In May, 2009 a review of my book on hypercomputation appeared in the Computing Reviews. Although I submitted a rebuttal to the review, it appeared slightly edited. So for reasons of completeness, I post my complete rebuttal here today.
It is known that disagreements in the academic world are quite common and constitute the essence of any scientific production. Everybody who is doing some scholar work is virtually exposed to criticism. Nevertheless, it is one thing to criticize one's work and another to present a piece of work in such a way that potential readers get the impression that the work is almost worthless! A typical example of this “reviewing technique” is to assert that an author fully and unconditionally subscribes to a particular idea, when, in fact, she/he explicitly states that one cannot be sure about the idea!
Apparently, Zenil's review is based on this “technique” and has almost fiercely tried to convince his readers that I practically have no idea what I am talking about! For example, he argues that I subscribe to the Lucas-Penrose argument (LPA) without saying that the book includes many counter-arguments to the LPA. Interestingly, Zenil states that I use Searle's ideas to “immediately acknowledge hypercomputation” (ergo, I believe in the validity of Searle's ideas) and at the same time he states that I do subscribe to the LPA, when it is known that Searle rejects the LPA! Unfortunately, this “technique” is employed in other parts of the review. In particular, when he talks about the space-time granularity, Zenil argues that “the author assumes that space and time are continuous--in spite of quantum mechanics.” First of all Schrödinger's equation assumes a continuous space and time so the non-granularity of space and time is self-evident. Nevertheless, in my work I was careful enough not to employ such seemingly knock-out arguments and so I have explicitly stated (on page 147) that “it is clear that for the time being, nobody really knows the truth regarding spacetime granularity.” In different words, although I do believe that space and time are continuous, still there is no scientific proof for this.
Another quite problematic part of Zenil's review is statements like the following:
“as it is acknowledged in the book itself, several models are missing and those included are only introductions. Consequently, the book is more a dictionary of models of hypercomputation that Syropoulos chose to include.”
Firstly, I would be really grateful to anybody who could bring to my attention serious models/proposals of hypercomputation. Of course any model/proposal that was suggested after the book was published, can be included in a future edition of the book. Secondly, I admit that in a couple of case I did not discuss some older ideas just because more recent ones describe systems based on the same principles in a more scientific and rigorous way. Thirdly, there is no discussion of hypermachines based on ideas that are very controversial.
It is true that I find it extremely naïve to believe to a Turing computable view of the mind/universe. However, when I try to summarize computationalism by saying that we are tiny Turing machines [that live in a “Turing-verse”!], I actually mean that our capabilities in thinking the very notion of computation are actually delimited by the capabilities of the Turing machine. In other words, we cannot compute more than a Turing machine (do not forget that computationalists believe that even feelings are computations). So, I have used this expression as a metaphor, that is, a figure of speech. Consequently, I did not expect (educated) readers to conclude that I think that anyone who subscribes to computationalism believes that people are literally Turing machines.
It is clear that computation has played, plays, and will play a very important role in our societies (we already live in an Information Society); but so does Newtonian mechanics as well, which, nevertheless, is not universally valid. Under the light of the Newtonian mechanics paradigm, let me state that I personally believe that hypercomputation is, in a certain sense, to classical computability theory what the theory of relativity is to classical mechanics.
Unfortunately, Zenil writes without asking himself if his interpretation is the only possible. For instance, he argues in the sequel that “there is no evidence that the [Church-Turing] thesis may be wrong, but a lot of evidence that it is correct.” This is true, however, at the same time there is so much evidence that space and time are continuous, but still Zenil does not accept the validity of this hypothesis! Also, let me remind that evidence is not enough; in science we need proofs. And that is why the Church-Turing thesis (CTT) stands as a hypothesis. Obviously, only when (and if) the CTT will be proved beyond any doubt to be valid, only then hypercomputation will have no place to stand!
In addition, I do not think that the section of the CTT has errors—since I do not believe in the validity of this thesis, I presented a number of different formulations without going into the details. We know that the thesis was originally formulated in 1935 when the only “models” of computation were the λ-calculus and general recursive functions; so we cannot speak about a thesis which is the result of “the convergence of the definitions of computation.”
Another serious mistake of Zenil's is to accuse me that I believe that “a hypercomputer is more feasible than a quantum computer.” I thank him for giving me issues to understand me differently and better! But even a simple reader of the book, I mean, even a reader who does not pretend to be a scholar, can quickly verify that (on page 10) I state that “I am convinced that future advances in technology will allow us sooner or later to build computers based on these paradigms,” where “these paradigms” refers to quantum computing, etc. Last, but certainly not least, the first chapter of the book concludes as follows:
The truth is always in the middle, and I agree fully with Christof Teuscher and Moshe Sipper  when they say: "So, hype or computation? At this juncture, it seems the jury is still out—but the trial promises to be riveting."
At this point I stop. What hurts me is not the critique. Perhaps even nor the interpretative injustice, nor the critical unfairness of Zenil (anyway, we cannot constraint the reading strategy of a reader, and nobody can understand more than she/he can: by reading, the reader re-writes what she/he reads). But I am sad to encounter one more time the transmutation of the critique into a means or an opportunity of getting authority.