Numbers have mathematically defined, formal meanings, which afford precision and objectivity. In practice, however, we show that round numbers are frequently used approximately, and this approximate use depends on magnitude. Across three analyses of British and American English, we demonstrate the following: (1) people use round numbers more often, and round to a greater extent, at higher magnitudes; (2) the distributional semantics of larger round numbers resemble those of indefinite hyperbolic numbers such as ‘gazillion’, which lack a precise value; and (3) larger jigsaw puzzles have greater discrepancies between round advertised piece counts and the actual values (e.g., advertising ‘13,200 pieces’ when the actual count is 13,224). We argue that the relationship between roundness, magnitude and approximation derives from the base-10 structure of English numerals, which renders powers of 10 structurally salient, creating hotspots for communicative functions such as approximation. We discuss how these communicative patterns align with the approximate number system, which cognitively represents larger quantities with increasing imprecision, making them harder to estimate and compare.

Social scientists express concerns that perspectives on new genetic engineering techniques, such as gene editing, are becoming polarized and entrenched and that those entrenched positions could hinder the formation of alliances needed to make the new technologies available. Without such alliances, potential solutions to agronomic challenges, food security, climate change, improving nutrition, and reducing food waste may never be implemented. This paper explores whether these competing perspectives are as entrenched as they are often portrayed. Through intensive interviews, I ask German scientists to share their perspectives on the European Court of Justice (ECJ) ruling that gene edited crops would be regulated the same as transgenic crops. Using the concepts of techno-optimism and techno-pessimism to analyze those scientists’ perspectives, I discover that both techno-optimistic and techno-pessimistic scientists are generally less entrenched and more reflective when presented with competing perspectives. Furthermore, four of the scientists offer potential policies and practices that could resolve some disputes and could even overcome obstacles to promoting social and ecological benefits from the new technologies.

The rational homology of the IA-automorphism group $\operatorname {IA}_n$ of the free group $F_n$ is still mysterious. We study the quotient of the rational homology of $\operatorname {IA}_n$ that is obtained as the image of the map induced by the abelianization map, which we call the Albanese homology of $\operatorname {IA}_n$. We obtain a representation-stable $\operatorname {GL}(n,\mathbb {Q})$-subquotient of the Albanese homology of $\operatorname {IA}_n$, which conjecturally coincides with the entire Albanese homology of $\operatorname {IA}_n$. In particular, we obtain a lower bound of the dimension of the Albanese homology of $\operatorname {IA}_n$ for each homological degree in a stable range. Moreover, we determine the entire third Albanese homology of $\operatorname {IA}_n$ for $n\ge 9$. We also study the Albanese homology of an analogue of $\operatorname {IA}_n$ for the outer automorphism group of $F_n$ and the Albanese homology of the Torelli groups of surfaces. Moreover, we study the relation between the Albanese homology of $\operatorname {IA}_n$ and the cohomology of $\operatorname {Aut}(F_n)$ with twisted coefficients.

Plantago fengdouensis, a species endemic to China’s Yangtze River Basin, was once presumed extinct in the wild as a result of the complete inundation of its native habitats following the construction of the Three Gorges Dam. Historically documented only on two riverine islets in Fengdu and Zhongxian counties of Chongqing, the species was last observed in 2003 before its habitats were permanently submerged, leading to its designation as the first documented herbaceous plant driven to extinction by the dam project. However, in 2023 a previously unknown population of > 200 individuals was discovered in Jiang’an County, Sichuan Province, representing the largest known wild population to date. From January to May 2023, 273 seeds were collected and conservation research was conducted in the botanical greenhouse of Yibin University. The key to the germination of P. fengdouensis seeds lies in the harvest period. Seeds with light brown seed coats that are not fully mature have the highest germination vitality. Through systematic germination trials, optimal conditions were identified as 24 h pretreatment with 1.0% gibberellin under 28 ℃ and 1,500 Lux illumination, achieving an 87.5% germination rate. During May–November 2024, nursery-grown seedlings were transplanted near the wild population, with an initial 89% establishment success and 98.5% survival after 12 months. These results suggest that P. fengdouensis populations can be effectively restored in situ through seed-based propagation, offering a model for conserving other threatened floodplain species.

Interpreting requires regular and frequent language switching and is thus likely beneficial to cognitive flexibility. However, advantage research found mixed results, probably due to two confounding factors: interpreter expertise and task differences. This study targeted the critical period of intermediate interpreter expertise and compared participants’ switching performance in the rule–based Wisconsin Card Sorting Test (WCST) and the cue-based colour–shape switching tasks (uni-/bivalent versions). Results showed that interpreting students at the pre-intermediate level outperformed bilingual controls in switch cost, and in WCST errors and global RT. With the same participants tested 1 year later and with interpreting students at the post-intermediate level, interpreters outperformed in mixing cost in the bivalent task and in WCST global RT. The findings of the colour–shape switching tasks (further confirmed by cue-based analysis) revealed a developmental transition of interpreters’ advantage from local switching to global monitoring, and a differential sensitivity of the tasks, with implications for studies on bilingual advantage.

The article is focused on friendship and collaboration between two prominent alpine climbers: Stipe Božić from Croatia and Viki Grošelj from Slovenia. Following their joint endeavors beginning in Yugoslavia and proceeding within the setting of independent countries, the article discusses different framings of alpinist expeditions on which they embarked together, which range from a common Yugoslav enterprise to a nationally separate narrative. Highlighting that their primary motivation for cooperation was in sharing goals and professional compatibility, the article explores how personal narratives are transformed into national narratives. Finally, the article touches upon the value of friendship research for exploring everyday nationhood.

Food literacy is important for understanding the factors that determine food choices, eating behaviours and diet quality. However, few studies have examined the relationship between food literacy, diet quality and food consumption. The present study aimed to examine this relationship in an adult population. This cross-sectional study included 639 adults (50·2 % female; age range: 19–65 years) at Ondokuz Mayıs University in Samsun, Türkiye. Participants completed the Short Food Literacy Questionnaire (SFLQ). Anthropometric measurements and 24-h food recall were recorded. Diet quality was assessed using the Healthy Eating Index (HEI)-2015. Total scores for vegetables and seafood and plant proteins (HEI-2015 components) were higher in the adequate–excellent food literacy group (2·9 (sd 2·25) v. 2·5 (sd 1·85), P = 0·041 and 12·8 (sd 12·51) v. 11·0 (sd 10·58), P = 0·040). Conversely, the refined grain scores were higher in the inadequate–limited food literacy group (3·6 (sd 5·77) v. 4·5 (sd 5·67), P = 0·041). In the regression model, the SFLQ score was positively associated with HEI-2015 scores (β = 0·364, P = 0·026) and total vegetable consumption (β = 0·029, P = 0·015). For each 1-point increase in the SFLQ score, the HEI-2015 score increased by 0·364 points on average (β = 0·364, P = 0·026). Furthermore, SFLQ scores were negatively associated with refined grain scores (β = −0·107, P = 0·001) and added sugar scores (β = −0·021, P = 0·042). Food literacy is an important factor associated with diet quality. Enhancing nutrition knowledge, skills and attitudes in adults may contribute to healthier eating behaviours.

This Article examines the legitimacy crisis in investment arbitration with a particular focus on Africa’s historical and contemporary experiences under the investor–state dispute settlement (ISDS) system. Tracing the colonial origins of international investment law, it argues that the structure and implementation of ISDS mechanisms have disproportionately disadvantaged African states. Through historical analysis, case law, and the reform agenda of UNCITRAL’s Working Group III, the Article highlights how Africa was both shaped by and now actively participates in shaping global investment law. While acknowledging colonial-era power asymmetries, the Article contends that the future lies in Africa’s strategic engagement with reform efforts. It concludes by proposing regionally grounded reforms and a shift in perspective that recognizes African states not as passive respondents, but as vital contributors to the evolution of investment arbitration.

Global mental health advances its commitment to rights-based care grounded in dignity, autonomy and freedom from coercion, assuming worth is inherent and support is a right. This Perspective aims to strengthen that agenda by adding a cultural-implementation lens: in many settings, everyday moral reasoning links worth to contribution (e.g., labour, perseverance and fulfilment of social obligations), creating a moral economy of worth in which legitimacy is earned, relational and conditional. Drawing on cross-cultural psychology, the article argues that contribution-based moralities are especially salient where three cultural dimensions co-occur: restraint, collectivism and long-term orientation. In such contexts, support can be morally misread as unearned reward, rest as indulgence and reduced functioning as moral failure, producing ethical dissonance that shapes help-seeking, clinical practice and policy uptake without implying rejection of human rights. Using Japan as an illustrative case, the article shows how norms of perseverance (ganbaru) and regulated dependence (amae) can intensify contingent self-worth, self-stigma, rapid-return expectations and family hesitation to seek support. To improve legitimacy and sustainability, five strategies are proposed: broaden what counts as contribution; frame recovery as stewardship for future participation; avoid morally triggering eligibility language; use culturally credible lived-experience narratives; and engage institutions across levels that shape moral judgement.

Among White Americans, have attitudes toward the Black Lives Matter (BLM) movement become increasingly polarized between 2016 and 2020, and was that polarization sustained through 2024? This study conceptualizes BLM polarization as a growing divergence in attitudes toward the movement—both in overall evaluations and in widening gaps across key orientations such as partisanship, racial resentment, social dominance orientation (SDO), and authoritarianism. Building upon recent work on partisan polarization, I examine individual-level changes in racial attitudes toward BLM over an extended time period and determine if partisanship or other socio-psychological predispositions predict this change. Through the use of the American National Election Studies (ANES) 2016–2020–2024 panel data, I find that BLM polarization occurred from 2016 to 2020 and remained robust from 2020 to 2024. Racial resentment, SDO, and authoritarianism also served as important factors associated with BLM polarization, alongside party affiliation.

For the third time in a century, the concept of critical minerals has become a central theme in international trade and security debates. Materials criticality discourse first arose in the late 1930s and 1940s. It was taken up again from the mid-1970s through to mid-1980s and has become ubiquitous in post-pandemic debates concerning the global energy transition in a context of escalating geopolitical volatility. This article examines the evolution of critical minerals discourse over a century, with a focus on these three periods. It seeks to identify the contexts in which criticality claims have emerged and to examine the politics of critical minerals discourse in this third wave. It argues that critical minerals discourse has evolved in response to geopolitical instability understood by the US to threaten its hegemony; and that critical minerals discourse in its third wave has thus far served four major political functions. First, critical minerals discourse has served as a rhetorical device for asserting that the security of the US and its allies lies in the defence of US hegemony, and not in the defence of international institutions and trade norms. Second, critical minerals discourse has served as an effective means of leveraging geopolitical instability in favour of extractive interests. Third, critical minerals discourse has worked to re-mystify the economics of market speculation and the predictability of state intervention in markets. Finally, critical minerals discourse has been used to leverage the existential urgency of the climate crisis in favour of elite and extractive interests and against local communities and ecosystems.