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.

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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
[200] 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.