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Chris Bernhardt

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Turing's Vision: The Birth of Computer Science Kindle Edition

by Chris Bernhardt (Author) Format: Kindle Edition

4.5 116 ratings

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An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phones

In 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing’s Vision, Chris Bernhardt explains the theory for the general reader, beginning with its foundations and systematically building to its surprising conclusions. He also views Turing’s theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing’s later work, and the birth of the modern computer.

Turing wanted to show that there were problems that were beyond any computer’s ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing’s ideas, Bernhardt examines 3 well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing’s problem concerning computable numbers.

Editorial Reviews

Review

The dazzling array of computer applications, from desktop to cell phone, has obscured the play of ideas that first set our modern era in motion. In this account, Bernhardt reveals the crucial contribution to these developments made by Alan Turing and other early computer scientists. A marvelous book.

(A. K. Dewdney, Professor Emeritus, Department of Computer Science, University of Western Ontario)

A fascinating account of Alan Turing's epic research paper, which kicked off the entire computer revolution. I'm particularly impressed by the amount of detail the author includes while keeping everything simple, transparent, and a pleasure to read.

(Ian Stewart, author of In Pursuit of the Unknown: 17 Equations That Changed the World)

Over the past several decades, Alan Turing, known as the father of computer science, has become an intellectual and cultural icon. Chris Bernhardt has written a very clear and accessible book that explains Turing's work, showing how his ideas have developed into some of the most important ideas in computer science today.

(Noson S. Yanofsky, author of The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us)

This is a delightful introduction for the lay reader to the ideas surrounding Alan Turing's great paper of 1936.

(Scott Aaronson, Associate Professor of Electrical Engineering and Computer Science, MIT)

About the Author

Chris Bernhardt is professor of mathematics at Fairfield University.

Product details

ASIN ‏ : ‎ B08BT6W6H7
Publisher ‏ : ‎ The MIT Press (May 13, 2016)
Publication date ‏ : ‎ May 13, 2016
Language ‏ : ‎ English
File size ‏ : ‎ 1186 KB
Text-to-Speech ‏ : ‎ Enabled
Screen Reader ‏ : ‎ Supported
Enhanced typesetting ‏ : ‎ Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Sticky notes ‏ : ‎ On Kindle Scribe
Print length ‏ : ‎ 249 pages

Best Sellers Rank: #475,302 in Kindle Store (See Top 100 in Kindle Store)
- #53 in Business & Management Technology History
- #91 in Computer & Technology Biographies
- #152 in Computing Industry History

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4.5 116 ratings

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Chris Bernhardt

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Chris Bernhardt is a professor emeritus of mathematics at Fairfield University. He received his PhD in mathematics from the University of Warwick.

His books are on the theory of computation — an area that encompasses mathematics, computer science and physics. This area contains many beautiful and counterintuitive ideas. Prof Bernhardt's aim is to introduce non-specialists to some of the most important of these by keeping everything as simple as possible.

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116 global ratings

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Vector

I absolutely love this book

Reviewed in the United States on November 19, 2016

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I absolutely love this book. Computer Science is my hobby, and a major part of my profession; thus making this book indispensable in terms of providing historical value to understanding CS roots. Reading this work has opened my mind to pioneers such as Charles Sanders Pierce, the father of pragmatism, and his numerous collections of philosophic, logical and mathematical writings. Furthermore, there is an endless array of notable reads that should be attempted; and not just by those who study computer science. For example, the writings of Euclid, George Boole, Russel Bertrand and much more. I highly recommend this to anyone who wants to "feel" what computer science truly is. Alan Turing's work is so influential and most people fail to realize its significance. Therefore do yourself the favor and pick this book up, you will not regret it, and likely it will help shape your mind as it did mine. Enjoy!

21 people found this helpful

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neuroscientist

Great book, unique book.

Reviewed in the United States on April 23, 2020

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Absolutely a great book. Highly recommend it. Great point to start learning about both Computer Science foundations and history. The only problems are some typos (e.g., words are sometimes repeated) throughout the book, which could have been easily edited .. and should still be edited. Great bibliography for further reading. Maybe ran out of gas a little by the end of the book, Turing's final result and its implications could have been broken down and expanded even more.

5 people found this helpful

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Mustard Seed Ministries

Too much and too little

Reviewed in the United States on January 20, 2024

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This is a curious book - which in some cases contain s technical w work beyond common understanding, yet is not detailed enough in other are. This may be due to t h e date of publication. The reader can decide

One person found this helpful

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Sami Al Suwailem

Wonderful!

Reviewed in the United States on November 9, 2017

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This is an excellent book on Turing and computability. It explains the halting problem in an intuitive and clear manner that I could not find in dozens of other books and papers. The author is able to highlight the important ideas that are the foundations of computability. The style is clear, readable and friendly. The length of the book is also very reasonable. I wish he explained more clearly the difference between the Entscheidungsproblem (proved impossible by Turing) and formal completeness (proved impossible by Godel). Nonetheless, this is an excellent book, for which I congratulate the author for such a wonderful work.

7 people found this helpful

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John Kirk

What an outstanding, ground-up view of the technology and ...

Reviewed in the United States on July 18, 2016

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What an outstanding, ground-up view of the technology and thinking that informs an increasing amount of how and what tools we use virtually every day to make decisions and, well, live.

6 people found this helpful

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Muhammad Bilal

Fun read

Reviewed in the United States on October 22, 2019

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I enjoyed reading it

One person found this helpful

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A. Menon

Understandable overview of the logic that framed moder day computer science

Reviewed in the United States on December 16, 2016

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Turing's Vision gives the reader an overview of the logic required to understand the foundations of computability and computer science. Most works on Turing for the popular audience focus on his remarkable life but in this book the author tries to convey the core ideas of what computability is how computation can take place and the limits on what is computable. The author gives a history of where mathematical logic stood at the turn of the century and takes the reader through how Turing solved a major outstanding problem posed by Hilbert.

The book is accessible to the general audience but this is a mathematical text so patience is often required. The book starts out by describing the world in the early 20th century from a mathematicians perspective. In particular the author covers topics like the goal of formalizing all of mathematics so that any statement could be proven or disproven within that system as well as the entscheidungsproblem, which was effectively the halting problem. The author goes through the foundations of arithmetic and gives a quick overview of things like Gödel's results on the incompleteness of any mathematical system to describe itself fully using its axioms. The author covers the history as well as people working on these logic questions and gives a rough overview of who was working on what to the reader. The author then goes on to describe finite automata, a computational system which can answer a wide array of questions and the author also shows what cannot be computed by finite automata. The author describes Turing machines and how they cover and extend the boundaries of what can be computed by finite automata as well as what things like polynomial time and NP problems are. Though not comprehensive the book remains accessible so its definitely quite refreshing for the non-mathematician reader. The author then spends time on some more formal mathematics, in particular lambda calculus, a system of computing that is equivalent to Turing's more intuitive machine. Parts of the book like this add to completeness but can be skipped over by the reader less interested in all the logical structure behind the ideas. The author spends time on how to correspond Turing machines to finite automata. It is quite remarkable how certain problems are easily solved in one system but incredibly complicated in others. Modern computer architecture is covered briefly so theory becomes practical but these details are covered quite casually. The author then goes back to logic to cover the initial question posed at the beginning and goes through logical paradoxes when one looks at sets which refer to themselves. This concept is shown to be relevant for programs which are trying to decide on whether programs will halt or not and that impossibility is why the halting problem cannot be solved. The mathematical side of the book is furthered toward the end as the author spends time on understanding diagonalization arguments that are required to follow Turing's original argument. The author then goes on to discuss what can be computed as a consequence of these results from counting and cardinality. The author ends with a brief history of Turing and his work and life, it is very brief so just ties actual events to the book.

Turing's Vision is a introduction to the foundational logic required to understand what a turing machine can and cannot do and what the nature of computation is. The reader gets a sense of the limits of what can be answered by a computer and why. There are other books which have a similar reader level like The Annotated Turing for example which are very good but this book focuses more on the logic side rather than deciphering the paper that Turing wrote. For the more technically inclined reader this is recommended but it is approachable for those who are willing to go through some more formal arguments

20 people found this helpful

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OKLAHOMA PANHANDLE STATE UNIVERSITY - OPSU

Turing

Reviewed in the United States on October 18, 2017

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Great bio.

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Allan D

Introduction to the mathematics of Turing's work

Reviewed in Canada on February 12, 2022

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This is an interesting introduction to some of the key mathematical work of Alan Turing (mostly his 1936 results on Computable Numbers and Turing Machines) relating it to both contemporary developments in logic (the lambda calculus) and later developments in computer science and related ideas like finite automata. The book is thus mostly an introduction to mathematical and computer science concepts but serves to give them some intellectual context also and even a little bit of social context for Turing's life and legacy.

The book begins with some discussion of mathematical logic, Hilbert's program (the Entscheidungsproblem) and the Godel results that Turing's work built on, responded and contributed to. Things like finite automata and the lambda calculus are worked though in preparation to lead the reader through Turing's laying out of his model of computing in terms of Turing machines and proof that the computable numbers are not effectively innumerable. Also other mathematical work such as Cantor's diagonalization argument are sketched out and worked through to the extent necessary to relate them to Turing's work. Some key elements of Turing's life and other work are summarized as are a few seminal instances from the origin of the computer, some philosophical issues around artificial intelligence and a final reflection on Turing's life and legacy.

The book is a fairly readable and understandable exposition of the mathematics. However at times I found the examples and work through of the problems a bit brief. I had some rather haphazard knowledge of the mathematics in Turing's work including my own attempt to read Turing's paper, but much of the mathematical logic and machine theory was new to me. There is a difficult balance between being comprehensible to the general reader (or at least the interested neophyte) and avoiding tedium in explaining the very simple but elaborate procedures involved. Also the depth and breadth of the discussion is limited. Careful reading would no doubt be rewarded with greater comprehension but I found I profitably read it without having to master all the technical nuance presented.

The history presented is often very schematic outside of tracing the pedigree of certain mathematical techniques there are just a few bits of greatest hits. The reader may come away with a somewhat inflated sense of Turing's role in the origin of actual computing machines (Turing's exact contributions to various elements is a matter of some dispute), a few interesting early machines are left unmentioned in the cursory round up of early computers but otherwise I did not notice any serious errors.

One person found this helpful

lynne knapp

Good book

Reviewed in the United Kingdom on March 5, 2022

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