The Reasons for a (Sometimes) Change of Mind

Often we experience a “change of mind” on some issue for which, at the time it was made, we are certain of its correctness. The central question we investigate in this presentation is: What valid reasons can be made for a “change of mind”? For example, scientific progress is made because older theories are replaced by better theories with the major reason being new evaluations and analyses of data and methodologies. We examine and discuss a broad range of issues for which a “change of mind” provides useful insights on the relevant topics. Examples include the interpretation and appreciation of modern art, selecting a queue when multi-possibilities exist, the Monty-Hall problem, and forgiveness for past deeds. Our primary tool for this study is the application of the concept of the “Rashomon effect”

Art Is I, Science Is We

The expression of the title has been used for some time to produce a concise summary of the major distinction between “art” and “science.” Our goal is to give a fuller and deeper understanding of this statement by discussing its meaning and interpretation within the context of a precise definition of science. We conclude that “Art is I, science is we,” captures accurately the fundamental difference between these two disciplines

The Reasons (Sometimes) for a Change of Mind

Often we experience a “change of mind” on some issue for which, at the time it was made, we are certain of its correctness. The central question we investigate in this presentation is: What valid reasons can be made for a “change of mind”? For example, scientific progress is made because older theories are replaced by better theories with the major reason being new evaluations and analyses of data and methodologies. We examine and discuss a broad range of issues for which a “change of mind” provides useful insights on the relevant topics. Examples include the interpretation and appreciation of modern art, selecting a queue when multi-possibilities exist, the Monty-Hall problem, and forgiveness for past deeds. Our primary tool for this study is the application of the concept of the “Rashomon effect”

The Level Structure of Mathematics: Some Implications

The creation of mathematical concepts and their simultaneous application arose through a set of structures: looking/comparison, counting, rational numbers, real and complex numbers, geometry/trigonometry, algebra, calculus, etc. We refer to this as the “level structure of mathematics (LSOM).” This presentation examines some of the consequences of this characterization and we discuss its implications for the teaching and learning of mathematics. We focus on several issues related to research in the mathematical based sciences, and the impact that LSOM has on enhancing or not the participation of students in STEM fields. Finally, we provide arguments to illustrate that the LSOM is a major cause of the low level of science literacy existing in the general educated public and examine roles that librarians can play in aiding educational professionals in the selection of appropriate text books for all levels of pre-college mathematics courses