Embracing Uncertainty: Reducing Predictive Precision in Bayesian Inference Enhances Novelty in Creative Design

Embracing Uncertainty: Reducing Predictive Precision in Bayesian Inference Enhances Novelty in Creative Design | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Embracing Uncertainty: Reducing Predictive Precision in Bayesian Inference Enhances Novelty in Creative Design Koji Koizumi, Hideyoshi Yanagisawa, Shimon Honda, Yoed Nissan Kenett, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9152871/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Creative design is an inquiry process that transforms unknowns into knowns while strategically accepting uncertainty to generate novelty. To understand this computationally, we applied the Inquiry Cycle Model (ICM), which extends the Free Energy Principle by positing that temporary increases in predictive uncertainty maximize long-term information gain. We investigated how modulating this uncertainty influences design ideation by conducting a double-blind, randomized controlled experiment using transcranial alternating current stimulation (tACS). By targeting right temporal alpha oscillations—a neural mechanism for inhibiting obvious semantic associations—we artificially lowered top-down predictive precision during divergent thinking. Results demonstrated that this intervention effectively enhanced self-reported originality in both problem-solving and problem-finding tasks. Crucially, the nature of this creative enhancement was fundamentally modulated by the baseline uncertainty of the task context. In more structured problem-solving scenarios, reducing predictive precision significantly increased objective, corpus-based Bayesian surprise (specifically, maximum information gain and optimal arousal). Conversely, in highly ambiguous problem-finding contexts where prior precision is inherently low, the intervention primarily amplified subjective, internal experiences of insight (aha strength) and confidence. These findings provide causal neurophysiological evidence linking right temporal alpha oscillations to predictive precision. Ultimately, they partially support the ICM and highlight the context-dependent role of predictive precision in fostering novelty during idea generation. This offers a mechanistic account of creative cognition based on the brain’s information-processing principles, laying the groundwork for evidence-based methodologies that deliberately regulate these cognitive states in design practice. Cognitive Neuroscience Architecture, Design and Planning Computational Neuroscience Psychology creative design free energy principle inquiry cycle model predictive precision transcranial alternating current stimulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Highlights Right temporal alpha oscillations relate to reduced Bayesian predictive precision. Reduced precision boosts information gain and arousal of Bayesian surprise. Reduced predictive precision via right temporal alpha tACS enhances idea originality. Task context clarity modulates the effect of reduced predictive precision. Findings validate the Inquiry Cycle Model for creative design cognition . 1 Introduction 1.1 Creative Design and the Predictive Brain Paradox Creative design is an act of expanding and transforming the design state space by introducing new perspectives or variables, thereby enabling the generation of unprecedented solutions. Such processes can transcend conventional frameworks, opening new domains and even triggering paradigm shifts. 1 In creative design, designers confronting uncertain challenges hypothesize, test, and evince solutions until achieving outcomes that are both novel and apt. 2 – 4 Design cognition research that seeks to elucidate such creative thinking processes has traditionally relied on cognitive psychological approaches such as protocol analysis, which revealed two key perspectives: design as a search process within a problem space, and as an exploratory process between problem and solution spaces. 5 These studies also highlighted the roles of multiple cognitive functions, including memory, associative processing, visual perception, and mental imagery, in design thinking. 6 More recently, neurophysiological tools such as eye tracking, heart rate monitoring, and brain imaging have enabled quantitative assessments of design cognition. 7 – 9 Concurrently, both design and creativity research have increasingly emphasized theory-driven, computational approaches that seek mechanistic explanations of creative cognition. 10 – 17 The Free Energy Principle (FEP), one of the most influential theoretical frameworks in neuroscience, provides a unifying account of perception, action, and learning. In essence, FEP describes the brain as a predictive machine that constantly minimizes prediction error (or “free energy”) by updating its internal model of the world via Bayesian inference. 18 This principle provides a lens for understanding design processes which begin with high uncertainty and progressively transform the unknown into the known. 19 However, a fundamental paradox arises: if the brain by default strives to reduce surprise and uncertainty, how can we account for creative design, a process in which one deliberately seeks out novelty and embraces uncertainty? This conundrum is analogous to the classic “dark room problem” in predictive brain theory (the question of why an agent driven to minimize surprise would not simply converge upon a state of minimal sensory input, dark room) and has been reformulated in the context of creativity as the “Enlightened Room Problem,” which asks how a strictly error-minimizing agent could ever act creatively. 20 Put simply, why would a self-organizing system driven to minimize surprise ever explore beyond the familiar, and how could it generate genuinely novel ideas given the constraints of its own predictive models? 1.2 The Inquiry Cycle Model: Strategic Resolution of Uncertainty and the Pursuit of Novelty The Inquiry Cycle Model (ICM) 21 resolves this paradox by extending the free-energy minimization framework over time, allowing an agent to tolerate temporary increases in uncertainty (entropy) if these are expected to yield greater net reductions of free energy in the long run. This aligns with recent creativity research. For instance, the “entropy modulation theory of creative exploration” posits that creativity depends on modulating entropy during cognitive search; 22 increasing predictive uncertainty raises entropy, enabling broader memory retrievals and more novel ideas. Similarly, the “matched filter hypothesis” suggests that during idea generation, the brain emphasizes data-driven (bottom-up) processing while suppressing knowledge-driven (top-down) control. 23 Loosening input filtering makes low-level information more accessible, facilitating creative thinking. These perspectives highlight that temporarily embracing uncertainty—via entropy modulation or loosened filtering—is fundamental to creativity. This supports the ICM’s tenet that strategic, short-lived increases in free energy are essential conditions for achieving global minimization over time, reframing creative exploration as a dynamic cycle of “convergence” toward order and “expansion” of uncertainty. This cyclical structure aligns with Peirce’s framework of explicative and ampliative reasoning. 24 Explicative reasoning (deduction) is a “convergent” process that derives consequences from existing premises to enhance internal consistency; this corresponds to long-term free-energy minimization. Conversely, ampliative reasoning is an “expansive” process that extends the inference space beyond existing premises. While this includes induction, its crucial exploratory mode is abduction, the sole inference capable of boldly introducing novel hypotheses via a logical leap. This abductive hypothesis formation expands knowledge of the real world, mapping directly to the temporary increase in free energy—the strategic "acceptance of uncertainty"—within the ICM. This logical consistency provides a theoretical foundation for understanding how the ICM facilitates creative inquiry beyond mere prediction error minimization. Indeed, widespread theoretical consensus posits that creative progress is a dynamic iteration of ampliative expansion and explicative validation. 14 , 25 – 27 In cognitive models, this cyclical interplay is directly mapped to idea generation and evaluation—collectively termed the two-fold model of creativity. 25 This dual-phase structure is supported by neuroimaging 28 , 29 and cognitive frameworks such as the “Geneplore” model 26 and Memory in Creative Ideation (MemiC). 14 , 27 These models commonly demonstrate that creativity emerges by iteratively alternating between exploring distant semantic networks to generate novel ideas and evaluating their effectiveness against existing knowledge. Thus, these cognitive processes dynamically build upon one another over time. Within the field of design research, this cyclic structure of ampliative expansion and explicative validation is historically regarded as the essence of design. 30 – 35 Its origins trace back to Page’s cyclical process of “Analysis, Synthesis, and Evaluation,” later systematized by Jones. 36 , 37 March subsequently applied Peirce’s inference modes to design via the Production-Deduction-Induction (PDI) model, explicitly mapping abduction to “production.” 33 This iterative refinement perspective is widely supported across various nomenclatures (e.g., Mesarović , 38 Watts, 39 Matsuoka et al. 40 ). Furthermore, Takeda et al. formalized design as an iterative logical process of abductive suggestion, deductive evaluation, and circumscription. 32 Crucially, circumscription dynamically rewrites premise knowledge in response to contradictions, extending the inference space rather than merely applying fixed knowledge. Similarly, Schön’s Reflection-in-action describes design as a “reflective conversation with the situation.” 3 When a designer’s “move” elicits unexpected “backtalk” (surprise), they reframe the problem on the spot and proceed to new exploration, navigating iterative stages of sensemaking and future framing. 41 – 43 Gero and Kannengiesser’s Function-Behavior-Structure (FBS) ontology describes this reflection as constructive memory driven by misalignment between the “expected” and “interpreted” worlds. This dynamic rewriting of the state space is fundamentally an act of ampliative inference. 44 A comparable rhythm is explicitly articulated in the British Design Council’s “Double Diamond” model, 45 where both problem-finding and problem-solving phases follow a divergence–convergence pattern. Thus, from computational logic to ontologies and practical reflection, design research universally recognizes this dynamic interplay of exploratory, ampliative expansion and convergent, explicative validation as the fundamental structure of design activity. The engine that intrinsically drives this cognitive cycle is the fundamental motivation directed toward information acquisition and the resolution of uncertainty: namely, "curiosity". 46–49 Recent research proposes frameworks like the Novelty-Seeking Model (NSM), which views novelty seeking as dynamically regulated by states of mind managing top-down and bottom-up processing. 50 , 51 Similarly, the Question-Asking in Information Seeking (QuInS) framework illustrates how recognizing a knowledge gap triggers iterative cycles of question formulation and evaluation. 52 Furthermore, Seiler and Dan distinguish between boredom—an information "hunger" driving broad, unspecific exploration—and curiosity—an "appetite" fostering targeted, knowledge-enriching behavior. 53 These functional distinctions manifest in specific knowledge-building styles: the “hunter” (tightly connected networks), the “busybody” (loosely connected, diverse topics), and the “dancer” (creative leaps across disconnected areas). 54 , 55 Recent advances allow these semantic memory structures to be quantified using graph-theoretical metrics. For example, the clustering coefficient (CC) reflects local interconnectedness; high CC coupled with short path lengths characterizes the “small-world” organization often seen in creative individuals. Global and local efficiency (GE, LE) represent information transmission ease, where shorter path lengths serve as a robust metric for semantic distance, 56 facilitating access to remote associations. Finally, modularity (Q) captures network segregation into subcommunities, where lower Q indicates more integrated, flexible semantic networks. 57 , 58 Together, these structural properties correlate with individual differences in creativity, particularly in tasks requiring remote associations and divergent thinking. 57 , 58 These diverse knowledge-building styles and their quantitative differences reflect two functionally distinct forms of epistemic desire. 59 , 60 The origins of this concept trace back to the classical definition by Berlyne, 61 who distinguished curiosity into "diversive curiosity," which seeks to avoid boredom and pursue broad stimulation or novelty, and "specific curiosity," which aims to resolve specific uncertainties or gaps in knowledge. 51 , 54 Crucially, these two forms of curiosity can be interpreted as having a functional correspondence with the aforementioned reasoning processes. Diversive curiosity is characterized by directing attention toward unknown territories that the current predictive model cannot capture—a trait that inherently aligns with the broad exploration sought by exploratory, ampliative reasoning. Conversely, specific curiosity seeks detailed information to reduce identified uncertainties, thereby supporting the model refinement driven by convergent, explicative reasoning. 54 The antagonistic interaction between these two curiosities regulates the agent's arousal level, configuring the design process as an inquiry cycle that autonomously transitions between "exploration of the unknown (entropy increase)" and "deepening of understanding (entropy decrease). 21 , 61 Thus, curiosity functions as a meta-cognitive controller that mediates the exploration-exploitation trade-off to maximize long-term information gain. 62 , 63 Computationally framing this exploration-exploitation cycle via prediction error minimization, Becker and Cabeza 64 and Van de Cruys et al. 65,66 provide critical insights. They posit that curiosity reflects expected information gain—estimating future model updates based on current prediction errors. In contrast, the aha experience corresponds to actual information gain when new information resolves the error, functioning as an intrinsic reward for updating the model. 66 This duality of actual and expected information gain aligns perfectly with the mathematical structure of the ICM. 21 Fig. 1 illustrates the overall process of free energy reduction and information gain in the ICM. In the ICM, the information gain obtained by recognizing the causal state underlying an observation is defined as Kullback-Leibler divergence ( \(\:KLD\) ), quantifies the epistemic value associated with recognizing an observation. It encompasses convergent processes that transform uncertainty into known facts and restore model consistency, such as Schön’s sensemaking process of situational “backtalk” 3 or mismatch resolution in the FBS framework. 44 It is specific curiosity that seeks the maximization of this \(\:KLD\) ; by converging excessive arousal (confusion) into order as if climbing the right side of the Wundt curve, 67 it computationally executes what Peirce termed "explicative reasoning" and model refinement. 24 Conversely, the maximum information gain expected from updating prior beliefs is defined as Bayesian Surprise ( \(\:BS\) ), termed the expected epistemic value arising from model update or learning. \(\:BS\) reflects the novelty of a recognized observation and has been shown to correlate with human surprise responses to novel stimuli. 68 Diversive curiosity drives the maximization of this \(\:BS\) , increasing arousal from a state of low arousal (boredom) by moving up the left side of the Wundt curve. 67 In design, this drives the active search for unknown variables to break existing constraints. The temporary increase in predictive uncertainty induced by pursuing \(\:BS\) aligns with entropy modulation and relaxed cognitive control. 22 , 23 Crucially, this state triggers Peirce’s ampliative reasoning (abduction). 24 Thus, \(\:BS\) maximization functions as a dynamic engine that expands the state space—the essence of creative design. 1 To provide a mathematical basis for these dynamics, analyses using a Gaussian generative model with a uniform noise likelihood (Fig. 2) demonstrate that these two types of information gain, along with their sum ( \(\:IG=KLD+BS\) ), form inverted-U shaped functions with respect to surprise \(\:S\) , which represents information about an observation (Fig. 3). Since \(\:S\) correlates with arousal potential, 68–70 these findings provide a formal mathematical foundation for Berlyne’s arousal potential theory, 61 demonstrating that hedonic value peaks at an optimal level of arousal on the Wundt curve. 67 In conclusion, the ICM realizes an ideal inquiry cycle where uncertainty dynamically fluctuates around optimal arousal via the alternating maximization of \(\:KLD\) (uncertainty resolution) and \(\:BS\) (novelty pursuit). 21 , 61 This framework provides a robust foundation seamlessly bridging psychological theories of curiosity, computational free-energy minimization, and design practice. It explains how designers transform the unknown into the known, achieving genuine creativity characterized by both novelty and aptness. Box 1 (Supplementary) summarizes the correspondence between these concepts, information-based metrics, and their cognitive interpretations. To formulate the core inquiry of this study, we draw upon theoretical predictions derived from the ICM. 21 Simulations manipulating prior variance ( \(\:{s}_{p}\) ) —the inverse of predictive precision—reveal two critical properties that form our computational hypotheses: Enhancement of Information Gain: Decreasing predictive precision (increasing \(\:{s}_{p}\) ) raises the maximum values of \(\:BS\) , \(\:KLD\) , and \(\:IG\) (Fig. 4A, Fig. 5), computationally facilitating both the exploration of the unknown (diversive curiosity) and the resolution of uncertainty (specific curiosity). Shift in Optimal Arousal: As prior variance increases, the surprise level maximizing \(\:BS\) (optimal surprise, \(\:{S}_{BS}\) ) rises, while the level maximizing \(\:KLD\) ( \(\:{S}_{KLD}\) ) decreases (Fig. 4B, Fig. 5). This expanded cognitive "tolerance" for higher surprise fosters broader exploration during divergent thinking. Consequently, we hypothesize that decreasing predictive precision during divergent thinking will increase both the maximum information gain and the optimal arousal of \(\:BS\) associated with novelty. The present study empirically tests these predictions by modulating neural activity. 1.3 Alpha Oscillations: A Neural Mechanism for Modulating Predictive Precision In creative design, commonsense solutions and habitual thinking can act as strong constraints, consistent with design fixation effects in which prior examples or entrenched knowledge bias subsequent ideation. 71 – 73 Within a predictive-processing framework, such constraints can be interpreted as high-precision priors—predictions shaped by past experience that are relatively resistant to updating. 20 , 74 , 75 To generate novel ideas, these strong predictions need to be attenuated, thereby allowing uncertainty and facilitating broader exploration of the solution space. This conceptualization closely aligns with the REBUS (relaxed beliefs under psychedelics) model. 76 Their framework formally demonstrates that relaxing the precision of high-level priors increases systemic entropy, thereby liberating the brain from rigid, entrenched networks and enabling highly flexible, divergent exploration. Thus, the essence of such creative thinking, often described as “getting rid of preconceptions” or “thinking outside the box” can be understood, within the ICM framework, as a strategic lowering of predictive precision to create a receptive state for the exploration of new information. In this context, an important question arises: what neural mechanisms regulate such adjustments in predictive precision during creative thinking? Cognitive neuroscience research over the past decades has shown that alpha oscillations (8–12 Hz) in EEG are involved in various cognitive processes, including the control of predictive precision. 77 , 78 In the visual cortex, increases in alpha activity have been reported to temporarily suppress the processing of visual input, allowing top-down predictions generated by the internal model to dominate. 79 , 80 Conversely, when alpha activity decreases, sensory information that does not match predictions is emphasized, prediction errors are amplified, and the updating of the internal model is facilitated.​ 81,82 This inhibitory function of alpha oscillations is not regarded as a passive state, but rather as a process of active inhibition. 83 Alpha oscillations are thought to modulate the precise timing of neuronal spiking (action potentials), thereby enhancing the signal-to-noise ratio. Through this mechanism, alpha activity functions as a sensory gate, blocking task-irrelevant information and controlling access to relevant information processing. 84 , 85 In creativity research, alpha oscillations are reported to play a central role. Reviews by Fink and Benedek synthesize these findings to comprehensively demonstrate the role of alpha oscillations in the neural basis of creative thinking. 86 Specifically, increased alpha activity is associated with internally directed attention, the suppression of sensory input, and the inhibition of obvious semantic associations. 86 During creative thinking, specifically divergent thinking, alpha power has been shown to increase in frontal and parietal regions. 87 , 88 Notably, highly creative individuals exhibit greater alpha enhancement and are able to sustain this increase for longer durations. 89 , 90 Furthermore, alpha power follows a characteristic temporal trajectory: it peaks at the onset of idea generation, subsequently decreases, and increases again immediately prior to the response. 91 This dynamic may reflect a process in which strong top-down control defines the search space during the initial phase, followed by the execution of the actual search. A recent study demonstrated that alpha power increases during the generation of distant semantic associations. Furthermore, they found that the explicit goal to be creative enhances alpha phase synchronisation from left to right temporal brain areas, reflecting top-down control of semantic search. 92 This alpha synchronization mediates internal attention by blocking external visual inputs and concentrating neural resources on internal mental imagery and modes of thought. 93 , 94 Indeed, it is known that simply closing one’s eyes to block visual input is sufficient to improve performance in divergent thinking. 95 Consistent with these mechanisms, alpha oscillations in the right hemisphere have been linked to the generation of original ideas. 87 , 91 , 96 – 98 Specifically, in insight tasks such as the remote associates test, higher alpha power in the right hemisphere immediately before hint presentation has been shown to predict subsequent successful solutions achieved through insight. 99 Moreover, immediately prior to arriving at a solution via a sudden “Aha!” experience rather than analytical reasoning, marked increases in alpha activity have been observed in the right parietal, right temporal, and occipital regions. 100 – 104 According to the hypothesis proposed by Klimesch et al., 85 this increased alpha amplitude in task-relevant regions facilitates inhibition by silencing weakly excited neural populations (representing noise or obvious associations), thereby allowing semantically distant and creative associations to emerge into consciousness. While the aforementioned EEG studies provide valuable insights into the neural correlates of ideation, many of these findings remain correlational. To establish whether alpha oscillations are a causal factor in creative thinking, it is necessary to verify causality using methods such as brain stimulation. Research using transcranial Alternating Current Stimulation (tACS), which can enhance neural oscillations at specific frequencies, is beginning to demonstrate this causality. 105 For instance, applying alpha-frequency tACS to the frontal lobe has been reported to improve divergent thinking performance, a result interpreted as a strengthening of inhibitory top-down control. 106 Furthermore, alpha tACS applied to parieto-occipital regions has been shown to strongly suppress external visual information and indirectly enhance Default Mode Network (DMN) activity, thereby promoting an internal mode of thought and improving the originality and elaboration of ideas. 107 Moreover, because tACS allows for frequency specification, it has been verified that the involvement in creativity is not merely due to electrical stimulation in itself, but is an effect specific to the "alpha rhythm." Grabner et al. compared alpha (10 Hz) and gamma (40 Hz) stimulation, proposing a framework to examine the specific functional role of the alpha band in creativity. 108 Beyond frequency specificity, a comprehensive understanding of creative mechanisms must also account for the specificity of the “stimulation site”. In this regard, the fact that the right temporal lobe is a critical region for processing semantic associations and retrieving conceptual knowledge cannot be overlooked. 109 – 112 Consistent with this anatomical and functional neural basis, there is accumulating evidence that stimulation of the right temporal region facilitates insight tasks. 113 In particular, Luft et al. causally demonstrated that alpha-frequency stimulation to the right temporal area inhibits strongly linked, obvious semantic associations, thereby facilitating connections to more remotely related concepts. 114 Furthermore, as a recent finding, Ghani et al. reported that up-regulating right temporal alpha oscillations guides the brain into a receptive state, which in turn promotes the occurrence of insight. 115 This concept of a "receptive brain state" aligns strongly with the mechanism of creative thinking discussed in this paper: lowering prediction precision to enable the exploration of novel information. Taken together, these findings suggest that alpha oscillations, especially in the right temporal region, constitute a neural basis for suppressing obvious semantic associations and enabling broad exploration within semantic space. Within the framework of the Bayesian brain hypothesis, such neural activity can be interpreted as a process that reduces predictive precision, thereby creating a cognitive state that facilitates the exploration of novel associations. 1.4 Objectives This study applied the ICM to the domain of creative design to examine how controlling uncertainty in the brain via tACS-induced right temporal alpha oscillations influences creativity and information content of ideas in problem-solving and problem-finding, particularly during divergent thinking processes. By associating these oscillations with reduced predictive precision, the present study links free-energy-based theoretical modeling with neurophysiological evidence, elucidating how uncertainty and information acquisition facilitate creative inquiry. The findings offer implications for evidence-based strategies to foster creativity in both educational and professional design contexts. 2 Materials and Methods 2.1 Participants We recruited 43 participants (22 females, aged 18–32 years, M = 21.1 years, SD = 2.8 years) from XXX. All participants were fluent in English and interested in design. Exclusion criteria included a history of neurological disorders, pregnancy, previous neurosurgical procedures, metal or medical implants, or consumption of alcohol or recreational drugs within 24 h of the session. Participants received course credit or £10/h. The research was approved by the College of Health, Medicine and Life Sciences Research Ethics Committee (DLS) at Brunel University of London (Reference: 44385-LR-Oct/2023-47425-2). All participants provided written informed consent after being informed of the study’s purpose. 2.2 Experimental design Participants were randomly assigned to one of the three conditions: left alpha (hemisphere control, N = 15 ); right alpha ( N = 13); right gamma (frequency control, N = 15). There were no significant differences in age or gender distribution across conditions (age: F (2,40) = 1.94, p = .157, η p 2 = .088; gender: X 2 (2, N = 43) = 1.34, p = .513). The experiment was conducted in a double-blind manner; neither participants nor experimenters knew the assigned stimulation conditions. Participants engaged in a design creativity task in each phase: before stimulation (Pre), during stimulation (Stim), and after stimulation (Post). In Pre phase, participants also completed a relatedness judgement task following the design creativity task. Figure 6A provides an overview of the experimental design. 2.3 EEG and tACS protocol Both EEG recording and tACS were conducted using a Starstim (Neuroelectrics, Barcelona, Spain) with twenty channels. During the Pre/Post phase, EEG was recorded at a 500 Hz sampling rate, with two reference electrodes (CMS and DRL) vertically aligned on the right cheekbone. During the Stim phase, high-definition tACS (HD-tACS) was applied to the temporal region at 2 mA (baseline–peak), with 6 s ramp periods. T7 (left) or T8 (right) served as the target electrode, with five surrounding electrodes as returns (20% each: left, F7/F3/Cz/P3/P7; right, F8/F4/Cz/P4/P8). Gamma stimulation was set at 35 Hz. Alpha stimulation used each participant’s individual alpha peak frequency (IAF), defined as the peak power in the 8–12 Hz band during divergent thinking in the Pre problem-solving task. Online estimates were approximately 8.3 Hz, but offline recalculation after preprocessing yielded slightly higher true IAFs (right: 9.50 Hz, left: 8.95 Hz), indicating that stimulation was delivered marginally below IAF. Electric-field simulations using Finite Element Method 116 (NIC v2.1.3.4 StimViewer) confirmed that the montage produced electric field strengths above the 0.3 mV/mm threshold for neuronal modulation (Fig. 6B). 117 2.4 Design creativity task This task evaluated design thinking using the Double Diamond design process model, 45 which emphasizes problem finding and problem solving through divergent and convergent thinking. Accordingly, the experiment included two components: a problem-solving task and a problem-finding task, each comprising divergent thinking (DT) and convergent thinking (CT) phases (Fig. 6C). Participants rested for 30 s before each task and received both oral and on-screen instructions. Different problems or themes were provided for each phase (Table 1 ), and responses were entered via keyboard. Table 1 Problems and Themes Used in the Design Creativity Tasks for Each Phase Task Phase Problems and Themes Problem-solving Pre People with hearing impairments may not notice fire alarms, leading to compromised safety. Stim People with visual impairments may not detect approaching quiet vehicles, leading to potential accidents. Post People with speech disorders may struggle with communication in emergencies, leading to delays in crucial assistance. Problem-finding Pre A future in 2050 where technological changes to the human body, such as gene editing and cybernetic enhancements, have advanced. Stim A future in 2050 where the technological advancements in transport, such as autonomous cars and unmanned aerial vehicles, have become commonplace. Post A future in 2050 where the technology enabling human colonization of Mars has advanced. 2.4.1 Problem-solving task Participants were presented with specific social problems and asked to be creative and come up with solutions while imagining the user’s perspective. This task included five phases: (1) problem scoping, listing as many requirements and constraints for solutions as possible (3 min); (2) evaluation of these items, rating their importance on a 7-point Likert scale and indicating which to retain (no time limit); (3) divergent thinking (DT), generating as many different and original solutions as possible (3 min); (4) solution evaluation, rating solutions for originality, confidence, and "aha experience" strength on a 7-point scale (no time limit); and (5) convergent thinking (CT), developing the most creative solution by elaborating on or combining ideas from the DT phase (5 min). 2.4.2 Problem-finding task Participants were presented with a specific theme envisioning the future in 2050 and asked to be creative and identify what kind of problems or issues might arise in such a future. This task consisted of three phases: (1) DT, listing as many different and original problems as possible (3 min); (2) idea evaluation, rating these problems for originality, confidence, and "aha experience" strength on a 7-point scale (no time limit); and (3) CT, identifying the most original and important potential problem, referring to their DT ideas (5 min). 2.5 Relatedness judgement task Before stimulation, participants intuitively rated the semantic relatedness of 20 words (190 pairs, Table 2 ) on a visual analogue scale from 0 (unrelated) to 100 (strongly related) (Fig. 6D). Semantic memory networks were constructed by representing words as nodes and edge weights as relatedness ratings, yielding weighted undirected networks. 58 To evaluate whether the stimulation groups possessed comparable baseline cognitive profiles before the intervention, we analyzed the structural properties of their semantic memory networks. Specifically, we calculated standard network properties, CC, GE, LE, and Q, which are known predictors of individual creativity, 57,58 and compared them across stimulation conditions using a permutation-based F-test with 10,000 iterations; data from two participants (one from left alpha, one from right gamma) were excluded due to system error. Table 2 Words Used in the Relatedness Judgement Task Near Words Far Words Irrelevant Words sound, infrared, wearable, touch, sensor, vibration, Bluetooth flag, microscope, compass, ant, perfume, chameleon, tap-dance book, basket, calendar, chair, mug, pencil The same 20 words also served as primes for the problem-solving task in the Stim phase. Seven were semantically close to the problem and served as direct hints (Near words), seven were distant and served as indirect hints (Far words), and six were unrelated (Irrelevant words). After the problem-solving task in the Stim phase, participants indicated whether each word was used as a hint in both DT and CT phase. Hint usage rates (proportion of "yes" responses) were averaged for each category (Near, Far, Irrelevant). We expected highest rates for Near words, followed by Far and Irrelevant, and tested this using a Kruskal–Wallis test with Dunn’s post-hoc multiple comparisons (Holm correction). Finally, we examined the effect of stimulation on hint usage rates for each category. Given that right temporal alpha oscillations actively inhibit strong semantic associations to promote distant concept exploration, 114 we hypothesized that Far-word usage would be greater in the right alpha condition than in controls, tested using a Friedman test with post-hoc Wilcoxon signed-rank tests (Holm correction). 2.6 Idea ratings The ideas generated in the design creativity task were evaluated using self-ratings and information-based metrics. Participants who provided only one idea during the DT phase in any of the three phases (Pre, Stim, Post) were excluded from this analysis due to insufficient divergent thinking. The final sample sizes were: Problem-solving task: left alpha ( N = 13), right alpha ( N = 13), right gamma ( N = 12); Problem-finding task: left alpha ( N = 14), right alpha ( N = 12), right gamma ( N = 14). 2.6.1 Self-ratings As described in Section 2.4, participants self-rated ideas from the DT phase. For each evaluation metric, we calculated within-participant averages for Pre, Stim, and Post phases. These averages were then Z-score normalized across participants, with outliers excluded using the interquartile range (IQR) approach. Since the problems and themes for each phase (Pre, Stim, Post) were fixed and presented in a predetermined order without counterbalancing (Table 1 ), we compared conditions using one-way ANOVA per phase rather than a mixed ANOVA. Significant effects were followed by post-hoc Dunnett’s tests (p-values adjusted via multivariate t-distribution) comparing the right alpha condition against both controls. 2.6.2 Information-based metrics We calculated Information-based metrics for ideas using a custom computational system based on the free energy principle, 118 using the English Wikipedia corpus (enwiki, September 2023). Computational system overview. The generative model is factorized as \(\:p\left(s,o\right)=p\left(o|s\right)p\left(s\right)\) . The prior \(\:p\left(s\right)\) represents the occurrence probability of prior words (starting point of ideation), defined as a set of words \(\:S=\left\{{s}_{i}|1\le\:i\le\:{N}_{s}\right\}\) . The observation model \(\:p\left(o|s\right)\) represents the probability of generating directional words (ideation directions) from these prior words, defined as a set of words \(\:O=\left\{{o}_{i}|1\le\:i\le\:{N}_{o}\right\}\) . Table 3 details the specific sets \(\:S\) and \(\:O\) used across all task phases. Table 3 Prior and Directional Word lists for Information-based metrics of ideas in the Design Creativity Tasks Task Phase \(\:S\) : Prior words Entropy \(\:O\) : Directional words Problem-solving Pre people, hearing, impairment, loss, deaf, deafness 8.39 notice, detect, aware, warning, alert, fire, alarm Stim people, visual, vision, impairment, loss, blind, blindness 9.22 detect, notice, aware, warning, alert, approaching, quiet, vehicle Post people, speech, disorder, impairment 8.83 understand, assistance, response, instruction, communication, emergency Problem-finding Pre evolution, human, body, future, gene, editing, cybernetic, enhancement, biotechnology, augmentation 9.27 problem, issue, risk, concern, constraint, threat, uncertainty Stim autonomous, transport, future, advancement, car, unmanned, vehicle, aircraft 9.79 problem, issue, risk, concern, constraint, threat, uncertainty Post migration, Mars, future, human, colonization, space, settlement 9.72 problem, issue, risk, concern, constraint, threat, uncertainty Prior distribution \(\:\varvec{p}\left(\varvec{s}\right)\) . To capture word polysemy and similarity, we smoothed the prior distribution using local co-occurrence. This was calculated by counting words within a ± 2-word window around the word \(\:s\) in each corpus sentence, excluding function words. To prevent underestimating \(\:s\) during smoothing, we included \(\:s\) itself in the occurrence count. The prior entropy, \(\:-\sum\:_{i=1}^{{N}_{s}}p\left({s}_{i}\right)\text{ln}p\left({s}_{i}\right)\) , measures the distribution’s spread, where higher entropy indicates lower precision. Across phases, entropy ranged from 8.39 to 9.22 for the problem-solving task and 9.27 to 9.79 for the problem-finding task (Table 3 ). Likelihood (observation model) \(\:\varvec{p}\left(\varvec{o}|\varvec{s}\right)\) . To calculate the probability of \(\:o\) given \(\:s\) , we used syntactic dependency relations to capture stronger grammatical connections than local co-occurrence. We performed dependency parsing on each corpus sentence, counting words dependent on the directional word \(\:o\) . To convert the resulting frequencies from both models into probability distributions, the co-occurrence frequency was expressed as \(\:C\left(x,y\right)/\left(C\left(x\right)C\left(y\right)\right)\) —where \(\:C\left(x,y\right)\) is the co-occurrence count, and \(\:C\left(x\right)\) , \(\:C\left(y\right)\) are the individual word counts—and subsequently normalized over \(\:y\) . Participant-derived word-level belief distribution \(\:{\varvec{q}}_{\varvec{i}}\left(\varvec{s}\right)\) . An idea was defined as a set of explicitly produced content words, \(\:W=\left\{{w}_{i}|1\le\:i\le\:{N}_{w}\right\}\) . For each word \(\:{w}_{i}\) , its precomputed corpus-based semantic distribution served as the individual word-level belief distribution \(\:{q}_{i}\left(s\right)\) . Idea-level metrics were derived by calculating the information-based metrics for each \(\:{q}_{i}\left(s\right)\) and averaging these values across \(\:W\) . This word-level computation was deliberately chosen over aggregating distributions beforehand to prevent the semantic dilution of highly original concepts; otherwise, the high surprise value of unique conceptual leaps could be smoothed out by more common words within the same idea. To isolate the core semantic vocabulary, standard stop words (including pronouns, conjunctions, prepositions, auxiliary verbs, and abbreviations) were excluded from \(\:W\) . Computing information-based metrics. Using \(\:p\left(s\right)\) , \(\:p\left(o|s\right)\) , and \(\:{q}_{i}\left(s\right)\) , we computed word-level metrics. \(\:{BS}_{i}\) was operationalized as the Kullback–Leibler divergence between the belief and the prior distributions: \(\:{BS}_{i}={D}_{KL}\left({q}_{i}\left(s\right)|p\left(s\right)\right)\) which quantifies the extent to which the participant-generated word-level belief distribution deviates from the semantic prior defined by the problem context. Surprise \(\:{S}_{i}\) measures deviation from the generative model: \(\:{S}_{i}={BS}_{i}+{U}_{i}\) . Here, \(\:{U}_{i}\:\) is an uncertainty term corresponding to the cross-entropy between \(\:{q}_{i}\left(s\right)\) and the observation model: \(\:{U}_{i}=-{\sum\:}_{s}{q}_{i}\left(s\right)\text{ln}p\left(o|s\right)\) . Idea-level metrics ( \(\:BS\) , \(\:S\) ) were then calculated by averaging these word-level values across all content words \(\:{w}_{i}\in\:W\) . Focusing on the DT phase across tasks and phases (Pre, Stim, and Post), we identified the maximum \(\:BS\) value among all ideas generated by each participant, defining it as max \(\:BS\) . The Surprise value of the specific idea that yielded this max \(\:BS\) was subsequently extracted and defined as \(\:{S}_{BS}\) . Statistical analysis. After Z-score normalization across participants and IQR-based outlier exclusion, metrics were compared across conditions using one-way ANOVA. Significant effects were followed by post-hoc Dunnett’s tests (p-values adjusted via multivariate t-distribution) comparing the right alpha condition against both controls. 3 Results 3.1 Relatedness judgement and the Acceptance of Semantically Distant Primes To confirm that there were no pre-existing differences in creativity between the stimulation groups, we conducted a permutation-based F-test on semantic memory network metrics. No significant differences were observed across conditions for any metric prior to stimulation. The observed F -statistics were: for CC, 0.314 ( p = .727); for GE, 0.267 ( p = .767); for LE, 0.136 ( p = .871); and for Q, 1.722 ( p = .187). To verify whether there was an expected gradation in the hint usage rates among the word categories (Near, Far, and Irrelevant) adopted in this study, we performed a Kruskal–Wallis test. Figure 7 shows the hint usage rate across word categories and conditions. As predicted, Near words had the highest rates (DT: Mdn = 41.86, IQR = 24.42; CT: Mdn = 37.21, IQR = 25.58), followed by Far (DT: Mdn = 2.33, IQR = 5.81; CT: Mdn = 2.33, IQR = 4.65), and Irrelevant words (DT: Mdn = 1.16, IQR = 2.33; CT: Mdn = 1.16, IQR = 2.33). We observed significant category differences in both DT, H (2) = 14.28, p < .001, η 2 = 0.752, and CT, H (2) = 15.70, p < .001, η 2 = 0.826. Post-hoc contrasts revealed Near words had significantly higher usage than both Far (DT: p = .020; CT: p = .022) and Irrelevant words (DT: p = .001; CT: p < .001). We observed no significant difference between Far and Irrelevant words (DT: p = .233; CT: p = .149). To evaluate the hypothesis that right temporal alpha stimulation promotes distant concept exploration by actively inhibiting obvious semantic associations, we conducted a Friedman test to examine the effect of stimulation on hint usage rates. The analysis revealed a significant main effect of stimulation specifically for Far words during the CT phase, X 2 (2) = 7.91, p = .019. However, post-hoc showed that the hint usage rate for Far words in the right alpha condition ( Mdn = 7.69, IQR = 3.85) was not significantly higher than the left alpha ( Mdn = 0.00, IQR = 6.67; p = .063) or right gamma ( Mdn = 0.00, IQR = 3.33; p = .063) conditions after Holm correction. There were no significant effects during the DT phase for Far words, X 2 (2) = 4.26, p = .119, and no significant effects of stimulation were observed for Near (DT: X 2 (2) = 2.00, p = .368; CT: X 2 (2) = 0.29, p = .867) or Irrelevant words (DT: X 2 (2) = 1.40, p = .497; CT: X 2 (2) = 0.00, p = 1.00). 3.2 Effects of Right Temporal Alpha Stimulation on Problem-Solving Task To evaluate the effect of right temporal alpha stimulation on ideas during the problem-solving task, we assessed subjective self-ratings and compared conditions using one-way ANOVA per phase. Figure 8 highlights changes in self-ratings during the DT phase of the problem-solving task. In Pre phase, we observed no significant differences across conditions for any evaluation metric: originality, F (2, 35) = 1.75, p = .188, η G 2 = 0.091; confidence, F (2, 35) = 1.19, p = .317, η G 2 = 0.064; aha strength, F (2, 35) = 1.22, p = .308, η G 2 = 0.065, indicating no pre-existing condition differences. In Stim phase, there were no significant differences between conditions for originality, F (2, 33) = 1.42, p = .257, η G 2 = 0.079; confidence, F (2, 35) = 1.96, p = .157, η G 2 = 0.101; or aha strength, F (2, 35) = 2.90, p = .068, η G 2 = 0.142. In Post phase, the effect of stimulation conditions was significant on self-rated originality, F (2, 35) = 5.04, p = .012, η G 2 = 0.224. Post-hoc contrasts identified significantly higher originality in the right alpha condition compared to both the left alpha condition, t (35) = 2.90, p = .012, Hedges’ g = 1.079, and the right gamma condition, t (35) = 2.55, p = .029, Hedges’ g = 1.301. In contrast, there were no significant differences for the other evaluation metrics, including confidence, F (2, 35) = 1.13, p = .336, η G 2 = 0.060; and aha strength, F (2, 35) = 3.05, p = .060, η G 2 = 0.148, across the conditions. Similarly, we analyzed the objective information-based metrics using the same one-way ANOVA approach. The results of the analysis on max \(\:BS\) during the DT phase of the problem-solving task are presented in Fig. 9A. In both Pre and Stim phase, no significant differences were observed between conditions: Pre phase, F (2, 33) = 0.04, p = .957, η G 2 = 0.003; Stim phase, F (2, 34) = 0.35, p = .706, η G 2 = 0.020. However, in Post phase, significant differences was observed, F (2, 34) = 4.16, p = .024, η G 2 = 0.197. Post-hoc contrasts revealed significantly higher max \(\:BS\) , t (34) = 2.32, p = .049, Hedges’ g = 0.890, in the right alpha condition compared to the left alpha condition. In contrast, no significant difference was found between the right alpha and the right gamma conditions, t (34) = 0.30, p = .938, Hedges’ g = 0.107. Figure 9B illustrates the results for \(\:{S}_{BS}\) during the DT phase of the problem-solving task. In both Pre and Stim phase, no significant differences were observed across conditions: Pre phase, F (2, 33) = 0.05, p = .956, η G 2 = 0.003; Stim phase, F (2, 34) = 0.35, p = .706, η G 2 = 0.020. In contrast, in Post phase, \(\:{S}_{BS}\) revealed significant effect, F (2, 34) = 4.14, p = .025, η G 2 = 0.196. Post-hoc tests indicated that the right alpha condition resulted in significantly higher \(\:{S}_{BS}\) compared to the left alpha condition, t (34) = 2.31, p = .049, Hedges’ g = 0.889. However, no significant differences in \(\:{S}_{BS}\) were observed between the right alpha and right gamma conditions, t (34) = 0.29, p = .939, Hedges’ g = 0.106. 3.3 Effects of Right Temporal Alpha Stimulation on Problem-Finding Task To evaluate the effect of right temporal alpha stimulation on ideas during the problem-finding task, we assessed subjective self-ratings and compared conditions using one-way ANOVA per phase. Figure 10 shows changes in self-ratings for ideas during the DT phase of the problem-finding task. First, similar to the problem-solving task, there were no significant differences between conditions in Pre phase for any evaluation metrics: originality, F (2, 37) = 2.58, p = .089, η G 2 = 0.123; confidence, F (2, 37) = 0.44, p = .646, η G 2 = 0.023; aha strength, F (2, 37) = 0.41, p = .666, η G 2 = 0.022. Second, in Stim phase, there were no significant differences between conditions for originality, F (2, 37) = 3.10, p = .057, η G 2 = 0.144; confidence, F (2, 37) = 2.41, p = .104, η G 2 = 0.115; or aha strength, F (2, 37) = 0.94, p = .040, η G 2 = 0.048. Finally, in Post phase, we observed a significant effect of stimulation condition on the originality, F (2, 37) = 6.18, p = .005, η G 2 = 0.250; confidence, F (2, 37) = 4.19, p = .023, η G 2 = 0.185; and aha strength, F (2, 37) = 4.17, p = .023, η G 2 = 0.184. Post-hoc comparisons revealed that originality was significantly higher in the right alpha condition than in both the left alpha condition, t (37) = 3.48, p = .003, Hedges’ g = 1.269, and the right gamma condition, t (37) = 2.31, p = .048, Hedges’ g = 0.993. For confidence, self-ratings in the right alpha condition were significantly higher than in the right gamma condition, t (37) = 2.77, p = .016, Hedges’ g = 1.267, but not significantly different from the left alpha condition, t (37) = 2.20, p = .062, Hedges’ g = 0.784. Aha strength was significantly higher in the right alpha condition compared to the left alpha condition, t (37) = 2.89, p = .012, Hedges’ g = 1.184, while the difference with the right gamma condition was not significant, t (37) = 1.48, p = .247, Hedges’ g = 0.587. Similarly, we analyzed the objective information-based metrics using the same one-way ANOVA approach. Figure 11 summarises the results of the analysis on information-based metrics (max \(\:BS\) and \(\:{S}_{BS}\) ) during the DT phase of the problem-finding task. Across all phases (Pre, Stim, and Post), no significant differences were found between conditions for either metric. For max \(\:BS\) (Fig. 11A), the main effect of condition was not significant in Pre phase, F (2, 30) = 0.90, p = .418, η G 2 = 0.057, Stim phase, F (2, 35) = 0.61, p = .550, η G 2 = 0.034, or Post phase, F (2, 35) = 0.18, p = .835, η G 2 = 0.010. Similarly, for \(\:{S}_{BS}\) (Fig. 11B), no significant main effects of condition were observed in Pre phase, F (2, 30) = 0.90, p = .418, η G 2 = 0.056, Stim phase, F (2, 35) = 0.61, p = .550, η G 2 = 0.034, or Post phase, F (2, 35) = 0.19, p = .830, η G 2 = 0.011. 4 Discussion The present study provides causal neurophysiological evidence linking right temporal alpha oscillations to the modulation of predictive precision during creative design cognition. Grounded in the FEP and the ICM, we hypothesized that decreasing predictive precision—computationally operationalized as an increase in prior variance—would facilitate the exploration of novel semantic spaces. By applying tACS at IAF to the right temporal lobe, we sought to temporarily attenuate top-down predictive constraints. The principal findings corroborate this overarching hypothesis: (1) during the problem-solving task, right temporal alpha stimulation significantly increased maximum information gain and optimal arousal of \(\:BS\) , alongside elevated self-ratings of originality; and (2) during the problem-finding task, stimulation enhanced subjective ratings of originality, confidence, and aha strength, despite an absence of significant changes in corpus-based objective information metrics. 4.1 Modulation of Predictive Precision in Problem-Solving In the problem-solving task, right temporal alpha stimulation led to a significant increase in \(\:BS\) ’s maximum information gain and its optimal arousal level compared to the hemispheric control (left temporal alpha). Furthermore, this stimulation enhanced the acceptance of semantically distant priming stimuli (Far words). These findings advance previous neurostimulation literature, which posits that right temporal alpha oscillations act as a neural mechanism for the active inhibition of obvious semantic associations. 114 , 115 Within the predictive processing framework, alpha oscillations have been shown to encode the precision of top-down predictions. 79 – 81 Strong predictions—shaped by habitual associations, established knowledge, or design fixation—act as high-precision priors that rigidly constrain the search space. 71 – 75 By artificially enhancing right temporal alpha rhythms, tACS effectively lowered the precision of these dominant prior beliefs, thereby increasing the variance of the probability distribution of the internal model. Computationally, this temporary reduction in precision expands the agent’s tolerance for higher surprise and promotes divergent exploration, directly resulting in the observed maximization of \(\:BS\) associated with highly original design solutions. 68 , 76 , 83 , 87 , 88 , 92 4.2 Task Context Dependency: Problem-Solving versus Problem-Finding While the problem-solving task exhibited robust increases in objective information metrics, the problem-finding task showed no significant changes in these corpus-based measures, despite a clear enhancement in subjective evaluations. This dissociation can be logically interpreted through the baseline informational characteristics of the tasks themselves. The prior distributions established for the problem-finding task inherently possessed higher entropy compared to the problem-solving task. Problem-finding requires navigating an ill-defined, highly ambiguous conceptual space with minimal external constraints, meaning the baseline prior precision is already low. 119 , 120 As illustrated in Fig. 4, because theoretical simulation indicates that maximum information gain and optimal arousal are highly sensitive to modifications in precision when prior precision is initially high, the impact of further reducing precision via alpha tACS was likely attenuated in the problem-finding condition. This attenuation aligns with the well-established state-dependency of non-invasive brain stimulation, where intervention outcomes are fundamentally bound by the baseline neural and cognitive state. 121 , 122 Conversely, the problem-solving task featured a structured problem-scoping phase that narrowed the context, establishing higher baseline precision. Thus, reducing predictive precision through right temporal alpha stimulation yielded a more pronounced shift in the exploration of the semantic space during problem-solving, as reflected in the information-based metrics. 123 These information-theoretic observations suggest that the clarity of prior knowledge or context in a task, namely how clearly the problem space is defined, is critical for information gain and creative exploration. 4.3 Dissociation Between Subjective Evaluations and Objective Metrics The observation that subjective ratings (originality, confidence, and aha strength) increased in the problem-finding task without corresponding increases in objective \(\:BS\) reflects a well-documented discrepancy between subjective and objective creativity measurements. 124 – 126 Information-based metrics calculated via a static Wikipedia corpus capture the semantic distance of concepts in generalized human knowledge. In contrast, subjective evaluations rely on the dynamic exploration of each participant’s idiosyncratic semantic memory networks. When the right temporal alpha tACS suppressed dominant associations, it allowed participants to internally explore more distant concepts. The sudden successful bridging of an ambiguous knowledge gap generates an instantaneous resolution of internal prediction errors. Neurobiologically, this sharp drop in uncertainty functions as an intrinsic reward mediated by dopaminergic pathways, which manifests consciously as a strong "Aha" experience and heightened confidence. 65 , 127 – 133 Therefore, the elevation in subjective scores suggests that the stimulation successfully promoted internal semantic restructuring and an active inference process, generating strong feelings of insight and originality, even when the generated ideas did not register as statistically distant within the generalized macro-corpus parameters. 4.4 Neurophysiological Mechanisms of Offline tACS Effects Notably, the significant effects of right temporal alpha stimulation on both information-based metrics and subjective ratings emerged during the Post phase rather than concurrently during the Stim phase. This temporal delay is consistent with recent literature delineating the mechanisms of tACS. While online effects are generally attributed to the immediate entrainment of endogenous oscillations, 134,135 offline aftereffects are driven by neuroplastic changes, specifically spike-timing-dependent plasticity (STDP) and strengthening the synapse through long-term potentiation (LTP). 136 , 137 Because the tACS in this study was administered at frequencies marginally below each participant’s true offline-calculated IAF, the stimulation likely satisfied the preconditions for STDP, whereby presynaptic activity consistently precedes postsynaptic firing, leading to robust synaptic strengthening. This extended plasticity facilitated the sustained state of reduced predictive precision necessary for the creative tasks performed after the stimulation ceased. 138 , 139 4.5 Limitations and Future Directions Several methodological limitations must be acknowledged when interpreting these findings. First, the relatively small sample size may have limited statistical power, given the high inter-individual variability in creative cognition 140 and individual responsiveness to tACS. 141 Second, while IAFs were utilized, the tACS protocol lacked real-time phase-locking to endogenous brain rhythms, which can introduce variability into the neuromodulatory outcomes. 142 Future studies leveraging closed-loop, phase-locked HD-tACS protocols concurrently with neuroimaging will be necessary to isolate precise spatiotemporal network dynamics. Finally, because the problem-finding task consistently followed the problem-solving task, the neuroplastic aftereffects of tACS might have gradually decayed. 138 Future experimental designs must counterbalance task order to definitively rule out time-dependent attenuation. Nevertheless, the observation of significant enhancements in subjective ratings strongly indicates that the neuromodulatory influence on internal evaluative processes remained robust even in the latter half of the experiment. Thus, the dissociation between objective metrics and subjective experiences observed in this task is more likely attributable to its inherently high baseline uncertainty, rather than merely the fading of stimulation effects. Beyond these methodological refinements, the present findings open critical avenues for advancing design research. While we utilized neurostimulation to artificially lower predictive precision, a fundamental question for design science is how designers can self-regulate this cognitive state. Future research must clarify the factors that modulate predictive precision. Recent cognitive models propose that creative thought is shaped by the interplay of deliberate and automatic constraints on spontaneous thought. 16 , 143 , 144 Building on this framework, it is highly promising to hypothesize that the predictive precision—which acts as a strong top-down constraint on the search space—targeted in our study is primarily modulated by "deliberate constraints" actively set by designers (e.g., goal-directedness, evaluative thinking) and "automatic constraints" operating unconsciously (e.g., preconceptions, expertise bias, emotional bias, and habitual thinking). As a subsequent step, future studies should investigate the extent to which these constraining factors can be actively relaxed or regulated without external brain stimulation, by employing established design strategies and ideation tools (e.g., forced associations, random word stimulation, or intentional reframing). Furthermore, the current study assessed isolated, short-term ideation tasks performed by individuals. However, real-world design typically unfolds over weeks or months, often within multidisciplinary teams. 43 , 145 Therefore, it is essential to investigate how the ICM and the mechanism of uncertainty modulation function within such complex, collaborative practical projects. Extending this research to highly ecologically valid settings will bridge the gap between neurocognitive principles and practical design processes. 5 Conclusion This study provides causal neurophysiological evidence bridging the theoretical frameworks of the Bayesian brain and the Inquiry Cycle Model (ICM) with the practical domain of creative design cognition. By demonstrating that upregulating right temporal alpha oscillations effectively lowers top-down predictive precision, our findings reveal a neural mechanism for relaxing rigid semantic priors to facilitate the generation of highly original ideas. Crucially, we highlight that the magnitude and nature of this creative enhancement are context-dependent, fundamentally modulated by the baseline uncertainty of the task. In more defined problem-solving scenarios, reducing precision significantly increases objective Bayesian surprise (maximum information gain and optimal arousal). Conversely, in highly ambiguous problem-finding contexts where prior precision is inherently low, the intervention primarily amplifies the internal, subjective experience of insight, confidence, and originality. Ultimately, by mapping these neurophysiological and information-theoretic dynamics onto the Free Energy Principle, this research offers a mechanistic understanding of how designers strategically embrace and resolve uncertainty to achieve genuinely novel solutions. Declarations Author contribution K.K.: Conceptualization, Methodology, Data curation, Investigation, Project administration, Validation, Formal analysis, Funding acquisition, Visualization, Software, Writing - Original Draft, Writing - Review & Editing. H.Y.: Conceptualization, Methodology, Funding acquisition, Writing - Review & Editing. S.H.: Software, Writing - Review & Editing. Y.N.K.: Conceptualization, Methodology, Software, Writing - Review & Editing. C.D.B.L.: Conceptualization, Methodology, Data curation, Investigation, Project administration, Validation, Resources, Supervision, Software, Writing - Review & Editing. All authors have read and approved the final version of the manuscript. Funding We were supported by JSPS Overseas Research Fellowships and JSPS KAKENHI Grant Number JP25H01132. Acknowledgements We thank Anum Hussain, Charlotte Basso, and Eleonora Canino for helping to collect EEG data. We also thank Kakeru Hashimoto for sharing the code that formed the basis of the information-theoretic calculations used in this study. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Ethics statement The research was approved by the College of Health, Medicine and Life Sciences Research Ethics Committee (DLS) at Brunel University of London (Reference: 44385-LR-Oct/2023-47425-2). Data availability statement The data and analysis code that support the findings of this study are openly available in OSF at https://doi.org/10.17605/OSF.IO/KRY8Q. Declaration of Generative AI and AI-assisted technologies in the writing process During the preparation of this work the authors used ChatGPT (OpenAI) and Gemini (Google) in order to improve the clarity and language quality of the manuscript. 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Koizumi","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-4573-8319","institution":"The University of Tokyo Graduate School of Engineering Department of Mechanical Engineering","correspondingAuthor":true,"prefix":"","firstName":"Koji","middleName":"","lastName":"Koizumi","suffix":""},{"id":607883329,"identity":"9e26f567-f5bc-4019-bc53-e68b67cc7d1a","order_by":1,"name":"Hideyoshi Yanagisawa","email":"","orcid":"https://orcid.org/0000-0002-0175-7537","institution":"The University of Tokyo Graduate School of Engineering Department of Mechanical Engineering","correspondingAuthor":false,"prefix":"","firstName":"Hideyoshi","middleName":"","lastName":"Yanagisawa","suffix":""},{"id":607883330,"identity":"000f2adb-1f8b-427a-9470-d1527750e3ac","order_by":2,"name":"Shimon Honda","email":"","orcid":"","institution":"The University of Tokyo Graduate School of Engineering Department of Mechanical Engineering","correspondingAuthor":false,"prefix":"","firstName":"Shimon","middleName":"","lastName":"Honda","suffix":""},{"id":607883331,"identity":"39c0289a-565e-4e0e-9d38-ceaafed10b49","order_by":3,"name":"Yoed Nissan Kenett","email":"","orcid":"https://orcid.org/0000-0003-3872-7689","institution":"Technion Israel Institute of Technology Faculty of Data and Decision Sciences","correspondingAuthor":false,"prefix":"","firstName":"Yoed","middleName":"Nissan","lastName":"Kenett","suffix":""},{"id":607883332,"identity":"a28e1086-d6d4-4320-bde5-e30a06bebd54","order_by":4,"name":"Caroline Di Bernardi Luft","email":"","orcid":"https://orcid.org/0000-0002-3293-3898","institution":"Brunel University of London College of Health, Medicine and Life Sciences","correspondingAuthor":false,"prefix":"","firstName":"Caroline","middleName":"Di Bernardi","lastName":"Luft","suffix":""}],"badges":[],"createdAt":"2026-03-17 23:08:59","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9152871/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9152871/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104961225,"identity":"46ad6a57-c9a7-4d8b-ba48-ec61caad139a","added_by":"auto","created_at":"2026-03-19 08:58:25","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":384124,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/9a0c0fd65ee07a0adb6d4d9c.png"},{"id":104961166,"identity":"473fd40a-98c9-45e7-b0f4-6828a5d27523","added_by":"auto","created_at":"2026-03-19 08:58:02","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":571846,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/73c121265bc19530104f8d8d.png"},{"id":104961172,"identity":"9aba17fb-57f6-41f5-a0db-ea70f05fd3b3","added_by":"auto","created_at":"2026-03-19 08:58:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":817731,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/5e17a4a9c88563f8877fbd95.png"},{"id":104961231,"identity":"a8b6ff3a-1c25-4739-9b56-4c23eb82ef2b","added_by":"auto","created_at":"2026-03-19 08:58:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1591172,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/8797fff281378f46a6966d1c.png"},{"id":104961068,"identity":"5027d234-45dc-4abe-9bc0-a25276736ea6","added_by":"auto","created_at":"2026-03-19 08:57:56","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":536758,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/1100d697aaf171760ae141ea.png"},{"id":104961182,"identity":"3b42f651-9e70-4318-9f8e-7c5734014a59","added_by":"auto","created_at":"2026-03-19 08:58:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":14612474,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/9c15fe077a4dcf750915e8a8.png"},{"id":104961277,"identity":"05653206-6c73-43e9-8c93-9cc15038f9dd","added_by":"auto","created_at":"2026-03-19 08:58:41","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2713738,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/ebe54f6002faa79a8ecce1ce.png"},{"id":104961232,"identity":"db51ce0d-9bc7-4eee-9ad6-c1c6a3883b3d","added_by":"auto","created_at":"2026-03-19 08:58:27","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2195221,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/6410f338fc6f715269791528.png"},{"id":104961226,"identity":"474d2a4f-f6db-43ea-8a19-f5c787a558e8","added_by":"auto","created_at":"2026-03-19 08:58:25","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1614406,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure9.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/6a472c26aa057b34c14970cc.png"},{"id":104961217,"identity":"9e08b457-b658-4064-ba7d-4e46af05f0b1","added_by":"auto","created_at":"2026-03-19 08:58:17","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":2362414,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure10.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/978a139274602782f86c3024.png"},{"id":105035181,"identity":"67f7120b-3039-42d8-9df6-a870b356b964","added_by":"auto","created_at":"2026-03-20 07:25:38","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":1704164,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Legend not included with this version.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Figure11.png","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/faee4d0e7e371b49301d50a4.png"},{"id":105562553,"identity":"3523324d-3144-4929-bdf7-475c5f78d133","added_by":"auto","created_at":"2026-03-27 12:42:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":30295347,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/a0168c71-c1fa-4938-824c-a6de27826778.pdf"},{"id":104961274,"identity":"f2d9df2e-8b71-439a-bd9c-e78961c5a7d3","added_by":"auto","created_at":"2026-03-19 08:58:41","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":464039,"visible":true,"origin":"","legend":"","description":"","filename":"6supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/d2be38679636059409d50d6b.docx"},{"id":104961119,"identity":"0291529c-867c-45b3-a3ab-7019ec41595a","added_by":"auto","created_at":"2026-03-19 08:57:59","extension":"tif","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":10835846,"visible":true,"origin":"","legend":"","description":"","filename":"graphicalabstract.tif","url":"https://assets-eu.researchsquare.com/files/rs-9152871/v1/3bdc50e0f02bcd657ace41f4.tif"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEmbracing Uncertainty: Reducing Predictive Precision in Bayesian Inference Enhances Novelty in Creative Design\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Highlights","content":"\u003cp\u003eRight temporal alpha oscillations relate to reduced Bayesian predictive precision.\u003c/p\u003e\n\u003cp\u003eReduced precision boosts information gain and arousal of Bayesian surprise.\u003c/p\u003e\n\u003cp\u003eReduced predictive precision via right temporal alpha tACS enhances idea originality.\u003c/p\u003e\n\u003cp\u003eTask context clarity modulates the effect of reduced predictive precision.\u003c/p\u003e\n\u003cp\u003eFindings validate the Inquiry Cycle Model for creative design cognition\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e"},{"header":"1 Introduction","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Creative Design and the Predictive Brain Paradox\u003c/h2\u003e \u003cp\u003eCreative design is an act of expanding and transforming the design state space by introducing new perspectives or variables, thereby enabling the generation of unprecedented solutions. Such processes can transcend conventional frameworks, opening new domains and even triggering paradigm shifts.\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e In creative design, designers confronting uncertain challenges hypothesize, test, and evince solutions until achieving outcomes that are both novel and apt.\u003csup\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e Design cognition research that seeks to elucidate such creative thinking processes has traditionally relied on cognitive psychological approaches such as protocol analysis, which revealed two key perspectives: design as a search process within a problem space, and as an exploratory process between problem and solution spaces.\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e These studies also highlighted the roles of multiple cognitive functions, including memory, associative processing, visual perception, and mental imagery, in design thinking.\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e More recently, neurophysiological tools such as eye tracking, heart rate monitoring, and brain imaging have enabled quantitative assessments of design cognition.\u003csup\u003e\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e Concurrently, both design and creativity research have increasingly emphasized theory-driven, computational approaches that seek mechanistic explanations of creative cognition.\u003csup\u003e\u003cspan additionalcitationids=\"CR11 CR12 CR13 CR14 CR15 CR16\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThe Free Energy Principle (FEP), one of the most influential theoretical frameworks in neuroscience, provides a unifying account of perception, action, and learning. In essence, FEP describes the brain as a predictive machine that constantly minimizes prediction error (or \u0026ldquo;free energy\u0026rdquo;) by updating its internal model of the world via Bayesian inference.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e This principle provides a lens for understanding design processes which begin with high uncertainty and progressively transform the unknown into the known.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e However, a fundamental paradox arises: if the brain by default strives to reduce surprise and uncertainty, how can we account for creative design, a process in which one deliberately seeks out novelty and embraces uncertainty? This conundrum is analogous to the classic \u0026ldquo;dark room problem\u0026rdquo; in predictive brain theory (the question of why an agent driven to minimize surprise would not simply converge upon a state of minimal sensory input, dark room) and has been reformulated in the context of creativity as the \u0026ldquo;Enlightened Room Problem,\u0026rdquo; which asks how a strictly error-minimizing agent could ever act creatively.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e Put simply, why would a self-organizing system driven to minimize surprise ever explore beyond the familiar, and how could it generate genuinely novel ideas given the constraints of its own predictive models?\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2 The Inquiry Cycle Model: Strategic Resolution of Uncertainty and the Pursuit of Novelty\u003c/h2\u003e \u003cp\u003eThe Inquiry Cycle Model (ICM)\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e resolves this paradox by extending the free-energy minimization framework over time, allowing an agent to tolerate temporary increases in uncertainty (entropy) if these are expected to yield greater net reductions of free energy in the long run. This aligns with recent creativity research. For instance, the \u0026ldquo;entropy modulation theory of creative exploration\u0026rdquo; posits that creativity depends on modulating entropy during cognitive search;\u003csup\u003e22\u003c/sup\u003e increasing predictive uncertainty raises entropy, enabling broader memory retrievals and more novel ideas. Similarly, the \u0026ldquo;matched filter hypothesis\u0026rdquo; suggests that during idea generation, the brain emphasizes data-driven (bottom-up) processing while suppressing knowledge-driven (top-down) control.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e Loosening input filtering makes low-level information more accessible, facilitating creative thinking. These perspectives highlight that temporarily embracing uncertainty\u0026mdash;via entropy modulation or loosened filtering\u0026mdash;is fundamental to creativity. This supports the ICM\u0026rsquo;s tenet that strategic, short-lived increases in free energy are essential conditions for achieving global minimization over time, reframing creative exploration as a dynamic cycle of \u0026ldquo;convergence\u0026rdquo; toward order and \u0026ldquo;expansion\u0026rdquo; of uncertainty. This cyclical structure aligns with Peirce\u0026rsquo;s framework of explicative and ampliative reasoning.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e Explicative reasoning (deduction) is a \u0026ldquo;convergent\u0026rdquo; process that derives consequences from existing premises to enhance internal consistency; this corresponds to long-term free-energy minimization. Conversely, ampliative reasoning is an \u0026ldquo;expansive\u0026rdquo; process that extends the inference space beyond existing premises. While this includes induction, its crucial exploratory mode is abduction, the sole inference capable of boldly introducing novel hypotheses via a logical leap. This abductive hypothesis formation expands knowledge of the real world, mapping directly to the temporary increase in free energy\u0026mdash;the strategic \"acceptance of uncertainty\"\u0026mdash;within the ICM. This logical consistency provides a theoretical foundation for understanding how the ICM facilitates creative inquiry beyond mere prediction error minimization.\u003c/p\u003e \u003cp\u003eIndeed, widespread theoretical consensus posits that creative progress is a dynamic iteration of ampliative expansion and explicative validation.\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e In cognitive models, this cyclical interplay is directly mapped to idea generation and evaluation\u0026mdash;collectively termed the two-fold model of creativity.\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e This dual-phase structure is supported by neuroimaging\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e and cognitive frameworks such as the \u0026ldquo;Geneplore\u0026rdquo; model\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e and Memory in Creative Ideation (MemiC).\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e These models commonly demonstrate that creativity emerges by iteratively alternating between exploring distant semantic networks to generate novel ideas and evaluating their effectiveness against existing knowledge. Thus, these cognitive processes dynamically build upon one another over time. Within the field of design research, this cyclic structure of ampliative expansion and explicative validation is historically regarded as the essence of design.\u003csup\u003e\u003cspan additionalcitationids=\"CR31 CR32 CR33 CR34\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e Its origins trace back to Page\u0026rsquo;s cyclical process of \u0026ldquo;Analysis, Synthesis, and Evaluation,\u0026rdquo; later systematized by Jones.\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e March subsequently applied Peirce\u0026rsquo;s inference modes to design via the Production-Deduction-Induction (PDI) model, explicitly mapping abduction to \u0026ldquo;production.\u0026rdquo;\u003csup\u003e33\u003c/sup\u003e This iterative refinement perspective is widely supported across various nomenclatures (e.g., Mesarović ,\u003csup\u003e38\u003c/sup\u003e Watts,\u003csup\u003e39\u003c/sup\u003e Matsuoka et al.\u003csup\u003e40\u003c/sup\u003e). Furthermore, Takeda et al. formalized design as an iterative logical process of abductive suggestion, deductive evaluation, and circumscription.\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e Crucially, circumscription dynamically rewrites premise knowledge in response to contradictions, extending the inference space rather than merely applying fixed knowledge. Similarly, Sch\u0026ouml;n\u0026rsquo;s Reflection-in-action describes design as a \u0026ldquo;reflective conversation with the situation.\u0026rdquo;\u003csup\u003e3\u003c/sup\u003e When a designer\u0026rsquo;s \u0026ldquo;move\u0026rdquo; elicits unexpected \u0026ldquo;backtalk\u0026rdquo; (surprise), they reframe the problem on the spot and proceed to new exploration, navigating iterative stages of sensemaking and future framing.\u003csup\u003e\u003cspan additionalcitationids=\"CR42\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e Gero and Kannengiesser\u0026rsquo;s Function-Behavior-Structure (FBS) ontology describes this reflection as constructive memory driven by misalignment between the \u0026ldquo;expected\u0026rdquo; and \u0026ldquo;interpreted\u0026rdquo; worlds. This dynamic rewriting of the state space is fundamentally an act of ampliative inference.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e A comparable rhythm is explicitly articulated in the British Design Council\u0026rsquo;s \u0026ldquo;Double Diamond\u0026rdquo; model,\u003csup\u003e45\u003c/sup\u003e where both problem-finding and problem-solving phases follow a divergence\u0026ndash;convergence pattern. Thus, from computational logic to ontologies and practical reflection, design research universally recognizes this dynamic interplay of exploratory, ampliative expansion and convergent, explicative validation as the fundamental structure of design activity.\u003c/p\u003e \u003cp\u003eThe engine that intrinsically drives this cognitive cycle is the fundamental motivation directed toward information acquisition and the resolution of uncertainty: namely, \"curiosity\".\u003csup\u003e46\u0026ndash;49\u003c/sup\u003e Recent research proposes frameworks like the Novelty-Seeking Model (NSM), which views novelty seeking as dynamically regulated by states of mind managing top-down and bottom-up processing.\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e,\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e Similarly, the Question-Asking in Information Seeking (QuInS) framework illustrates how recognizing a knowledge gap triggers iterative cycles of question formulation and evaluation.\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e Furthermore, Seiler and Dan distinguish between boredom\u0026mdash;an information \"hunger\" driving broad, unspecific exploration\u0026mdash;and curiosity\u0026mdash;an \"appetite\" fostering targeted, knowledge-enriching behavior.\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e These functional distinctions manifest in specific knowledge-building styles: the \u0026ldquo;hunter\u0026rdquo; (tightly connected networks), the \u0026ldquo;busybody\u0026rdquo; (loosely connected, diverse topics), and the \u0026ldquo;dancer\u0026rdquo; (creative leaps across disconnected areas).\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e Recent advances allow these semantic memory structures to be quantified using graph-theoretical metrics. For example, the clustering coefficient (CC) reflects local interconnectedness; high CC coupled with short path lengths characterizes the \u0026ldquo;small-world\u0026rdquo; organization often seen in creative individuals. Global and local efficiency (GE, LE) represent information transmission ease, where shorter path lengths serve as a robust metric for semantic distance,\u003csup\u003e56\u003c/sup\u003e facilitating access to remote associations. Finally, modularity (Q) captures network segregation into subcommunities, where lower Q indicates more integrated, flexible semantic networks.\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e,\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e Together, these structural properties correlate with individual differences in creativity, particularly in tasks requiring remote associations and divergent thinking.\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e,\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThese diverse knowledge-building styles and their quantitative differences reflect two functionally distinct forms of epistemic desire.\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e,\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e The origins of this concept trace back to the classical definition by Berlyne,\u003csup\u003e61\u003c/sup\u003e who distinguished curiosity into \"diversive curiosity,\" which seeks to avoid boredom and pursue broad stimulation or novelty, and \"specific curiosity,\" which aims to resolve specific uncertainties or gaps in knowledge.\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e Crucially, these two forms of curiosity can be interpreted as having a functional correspondence with the aforementioned reasoning processes. Diversive curiosity is characterized by directing attention toward unknown territories that the current predictive model cannot capture\u0026mdash;a trait that inherently aligns with the broad exploration sought by exploratory, ampliative reasoning. Conversely, specific curiosity seeks detailed information to reduce identified uncertainties, thereby supporting the model refinement driven by convergent, explicative reasoning.\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e The antagonistic interaction between these two curiosities regulates the agent's arousal level, configuring the design process as an inquiry cycle that autonomously transitions between \"exploration of the unknown (entropy increase)\" and \"deepening of understanding (entropy decrease).\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e Thus, curiosity functions as a meta-cognitive controller that mediates the exploration-exploitation trade-off to maximize long-term information gain.\u003csup\u003e\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e,\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e Computationally framing this exploration-exploitation cycle via prediction error minimization, Becker and Cabeza\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e and Van de Cruys et al.\u003csup\u003e65,66\u003c/sup\u003e provide critical insights. They posit that curiosity reflects expected information gain\u0026mdash;estimating future model updates based on current prediction errors. In contrast, the aha experience corresponds to actual information gain when new information resolves the error, functioning as an intrinsic reward for updating the model.\u003csup\u003e\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThis duality of actual and expected information gain aligns perfectly with the mathematical structure of the ICM.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e Fig.\u0026nbsp;1 illustrates the overall process of free energy reduction and information gain in the ICM. In the ICM, the information gain obtained by recognizing the causal state underlying an observation is defined as Kullback-Leibler divergence (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:KLD\\)\u003c/span\u003e\u003c/span\u003e), quantifies the epistemic value associated with recognizing an observation. It encompasses convergent processes that transform uncertainty into known facts and restore model consistency, such as Sch\u0026ouml;n\u0026rsquo;s sensemaking process of situational \u0026ldquo;backtalk\u0026rdquo;\u003csup\u003e3\u003c/sup\u003e or mismatch resolution in the FBS framework.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e It is specific curiosity that seeks the maximization of this \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:KLD\\)\u003c/span\u003e\u003c/span\u003e; by converging excessive arousal (confusion) into order as if climbing the right side of the Wundt curve,\u003csup\u003e67\u003c/sup\u003e it computationally executes what Peirce termed \"explicative reasoning\" and model refinement.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e Conversely, the maximum information gain expected from updating prior beliefs is defined as Bayesian Surprise (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e), termed the expected epistemic value arising from model update or learning. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e reflects the novelty of a recognized observation and has been shown to correlate with human surprise responses to novel stimuli.\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u003c/sup\u003e Diversive curiosity drives the maximization of this \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e, increasing arousal from a state of low arousal (boredom) by moving up the left side of the Wundt curve.\u003csup\u003e\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e In design, this drives the active search for unknown variables to break existing constraints. The temporary increase in predictive uncertainty induced by pursuing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e aligns with entropy modulation and relaxed cognitive control.\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e Crucially, this state triggers Peirce\u0026rsquo;s ampliative reasoning (abduction).\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e Thus, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e maximization functions as a dynamic engine that expands the state space\u0026mdash;the essence of creative design.\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e To provide a mathematical basis for these dynamics, analyses using a Gaussian generative model with a uniform noise likelihood (Fig.\u0026nbsp;2) demonstrate that these two types of information gain, along with their sum (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:IG=KLD+BS\\)\u003c/span\u003e\u003c/span\u003e), form inverted-U shaped functions with respect to surprise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e, which represents information about an observation (Fig.\u0026nbsp;3). Since \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e correlates with arousal potential,\u003csup\u003e68\u0026ndash;70\u003c/sup\u003e these findings provide a formal mathematical foundation for Berlyne\u0026rsquo;s arousal potential theory,\u003csup\u003e61\u003c/sup\u003e demonstrating that hedonic value peaks at an optimal level of arousal on the Wundt curve.\u003csup\u003e\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e In conclusion, the ICM realizes an ideal inquiry cycle where uncertainty dynamically fluctuates around optimal arousal via the alternating maximization of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:KLD\\)\u003c/span\u003e\u003c/span\u003e (uncertainty resolution) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e (novelty pursuit).\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e\u003c/sup\u003e This framework provides a robust foundation seamlessly bridging psychological theories of curiosity, computational free-energy minimization, and design practice. It explains how designers transform the unknown into the known, achieving genuine creativity characterized by both novelty and aptness. Box 1 (Supplementary) summarizes the correspondence between these concepts, information-based metrics, and their cognitive interpretations.\u003c/p\u003e \u003cp\u003eTo formulate the core inquiry of this study, we draw upon theoretical predictions derived from the ICM.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e Simulations manipulating prior variance (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{s}_{p}\\)\u003c/span\u003e\u003c/span\u003e) \u0026mdash;the inverse of predictive precision\u0026mdash;reveal two critical properties that form our computational hypotheses:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eEnhancement of Information Gain: Decreasing predictive precision (increasing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{s}_{p}\\)\u003c/span\u003e\u003c/span\u003e) raises the maximum values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:KLD\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:IG\\)\u003c/span\u003e\u003c/span\u003e (Fig.\u0026nbsp;4A, Fig.\u0026nbsp;5), computationally facilitating both the exploration of the unknown (diversive curiosity) and the resolution of uncertainty (specific curiosity).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eShift in Optimal Arousal: As prior variance increases, the surprise level maximizing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e (optimal surprise, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e) rises, while the level maximizing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:KLD\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{KLD}\\)\u003c/span\u003e\u003c/span\u003e) decreases (Fig.\u0026nbsp;4B, Fig.\u0026nbsp;5). This expanded cognitive \"tolerance\" for higher surprise fosters broader exploration during divergent thinking.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eConsequently, we hypothesize that decreasing predictive precision during divergent thinking will increase both the maximum information gain and the optimal arousal of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e associated with novelty. The present study empirically tests these predictions by modulating neural activity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Alpha Oscillations: A Neural Mechanism for Modulating Predictive Precision\u003c/h2\u003e \u003cp\u003eIn creative design, commonsense solutions and habitual thinking can act as strong constraints, consistent with design fixation effects in which prior examples or entrenched knowledge bias subsequent ideation.\u003csup\u003e\u003cspan additionalcitationids=\"CR72\" citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e Within a predictive-processing framework, such constraints can be interpreted as high-precision priors\u0026mdash;predictions shaped by past experience that are relatively resistant to updating.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e,\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e\u003c/sup\u003e To generate novel ideas, these strong predictions need to be attenuated, thereby allowing uncertainty and facilitating broader exploration of the solution space. This conceptualization closely aligns with the REBUS (relaxed beliefs under psychedelics) model.\u003csup\u003e\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u003c/sup\u003e Their framework formally demonstrates that relaxing the precision of high-level priors increases systemic entropy, thereby liberating the brain from rigid, entrenched networks and enabling highly flexible, divergent exploration. Thus, the essence of such creative thinking, often described as \u0026ldquo;getting rid of preconceptions\u0026rdquo; or \u0026ldquo;thinking outside the box\u0026rdquo; can be understood, within the ICM framework, as a strategic lowering of predictive precision to create a receptive state for the exploration of new information.\u003c/p\u003e \u003cp\u003eIn this context, an important question arises: what neural mechanisms regulate such adjustments in predictive precision during creative thinking? Cognitive neuroscience research over the past decades has shown that alpha oscillations (8\u0026ndash;12 Hz) in EEG are involved in various cognitive processes, including the control of predictive precision.\u003csup\u003e\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e,\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e\u003c/sup\u003e In the visual cortex, increases in alpha activity have been reported to temporarily suppress the processing of visual input, allowing top-down predictions generated by the internal model to dominate.\u003csup\u003e\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e,\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e Conversely, when alpha activity decreases, sensory information that does not match predictions is emphasized, prediction errors are amplified, and the updating of the internal model is facilitated.​\u003csup\u003e81,82\u003c/sup\u003e This inhibitory function of alpha oscillations is not regarded as a passive state, but rather as a process of active inhibition.\u003csup\u003e\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e\u003c/sup\u003e Alpha oscillations are thought to modulate the precise timing of neuronal spiking (action potentials), thereby enhancing the signal-to-noise ratio. Through this mechanism, alpha activity functions as a sensory gate, blocking task-irrelevant information and controlling access to relevant information processing.\u003csup\u003e\u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e,\u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eIn creativity research, alpha oscillations are reported to play a central role. Reviews by Fink and Benedek synthesize these findings to comprehensively demonstrate the role of alpha oscillations in the neural basis of creative thinking.\u003csup\u003e\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e\u003c/sup\u003e Specifically, increased alpha activity is associated with internally directed attention, the suppression of sensory input, and the inhibition of obvious semantic associations.\u003csup\u003e\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e\u003c/sup\u003e During creative thinking, specifically divergent thinking, alpha power has been shown to increase in frontal and parietal regions.\u003csup\u003e\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e,\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e\u003c/sup\u003e Notably, highly creative individuals exhibit greater alpha enhancement and are able to sustain this increase for longer durations.\u003csup\u003e\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e,\u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e\u003c/sup\u003e Furthermore, alpha power follows a characteristic temporal trajectory: it peaks at the onset of idea generation, subsequently decreases, and increases again immediately prior to the response.\u003csup\u003e\u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e\u003c/sup\u003e This dynamic may reflect a process in which strong top-down control defines the search space during the initial phase, followed by the execution of the actual search. A recent study demonstrated that alpha power increases during the generation of distant semantic associations. Furthermore, they found that the explicit goal to be creative enhances alpha phase synchronisation from left to right temporal brain areas, reflecting top-down control of semantic search.\u003csup\u003e\u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e92\u003c/span\u003e\u003c/sup\u003e This alpha synchronization mediates internal attention by blocking external visual inputs and concentrating neural resources on internal mental imagery and modes of thought.\u003csup\u003e\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e93\u003c/span\u003e,\u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e94\u003c/span\u003e\u003c/sup\u003e Indeed, it is known that simply closing one\u0026rsquo;s eyes to block visual input is sufficient to improve performance in divergent thinking.\u003csup\u003e\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e95\u003c/span\u003e\u003c/sup\u003e Consistent with these mechanisms, alpha oscillations in the right hemisphere have been linked to the generation of original ideas.\u003csup\u003e\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e,\u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e,\u003cspan additionalcitationids=\"CR97\" citationid=\"CR96\" class=\"CitationRef\"\u003e96\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR98\" class=\"CitationRef\"\u003e98\u003c/span\u003e\u003c/sup\u003e Specifically, in insight tasks such as the remote associates test, higher alpha power in the right hemisphere immediately before hint presentation has been shown to predict subsequent successful solutions achieved through insight.\u003csup\u003e\u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e99\u003c/span\u003e\u003c/sup\u003e Moreover, immediately prior to arriving at a solution via a sudden \u0026ldquo;Aha!\u0026rdquo; experience rather than analytical reasoning, marked increases in alpha activity have been observed in the right parietal, right temporal, and occipital regions.\u003csup\u003e\u003cspan additionalcitationids=\"CR101 CR102 CR103\" citationid=\"CR100\" class=\"CitationRef\"\u003e100\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e104\u003c/span\u003e\u003c/sup\u003e According to the hypothesis proposed by Klimesch et al.,\u003csup\u003e85\u003c/sup\u003e this increased alpha amplitude in task-relevant regions facilitates inhibition by silencing weakly excited neural populations (representing noise or obvious associations), thereby allowing semantically distant and creative associations to emerge into consciousness. While the aforementioned EEG studies provide valuable insights into the neural correlates of ideation, many of these findings remain correlational. To establish whether alpha oscillations are a causal factor in creative thinking, it is necessary to verify causality using methods such as brain stimulation. Research using transcranial Alternating Current Stimulation (tACS), which can enhance neural oscillations at specific frequencies, is beginning to demonstrate this causality.\u003csup\u003e\u003cspan citationid=\"CR105\" class=\"CitationRef\"\u003e105\u003c/span\u003e\u003c/sup\u003e For instance, applying alpha-frequency tACS to the frontal lobe has been reported to improve divergent thinking performance, a result interpreted as a strengthening of inhibitory top-down control.\u003csup\u003e\u003cspan citationid=\"CR106\" class=\"CitationRef\"\u003e106\u003c/span\u003e\u003c/sup\u003e Furthermore, alpha tACS applied to parieto-occipital regions has been shown to strongly suppress external visual information and indirectly enhance Default Mode Network (DMN) activity, thereby promoting an internal mode of thought and improving the originality and elaboration of ideas.\u003csup\u003e\u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e107\u003c/span\u003e\u003c/sup\u003e Moreover, because tACS allows for frequency specification, it has been verified that the involvement in creativity is not merely due to electrical stimulation in itself, but is an effect specific to the \"alpha rhythm.\" Grabner et al. compared alpha (10 Hz) and gamma (40 Hz) stimulation, proposing a framework to examine the specific functional role of the alpha band in creativity.\u003csup\u003e\u003cspan citationid=\"CR108\" class=\"CitationRef\"\u003e108\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eBeyond frequency specificity, a comprehensive understanding of creative mechanisms must also account for the specificity of the \u0026ldquo;stimulation site\u0026rdquo;. In this regard, the fact that the right temporal lobe is a critical region for processing semantic associations and retrieving conceptual knowledge cannot be overlooked.\u003csup\u003e\u003cspan additionalcitationids=\"CR110 CR111\" citationid=\"CR109\" class=\"CitationRef\"\u003e109\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR112\" class=\"CitationRef\"\u003e112\u003c/span\u003e\u003c/sup\u003e Consistent with this anatomical and functional neural basis, there is accumulating evidence that stimulation of the right temporal region facilitates insight tasks.\u003csup\u003e\u003cspan citationid=\"CR113\" class=\"CitationRef\"\u003e113\u003c/span\u003e\u003c/sup\u003e In particular, Luft et al. causally demonstrated that alpha-frequency stimulation to the right temporal area inhibits strongly linked, obvious semantic associations, thereby facilitating connections to more remotely related concepts.\u003csup\u003e\u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e114\u003c/span\u003e\u003c/sup\u003e Furthermore, as a recent finding, Ghani et al. reported that up-regulating right temporal alpha oscillations guides the brain into a receptive state, which in turn promotes the occurrence of insight.\u003csup\u003e\u003cspan citationid=\"CR115\" class=\"CitationRef\"\u003e115\u003c/span\u003e\u003c/sup\u003e This concept of a \"receptive brain state\" aligns strongly with the mechanism of creative thinking discussed in this paper: lowering prediction precision to enable the exploration of novel information. Taken together, these findings suggest that alpha oscillations, especially in the right temporal region, constitute a neural basis for suppressing obvious semantic associations and enabling broad exploration within semantic space. Within the framework of the Bayesian brain hypothesis, such neural activity can be interpreted as a process that reduces predictive precision, thereby creating a cognitive state that facilitates the exploration of novel associations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e1.4 Objectives\u003c/h2\u003e \u003cp\u003eThis study applied the ICM to the domain of creative design to examine how controlling uncertainty in the brain via tACS-induced right temporal alpha oscillations influences creativity and information content of ideas in problem-solving and problem-finding, particularly during divergent thinking processes. By associating these oscillations with reduced predictive precision, the present study links free-energy-based theoretical modeling with neurophysiological evidence, elucidating how uncertainty and information acquisition facilitate creative inquiry. The findings offer implications for evidence-based strategies to foster creativity in both educational and professional design contexts.\u003c/p\u003e \u003c/div\u003e"},{"header":"2 Materials and Methods","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants\u003c/h2\u003e \u003cp\u003eWe recruited 43 participants (22 females, aged 18\u0026ndash;32 years, \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;21.1 years, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.8 years) from XXX. All participants were fluent in English and interested in design. Exclusion criteria included a history of neurological disorders, pregnancy, previous neurosurgical procedures, metal or medical implants, or consumption of alcohol or recreational drugs within 24 h of the session. Participants received course credit or \u0026pound;10/h. The research was approved by the College of Health, Medicine and Life Sciences Research Ethics Committee (DLS) at Brunel University of London (Reference: 44385-LR-Oct/2023-47425-2). All participants provided written informed consent after being informed of the study\u0026rsquo;s purpose.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental design\u003c/h2\u003e \u003cp\u003eParticipants were randomly assigned to one of the three conditions: left alpha (hemisphere control, \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15 ); right alpha (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;13); right gamma (frequency control, \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15). There were no significant differences in age or gender distribution across conditions (age: \u003cem\u003eF\u003c/em\u003e(2,40)\u0026thinsp;=\u0026thinsp;1.94, \u003cem\u003ep\u003c/em\u003e = .157, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.088; gender: \u003cem\u003eX\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e(2, \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;43)\u0026thinsp;=\u0026thinsp;1.34, \u003cem\u003ep\u003c/em\u003e = .513). The experiment was conducted in a double-blind manner; neither participants nor experimenters knew the assigned stimulation conditions. Participants engaged in a design creativity task in each phase: before stimulation (Pre), during stimulation (Stim), and after stimulation (Post). In Pre phase, participants also completed a relatedness judgement task following the design creativity task. Figure\u0026nbsp;6A provides an overview of the experimental design.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.3 EEG and tACS protocol\u003c/h2\u003e \u003cp\u003eBoth EEG recording and tACS were conducted using a Starstim (Neuroelectrics, Barcelona, Spain) with twenty channels. During the Pre/Post phase, EEG was recorded at a 500 Hz sampling rate, with two reference electrodes (CMS and DRL) vertically aligned on the right cheekbone. During the Stim phase, high-definition tACS (HD-tACS) was applied to the temporal region at 2 mA (baseline\u0026ndash;peak), with 6 s ramp periods. T7 (left) or T8 (right) served as the target electrode, with five surrounding electrodes as returns (20% each: left, F7/F3/Cz/P3/P7; right, F8/F4/Cz/P4/P8). Gamma stimulation was set at 35 Hz. Alpha stimulation used each participant\u0026rsquo;s individual alpha peak frequency (IAF), defined as the peak power in the 8\u0026ndash;12 Hz band during divergent thinking in the Pre problem-solving task. Online estimates were approximately 8.3 Hz, but offline recalculation after preprocessing yielded slightly higher true IAFs (right: 9.50 Hz, left: 8.95 Hz), indicating that stimulation was delivered marginally below IAF. Electric-field simulations using Finite Element Method\u003csup\u003e\u003cspan citationid=\"CR116\" class=\"CitationRef\"\u003e116\u003c/span\u003e\u003c/sup\u003e (NIC v2.1.3.4 StimViewer) confirmed that the montage produced electric field strengths above the 0.3 mV/mm threshold for neuronal modulation (Fig.\u0026nbsp;6B).\u003csup\u003e\u003cspan citationid=\"CR117\" class=\"CitationRef\"\u003e117\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Design creativity task\u003c/h2\u003e \u003cp\u003eThis task evaluated design thinking using the Double Diamond design process model,\u003csup\u003e45\u003c/sup\u003e which emphasizes problem finding and problem solving through divergent and convergent thinking. Accordingly, the experiment included two components: a problem-solving task and a problem-finding task, each comprising divergent thinking (DT) and convergent thinking (CT) phases (Fig.\u0026nbsp;6C). Participants rested for 30 s before each task and received both oral and on-screen instructions. Different problems or themes were provided for each phase (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and responses were entered via keyboard.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eProblems and Themes Used in the Design Creativity Tasks for Each Phase\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTask\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eProblems and Themes\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eProblem-solving\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeople with hearing impairments may not notice fire alarms, leading to compromised safety.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeople with visual impairments may not detect approaching quiet vehicles, leading to potential accidents.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeople with speech disorders may struggle with communication in emergencies, leading to delays in crucial assistance.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eProblem-finding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA future in 2050 where technological changes to the human body, such as gene editing and cybernetic enhancements, have advanced.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA future in 2050 where the technological advancements in transport, such as autonomous cars and unmanned aerial vehicles, have become commonplace.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA future in 2050 where the technology enabling human colonization of Mars has advanced.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1 Problem-solving task\u003c/h2\u003e \u003cp\u003eParticipants were presented with specific social problems and asked to be creative and come up with solutions while imagining the user\u0026rsquo;s perspective. This task included five phases: (1) problem scoping, listing as many requirements and constraints for solutions as possible (3 min); (2) evaluation of these items, rating their importance on a 7-point Likert scale and indicating which to retain (no time limit); (3) divergent thinking (DT), generating as many different and original solutions as possible (3 min); (4) solution evaluation, rating solutions for originality, confidence, and \"aha experience\" strength on a 7-point scale (no time limit); and (5) convergent thinking (CT), developing the most creative solution by elaborating on or combining ideas from the DT phase (5 min).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2 Problem-finding task\u003c/h2\u003e \u003cp\u003eParticipants were presented with a specific theme envisioning the future in 2050 and asked to be creative and identify what kind of problems or issues might arise in such a future. This task consisted of three phases: (1) DT, listing as many different and original problems as possible (3 min); (2) idea evaluation, rating these problems for originality, confidence, and \"aha experience\" strength on a 7-point scale (no time limit); and (3) CT, identifying the most original and important potential problem, referring to their DT ideas (5 min).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Relatedness judgement task\u003c/h2\u003e \u003cp\u003eBefore stimulation, participants intuitively rated the semantic relatedness of 20 words (190 pairs, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) on a visual analogue scale from 0 (unrelated) to 100 (strongly related) (Fig.\u0026nbsp;6D). Semantic memory networks were constructed by representing words as nodes and edge weights as relatedness ratings, yielding weighted undirected networks.\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e To evaluate whether the stimulation groups possessed comparable baseline cognitive profiles before the intervention, we analyzed the structural properties of their semantic memory networks. Specifically, we calculated standard network properties, CC, GE, LE, and Q, which are known predictors of individual creativity,\u003csup\u003e57,58\u003c/sup\u003e and compared them across stimulation conditions using a permutation-based F-test with 10,000 iterations; data from two participants (one from left alpha, one from right gamma) were excluded due to system error.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eWords Used in the Relatedness Judgement Task\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNear Words\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFar Words\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIrrelevant Words\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esound, infrared, wearable, touch, sensor, vibration, Bluetooth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eflag, microscope, compass, ant, perfume, chameleon, tap-dance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebook, basket, calendar, chair, mug, pencil\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe same 20 words also served as primes for the problem-solving task in the Stim phase. Seven were semantically close to the problem and served as direct hints (Near words), seven were distant and served as indirect hints (Far words), and six were unrelated (Irrelevant words). After the problem-solving task in the Stim phase, participants indicated whether each word was used as a hint in both DT and CT phase. Hint usage rates (proportion of \"yes\" responses) were averaged for each category (Near, Far, Irrelevant). We expected highest rates for Near words, followed by Far and Irrelevant, and tested this using a Kruskal\u0026ndash;Wallis test with Dunn\u0026rsquo;s post-hoc multiple comparisons (Holm correction).\u003c/p\u003e \u003cp\u003eFinally, we examined the effect of stimulation on hint usage rates for each category. Given that right temporal alpha oscillations actively inhibit strong semantic associations to promote distant concept exploration,\u003csup\u003e114\u003c/sup\u003e we hypothesized that Far-word usage would be greater in the right alpha condition than in controls, tested using a Friedman test with post-hoc Wilcoxon signed-rank tests (Holm correction).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Idea ratings\u003c/h2\u003e \u003cp\u003eThe ideas generated in the design creativity task were evaluated using self-ratings and information-based metrics. Participants who provided only one idea during the DT phase in any of the three phases (Pre, Stim, Post) were excluded from this analysis due to insufficient divergent thinking. The final sample sizes were: Problem-solving task: left alpha (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;13), right alpha (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;13), right gamma (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;12); Problem-finding task: left alpha (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;14), right alpha (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;12), right gamma (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;14).\u003c/p\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e2.6.1 Self-ratings\u003c/h2\u003e \u003cp\u003eAs described in Section 2.4, participants self-rated ideas from the DT phase. For each evaluation metric, we calculated within-participant averages for Pre, Stim, and Post phases. These averages were then Z-score normalized across participants, with outliers excluded using the interquartile range (IQR) approach. Since the problems and themes for each phase (Pre, Stim, Post) were fixed and presented in a predetermined order without counterbalancing (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), we compared conditions using one-way ANOVA per phase rather than a mixed ANOVA. Significant effects were followed by post-hoc Dunnett\u0026rsquo;s tests (p-values adjusted via multivariate t-distribution) comparing the right alpha condition against both controls.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e2.6.2 Information-based metrics\u003c/h2\u003e \u003cp\u003eWe calculated Information-based metrics for ideas using a custom computational system based on the free energy principle,\u003csup\u003e118\u003c/sup\u003e using the English Wikipedia corpus (enwiki, September 2023).\u003c/p\u003e \u003cp\u003e \u003cb\u003eComputational system overview.\u003c/b\u003e The generative model is factorized as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(s,o\\right)=p\\left(o|s\\right)p\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e. The prior \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the occurrence probability of \u003cem\u003eprior words\u003c/em\u003e (starting point of ideation), defined as a set of words \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S=\\left\\{{s}_{i}|1\\le\\:i\\le\\:{N}_{s}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e. The observation model \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(o|s\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the probability of generating \u003cem\u003edirectional words\u003c/em\u003e (ideation directions) from these prior words, defined as a set of words \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:O=\\left\\{{o}_{i}|1\\le\\:i\\le\\:{N}_{o}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e details the specific sets \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:O\\)\u003c/span\u003e\u003c/span\u003e used across all task phases.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003ePrior and Directional Word lists for Information-based metrics of ideas in the Design Creativity Tasks\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTask\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e: Prior words\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEntropy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:O\\)\u003c/span\u003e\u003c/span\u003e: Directional words\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eProblem-solving\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epeople, hearing, impairment,\u003c/p\u003e \u003cp\u003eloss, deaf, deafness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003enotice, detect, aware,\u003c/p\u003e \u003cp\u003ewarning, alert, fire, alarm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epeople, visual, vision, impairment,\u003c/p\u003e \u003cp\u003eloss, blind, blindness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003edetect, notice, aware, warning,\u003c/p\u003e \u003cp\u003ealert, approaching, quiet, vehicle\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epeople, speech, disorder, impairment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eunderstand, assistance, response,\u003c/p\u003e \u003cp\u003einstruction, communication, emergency\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eProblem-finding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eevolution, human, body, future, gene,\u003c/p\u003e \u003cp\u003eediting, cybernetic, enhancement,\u003c/p\u003e \u003cp\u003ebiotechnology, augmentation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eproblem, issue, risk, concern,\u003c/p\u003e \u003cp\u003econstraint, threat, uncertainty\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eautonomous, transport, future,\u003c/p\u003e \u003cp\u003eadvancement, car, unmanned,\u003c/p\u003e \u003cp\u003evehicle, aircraft\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eproblem, issue, risk, concern,\u003c/p\u003e \u003cp\u003econstraint, threat, uncertainty\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003emigration, Mars, future, human,\u003c/p\u003e \u003cp\u003ecolonization, space, settlement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eproblem, issue, risk, concern,\u003c/p\u003e \u003cp\u003econstraint, threat, uncertainty\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003ePrior distribution\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{p}\\left(\\varvec{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e. To capture word polysemy and similarity, we smoothed the prior distribution using local co-occurrence. This was calculated by counting words within a\u0026thinsp;\u0026plusmn;\u0026thinsp;2-word window around the word \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\)\u003c/span\u003e\u003c/span\u003e in each corpus sentence, excluding function words. To prevent underestimating \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\)\u003c/span\u003e\u003c/span\u003e during smoothing, we included \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\)\u003c/span\u003e\u003c/span\u003e itself in the occurrence count.\u003c/p\u003e \u003cp\u003eThe prior entropy, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\sum\\:_{i=1}^{{N}_{s}}p\\left({s}_{i}\\right)\\text{ln}p\\left({s}_{i}\\right)\\)\u003c/span\u003e\u003c/span\u003e, measures the distribution\u0026rsquo;s spread, where higher entropy indicates lower precision. Across phases, entropy ranged from 8.39 to 9.22 for the problem-solving task and 9.27 to 9.79 for the problem-finding task (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eLikelihood (observation model)\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{p}\\left(\\varvec{o}|\\varvec{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e. To calculate the probability of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:o\\)\u003c/span\u003e\u003c/span\u003e given \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\)\u003c/span\u003e\u003c/span\u003e, we used syntactic dependency relations to capture stronger grammatical connections than local co-occurrence. We performed dependency parsing on each corpus sentence, counting words dependent on the directional word \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:o\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo convert the resulting frequencies from both models into probability distributions, the co-occurrence frequency was expressed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(x,y\\right)/\\left(C\\left(x\\right)C\\left(y\\right)\\right)\\)\u003c/span\u003e\u003c/span\u003e\u0026mdash;where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(x,y\\right)\\)\u003c/span\u003e\u003c/span\u003e is the co-occurrence count, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(y\\right)\\)\u003c/span\u003e\u003c/span\u003e are the individual word counts\u0026mdash;and subsequently normalized over \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eParticipant-derived word-level belief distribution\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{q}}_{\\varvec{i}}\\left(\\varvec{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e. An idea was defined as a set of explicitly produced content words, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W=\\left\\{{w}_{i}|1\\le\\:i\\le\\:{N}_{w}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e. For each word \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{i}\\)\u003c/span\u003e\u003c/span\u003e, its precomputed corpus-based semantic distribution served as the individual word-level belief distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{i}\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e. Idea-level metrics were derived by calculating the information-based metrics for each \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{i}\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e and averaging these values across \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\)\u003c/span\u003e\u003c/span\u003e. This word-level computation was deliberately chosen over aggregating distributions beforehand to prevent the semantic dilution of highly original concepts; otherwise, the high surprise value of unique conceptual leaps could be smoothed out by more common words within the same idea. To isolate the core semantic vocabulary, standard stop words (including pronouns, conjunctions, prepositions, auxiliary verbs, and abbreviations) were excluded from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eComputing information-based metrics.\u003c/b\u003e Using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left(o|s\\right)\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{i}\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e, we computed word-level metrics.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{BS}_{i}\\)\u003c/span\u003e \u003c/span\u003e was operationalized as the Kullback\u0026ndash;Leibler divergence between the belief and the prior distributions: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{BS}_{i}={D}_{KL}\\left({q}_{i}\\left(s\\right)|p\\left(s\\right)\\right)\\)\u003c/span\u003e\u003c/span\u003e which quantifies the extent to which the participant-generated word-level belief distribution deviates from the semantic prior defined by the problem context. Surprise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{i}\\)\u003c/span\u003e\u003c/span\u003e measures deviation from the generative model: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{i}={BS}_{i}+{U}_{i}\\)\u003c/span\u003e\u003c/span\u003e. Here, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{U}_{i}\\:\\)\u003c/span\u003e\u003c/span\u003eis an uncertainty term corresponding to the cross-entropy between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{i}\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e and the observation model: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{U}_{i}=-{\\sum\\:}_{s}{q}_{i}\\left(s\\right)\\text{ln}p\\left(o|s\\right)\\)\u003c/span\u003e\u003c/span\u003e. Idea-level metrics (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e) were then calculated by averaging these word-level values across all content words \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{i}\\in\\:W\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFocusing on the DT phase across tasks and phases (Pre, Stim, and Post), we identified the maximum \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e value among all ideas generated by each participant, defining it as max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e. The Surprise value of the specific idea that yielded this max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e was subsequently extracted and defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStatistical analysis.\u003c/b\u003e After Z-score normalization across participants and IQR-based outlier exclusion, metrics were compared across conditions using one-way ANOVA. Significant effects were followed by post-hoc Dunnett\u0026rsquo;s tests (p-values adjusted via multivariate t-distribution) comparing the right alpha condition against both controls.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Relatedness judgement and the Acceptance of Semantically Distant Primes\u003c/h2\u003e \u003cp\u003eTo confirm that there were no pre-existing differences in creativity between the stimulation groups, we conducted a permutation-based F-test on semantic memory network metrics. No significant differences were observed across conditions for any metric prior to stimulation. The observed \u003cem\u003eF\u003c/em\u003e-statistics were: for CC, 0.314 (\u003cem\u003ep\u003c/em\u003e = .727); for GE, 0.267 (\u003cem\u003ep\u003c/em\u003e = .767); for LE, 0.136 (\u003cem\u003ep\u003c/em\u003e = .871); and for Q, 1.722 (\u003cem\u003ep\u003c/em\u003e = .187).\u003c/p\u003e \u003cp\u003eTo verify whether there was an expected gradation in the hint usage rates among the word categories (Near, Far, and Irrelevant) adopted in this study, we performed a Kruskal\u0026ndash;Wallis test. Figure\u0026nbsp;7 shows the hint usage rate across word categories and conditions. As predicted, Near words had the highest rates (DT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;41.86, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;24.42; CT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;37.21, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;25.58), followed by Far (DT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.33, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.81; CT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.33, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.65), and Irrelevant words (DT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.16, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.33; CT: \u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.16, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.33). We observed significant category differences in both DT, \u003cem\u003eH\u003c/em\u003e(2)\u0026thinsp;=\u0026thinsp;14.28, \u003cem\u003ep\u003c/em\u003e \u0026lt; .001, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.752, and CT, \u003cem\u003eH\u003c/em\u003e(2)\u0026thinsp;=\u0026thinsp;15.70, \u003cem\u003ep\u003c/em\u003e \u0026lt; .001, \u003cem\u003eη\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.826. Post-hoc contrasts revealed Near words had significantly higher usage than both Far (DT: \u003cem\u003ep\u003c/em\u003e = .020; CT: \u003cem\u003ep\u003c/em\u003e = .022) and Irrelevant words (DT: \u003cem\u003ep\u003c/em\u003e = .001; CT: \u003cem\u003ep\u003c/em\u003e \u0026lt; .001). We observed no significant difference between Far and Irrelevant words (DT: \u003cem\u003ep\u003c/em\u003e = .233; CT: \u003cem\u003ep\u003c/em\u003e = .149).\u003c/p\u003e \u003cp\u003eTo evaluate the hypothesis that right temporal alpha stimulation promotes distant concept exploration by actively inhibiting obvious semantic associations, we conducted a Friedman test to examine the effect of stimulation on hint usage rates. The analysis revealed a significant main effect of stimulation specifically for Far words during the CT phase, \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;7.91, \u003cem\u003ep\u003c/em\u003e = .019. However, post-hoc showed that the hint usage rate for Far words in the right alpha condition (\u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;7.69, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.85) was not significantly higher than the left alpha (\u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.67; \u003cem\u003ep\u003c/em\u003e = .063) or right gamma (\u003cem\u003eMdn\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00, \u003cem\u003eIQR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.33; \u003cem\u003ep\u003c/em\u003e = .063) conditions after Holm correction. There were no significant effects during the DT phase for Far words, \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;4.26, \u003cem\u003ep\u003c/em\u003e = .119, and no significant effects of stimulation were observed for Near (DT: \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;2.00, \u003cem\u003ep\u003c/em\u003e = .368; CT: \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;0.29, \u003cem\u003ep\u003c/em\u003e = .867) or Irrelevant words (DT: \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;1.40, \u003cem\u003ep\u003c/em\u003e = .497; CT: \u003cem\u003eX\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e(2)\u0026thinsp;=\u0026thinsp;0.00, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.00).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Effects of Right Temporal Alpha Stimulation on Problem-Solving Task\u003c/h2\u003e \u003cp\u003eTo evaluate the effect of right temporal alpha stimulation on ideas during the problem-solving task, we assessed subjective self-ratings and compared conditions using one-way ANOVA per phase. Figure\u0026nbsp;8 highlights changes in self-ratings during the DT phase of the problem-solving task. In Pre phase, we observed no significant differences across conditions for any evaluation metric: originality, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;1.75, \u003cem\u003ep\u003c/em\u003e = .188, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.091; confidence, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;1.19, \u003cem\u003ep\u003c/em\u003e = .317, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.064; aha strength, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;1.22, \u003cem\u003ep\u003c/em\u003e = .308, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.065, indicating no pre-existing condition differences. In Stim phase, there were no significant differences between conditions for originality, \u003cem\u003eF\u003c/em\u003e(2, 33)\u0026thinsp;=\u0026thinsp;1.42, \u003cem\u003ep\u003c/em\u003e = .257, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.079; confidence, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;1.96, \u003cem\u003ep\u003c/em\u003e = .157, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.101; or aha strength, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;2.90, \u003cem\u003ep\u003c/em\u003e = .068, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.142. In Post phase, the effect of stimulation conditions was significant on self-rated originality, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;5.04, \u003cem\u003ep\u003c/em\u003e = .012, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.224. Post-hoc contrasts identified significantly higher originality in the right alpha condition compared to both the left alpha condition, \u003cem\u003et\u003c/em\u003e(35)\u0026thinsp;=\u0026thinsp;2.90, \u003cem\u003ep\u003c/em\u003e = .012, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.079, and the right gamma condition, \u003cem\u003et\u003c/em\u003e(35)\u0026thinsp;=\u0026thinsp;2.55, \u003cem\u003ep\u003c/em\u003e = .029, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.301. In contrast, there were no significant differences for the other evaluation metrics, including confidence, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;1.13, \u003cem\u003ep\u003c/em\u003e = .336, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.060; and aha strength, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;3.05, \u003cem\u003ep\u003c/em\u003e = .060, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.148, across the conditions.\u003c/p\u003e \u003cp\u003eSimilarly, we analyzed the objective information-based metrics using the same one-way ANOVA approach. The results of the analysis on max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e during the DT phase of the problem-solving task are presented in Fig.\u0026nbsp;9A. In both Pre and Stim phase, no significant differences were observed between conditions: Pre phase, \u003cem\u003eF\u003c/em\u003e(2, 33)\u0026thinsp;=\u0026thinsp;0.04, \u003cem\u003ep\u003c/em\u003e = .957, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.003; Stim phase, \u003cem\u003eF\u003c/em\u003e(2, 34)\u0026thinsp;=\u0026thinsp;0.35, \u003cem\u003ep\u003c/em\u003e = .706, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.020. However, in Post phase, significant differences was observed, \u003cem\u003eF\u003c/em\u003e(2, 34)\u0026thinsp;=\u0026thinsp;4.16, \u003cem\u003ep\u003c/em\u003e = .024, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.197. Post-hoc contrasts revealed significantly higher max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003et\u003c/em\u003e(34)\u0026thinsp;=\u0026thinsp;2.32, \u003cem\u003ep\u003c/em\u003e = .049, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.890, in the right alpha condition compared to the left alpha condition. In contrast, no significant difference was found between the right alpha and the right gamma conditions, \u003cem\u003et\u003c/em\u003e(34)\u0026thinsp;=\u0026thinsp;0.30, \u003cem\u003ep\u003c/em\u003e = .938, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.107. Figure\u0026nbsp;9B illustrates the results for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e during the DT phase of the problem-solving task. In both Pre and Stim phase, no significant differences were observed across conditions: Pre phase, \u003cem\u003eF\u003c/em\u003e(2, 33)\u0026thinsp;=\u0026thinsp;0.05, \u003cem\u003ep\u003c/em\u003e = .956, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.003; Stim phase, \u003cem\u003eF\u003c/em\u003e(2, 34)\u0026thinsp;=\u0026thinsp;0.35, \u003cem\u003ep\u003c/em\u003e = .706, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.020. In contrast, in Post phase, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e revealed significant effect, \u003cem\u003eF\u003c/em\u003e(2, 34)\u0026thinsp;=\u0026thinsp;4.14, \u003cem\u003ep\u003c/em\u003e = .025, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.196. Post-hoc tests indicated that the right alpha condition resulted in significantly higher \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e compared to the left alpha condition, \u003cem\u003et\u003c/em\u003e(34)\u0026thinsp;=\u0026thinsp;2.31, \u003cem\u003ep\u003c/em\u003e = .049, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.889. However, no significant differences in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e were observed between the right alpha and right gamma conditions, \u003cem\u003et\u003c/em\u003e(34)\u0026thinsp;=\u0026thinsp;0.29, \u003cem\u003ep\u003c/em\u003e = .939, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.106.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e3.3 \u003cb\u003eEffects of Right Temporal Alpha Stimulation on Problem-Finding Task\u003c/b\u003e\u003c/h2\u003e \u003cp\u003eTo evaluate the effect of right temporal alpha stimulation on ideas during the problem-finding task, we assessed subjective self-ratings and compared conditions using one-way ANOVA per phase. Figure\u0026nbsp;10 shows changes in self-ratings for ideas during the DT phase of the problem-finding task. First, similar to the problem-solving task, there were no significant differences between conditions in Pre phase for any evaluation metrics: originality, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;2.58, \u003cem\u003ep\u003c/em\u003e = .089, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.123; confidence, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;0.44, \u003cem\u003ep\u003c/em\u003e = .646, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.023; aha strength, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;0.41, \u003cem\u003ep\u003c/em\u003e = .666, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.022. Second, in Stim phase, there were no significant differences between conditions for originality, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;3.10, \u003cem\u003ep\u003c/em\u003e = .057, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.144; confidence, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;2.41, \u003cem\u003ep\u003c/em\u003e = .104, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.115; or aha strength, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;0.94, \u003cem\u003ep\u003c/em\u003e = .040, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.048. Finally, in Post phase, we observed a significant effect of stimulation condition on the originality, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;6.18, \u003cem\u003ep\u003c/em\u003e = .005, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.250; confidence, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;4.19, \u003cem\u003ep\u003c/em\u003e = .023, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.185; and aha strength, \u003cem\u003eF\u003c/em\u003e(2, 37)\u0026thinsp;=\u0026thinsp;4.17, \u003cem\u003ep\u003c/em\u003e = .023, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.184. Post-hoc comparisons revealed that originality was significantly higher in the right alpha condition than in both the left alpha condition, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;3.48, \u003cem\u003ep\u003c/em\u003e = .003, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.269, and the right gamma condition, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;2.31, \u003cem\u003ep\u003c/em\u003e = .048, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.993. For confidence, self-ratings in the right alpha condition were significantly higher than in the right gamma condition, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;2.77, \u003cem\u003ep\u003c/em\u003e = .016, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.267, but not significantly different from the left alpha condition, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;2.20, \u003cem\u003ep\u003c/em\u003e = .062, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.784. Aha strength was significantly higher in the right alpha condition compared to the left alpha condition, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;2.89, \u003cem\u003ep\u003c/em\u003e = .012, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.184, while the difference with the right gamma condition was not significant, \u003cem\u003et\u003c/em\u003e(37)\u0026thinsp;=\u0026thinsp;1.48, \u003cem\u003ep\u003c/em\u003e = .247, Hedges\u0026rsquo; \u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.587.\u003c/p\u003e \u003cp\u003eSimilarly, we analyzed the objective information-based metrics using the same one-way ANOVA approach. Figure\u0026nbsp;11 summarises the results of the analysis on information-based metrics (max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e) during the DT phase of the problem-finding task. Across all phases (Pre, Stim, and Post), no significant differences were found between conditions for either metric. For max \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e (Fig.\u0026nbsp;11A), the main effect of condition was not significant in Pre phase, \u003cem\u003eF\u003c/em\u003e(2, 30)\u0026thinsp;=\u0026thinsp;0.90, \u003cem\u003ep\u003c/em\u003e = .418, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.057, Stim phase, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;0.61, \u003cem\u003ep\u003c/em\u003e = .550, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.034, or Post phase, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;0.18, \u003cem\u003ep\u003c/em\u003e = .835, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.010. Similarly, for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{BS}\\)\u003c/span\u003e\u003c/span\u003e (Fig.\u0026nbsp;11B), no significant main effects of condition were observed in Pre phase, \u003cem\u003eF\u003c/em\u003e(2, 30)\u0026thinsp;=\u0026thinsp;0.90, \u003cem\u003ep\u003c/em\u003e = .418, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.056, Stim phase, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;0.61, \u003cem\u003ep\u003c/em\u003e = .550, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.034, or Post phase, \u003cem\u003eF\u003c/em\u003e(2, 35)\u0026thinsp;=\u0026thinsp;0.19, \u003cem\u003ep\u003c/em\u003e = .830, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003eG\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.011.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe present study provides causal neurophysiological evidence linking right temporal alpha oscillations to the modulation of predictive precision during creative design cognition. Grounded in the FEP and the ICM, we hypothesized that decreasing predictive precision\u0026mdash;computationally operationalized as an increase in prior variance\u0026mdash;would facilitate the exploration of novel semantic spaces. By applying tACS at IAF to the right temporal lobe, we sought to temporarily attenuate top-down predictive constraints. The principal findings corroborate this overarching hypothesis: (1) during the problem-solving task, right temporal alpha stimulation significantly increased maximum information gain and optimal arousal of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e, alongside elevated self-ratings of originality; and (2) during the problem-finding task, stimulation enhanced subjective ratings of originality, confidence, and aha strength, despite an absence of significant changes in corpus-based objective information metrics.\u003c/p\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Modulation of Predictive Precision in Problem-Solving\u003c/h2\u003e \u003cp\u003eIn the problem-solving task, right temporal alpha stimulation led to a significant increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e\u0026rsquo;s maximum information gain and its optimal arousal level compared to the hemispheric control (left temporal alpha). Furthermore, this stimulation enhanced the acceptance of semantically distant priming stimuli (Far words). These findings advance previous neurostimulation literature, which posits that right temporal alpha oscillations act as a neural mechanism for the active inhibition of obvious semantic associations.\u003csup\u003e\u003cspan citationid=\"CR114\" class=\"CitationRef\"\u003e114\u003c/span\u003e,\u003cspan citationid=\"CR115\" class=\"CitationRef\"\u003e115\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eWithin the predictive processing framework, alpha oscillations have been shown to encode the precision of top-down predictions.\u003csup\u003e\u003cspan additionalcitationids=\"CR80\" citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e\u003c/sup\u003e Strong predictions\u0026mdash;shaped by habitual associations, established knowledge, or design fixation\u0026mdash;act as high-precision priors that rigidly constrain the search space.\u003csup\u003e\u003cspan additionalcitationids=\"CR72 CR73 CR74\" citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e\u003c/sup\u003e By artificially enhancing right temporal alpha rhythms, tACS effectively lowered the precision of these dominant prior beliefs, thereby increasing the variance of the probability distribution of the internal model. Computationally, this temporary reduction in precision expands the agent\u0026rsquo;s tolerance for higher surprise and promotes divergent exploration, directly resulting in the observed maximization of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e associated with highly original design solutions.\u003csup\u003e\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e,\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e,\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e,\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e,\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e,\u003cspan citationid=\"CR92\" class=\"CitationRef\"\u003e92\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Task Context Dependency: Problem-Solving versus Problem-Finding\u003c/h2\u003e \u003cp\u003eWhile the problem-solving task exhibited robust increases in objective information metrics, the problem-finding task showed no significant changes in these corpus-based measures, despite a clear enhancement in subjective evaluations. This dissociation can be logically interpreted through the baseline informational characteristics of the tasks themselves. The prior distributions established for the problem-finding task inherently possessed higher entropy compared to the problem-solving task. Problem-finding requires navigating an ill-defined, highly ambiguous conceptual space with minimal external constraints, meaning the baseline prior precision is already low.\u003csup\u003e\u003cspan citationid=\"CR119\" class=\"CitationRef\"\u003e119\u003c/span\u003e,\u003cspan citationid=\"CR120\" class=\"CitationRef\"\u003e120\u003c/span\u003e\u003c/sup\u003e As illustrated in Fig.\u0026nbsp;4, because theoretical simulation indicates that maximum information gain and optimal arousal are highly sensitive to modifications in precision when prior precision is initially high, the impact of further reducing precision via alpha tACS was likely attenuated in the problem-finding condition. This attenuation aligns with the well-established state-dependency of non-invasive brain stimulation, where intervention outcomes are fundamentally bound by the baseline neural and cognitive state.\u003csup\u003e\u003cspan citationid=\"CR121\" class=\"CitationRef\"\u003e121\u003c/span\u003e,\u003cspan citationid=\"CR122\" class=\"CitationRef\"\u003e122\u003c/span\u003e\u003c/sup\u003e Conversely, the problem-solving task featured a structured problem-scoping phase that narrowed the context, establishing higher baseline precision. Thus, reducing predictive precision through right temporal alpha stimulation yielded a more pronounced shift in the exploration of the semantic space during problem-solving, as reflected in the information-based metrics.\u003csup\u003e\u003cspan citationid=\"CR123\" class=\"CitationRef\"\u003e123\u003c/span\u003e\u003c/sup\u003e These information-theoretic observations suggest that the clarity of prior knowledge or context in a task, namely how clearly the problem space is defined, is critical for information gain and creative exploration.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Dissociation Between Subjective Evaluations and Objective Metrics\u003c/h2\u003e \u003cp\u003eThe observation that subjective ratings (originality, confidence, and aha strength) increased in the problem-finding task without corresponding increases in objective \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:BS\\)\u003c/span\u003e\u003c/span\u003e reflects a well-documented discrepancy between subjective and objective creativity measurements.\u003csup\u003e\u003cspan additionalcitationids=\"CR125\" citationid=\"CR124\" class=\"CitationRef\"\u003e124\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR126\" class=\"CitationRef\"\u003e126\u003c/span\u003e\u003c/sup\u003e Information-based metrics calculated via a static Wikipedia corpus capture the semantic distance of concepts in generalized human knowledge. In contrast, subjective evaluations rely on the dynamic exploration of each participant\u0026rsquo;s idiosyncratic semantic memory networks.\u003c/p\u003e \u003cp\u003eWhen the right temporal alpha tACS suppressed dominant associations, it allowed participants to internally explore more distant concepts. The sudden successful bridging of an ambiguous knowledge gap generates an instantaneous resolution of internal prediction errors. Neurobiologically, this sharp drop in uncertainty functions as an intrinsic reward mediated by dopaminergic pathways, which manifests consciously as a strong \"Aha\" experience and heightened confidence.\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e,\u003cspan additionalcitationids=\"CR128 CR129 CR130 CR131 CR132\" citationid=\"CR127\" class=\"CitationRef\"\u003e127\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR133\" class=\"CitationRef\"\u003e133\u003c/span\u003e\u003c/sup\u003e Therefore, the elevation in subjective scores suggests that the stimulation successfully promoted internal semantic restructuring and an active inference process, generating strong feelings of insight and originality, even when the generated ideas did not register as statistically distant within the generalized macro-corpus parameters.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Neurophysiological Mechanisms of Offline tACS Effects\u003c/h2\u003e \u003cp\u003eNotably, the significant effects of right temporal alpha stimulation on both information-based metrics and subjective ratings emerged during the Post phase rather than concurrently during the Stim phase. This temporal delay is consistent with recent literature delineating the mechanisms of tACS. While online effects are generally attributed to the immediate entrainment of endogenous oscillations,\u003csup\u003e134,135\u003c/sup\u003e offline aftereffects are driven by neuroplastic changes, specifically spike-timing-dependent plasticity (STDP) and strengthening the synapse through long-term potentiation (LTP).\u003csup\u003e\u003cspan citationid=\"CR136\" class=\"CitationRef\"\u003e136\u003c/span\u003e,\u003cspan citationid=\"CR137\" class=\"CitationRef\"\u003e137\u003c/span\u003e\u003c/sup\u003e Because the tACS in this study was administered at frequencies marginally below each participant\u0026rsquo;s true offline-calculated IAF, the stimulation likely satisfied the preconditions for STDP, whereby presynaptic activity consistently precedes postsynaptic firing, leading to robust synaptic strengthening. This extended plasticity facilitated the sustained state of reduced predictive precision necessary for the creative tasks performed after the stimulation ceased.\u003csup\u003e\u003cspan citationid=\"CR138\" class=\"CitationRef\"\u003e138\u003c/span\u003e,\u003cspan citationid=\"CR139\" class=\"CitationRef\"\u003e139\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Limitations and Future Directions\u003c/h2\u003e \u003cp\u003eSeveral methodological limitations must be acknowledged when interpreting these findings. First, the relatively small sample size may have limited statistical power, given the high inter-individual variability in creative cognition\u003csup\u003e\u003cspan citationid=\"CR140\" class=\"CitationRef\"\u003e140\u003c/span\u003e\u003c/sup\u003e and individual responsiveness to tACS.\u003csup\u003e\u003cspan citationid=\"CR141\" class=\"CitationRef\"\u003e141\u003c/span\u003e\u003c/sup\u003e Second, while IAFs were utilized, the tACS protocol lacked real-time phase-locking to endogenous brain rhythms, which can introduce variability into the neuromodulatory outcomes.\u003csup\u003e\u003cspan citationid=\"CR142\" class=\"CitationRef\"\u003e142\u003c/span\u003e\u003c/sup\u003e Future studies leveraging closed-loop, phase-locked HD-tACS protocols concurrently with neuroimaging will be necessary to isolate precise spatiotemporal network dynamics. Finally, because the problem-finding task consistently followed the problem-solving task, the neuroplastic aftereffects of tACS might have gradually decayed.\u003csup\u003e\u003cspan citationid=\"CR138\" class=\"CitationRef\"\u003e138\u003c/span\u003e\u003c/sup\u003e Future experimental designs must counterbalance task order to definitively rule out time-dependent attenuation. Nevertheless, the observation of significant enhancements in subjective ratings strongly indicates that the neuromodulatory influence on internal evaluative processes remained robust even in the latter half of the experiment. Thus, the dissociation between objective metrics and subjective experiences observed in this task is more likely attributable to its inherently high baseline uncertainty, rather than merely the fading of stimulation effects.\u003c/p\u003e \u003cp\u003eBeyond these methodological refinements, the present findings open critical avenues for advancing design research. While we utilized neurostimulation to artificially lower predictive precision, a fundamental question for design science is how designers can self-regulate this cognitive state. Future research must clarify the factors that modulate predictive precision. Recent cognitive models propose that creative thought is shaped by the interplay of deliberate and automatic constraints on spontaneous thought.\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR143\" class=\"CitationRef\"\u003e143\u003c/span\u003e,\u003cspan citationid=\"CR144\" class=\"CitationRef\"\u003e144\u003c/span\u003e\u003c/sup\u003e Building on this framework, it is highly promising to hypothesize that the predictive precision\u0026mdash;which acts as a strong top-down constraint on the search space\u0026mdash;targeted in our study is primarily modulated by \"deliberate constraints\" actively set by designers (e.g., goal-directedness, evaluative thinking) and \"automatic constraints\" operating unconsciously (e.g., preconceptions, expertise bias, emotional bias, and habitual thinking). As a subsequent step, future studies should investigate the extent to which these constraining factors can be actively relaxed or regulated without external brain stimulation, by employing established design strategies and ideation tools (e.g., forced associations, random word stimulation, or intentional reframing).\u003c/p\u003e \u003cp\u003eFurthermore, the current study assessed isolated, short-term ideation tasks performed by individuals. However, real-world design typically unfolds over weeks or months, often within multidisciplinary teams.\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR145\" class=\"CitationRef\"\u003e145\u003c/span\u003e\u003c/sup\u003e Therefore, it is essential to investigate how the ICM and the mechanism of uncertainty modulation function within such complex, collaborative practical projects. Extending this research to highly ecologically valid settings will bridge the gap between neurocognitive principles and practical design processes.\u003c/p\u003e \u003c/div\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eThis study provides causal neurophysiological evidence bridging the theoretical frameworks of the Bayesian brain and the Inquiry Cycle Model (ICM) with the practical domain of creative design cognition. By demonstrating that upregulating right temporal alpha oscillations effectively lowers top-down predictive precision, our findings reveal a neural mechanism for relaxing rigid semantic priors to facilitate the generation of highly original ideas. Crucially, we highlight that the magnitude and nature of this creative enhancement are context-dependent, fundamentally modulated by the baseline uncertainty of the task. In more defined problem-solving scenarios, reducing precision significantly increases objective Bayesian surprise (maximum information gain and optimal arousal). Conversely, in highly ambiguous problem-finding contexts where prior precision is inherently low, the intervention primarily amplifies the internal, subjective experience of insight, confidence, and originality. Ultimately, by mapping these neurophysiological and information-theoretic dynamics onto the Free Energy Principle, this research offers a mechanistic understanding of how designers strategically embrace and resolve uncertainty to achieve genuinely novel solutions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eK.K.: Conceptualization, Methodology, Data curation, Investigation, Project administration, Validation, Formal analysis, Funding acquisition, Visualization, Software, Writing - Original Draft, Writing - Review \u0026amp; Editing.\u003c/p\u003e\n\u003cp\u003eH.Y.: Conceptualization, Methodology, Funding acquisition, Writing - Review \u0026amp; Editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eS.H.: Software, Writing - Review \u0026amp; Editing.\u003c/p\u003e\n\u003cp\u003eY.N.K.: Conceptualization, Methodology, Software, Writing - Review \u0026amp; Editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eC.D.B.L.: Conceptualization, Methodology, Data curation, Investigation, Project administration, Validation, Resources, Supervision, Software, Writing - Review \u0026amp; Editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll authors have read and approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe were supported by JSPS Overseas Research Fellowships and JSPS KAKENHI Grant Number JP25H01132.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank Anum Hussain, Charlotte Basso, and Eleonora Canino for helping to collect EEG data. We also thank Kakeru Hashimoto for sharing the code that formed the basis of the information-theoretic calculations used in this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics statement\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe research was approved by the College of Health, Medicine and Life Sciences Research Ethics Committee (DLS) at Brunel University of London (Reference: 44385-LR-Oct/2023-47425-2).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe data and analysis code that support the findings of this study are openly available in OSF at https://doi.org/10.17605/OSF.IO/KRY8Q.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of Generative AI and AI-assisted technologies in the writing process\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDuring the preparation of this work the authors used ChatGPT (OpenAI) and Gemini (Google) in order to improve the clarity and language quality of the manuscript. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eGero J.S. 2000. Computational Models of Innovative and Creative Design Processes. \u003cem\u003eTechnological Forecasting and Social Change\u003c/em\u003e \u003cstrong\u003e64\u003c/strong\u003e: 183\u0026ndash;196. https://doi.org/10.1016/S0040-1625(99)00105-5\u003c/li\u003e\n\u003cli\u003eBuchanan R. 1992. Wicked problems in design thinking. \u003cem\u003eDesign issues\u003c/em\u003e \u003cstrong\u003e8\u003c/strong\u003e: 5\u0026ndash;21.\u003c/li\u003e\n\u003cli\u003eSch\u0026ouml;n D.A. 1983. \u0026ldquo;\u003cem\u003eThe reflective practitioner: how professionals think in action\u003c/em\u003e.\u0026rdquo; New York: Basic Books.\u003c/li\u003e\n\u003cli\u003eSarkar P. \u0026amp; A. Chakrabarti. 2011. 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Updating the dynamic framework of thought: Creativity and psychedelics. \u003cem\u003eNeuroImage\u003c/em\u003e \u003cstrong\u003e213\u003c/strong\u003e: 116726\u0026ndash;116726. https://doi.org/10.1016/j.neuroimage.2020.116726\u003c/li\u003e\n\u003cli\u003eBucciarelli L.L. 1994. \u0026ldquo;\u003cem\u003eDesigning engineers\u003c/em\u003e.\u0026rdquo; MIT press.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Brunel University of London College of Health, Medicine and Life Sciences","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"creative design, free energy principle, inquiry cycle model, predictive precision, transcranial alternating current stimulation","lastPublishedDoi":"10.21203/rs.3.rs-9152871/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9152871/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCreative design is an inquiry process that transforms unknowns into knowns while strategically accepting uncertainty to generate novelty. To understand this computationally, we applied the Inquiry Cycle Model (ICM), which extends the Free Energy Principle by positing that temporary increases in predictive uncertainty maximize long-term information gain. We investigated how modulating this uncertainty influences design ideation by conducting a double-blind, randomized controlled experiment using transcranial alternating current stimulation (tACS). By targeting right temporal alpha oscillations\u0026mdash;a neural mechanism for inhibiting obvious semantic associations\u0026mdash;we artificially lowered top-down predictive precision during divergent thinking.\u003c/p\u003e \u003cp\u003eResults demonstrated that this intervention effectively enhanced self-reported originality in both problem-solving and problem-finding tasks. Crucially, the nature of this creative enhancement was fundamentally modulated by the baseline uncertainty of the task context. In more structured problem-solving scenarios, reducing predictive precision significantly increased objective, corpus-based Bayesian surprise (specifically, maximum information gain and optimal arousal). Conversely, in highly ambiguous problem-finding contexts where prior precision is inherently low, the intervention primarily amplified subjective, internal experiences of insight (aha strength) and confidence.\u003c/p\u003e \u003cp\u003eThese findings provide causal neurophysiological evidence linking right temporal alpha oscillations to predictive precision. Ultimately, they partially support the ICM and highlight the context-dependent role of predictive precision in fostering novelty during idea generation. This offers a mechanistic account of creative cognition based on the brain\u0026rsquo;s information-processing principles, laying the groundwork for evidence-based methodologies that deliberately regulate these cognitive states in design practice.\u003c/p\u003e","manuscriptTitle":"Embracing Uncertainty: Reducing Predictive Precision in Bayesian Inference Enhances Novelty in Creative Design","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-19 08:54:56","doi":"10.21203/rs.3.rs-9152871/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a34f8735-e9e4-4ad7-b2d9-2f6f983a9a7c","owner":[],"postedDate":"March 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":64683995,"name":"Cognitive Neuroscience"},{"id":64683996,"name":"Architecture, Design and Planning"},{"id":64683997,"name":"Computational Neuroscience"},{"id":64683998,"name":"Psychology"}],"tags":[],"updatedAt":"2026-03-19T08:54:56+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-19 08:54:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9152871","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9152871","identity":"rs-9152871","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}