In The Unknowable I use LISP to compare my work on incompleteness with that of G6del and Turing, and in The Limits of Mathematics I use LISP to discuss my work on incompleteness in more detail. In this book we'll use LISP to explore my theory of randomness, called algorithmic information theory (AIT). And when I say "explore" I mean it! This book is full of exercises for the reader, ranging from the mathematical equivalent oftrivial "fin ger warm-ups" for pianists, to substantial programmi...

Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level.For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a que...

This book explores the meaning of life for Israelis living along the Gaza border before and after October 7th. It brings together residents’ personal stories and photographs, alongside their creative social media posts.This second edition builds on a groundbreaking longitudinal study conducted between 2018 and 2021, which examined how people made sense of their lives after two decades of ongoing conflict. Now expanded with new research carried out in the wake of the Hamas terror at...

Personal narratives of genocide and intractable war can provide valuable insights around notions of collective identity, perceptions of the 'enemy,' intergenerational coping with massive social trauma, and sustainable peace and reconciliation. Written in an accessible and narrative style, this book demonstrates how the sharing of and listening to personal experiences deepens understandings of the long-term psychosocial impacts of genocide and war on direct victims and their descendants in ...

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines.The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as...

This book explores the meaning of life for Israelis from communities bordering the Gaza Strip, whose lives are bound to the intractable conflict between Israel and the Hamas regime. Based on a psychosocial qualitative study of narrative interviews, photographs, YouTube videos, and Facebook posts created by residents, the book presents the life stories of ordinary people, their perspectives of patriotism and Zionism, and their perceptions of the Gazan Palestinians. Routine Emergency capture...

The instant New York Times bestseller about humanity's place in the universe—and how we understand it.“Vivid...impressive....Splendidly informative.”—The New York Times“Succeeds spectacularly.”—Science“A tour de force.”—SalonAlready internationally acclaimed for his elegant, lucid writing on the most challenging notions in modern physics, Sean Carroll is emerging as one of t...

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation invaluable. All the information included is practical, rarely used results are excluded. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference! If you don't have a lot of time but want to excel in class, this book helps you: Brush up before tests Find answers fast Learn key formulas and tables Study quickly and more effect...

Written by noted quantum computing theorist Scott Aaronson, this book takes readers on a tour through some of the deepest ideas of maths, computer science and physics. Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of ...

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of fa...

This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and ...

This book provides a historic overview of what is defined as "soft computing" with its techniques: neural networks, fuzzy logic, genetic algorithms and cellular automata.