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Chaos theory is a branch of classical physics, founded in the 1960s-70s, that studies systems whose solutions are sensitively dependent on their initial conditions. For many, it is surprising that chaos theory arrived so late. However, through the work of Henri Poincaré, we know that much of the math of chaos was understood by some 70 years prior. Furthermore, through the writings of Poincaré's colleagues – Jacques Hadamard and Pierre Duhem – we also see a detailed understanding of the chaos found in his work. They also have explicit reasons of why the math of chaos was to be ignored. It was a strict form of empiricism – positivism – causing them to label chaos as “useless” and “meaningless” mathematics because it was thought to be ungrounded in experience. In this paper, I describe how the empiricist tenets of positivism exiled chaos from physics following Poincaré.

This reply is also a friendly introduction to the impossibility of emergence of preferred structures from the Hamiltonian $\mathsf{H}$ and the unit vector $|\psi\rangle$ only. The obstructions to emergence are illustrated on the concrete construction of a tensor product structure (TPS) from Soulas et al., 2025 ( arXiv:2512.07468v2 ). Soulas et al. offer their TPS as a counterexample to the proof from Stoica, 2022a ( arXiv:2102.08620 ) that structures constructed only from $\mathsf{H}$ and $|\psi\rangle$ either contradict physical observations or can't describe them unambiguously. Soulas et al.'s construction of a unique TPS can't be both invariant and compatible with physical observations, so it can't be a counterexample. Its incompatibility becomes visible by examining how the relation between $|\psi(t)\rangle$ and the TPS, encoding the entanglement, changes in time. Therefore their TPS doesn't refute, but confirms (Stoica, 2022a). Besides this, since Soulas et al.'s method to construct preferred structures consists of choosing their invariants, by the same logic one could claim as well that the masses of elementary particles emerge uniquely just by fixing their values by hand. Soulas et al.'s construction is concrete and can illustrate the major obstructions for emergent structures, confirming them despite doing the best possible to avoid them. This makes it an excellent pedagogical tool to illustrate the trilemma, but also the relational and structural aspects of quantum theory and its symmetries.

The cognitive scientist Donald Hoffman argues that we don't perceive reality: spacetime, objects, colors, sounds, tastes, and so forth, are all merely an interface that we evolved to track evolutionary fitness rather than to perceive truths about external reality. In this paper, I expound on his argument, then I extend it, primarily, by looking at key ideas in physics that are quite germane to it. Among the topics in physics that I discuss are black holes, the holographic principle, string theory, duality, quantum gravity, and special relativity. I discuss these ideas from physics with an eye to their relevance for Hoffman's view.

The rapid advancement of LLMs has generated growing interest in their potential role in physics education and assessment, yet a focused evaluation of their performance on multi-faceted, free-response physics problems remains underexplored. In this study, we systematically evaluate the performance of four widely accessible AI systems-ChatGPT 4.1 mini, Gemini 2.5 Flash, Claude 4.0 Sonnet, and DeepSeek R1-on AP Physics 1 and 2 free-response questions administered between 2015 and 2025. Model-generated solutions were produced under standardized exam-style prompting and evaluated by three independent physics experts using official College Board scoring guidelines. All models achieved relatively high mean scores (82-92%), indicating strong capability in structured algebraic problem solving. However, substantial year-to-year variability was observed, particularly for AP Physics 1, where statistical testing revealed no consistent performance hierarchy among models. In contrast, AP Physics 2 results showed statistically significant differences, with Gemini and DeepSeek demonstrating more consistent performance than Claude. A qualitative analysis revealed recurring error patterns across all models, including misinterpretation of diagrams and graphs, incorrect graph construction, incorrect reasoning about vector direction, circuit topology errors, partial and misleading qualitative explanations, and difficulties applying three-dimensional concepts such as the right-hand rule. These findings suggest that while contemporary AI systems can effectively support routine physics problem solving, they remain limited in tasks requiring spatial reasoning, visual interpretation, and conceptual integration. The results highlight both the instructional potential and current pedagogical limitations of AI-assisted learning tools in physics education.

The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical, graphical or approximate analytic methods. Here we investigate the less explored problem of a particle in a semi-infinite potential well. The energy eigenvalues, which are also determined by a transcendental equation, are found by a standard graphical method, and a simple rule that yields the number of stationary states is provided. Next a simplification of the aforementioned transcendental equation is attempted. During the process pitfalls are encountered and a purportedly simpler graphical treatment of the problem given in the solutions manual to a fine textbook is shown to be flawed. A more careful analysis brings forth the correct simplification, which is shown to be particularly suitable for finding highly accurate approximations to the energy levels. Finally, a class of exact solutions is produced, the associated normalized eigenfunctions are constructed and the probability of finding the particle inside the well is computed.

Generative artificial intelligence (genAI) is becoming increasingly prevalent and capable in physics, particularly for programming-related tasks. How, then, does genAI affect students' computational modeling? We interviewed 19 undergraduate students who had recently completed an open-ended computational assignment that encouraged the use of genAI, asking them how they used it. We then conducted a thematic analysis of these interviews using a framework for computational modeling in physics. We found that genAI significantly impacts several aspects of students' computational modeling, such as the planning, implementing, and debugging of computational models. GenAI can also help students find resources and introduce them to new computational tools. Productive use of genAI was associated with students limiting its use to small steps in the modeling process and consistently double-checking the formulas, explanations, and code it provided. We also identified challenges students faced due to an over-reliance on genAI, such as working from false model assumptions and not spending time learning the fundamentals of computational modeling, especially debugging. Finally, we discuss implications for teaching, such as the need to teach students how to use genAI productively and to urge them to plan before they code. We also highlight the continued value of low-stakes assessment and teaching assistants for teaching computational modeling, as the task remains difficult even with the introduction of genAI.

One of the most interesting questions that astronomy can hope to answer is: are we alone in our Milky Way galaxy? A detection of an electromagnetic (EM) signal generated by an extraterrestrial technological intelligence (ETI), or the presence in our solar system of an alien probe, would answer this question in the affirmative. Purposeful interstellar communication is a 2-way street - the transmitting and receiving technological intelligence (TI) both need to do its part. As the receiving TI, our EM search programs should incorporate a model of what a transmitting TI is likely to be doing. Published searches for extraterrestrial technological intelligence (SETI) have generally not done so and, thus, have often been sub-optimally designed. We propose an improved search technique that more closely corresponds to astronomical surveys that have been undertaken for reasons that have nothing to do with SETI. Published non-SETI radio and optical surveys are sufficiently extensive that they already supply meaningful constraints on the prevalence of nearby purposely communicative alien civilizations. Purposeful communication can also include the sending of spaceships (probes). The absence of evidence for alien probes in the solar system suggests that no alien civilization has passed within 100 light-years of Earth during the past few billion years.

The cognitive scientist Donald Hoffman argues that we don't perceive reality: spacetime, objects, colors, sounds, tastes, and so forth, are all merely an interface that we evolved to track evolutionary fitness rather than to perceive truths about external reality. In this paper, I expound on his argument, then I extend it, primarily, by looking at key ideas in physics that are quite germane to it. Among the topics in physics that I discuss are black holes, the holographic principle, string theory, duality, quantum gravity, and special relativity. I discuss these ideas from physics with an eye to their relevance for Hoffman's view.

VAM ({\it velocità ascensionale media}) is a measurement that quantifies a cyclist's climbing ability. We show that to minimize the time to attain a given height gain –  which is tantamount to maximizing VAM –  a cyclist should climb as steep a constant-grade hill as possible. Apart from the power-to-weight ratio, the limit of steepness is imposed by such factors as the efficiency of pedalling, which is related to feasible cadence, maintaining balance, preventing lifting of the front, and skidding of the rear, wheel. This article is focused on consequences of the power available to the cyclist, which can be viewed as a necessary condition to examine other aspects of climbing strategy. We show that –  for given start and end points, and for any fixed average-power constraint –  the brachistochrone, which is the trajectory of minimum ascent time, is the straight line connecting these points, covered with a constant speed, which along such a line is equivalent to a constant power. This is in contrast to the classical solution of a descent brachistochrone under gravity, which is a cycloid along which the speed is not constant.