Uncomputable

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Uncomputable

Alexander Galloway
Uncomputable Book PDF

Author : Alexander Galloway
Publisher : Verso Books
Page : 289 pages
File Size : 45,5 Mb
Release : 2021-11-02
Category : Social Science
ISBN : 9781839764004

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Uncomputable by Alexander Galloway Pdf

A journey through the uncomputable remains of computer history Narrating some lesser known episodes from the deep history of digital machines, Alexander R. Galloway explains the technology that drives the world today, and the fascinating people who brought these machines to life. With an eye to both the computable and the uncomputable, Galloway shows how computation emerges or fails to emerge, how the digital thrives but also atrophies, how networks interconnect while also fray and fall apart. By re-building obsolete technology using today's software, the past comes to light in new ways, from intricate algebraic patterns woven on a hand loom, to striking artificial-life simulations, to war games and back boxes. A description of the past, this book is also an assessment of all that remains uncomputable as we continue to live in the aftermath of the long digital age.

Undecidability, Uncomputability, and Unpredictability

Anthony Aguirre,Zeeya Merali,David Sloan
Undecidability Uncomputability and Unpredictability Book PDF

Author : Anthony Aguirre,Zeeya Merali,David Sloan
Publisher : Springer Nature
Page : 181 pages
File Size : 40,6 Mb
Release : 2021-08-20
Category : Science
ISBN : 9783030703547

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Undecidability, Uncomputability, and Unpredictability by Anthony Aguirre,Zeeya Merali,David Sloan Pdf

For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​

Your Brain Is (Almost) Perfect

Read Montague
Your Brain Is Almost Perfect Book PDF

Author : Read Montague
Publisher : Penguin
Page : 352 pages
File Size : 50,6 Mb
Release : 2007-09-25
Category : Science
ISBN : 9781101665619

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Your Brain Is (Almost) Perfect by Read Montague Pdf

"A fascinating introduction" (Steven Pinker) to the science of decision-making One of the leading thinkers in the computational neuroscience revolution offers a brilliant new perspective on the mind?s decision-making process. Why do we make the choices we make? How can science explain free will? If our brains are like slow computers originally programmed for survival with goals like food, water, and sex, why do we make choices that go against our own biological best interests? Where do values come from? What role do emotions play? From how we decide what we consume to the romantic, ethical, and financial choices we make, Read Montague guides readers through a new approach to the mind that is both entertaining and illuminating.

Computability and Complexity

Neil D. Jones
Computability and Complexity Book PDF

Author : Neil D. Jones
Publisher : MIT Press
Page : 494 pages
File Size : 51,9 Mb
Release : 1997
Category : Computers
ISBN : 0262100649

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Computability and Complexity by Neil D. Jones Pdf

Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a shift away from the Turing machine- and G�del number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems. According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models. New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs. Foundations of Computing series

Quantum, Probability, Logic

Meir Hemmo,Orly Shenker
Quantum Probability Logic Book PDF

Author : Meir Hemmo,Orly Shenker
Publisher : Springer Nature
Page : 635 pages
File Size : 40,6 Mb
Release : 2020-04-07
Category : Science
ISBN : 9783030343163

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Quantum, Probability, Logic by Meir Hemmo,Orly Shenker Pdf

This volume provides a broad perspective on the state of the art in the philosophy and conceptual foundations of quantum mechanics. Its essays take their starting point in the work and influence of Itamar Pitowsky, who has greatly influenced our understanding of what is characteristically non-classical about quantum probabilities and quantum logic, and this serves as a vantage point from which they reflect on key ongoing debates in the field. Readers will find a definitive and multi-faceted description of the major open questions in the foundations of quantum mechanics today, including: Is quantum mechanics a new theory of (contextual) probability? Should the quantum state be interpreted objectively or subjectively? How should probability be understood in the Everett interpretation of quantum mechanics? What are the limits of the physical implementation of computation? The impact of this volume goes beyond the exposition of Pitowsky’s influence: it provides a unique collection of essays by leading thinkers containing profound reflections on the field. Chapter 1. Classical logic, classical probability, and quantum mechanics (Samson Abramsky) Chapter 2. Why Scientific Realists Should Reject the Second Dogma of Quantum Mechanic (Valia Allori) Chapter 3. Unscrambling Subjective and Epistemic Probabilities (Guido Bacciagaluppi) Chapter 4. Wigner’s Friend as a Rational Agent (Veronika Baumann, Časlav Brukner) Chapter 5. Pitowsky's Epistemic Interpretation of Quantum Mechanics and the PBR Theorem (Yemima Ben-Menahem) Chapter 6. On the Mathematical Constitution and Explanation of Physical Facts (Joseph Berkovitz) Chapter 7. Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle (Harvey R. Brown, Gal Ben Porath) Chapter 8. ‘Two Dogmas’ Redu (Jeffrey Bub) Chapter 9. Physical Computability Theses (B. Jack Copeland, Oron Shagrir) Chapter 10. Agents in Healey’s Pragmatist Quantum Theory: A Comparison with Pitowsky’s Approach to Quantum Mechanics (Mauro Dorato) Chapter 11. Quantum Mechanics As a Theory of Observables and States and, Thereby, As a Theory of Probability (John Earman, Laura Ruetsche) Chapter 12. The Measurement Problem and two Dogmas about Quantum Mechanic (Laura Felline) Chapter 13. There Is More Than One Way to Skin a Cat: Quantum Information Principles In a Finite World(Amit Hagar) Chapter 14. Is Quantum Mechanics a New Theory of Probability? (Richard Healey) Chapter 15. Quantum Mechanics as a Theory of Probability (Meir Hemmo, Orly Shenker) Chapter 16. On the Three Types of Bell's Inequalities (Gábor Hofer-Szabó) Chapter 17. On the Descriptive Power of Probability Logic (Ehud Hrushovski) Chapter 18. The Argument against Quantum Computers (Gil Kalai) Chapter 19. Why a Relativistic Quantum Mechanical World Must be Indeterministic (Avi Levy, Meir Hemmo) Chapter 20. Subjectivists about Quantum Probabilities Should be Realists about Quantum States (Wayne C. Myrvold) Chapter 21. The Relativistic Einstein-Podolsky-Rosen Argument (Michael Redhead) Chapter 22. What price statistical independence? How Einstein missed the photon.(Simon Saunders) Chapter 23. How (Maximally) Contextual is Quantum Mechanics? (Andrew W. Simmons) Chapter 24. Roots and (Re)Sources of Value (In)Definiteness Versus Contextuality (Karl Svozil) Chapter 25: Schrödinger’s Reaction to the EPR Paper (Jos Uffink) Chapter 26. Derivations of the Born Rule (Lev Vaidman) Chapter 27. Dynamical States and the Conventionality of (Non-) Classicality (Alexander Wilce).

What Can Be Computed?

John MacCormick
What Can Be Computed Book PDF

Author : John MacCormick
Publisher : Princeton University Press
Page : 408 pages
File Size : 43,5 Mb
Release : 2018-05-15
Category : Computers
ISBN : 9781400889846

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What Can Be Computed? by John MacCormick Pdf

An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com

Maths 1001

Dr Richard Elwes,Richard Elwes
Maths 1001 Book PDF

Author : Dr Richard Elwes,Richard Elwes
Publisher : Greenfinch
Page : 577 pages
File Size : 49,8 Mb
Release : 2017-07-06
Category : Mathematics
ISBN : 9781786486950

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Maths 1001 by Dr Richard Elwes,Richard Elwes Pdf

The ultimate smart reference to the world of mathematics - from quadratic equations and Pythagoras' Theorem to chaos theory and quantum computing. Maths 1001 provides clear and concise explanations of the most fascinating and fundamental mathematical concepts. Distilled into 1001 bite-sized mini-essays arranged thematically, this unique reference book moves steadily from the basics through to the most advanced of ideas, making it the ideal guide for novices and mathematics enthusiasts. Whether used as a handy reference, an informal self-study course or simply as a gratifying dip-in, this book offers - in one volume - a world of mathematical knowledge for the general reader. Maths 1001 is an incredibly comprehensive guide, spanning all of the key mathematical fields including Numbers, Geometry, Algebra, Analysis, Discrete Mathematics, Logic and the Philosophy of Maths, Applied Mathematics, Statistics and Probability and Puzzles and Mathematical Games. From zero and infinity to relativity and Godel's proof that maths is incomplete, Dr Richard Elwes explains the key concepts of mathematics in the simplest language with a minimum of jargon. Along the way he reveals mathematical secrets such as how to count to 1023 using just 10 fingers and how to make an unbreakable code, as well as answering such questions as: Are imaginary numbers real? How can something be both true and false? Why is it impossible to draw an accurate map of the world? And how do you get your head round the mind-bending Monty Hall problem? Extensive, enlightening and entertaining, this really is the only maths book anyone would ever need to buy.

The Incomputable

S. Barry Cooper,Mariya I. Soskova
The Incomputable Book PDF

Author : S. Barry Cooper,Mariya I. Soskova
Publisher : Springer
Page : 292 pages
File Size : 54,9 Mb
Release : 2017-05-05
Category : Computers
ISBN : 9783319436692

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The Incomputable by S. Barry Cooper,Mariya I. Soskova Pdf

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

The Nature of Physical Computation

Oron Shagrir
The Nature of Physical Computation Book PDF

Author : Oron Shagrir
Publisher : Oxford University Press
Page : 319 pages
File Size : 46,9 Mb
Release : 2022
Category : Computers
ISBN : 9780197552384

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The Nature of Physical Computation by Oron Shagrir Pdf

Computing systems are ubiquitous in contemporary life. Even the brain is thought to be a computing system of sorts. But what does it mean to say that a given organ or system "computes"? What is it about laptops, smartphones, and nervous systems that they are deemed to compute - and why does itseldom occur to us to describe stomachs, hurricanes, rocks, or chairs that way? These questions are key to laying the conceptual foundations of computational sciences, including computer science and engineering, and the cognitive and neural sciences.Oron Shagrir here provides an extended argument for the semantic view of computation, which states that semantic properties are involved in the nature of computing systems. The first part of the book provides general background. Although different in scope, these chapters have a common theme-namely,that the linkage between the mathematical theory of computability and the notion of physical computation is weak. The second part of the book reviews existing non-semantic accounts of physical computation. Shagrir analyze three influential accounts in greater depth and argues that none of theseaccounts is satisfactory, but each of them highlights certain key features of physical computation that he eventually adopts in his own semantic account of physical computation - a view that rests on a phenomenon known as simultaneous implementation (or "indeterminacy of computation"). Shagrircompletes the characterization of his account of computation and highlights the distinctive feature of computational explanations.

Mind of God

P. C. W. Davies
Mind of God Book PDF

Author : P. C. W. Davies
Publisher : Simon and Schuster
Page : 260 pages
File Size : 45,9 Mb
Release : 1993-03-05
Category : Religion
ISBN : 9780671797188

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Mind of God by P. C. W. Davies Pdf

Exploration of whether modern science can provide the key that will unlock all the secrets of existence.

Artificial Psychology

Jay Friedenberg
Artificial Psychology Book PDF

Author : Jay Friedenberg
Publisher : Psychology Press
Page : 312 pages
File Size : 55,8 Mb
Release : 2010-10-18
Category : Psychology
ISBN : 9781136873881

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Artificial Psychology by Jay Friedenberg Pdf

Is it possible to construct an artificial person? Researchers in the field of artificial intelligence have for decades been developing computer programs that emulate human intelligence. This book goes beyond intelligence and describes how close we are to recreating many of the other capacities that make us human. These abilities include learning, creativity, consciousness, and emotion. The attempt to understand and engineer these abilities constitutes the new interdisciplinary field of artificial psychology, which is characterized by contributions from philosophy, cognitive psychology, neuroscience, computer science, and robotics. This work is intended for use as a main or supplementary introductory textbook for a course in cognitive psychology, cognitive science, artificial intelligence, or the philosophy of mind. It examines human abilities as operating requirements that an artificial person must have and analyzes them from a multidisciplinary approach. The book is comprehensive in scope, covering traditional topics like perception, memory, and problem solving. However, it also describes recent advances in the study of free will, ethical behavior, affective architectures, social robots, and hybrid human-machine societies.

The Hidden Pattern

Ben Goertzel
The Hidden Pattern Book PDF

Author : Ben Goertzel
Publisher : Universal-Publishers
Page : 422 pages
File Size : 45,5 Mb
Release : 2006
Category : Computers
ISBN : 9781581129892

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The Hidden Pattern by Ben Goertzel Pdf

The Hidden Pattern presents a novel philosophy of mind, intended to form a coherent conceptual framework within which it is possible to understand the diverse aspects of mind and intelligence in a unified way. The central concept of the philosophy presented is the concept of "pattern" minds and the world they live in and co-create are viewed as patterned systems of patterns, evolving over time, and various aspects of subjective experience and individual and social intelligence are analyzed in detail in this light. Many of the ideas presented are motivated by recent research in artificial intelligence and cognitive science, and the author's own AI research is discussed in moderate detail in one chapter. However, the scope of the book is broader than this, incorporating insights from sources as diverse as Vedantic philosophy, psychedelic psychotherapy, Nietzschean and Peircean metaphysics and quantum theory. One of the unique aspects of the patternist approach is the way it seamlessly fuses the mechanistic, engineering-oriented approach to intelligence and the introspective, experiential approach to intelligence.

Computable Economics

Kumaraswamy Velupillai
Computable Economics Book PDF

Author : Kumaraswamy Velupillai
Publisher : Unknown
Page : 250 pages
File Size : 50,7 Mb
Release : 2000
Category : Business & Economics
ISBN : 0198295278

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Computable Economics by Kumaraswamy Velupillai Pdf

In the field of economic analysis, computability in the formation of economic hypotheses is seen as the way forward. In this book, Professor Velupillai implements a theoretical research program along these lines. Choice theory, learning rational expectations equlibria, the persistence of adaptive behavior, arithmetical games, aspects of production theory, and economic dynamics are given recursion theoretic (i.e. computable) interpretations.

Goedel's Way

Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa
Goedel s Way Book PDF

Author : Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa
Publisher : CRC Press
Page : 160 pages
File Size : 53,7 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781136587641

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Goedel's Way by Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa Pdf

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 something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

The Physical Signature of Computation

Neal G Anderson,Professor of Electrical & Computer Engineering Neal G Anderson,Curators' Distinguished Professor of Philosophy Gualtiero Piccinini
The Physical Signature of Computation Book PDF

Author : Neal G Anderson,Professor of Electrical & Computer Engineering Neal G Anderson,Curators' Distinguished Professor of Philosophy Gualtiero Piccinini
Publisher : Oxford University Press
Page : 343 pages
File Size : 51,6 Mb
Release : 2024-09
Category : Language Arts & Disciplines
ISBN : 9780198833642

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The Physical Signature of Computation by Neal G Anderson,Professor of Electrical & Computer Engineering Neal G Anderson,Curators' Distinguished Professor of Philosophy Gualtiero Piccinini Pdf

Anderson and Piccinini offer the most systematic, rigorous, and comprehensive account of computational implementation to date. Their robust mapping account holds that the key for establishing that a computation is physically implemented is that the physical states bear neither more nor less information than the computational states they map onto.