Hypercomputation: Computing Beyond the Church-Turing Barrier

by Apostolos Syropoulos

This book provides a thorough description of hypercomputation. It covers all attempts at devising conceptual hypermachines and all new promising computational paradigms that may eventually lead to the construction of a hypermachine. Readers will gain a deeper understanding of what computability is, and why the Church-Turing thesis poses an arbitrary limit to what can be actually computed. Hypercomputing is a relatively novel idea. However, the book’s most important features are its description of the various attempts of hypercomputation, from trial-and-error machines to the exploration of the human mind, if we treat it as a computing device.

Genres: Computer Science

270 pages, Hardcover

First published January 1, 2008

Reviews

[Anthony O'Connor · Rating 3 out of 5]

Could have been good

Could have been good.
Fascinating topic. What lies beyond Turing Computable?
The book discusses
Infinite time Turing Machines and possible implementations using relativistic properties of space-time.
Computation on the real numbers with possible implementations using continuous/analog devices.
Naturally occurring non-computable processes.
And much else.
Possibly should have left alone the question of whether or not the ‘mind’ is non-computable and the nature of consciousness. Very Bright minds have badly sunk in these stormy seas. Hey Roger?
If you try to say too much about everything you end up saying less.

Unfortunately the book is very poorly written. It can’t make up its mind whether it’s a general popular exposition, a graduate level text book or a series of advanced research papers.
It comes across as plodding and amateurish whilst frequently descending into jargon/symbol thick gibberish.
Which I freely admit I can’t follow.
You can’t suddenly get that technical without providing adequate background and preparation.
Now I could go off and do that independently but Given what I see I’m not confident that it’s worth the effort.

Anyway it’s definitely worth browsing through noting the subjects, a few key ideas and some of the references which hopefully will be clearer and more readily comprehensible.

A for effort though. Fascinating subject. Fascinating questions.

[Philip Naw · Rating 4 out of 5]

Pros: This book is long due, and it truly does cover a wide range of material under the heading of 'Hypercomputation.' Personally, I loved the first couple chapters (especially the infinite time turing machines) and the last couple chapters (like the section on supertasks and black holes). There are interpretations of hypercomputation related to physics, analog systems, computers, machines, and so I would recommend this book to anyone with a firm footing in any of these areas related to hypercomputation.

Cons: While the book is actually quite enjoyable to read, it contains no proofs, just results. Some of the results are stated suddenly in a foreign system of symbols, and very little is done to break down some of the monster expressions that appear out of nowhere. However, I have studied computability and logic beforehand, so I was able to enjoy this book quite well despite this somewhat serious drawback. If you are new to theoretical computer science, perhaps this book is not for you, unless you are patient maybe. But if you have a good footing then I definitely recommend it.

[Jason Kowalski · Rating 4 out of 5]

Hypercomputation is a fascinating concept in computer science, and there aren't many books available for beginners. This one is quite good, but some parts require extensive prior knowledge, while others are too shallow. Nonetheless, I still think it's worth reading.

[Nick Black]

Amazon 2009-06-18. Moving dangerously close to Jürgen Schmidhuber-type nu-hermetics, but let's give it a chance.