Related papers: Making Meaning with Math in Physics: A semantic an…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
Computational thinking is a way of reasoning about the world in terms of data. This mindset channels number crunching toward an ambition to discover knowledge through logic, models and simulations. Here we show how computational cognitive…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour,…
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Mathematical approaches to modeling the mind since the 1950s are reviewed. Difficulties faced by these approaches are related to the fundamental incompleteness of logic discovered by K. G\"odel. A recent mathematical advancement, dynamic…
The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered…
Traditionally, semantics has been seen as a feature of human language. The advent of the information era has led to its widespread redefinition as an information feature. Contrary to this praxis, I define semantics as a special kind of…
Computer graphics, often associated with films, games, and visual effects, has long been a powerful tool for addressing scientific challenges--from its origins in 3D visualization for medical imaging to its role in modern computational…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
Two transformative waves of computing have redefined the way we approach science. The first wave came with the birth of the digital computer, which enabled scientists to numerically simulate their models and analyze massive datasets. This…
We integrate foundational theories of meaning with a mathematical formalism of artificial general intelligence (AGI) to offer a comprehensive mechanistic explanation of meaning, communication, and symbol emergence. This synthesis holds…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
A formal theory of meaning (the process of knowledge accumulation) as multiplicative chaos is proposed. The epistemological process is understood as the process of subjective extraction of some knowledge from the incoming information. The…