Related papers: Thinking Inside and Outside the Box
In the particle in the box problem, the particle is not in both boxes at the same time as some would have you believe. It is a set definition situation with the two boxes being part of a set that also contains a particle. Set and subset…
Space, time, and additional dimensions spawn remarkable complexity in optics. We encourage pairing black-box simulation and design tools with a complementary tool: understanding.
Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this "extensive" faculty conduct most mathematics research, their interests are the most heavily…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…
When language models answer open-ended problems, they implicitly make hidden decisions that shape their outputs, leaving users with uncontextualized answers rather than a working map of the problem; drawing on multiverse analysis from…
Cyberspace is being more and more tightly linked to the physical space and socioeconomic space to emerge a cyber-physical-socioeconomic space, where humans, machines and physical objects in the natural environment interact with each other,…
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some…
Learning to code, and more broadly, learning about computer science is a growing field of activity and research. Under the label of computational thinking, computational concepts are increasingly used as cognitive tools in many subject…
Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored.…
Human consciousness has been a long-lasting mystery for centuries, while machine intelligence and consciousness is an arduous pursuit. Researchers have developed diverse theories for interpreting the consciousness phenomenon in human brains…
The diffusion of artificial intelligence (AI) applications in organizations and society has fueled research on explaining AI decisions. The explainable AI (xAI) field is rapidly expanding with numerous ways of extracting information and…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
Entanglement, a puzzle since Einstein's time, has become increasingly crucial with the rise of quantum computation. But what exactly is it? Historically , entanglement can be precisely defined, but only negatively. In this article, we…
People leverage group discussions to collaborate in order to solve complex tasks, e.g. in project meetings or hiring panels. By doing so, they engage in a variety of conversational strategies where they try to convince each other of the…
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…
We demonstrate that users may be prone to place an inordinate amount of trust in black box algorithms that are framed as intelligent. We deploy an algorithm that purportedly assesses the positivity and negativity of a users' writing…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Black box systems for automated decision making, often based on machine learning over (big) data, map a user's features into a class or a score without exposing the reasons why. This is problematic not only for lack of transparency, but…
Recent progress in artificial intelligence (AI) has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video…