Related papers: Thinking Inside and Outside the Box
Recent work on interpretability in machine learning and AI has focused on the building of simplified models that approximate the true criteria used to make decisions. These models are a useful pedagogical device for teaching trained…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
An analysis of several important aspects of competition or conflict in games, social choice and decision theory is presented. Inherent difficulties and complexities in cooperation are highlighted. These have over the years led to a certain…
Most creative outputs are readily classified as belonging to a particular domain such as art, music, or technology. But does that mean the creative thinking that goes into creative projects respects these conventional domain boundaries?…
Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.
I use spin as a guide through the labyrinth of possibilities and ideas that go beyond the established understanding of the fundamental interactions.
Exploring the capabilities of Large Language Models (LLMs) in puzzle solving unveils critical insights into their potential and challenges in AI, marking a significant step towards understanding their applicability in complex reasoning…
The Snake-in-the-Box problem is that of finding a longest induced path in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced cycle in…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying mathematics and describe how they are naturally associated…
A robot operating in isolation needs to reason over the uncertainty in its model of the world and adapt its own actions to account for this uncertainty. Similarly, a robot interacting with people needs to reason over its uncertainty over…
We investigate the Dots and Boxes game, also known as ``Strings and Coins,'' for certain specific families of graphs. These include complete graphs, wheel graphs, and friendship graphs.
As machine learning is increasingly deployed in high-stakes contexts affecting people's livelihoods, there have been growing calls to open the black box and to make machine learning algorithms more explainable. Providing useful explanations…
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we…
The primary objective of this note is to revisit the two envelope problem and propose a simple resolution. It is argued that the paradox arises from the ambiguity associated with the money content $x of the chosen envelope. When X=x is…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
Black box machine learning models are currently being used for high stakes decision-making throughout society, causing problems throughout healthcare, criminal justice, and in other domains. People have hoped that creating methods for…
Theory of Mind is an essential ability of humans to infer the mental states of others. Here we provide a coherent summary of the potential, current progress, and problems of deep learning approaches to Theory of Mind. We highlight that many…
The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are…