A Calculus of Ideas

A Calculus of Ideas
Author: Ulf Grenander
Publisher: World Scientific
Total Pages: 236
Release: 2012
Genre: Computers
ISBN: 981438318X

Download A Calculus of Ideas Book in PDF, Epub and Kindle

This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.

A Calculus of Ideas

A Calculus of Ideas
Author: Ulf Grenander
Publisher: World Scientific
Total Pages: 236
Release: 2012
Genre: Computers
ISBN: 9814383198

Download A Calculus of Ideas Book in PDF, Epub and Kindle

This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.

Calculus Of Ideas, A: A Mathematical Study Of Human Thought

Calculus Of Ideas, A: A Mathematical Study Of Human Thought
Author: Ulf Grenander
Publisher: World Scientific
Total Pages: 236
Release: 2012-08-10
Genre: Mathematics
ISBN: 9814439118

Download Calculus Of Ideas, A: A Mathematical Study Of Human Thought Book in PDF, Epub and Kindle

This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.

Mathematics for Human Flourishing

Mathematics for Human Flourishing
Author: Francis Su
Publisher: Yale University Press
Total Pages: 287
Release: 2020-01-07
Genre: Mathematics
ISBN: 0300237138

Download Mathematics for Human Flourishing Book in PDF, Epub and Kindle

"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Handbook of Abductive Cognition

Handbook of Abductive Cognition
Author: Lorenzo Magnani
Publisher: Springer Nature
Total Pages: 1921
Release: 2023-03-31
Genre: Technology & Engineering
ISBN: 3031101359

Download Handbook of Abductive Cognition Book in PDF, Epub and Kindle

This Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group of internationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.

Numbers and the World

Numbers and the World
Author: David Mumford
Publisher: American Mathematical Society
Total Pages: 259
Release: 2023-09-27
Genre: Mathematics
ISBN: 1470470519

Download Numbers and the World Book in PDF, Epub and Kindle

This book is a collection of essays written by a distinguished mathematician with a very long and successful career as a researcher and educator working in many areas of pure and applied mathematics. The author writes about everything he found exciting about math, its history, and its connections with art, and about how to explain it when so many smart people (and children) are turned off by it. The three longest essays touch upon the foundations of mathematics, upon quantum mechanics and Schrödinger's cat phenomena, and upon whether robots will ever have consciousness. Each of these essays includes some unpublished material. The author also touches upon his involvement with and feelings about issues in the larger world. The author's main goal when preparing the book was to convey how much he loves math and its sister fields.

On the Logos: A Naïve View on Ordinary Reasoning and Fuzzy Logic

On the Logos: A Naïve View on Ordinary Reasoning and Fuzzy Logic
Author: Enric Trillas
Publisher: Springer
Total Pages: 214
Release: 2017-05-05
Genre: Technology & Engineering
ISBN: 3319560530

Download On the Logos: A Naïve View on Ordinary Reasoning and Fuzzy Logic Book in PDF, Epub and Kindle

This book offers an inspiring and naïve view on language and reasoning. It presents a new approach to ordinary reasoning that follows the author’s former work on fuzzy logic. Starting from a pragmatic scientific view on meaning as a quantity, and the common sense reasoning from a primitive notion of inference, which is shared by both laypeople and experts, the book shows how this can evolve, through the addition of more and more suppositions, into various formal and specialized modes of precise, imprecise, and approximate reasoning. The logos are intended here as a synonym for rationality, which is usually shown by the processes of questioning, guessing, telling, and computing. Written in a discursive style and without too many technicalities, the book presents a number of reflections on the study of reasoning, together with a new perspective on fuzzy logic and Zadeh’s “computing with words” grounded in both language and reasoning. It also highlights some mathematical developments supporting this view. Lastly, it addresses a series of questions aimed at fostering new discussions and future research into this topic. All in all, this book represents an inspiring read for professors and researchers in computer science, and fuzzy logic in particular, as well as for psychologists, linguists and philosophers.

Robot Memetics

Robot Memetics
Author: Walt Truszkowski
Publisher: Springer Nature
Total Pages: 82
Release: 2020-01-30
Genre: Technology & Engineering
ISBN: 3030379523

Download Robot Memetics Book in PDF, Epub and Kindle

This book provides a novel perspective on the concept of memetics as applied to the development and evolution of intelligent robots and robotic communities/cultures. It provides a framework for the emergence of a hybrid community of people and intelligent robots collaborating to realize mutual benefits and scientific objectives. It aims to show that as the hybrid community emerges, so does its culture. Once this foundational work is done, the book illustrates the robot memetic ideas in the context of a space exploration scenario based on the development and operation of a human/robot settlement on Mars.

The Genesis of Logic

The Genesis of Logic
Author: Enric Trillas
Publisher: Springer Nature
Total Pages: 119
Release:
Genre:
ISBN: 3031550404

Download The Genesis of Logic Book in PDF, Epub and Kindle

How Humans Learn to Think Mathematically

How Humans Learn to Think Mathematically
Author: David Tall
Publisher: Cambridge University Press
Total Pages: 483
Release: 2013-09-02
Genre: Education
ISBN: 1107035708

Download How Humans Learn to Think Mathematically Book in PDF, Epub and Kindle

How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.