According to 4E cognitive science, our cognitive capacities depend on, and have been transformed by, the environments we have made. Most early works of 4E cognitive science tend to focus on the upside of agent-environment interactions: They have made us smarter and allowed us to do more, despite the same, limited brain (and body) power. However, the recent critical turn focuses on the downsides of agent-environment interactions. Critical 4E cognitive science, as we call this emerging research program, adopts the 4E frameworks and concepts but with a critical lens: questioning its hidden assumptions and leveraging its theoretical resources for social criticism. In particular, we distinguish two kinds of normative critique that bring out the downsides of agent-environment interactions. Prudential critiques focus on how agent-environment interactions can shape an agent's cognition to undermine their own interests. Political critiques focus on how agent-environment interactions can shape an agent's cognition to contribute to the reinforcement and exacerbation of unjust social forces.
Featured Application Wind-tunnel tests and trajectory analyses of Trionda, the 2026 World Cup ball, are compared with previous World Cup balls.Abstract Wind-tunnel experiments were conducted on Trionda, the official match ball of the 2026 FIFA World Cup. Aerodynamic force coefficients derived from these measurements were incorporated into numerical trajectory simulations of kicked balls. The resulting aerodynamic characteristics and simulated flight behavior were compared with those of the four previous World Cup match balls: Al Rihla (2022), Telstar 18 (2018), Brazuca (2014), and Jabulani (2010). Relative to its predecessors, Trionda exhibits a drag crisis at lower flow speeds, consistent with an apparently rougher surface. Although its turbulent-regime drag coefficient is more stable than those of earlier designs, its magnitude is modestly larger. Trajectory simulations therefore indicate the potential for small but perceptible reductions in range for long kicks. This study therefore provides the first aerodynamic characterization of the 2026 FIFA World Cup match ball (Trionda) and places its drag-crisis behavior and flight characteristics in direct quantitative comparison with those of recent World Cup balls examined under identical experimental conditions.
Cactus networks were introduced by Lam as a generalization of planar electrical networks. He defined a map from these networks to the Grassmannian Gr($n+1,2n$) and showed that the image of this map, $\mathcal X_n$ lies inside the totally nonnegative part of this Grassmannian. In this paper, we show that $\mathcal X_n$ is exactly the elements of Gr($n+1,2n$) that are both totally nonnegative and isotropic for a particular skew-symmetric bilinear form. For certain classes of cactus networks, we also explicitly describe how to turn response matrices and effective resistance matrices into points of Gr($n+1,2n$) given by Lam's map. Finally, we discuss how our work relates to earlier studies of total positivity for Lagrangian Grassmannians.
Call it football, futbol, calcio, or soccer, there is some striking science behind the Beautiful Game and its sophisticated sphere.
