Mindmatics

A Nexus of Ideas

verfasst von: Yair Neuman

Verlag: Springer Nature Switzerland

Buchreihe : Mathematics in Mind

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis

Über dieses Buch

Mindmatics invites readers into a captivating exploration where the boundaries between mind and mathematics dissolve. Professor Neuman delves into the profound connections between cognitive processes and mathematical expression in this groundbreaking work. From how children grasp abstract concepts to symmetry's role in art and mathematics, this book uncovers the hidden structures that shape our understanding of the world. With insightful discussions on the relationship between poetry and mathematics and the essential role of the unconscious in fostering mathematical imagination, Mindmatics offers a unique perspective on the interplay of thought, creativity, and logic. This book is a must-read for anyone curious about the deeper links between the human mind and the mathematical universe.

Inhaltsverzeichnis

Frontmatter

Chapter 1. The Root of Mind and Mathematics

Abstract

The root of the mind is the primary distinction, and the mind unfolds through similarities, differences, similarities of differences, and differences of similarities. We will learn about these ideas and about the mind as a sign-mediated system. These ideas and their manifestations in the mind and mathematics are discussed and illustrated through various examples, from the similarity of a sausage and a dachshund to Boole’s fundamental law of thought.

Yair Neuman

Chapter 2. Equality, Similarity, and Transformations

Abstract

The equality sign (i.e., “=”), the idea of identity, and repetition are discussed. I explain how repetition stands at the heart of identity and point out the similarity of repetition in mathematics, psychology, and the arts. By discussing iterated function systems, fixed points, and invariant sets, the reader will learn that the equality sign in mathematics indicates a symmetry expressed under certain transformations. This chapter takes us on a journey from mathematics to psychoanalysis and poetry.

Yair Neuman

Chapter 3. Mind and Mathematics in an Event-Centered Approach

Abstract

The mind isn’t reducible to sensorimotor experiences, and neither is mathematics. In this chapter, I argue that sign-based processes are the foundations of both mind and mathematics and explain this idea through the concept of the variable, which allows us to imagine and explore multiple possibilities beyond the concrete. The mind is presented through an event-centered approach, according to which events, interactions, and transformations should be the focus of our analysis. This thesis is illustrated by word meanings and multiplication. The chapter also discusses linear transformations, liquid cats, and the reasons why narrow-minded educators may be dissatisfied with genies.

Yair Neuman

Chapter 4. Symmetry, the Unconscious, and Imagination

Abstract

Symmetry is expressed in mathematics, psychology, and the arts. In this chapter, I inquire about the symmetry dynamic of the unconscious, as explained by Matte-Blanco, and point to the importance of this mind system in supporting imagination. We will meet aliens at a galactic family gathering and the Frog Prince, and see how projection matrices can model the way our minds move between different dimensionalities.

Yair Neuman

Chapter 5. Imagination, Mathematics, and Mysticism

Abstract

This concluding chapter takes us on a journey from poetry to mysticism. It opens by showing how four ancient forms of interpretation can be used to exercise imagination. It then goes on to show how complex numbers added another possible type of number to algebra and explains how this may help us deal with a Kushiya arising from Boole’s fundamental law of thought. The chapter concludes by reflecting on the intersection of mind, mathematics, and mysticism.

Yair Neuman

Chapter 6. Epilogue

Abstract

The epilogue reflects on concluding the book, comparing it to summarizing a concert. I summarize the book as a journey through mind, mathematics, and imagination, highlighting their profound interconnectedness. Ultimately, the book aims to deepen our understanding of the mind and mathematics, inspiring further exploration of the intricate dance of distinction, signification, and transformation within the human cognitive landscape.

Yair Neuman

Backmatter

Titel: Mindmatics
verfasst von: Yair Neuman
Verlag: Springer Nature Switzerland
Electronic ISBN: 978-3-031-74955-1
Print ISBN: 978-3-031-74954-4
DOI: https://doi.org/10.1007/978-3-031-74955-1