March 11, 2017
Download Ebook , by Chris Bernhardt
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, by Chris Bernhardt
Download Ebook , by Chris Bernhardt
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Product details
File Size: 1264 KB
Print Length: 209 pages
Publisher: The MIT Press (May 13, 2016)
Publication Date: May 13, 2016
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B01FTF81TM
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Amazon Best Sellers Rank:
#359,329 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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!
The best thing about this book is it will leave you hungering for more details from e.g. Martin Davis' Computability and Unsolvability.A Turing Machine in this book is described differently from what you'd find in Charles Petzold's The Annotated Turing. Instead of being in tabular form it's described by a "state diagram." These diagrams are introduced to describe finite automata, and a Turing Machine is presented as a finite automaton with additional capabilities. So in addition to accepting and non-accepting states that halt, a TM can also diverge (not halt). It's an appealing way to learn about TMs.The author is a mathematician, but you don't need experience reading definition-theorem-proof textbooks. In fact there's a section toward the end of the book titled Proof by Contradiction containing a thorough proof that sqrt(2) is not a rational number.I had a few "that's cool as s**t" moments while reading the book. One example is the tag system for the modified Collatz function.There were a couple places in the book I found unconvincing due to the introduction of an underspecified new type of TM. The multi-tape TM in the section RAMs Can Be Emulated by Turing Machines, Chap 6. And the TM that depends on the results of two other TMs running simultaneously in parallel in the proof on page 117.Professor Bernhardt is an excellent writer and Turing's Vision is a fine introduction to computation.
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.
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
good story
I was hoping for more about the development of computer technology, sort of a timeline. The author tried to simplify the concepts and terms used in this field, but I still had trouble following it. But that's because of my own limitations grasping abstract processes.
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.
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