of interactions across time scales The first 999-word sequence of word RTs (Figure 5) exhibited multifractal-spectrum widths significantly different from 50 corresponding surrogates’ multifractal-spectrum widths (Figure 6) for 32 of 34 participants (i.e., 94%) as indicated by tMF. We do not interpret the difference of two participants’ reading except to use t-statistics as predictors in subsequent modeling of postsurprise RT. It is not customary for 100% of series to show significant difference from surrogates. Groups did not differ in multifractal-spectrum width, t(32) ¼ 1.54, p ¼ .13. Prereveal word RTs had only marginally wider spectra related to surrogate series, t(32) ¼ 1.90, p ¼ .07, in the stereotype-unfulfilled group (M ¼ 10.64, SE ¼ 2.50) than for the stereotype-fulfilled group (M ¼ 4.88, SE ¼ 3.55).3 3 We thank reviewer J. G. Holden for sharing the observation that buffering processes in the computer registering key presses from a keyboard can result in artefactual differences in key-press latencies in the span of ^7.5 ms. We would hope that our multifractal estimates were not reflective of such artefactual differences in key-press latencies. To address this concern, we compared our multifractal-spectra calculations for the measured RT series to multifractal-spectra calculations for a simulation of RT series with added noise to resemble the unsystematic variability dependent on key-press buffering. Specifically, this simulation consisted of the measured RT series plus a white-noise process as long as the measured series but having zero mean and SD of 7.5 ms. If the multifractal spectra calculations were contaminated by the 7.5-ms buffering, then we would have expected the multifractal spectra calculations to differ with and without the addition of the zero-mean, 7.5-ms SD. However, our simulation showed no evidence of a difference with or without the 7.5-ms SD noise. In both cases, the multifractal spectra showed a mean width of .149 and an SD of .068. Further, the multifractal spectra for the series with and without the simulated buffering correlated at r ¼ .987.

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Figure 6. Example multifractal spectrum for an original prereveal (words 1 –999) word RT series (black) and for 10 surrogate series preserving the linear autocorrelation but destroying original sequence (gray). The black curve is wider than the average spectrum for surrogate series, suggesting interactions across time scales in original series that do not follow simply from linear autocorrelation.

RTs slow down immediately after the 1,000th-word gender reveal in unfulfilled-stereotype story Mean word RTs over words 1,000 to 1,015 show that groups were not significantly different on the 1,000th word revealing the protagonist’s gender (Figure 7). The sharp increase in word RT immediately after the 1,000th word gradually diminished over the subsequent 4 words. We examine n þ 15 words given that predictability effects in self-paced reading show spillover effects on subsequent RTs (Smith & Levy, 2013). Hypothesis 1: Prereveal multifractal interactivity across time scales and prereveal reading speed together moderate the postreveal changes in RTs An LME tested effects of reading speed (MeanRT) and multifractal interactions across scales (tMF) from words 1 to 999 on short-range change of word RTs (Table 1, Figure 7). Logarithmic transformation

Figure 7. Mean word RTs in the stereotype-fulfilling (gray) or stereotype-unfulfilling (black) story for words 1,000 to 1,015 with standard error bars for each word. Actual excerpts from the two stories appears below the horizontal axis in colors corresponding to the plots.

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Table 1. Coefficients for LME model for effect of prereveal multifractal interactions across scales (i.e., multifractal-spectrum t-statistic comparing original with surrogate spectrum widths) on quartic polynomial trajectory of postreveal rise and decay of RTs. Predictor Intercept tMF Postsurprise MeanRT Words(Linear) Words(Quadratic) Words(Cubic) Words(Quartic) tMF £ Postsurprise tMF £ MeanRT Postsurprise £ MeanRT MeanRT £ Words(Linear) MeanRT £ Words(Quadratic) MeanRT £ Words(Cubic) MeanRT £ Words(Quartic) tMF £ Words(Linear) tMF £ Words(Quadratic) tMF £ Words(Cubic) tMF £ Words(Quartic) Postsurprise £ Words(Linear) Postsurprise £ Words(Quadratic) Postsurprise £ Words(Cubic) Postsurprise £ Words(Quartic) tMF £ Postsurprise £ MeanRT tMF £ MeanRT £ Words(Linear) tMF £ MeanRT £ Words(Quadratic) tMF £ MeanRT £ Words(Cubic) tMF £ MeanRT £ Words(Quartic) Postsurprise £ MeanRT £ Words(Linear) Postsurprise £ MeanRT £ Words(Quadratic) Postsurprise £ MeanRT £ Words(Cubic) Postsurprise £ MeanRT £ Words(Quartic) tMF £ Postsurprise £ Words(Linear) tMF £ Postsurprise £ Words(Quadratic) tMF £ Postsurprise £ Words(Cubic) tMF £ Postsurprise £ Words(Quartic) tMF £ Postsurprise £ MeanRT £ Words(Linear) tMF £ Postsurprise £ MeanRT £ Words(Quadratic) tMF £ Postsurprise £ MeanRT £ Words(Cubic) tMF £ Postsurprise £ MeanRT £ Words(Quartic)

B

SE

p for B

22LL ¼ x2(1)

p for x2(1)

22.12 2.01 2.84 1.71 4.20 1.56 22.56 24.19 .09 .04 3.92 22.79 24.00 21.03 6.05 2.05 .01 .03 2.06 212.17 4.72 5.04 28.21 2.35 .28 .05 .03 .32 21.68 26.65 217.82 31.81 .76 2.51 .01 .82 22.06 1.18 .03 23.06

.15 .01 .51 .37 1.42 1.42 1.42 1.42 .04 .04 1.48 3.63 3.63 3.63 3.63 .12 .12 .12 .12 4.93 4.93 4.93 4.93 .11 .36 .36 .36 .36 14.37 14.37 14.37 14.37 .37 .37 .37 .37 1.11 1.11 1.11 1.11

,.0001 .80 .11 ,.0001 ,.01 .27 .07 ,.01 ,.05 .24 ,.05 .44 .27 .78 .10 .69 .97 .79 .62 ,.05 .34 .31 .10 ,.01 .45 .89 .93 .37 .13 .64 .22 ,.05 ,.05 .17 .97 ,.05 .06 .29 .98 ,.01

.07 2.85 17.43 9.41 1.31 3.51 9.37 5.44 1.49 6.86 .64 1.32 .09 3.01 .17 .00 .08 .27 6.56 .99 1.13 3.00 8.91 .63 .02 .01 .86 2.46 .23 1.67 5.29 4.53 2.06 .00 5.36 3.74 1.24 .00 8.21

.79 .09 ,.0001 ,.01 .25 .06 ,.01 ,.05 .22 ,.01 .42 .25 .77 .08 .68 .96 .78 .60 ,.05 .32 .29 .08 ,.01 .43 .89 .92 .35 .12 .63 .20 ,.05 ,.05 .15 .97 ,.05 .05 .27 .98 ,.01

minimized effects of skew on regression estimates, even though patterns of significance were identical for raw data. We omit lexical-feature predictors because texts were identical (Figure 7). The RTs’ quartic profile times served as a baseline for modeling group and multifractal effects. For stereotype-fulfilled group, prereveal reading speed predicted postreveal speed The only significant predictors in Table 1 without postsurprise are for MeanRT, Words(Linear), and Words(Quartic), indicating that the only significant differences in the top panel of Figure 8 are, first, that slower reading of words 1 to 999 predicted slower reading and, second, that a negative quartic effect tempered linear slowing of reading. For stereotype-unfulfilled group, prereveal tMF accentuated effects of reading speed on reaction to the revealing of protagonist gender Significant interactions among postsurprise, tMF, MeanRT, and Words(Linear, Cubic, and Quartic) indicate that stronger multifractal interactions across time scales (i.e., tMF) accentuated prereveal aspects of MeanRT during words 1,001 to 1015 (bottom panel of Figure 8).

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Figure 8. Model predictions for coefficients in Table 1 describing mean postreveal trajectory in logarithmically scaled RT. These plots describe the interaction between prereveal tMF and prereveal mean reading speed for predicting word RTs after the 1,000th word revealing the protagonist’s gender, showing word RTs for slow and fast readers (third and first quartiles of prereveal mean RT) in gray and black curves. Solid and dashed curves indicate model predictions for participants exhibiting prereveal word RTs with high and low tMF (i.e., third and first quartile).

Faster prereveal readers during postreveal words 1,001 to 1,015. Readers with low prereveal MeanRT continued to read quickly, but readers with higher tMF showed marginally faster reading initially and less of the subsequent rise and fall in MeanRT that those readers with low tMF exhibited. Slower prereveal readers during postreveal words 1,001 to 1,015. Readers with high prereveal MeanRT showed greater increase in word RT, suggesting they may have been more surprised by the protagonist’s revealed gender. Initial bursts in word RT decayed much faster for these slower readers with lower prereveal tMF but also decayed much less and led to subsequent increases around word 1,010. Meanwhile, slower readers with higher tMF exhibited slower but much deeper decays of the postreveal increase. By word 1,008, slower/stronger-interaction-across-time scale readers ended up progressing faster even than those readers with greater prereveal reading speeds. Hypothesis 2: Postreveal reading exhibits stronger evidence of multifractal interactivity Table 2 reports coefficients from an LME modeling the effect of postreveal surprise for the stereotypeunfulfilled group on postreveal tMF, for the entire second half of the text (i.e., words 1,001 – 2,000) above and beyond effects of original postreveal multifractal-spectrum width and of postreveal standard deviation. Finding one’s stereotypes unfulfilled strengthens multifractal interactions across time scales (Figure 9), diminishing only as multifractal spectra widen due to higher standard deviation. Table 2. Coefficients for LME model for effects of postreveal WMF, stereotype fulfillment (postsurprise), and SD of word RT on postreveal tMF. Predictor Intercept SD WMF Postsurprise SD £ WMF SD £ Postsurprise WMF £ Postsurprise SD £ WMF £ Postsurprise

B

SE

p

22LL ¼ x2(1)

p for x2(1)

212.59 8.60 148.98 215.74 296.96 148.57 122.75 2910.90

3.40 11.38 38.68 11.04 65.75 60.52 81.17 372.71

, .05 .46 , .001 .17 .15 ,.05 .14 ,.05

.63 14.90 1.93 2.36 6.30 2.23 6.29

.43 , .001 .16 .12 ,.05 .14 ,.05

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Figure 9. Model predictions for the postreveal tMF strength of interactions across time scale. Plots compare model predictions for participants reading the stereotype-fulfilling story (gray) with model predictions for participants reading the stereotype-unfulfilling story and exhibiting high postreveal standard deviations (third quartile; black solid line) or low postreveal standard deviations (first quartile; black dashed line) of word RTs.

Discussion The present work investigates reading behavior in terms of multifractal structure in word RTs. Hypothesis 1 predicted that multifractal interactions across scales would moderate the increase and subsequent decay in word RTs after failure of expectations built over previous text. Hypothesis 2 predicted that unfulfilled expectations would intensify multifractal evidence of interactions across scales over the rest of the story. Results supported both predictions. These findings are consonant with previous research in reading (Wallot et al., 2014) but also in other cognitive domains alike: Violation of expectation has appeared as the surprising induction of a novel rule, both in gear-system problems (Stephen, Boncoddo, Magnuson, & Dixon, 2009) and in dimensional card-sort tasks (Stephen, Anastas, & Dixon, 2012). What distinguishes participants experiencing the surprising “aha!” moment is a capacity for greater multifractality in their exploratory movements during the task, reflecting stronger nonlinear hierarchical structure in their approach to the task. Multifractal evidence of interactions across time scales reflects the attentive poise of readers navigating a text and anticipating new words. Over the first half of our text, multifractality captures the interlacing of multiple scales as readers construct expectations. Over the second half, multifractality captured how surprised readers became newly vigilant to this interlacing of information across scales. Our results reaffirm that cognitive experience of novelty depends on the interactions across time scales, amid relatively short- and relatively long-range structure in the task environment (Dixon, Holden, Mirman, & Stephen, 2012). Our results further highlight that effects of surprise are not confined to relatively local pockets of text (Smith & Levy, 2013) but have long-lasting effects on how the cognitive system coordinates, both thriving on and contributing to the multifractal structure of reading processes. Might the role of multifractal fluctuations here indicate probabilistic epigenesis in reading? We speculate that multifractal interactions across scales observed in the reading process might proceed from a Gottliebian (2007) probabilistic-epigenetic framework in which the reading experience is an ongoing, dynamic interweaving of task context, reader intent, perceptual search, and physiological processes. Gottlieb’s (2007) work uncovered the fact that so-called innate behaviors reducible to genetic contributions would actually disappear with the removal of nonobvious factors such as embryo

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vocalizations inside the unhatched shell. Echoing Turing’s (1952) insights Gottlieb’s conclusion was that patterned behavior arose due to co-acting and co-developing (or co-evolving) factors. There is a cultural agreement that cognitive feats such as reading rely on more than genetic factors, but reading may follow from just the same sort of interlacing of multiple scales that Gottlieb (2007) envisioned (Dixon et al., 2012). Genetics provides a framework for the necessary tissues for the eye, for the nerves, for the brain, and for the articulatory tools that let us pronounce any word and so embody any text. In addition to cortical structures and nervous apparatus needed for vision, we have years of experience with our languages and our domains to learn what to expect in a given piece of text. As the foregoing literature has suggested, expectations about a text are built at many scales. We continue building and rebuilding them as we read, particularly when new information takes us by surprise. Probabilistic epigenesis provides a ready nonlinear framework where experiences at many scales can continually reshape the structure underlying smart behaviors. We address interactions across scales as a key player in the development and disassembly of expectations for reading text. Our general hypothesis was that surprise for reader expectations will manifest in the interaction of multifractal indicators with more mainstream predictors. Our general finding is twofold: first, that multifractal modeling of presurprise variability in RTs can, with mainstream measures like average reading speed, predict a small subset of postsurprise RTs and, second, that surprising a reader’s expectations can subsequently increase the multifractal evidence of interactions across scales over the rest of the text. Reading appears here to be a gradual developing process and discourse as a multiscaled hierarchy, prone to expectations or surprise at each scale but flexible because of interactions across those scales.

Funding C. B., H. B., E. E., and D. G. K.-S. acknowledge the generous support of Grinnell College’s Mentored Advanced Project program.

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