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arXiv2026

Half Strong Ill-Posedness of $2 \frac{1}{2}$D Electron Magnetohydrodynamics with Fractional Resistivity

We study the $2\frac{1}{2}$D electron magnetohydrodynamics (MHD): the electron MHD system that has $3$D magnetic field but is independent of $z$-variable. We establish a "half" strong ill-posedness result in $2\frac{1}{2}$D electron MHD with fractional resistivity $(-\Delta)^\alpha$ in the supercritical Sobolev space $H^{\beta}\times H^{\beta-1}$ for $3<\beta<4-2\alpha$. Specifically, we construct small initial data $(a_0,b_0)$ whose solution develops a norm inflation in $a$ but the norm of $b$ remains small.

math.AP↗

arXiv2025

"It makes you think": Provocations Help Restore Critical Thinking to AI-Assisted Knowledge Work

Recent research suggests that the use of Generative AI tools may result in diminished critical thinking during knowledge work. We study the effect on knowledge work of provocations: brief textual prompts that offer critiques for and propose alternatives to AI suggestions. We conduct a between-subjects study (n=24) in which participants completed AI-assisted shortlisting tasks with and without provocations. We find that provocations can induce critical and metacognitive thinking. We derive five dimensions that impact the user experience of provocations: task urgency, task importance, user expertise, provocation actionability, and user responsibility. We connect our findings to related work on design frictions, microboundaries, and distributed cognition. We draw design implications for critical thinking interventions in AI-assisted knowledge work.

cs.HC↗

arXiv2024

When Copilot Becomes Autopilot: Generative AI's Critical Risk to Knowledge Work and a Critical Solution

Generative AI, with its tendency to "hallucinate" incorrect results, may pose a risk to knowledge work by introducing errors. On the other hand, it may also provide unprecedented opportunities for users, particularly non-experts, to learn and apply advanced software features and greatly increase the scope and complexity of tasks they can successfully achieve. As an example of a complex knowledge workflow that is subject to risks and opportunities from generative AI, we consider the spreadsheet. AI hallucinations are an important challenge, but they are not the greatest risk posed by generative AI to spreadsheet workflows. Rather, as more work can be safely delegated to AI, the risk is that human critical thinking -- the ability to holistically and rigorously evaluate a problem and its solutions -- is degraded in the process. The solution is to design the interfaces of generative AI systems deliberately to foster and encourage critical thinking in knowledge work, building primarily on a long history of research on critical thinking tools for education. We discuss a prototype system for the activity of critical shortlisting in spreadsheets. The system uses generative AI to suggest shortlisting criteria and applies these criteria to sort rows in a spreadsheet. It also generates "provocations": short text snippets that critique the AI-generated criteria, highlighting risks, shortcomings, and alternatives. Our prototype opens up a rich and completely unexplored design space of critical thinking tools for modern AI-assisted knowledge work. We outline a research agenda for AI as a critic or provocateur, including questions about where and when provocations should appear, their form and content, and potential design trade-offs.

cs.HC↗