Related papers: From conjecture generation by maintaining dragging…
In this paper, we introduce and develop the theory of the Collatz process and the method of dynamical balls. We leverage this theory to study the Collatz conjecture. This theory also has a subtle connection with the infamous problem of the…
Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity…
MacGyvering is defined as creating or repairing something in an inventive or improvised way by utilizing objects that are available at hand. In this paper, we explore a subset of Macgyvering problems involving tool construction, i.e.,…
Repeated interaction between individuals is the main mechanism for maintaining cooperation in social dilemma situations. Variants of tit-for-tat (repeating the previous action of the opponent) and the win-stay lose-shift strategy are known…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We investigate the reasons of having confidence in mathematical theorems. The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to this confidence. Opposing…
The use of language-model-based question-answering systems to aid humans in completing difficult tasks is limited, in part, by the unreliability of the text these systems generate. Using hard multiple-choice reading comprehension questions…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
This work focuses on a theoretical analysis of a well-known inertia demonstration, which uses a weight suspended by a string with an extra string that hangs below the weight. The point in question is which string, the upper or lower, will…
Teaching an agent to perform new tasks using natural language can easily be hindered by ambiguities in interpretation. When a teacher provides an instruction to a learner about an object by referring to its features, the learner can…
The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights. I make this association for the simplest reasonable model of random juggling and compute the steady state probabilities…
Emergence and maintenance of excitability is often phrased in terms of arriving at and remaining about a manifold of 'solutions' embedded in a high dimensional parameter space. Alongside studies that extend traditional focus on…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Nudging participants with text-based reflective nudges enhances deliberation quality on online deliberation platforms. The effectiveness of multimodal reflective nudges, however, remains largely unexplored. Given the multi-sensory nature of…
In this course, I talk about the source of mathematical constructivism and its role in the future development of theoretical physics. I describe what physical constructivism is and why it is necessary for the penetration of exact methods of…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…
Numerical simulations in two space dimensions are used to examine the dynamics, transport, and equilibrium behaviors of a neutrally buoyant circular object immersed in an active suspension within a larger closed circular container. The…
Although reinforcement learning has seen tremendous success recently, this kind of trial-and-error learning can be impractical or inefficient in complex environments. The use of demonstrations, on the other hand, enables agents to benefit…
The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…