Iconic Arithmetic Volume II: Symbolic and Postsymbolic Formal Foundations - Couverture souple

Bricken Ph.D., William

Couverture souple

ISBN 10 : 1732485143 ISBN 13 : 9781732485143

Editeur : Unary press, 2019

Synopsis

Volume II of this series explores the unique structural characteristics of James algebra, a void-based iconic system inspired by the work of Charles Sanders Peirce, George Spencer Brown and Louis Kauffman. This volume defines the concepts of equality, substitution and concurrency for pattern-based transformation of nested containers. Substitution is sufficient mechanism to implement numeric operations. Iconic representation encourages parallel numeric computation. Boundary mathematics itself is constructed from difference rather than number. It mixes both numeric and non-numeric form.

A central objective of Volume II is to place James algebra within the context of the formal structure of arithmetic developed by Hilbert, Frege and Peano at the turn of the twentieth century. Peano’s axiomatic definition of numbers is substantively simplified. Presburger arithmetic, Robinson arithmetic and Primitive Recursive Arithmetic are restructured by removing the assumptions of string-based notation. The nature of formal systems and symbolic computation is then examined from an iconic perspective, leading to the elimination of set theory, propositional and predicate logic, and functional thinking as necessities of formal structure.

Volume I (ISBN 9781732485136) of this series explores iconic arithmetic from the perspectives of historical evolution, formal mathematics, computer science and mathematics education. Volume III (ISBN 9781732485150) shows how James algebra can organize and integrate non-numeric concepts such as infinity and indeterminism, and introduces a new additive imaginary number J that underlies √–1.

Iconic Arithmetic helps us to transition into a postsymbolic world of interactive information. The innovative perspectives will be fully rewarding to scholars interested in unique mathematical ideas, to students who question conventional mathematics, to educators and designers hoping to enhance creativity, to computer scientists seeking powerful new techniques, to folks who trust their senses more than their memory, to those whose intellectual approach to the world is visual, tactile and experiential, and to explorers of the evolution of philosophy and cognition.

Détails de l'édition

• Éditeur: Unary press
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 1732485143
• ISBN 13: 9781732485143
• Reliure: Broché
• Nombre de pages: 452
• Coordonnées du fabricant: Manufactured by Amazon on behalf of the author; https://www.amazon.fr/hz/contact-us; ; c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy; Luxembourg; L-1855; Luxembourg