Hypercomputation.info

I had the impression that the Church-Turing thesis has not been proven, but a recent posting to the Arxiv server claimed otherwise. In partricular, Nachum Dershowitz and Evgenia Falkovic in their extended abstract entitled " A Formalization and Proof of the Extended Church-Turing Thesis " claim that they offer a proof of the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. Interestingly, this proof uses the notion of classical algorithm which is a time-sequential state-transition system, whose transitions are partial functions on its states. But obviously, this is not an algorithm but something that someone calls a classical algorithm. Now if one has a deep desire to prove the Church-Turing thesis, then she can formulate and prove it inside Eff , that is, the effective topos (see Categorical Logic and Type Theory , p. 402)! In a nutshell, no I don't think this paper is a proof of the CTT.

Today I received an e-mail notification about a new book entitled A Computable Universe: Understanding and Exploring Nature as Computation . According to the publisher, the book It focuses on two main questions: What is computation? How does nature compute? Obviously there is an oxymoron here—if one does not know what  computation is, then it makes absolutely no sense to say anything about nature's computational capabilities! Notwithstanding, I find extremely naive the idea of a computable universe. To me it is more science fiction than science. But I have argued against this absurd idea elsewhere, so I will say no more here. PS The book's site states that "contributors are world-renowned experts", in what respect is the editor a world-renowned expert?

Recently, Jérémie Cabessa and Hava T. Siegelmann published a paper entitled The Computational Power of Interactive Recurrent Neural Networks . In this paper, the authors discuss a new form of interactive recurrent neural networks that are able to interact with other systems and/or the environment. These neural networks are shown to be strictly more powerful than interactive Turing machines, which implies that they have hypercomputational capabilities.

In a recent paper entitled Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity , which was posted to ArXiv , it is discussed whether it is possible to hypercompute in an ordinary spacetime. The authors conclude that this is possible provided that there are elementary particles that can travel faster than the light. Whether this is possible is another problem. Nevertheless, let me say that in a recent paper entitled Measurement of the neutrino velocity with the OPERA detector in the CNGS beam it is argued that neutrinos can travel faster than the light. PS It was shown that neutrinos do not travel faster than light.

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 t...

Recently, Matthew P. Szudzik posted an article to the arXiv  server that is entitled " Is Turing's Thesis the Consequence of a More General Physical Principle? " Szudzik ivnestigates Robert Rosen’s hypotheses, which were put forth in " Church’s thesis and its relation to the concept of realizability in biology and physics ". Roughly, one can say that these hypotheses state that the universe is discrete, deterministic, and computable.  A direct consequence of these hypotheses is the Church-Turing Thesis. Szudzik recognizes that these hypptheses are not correct and, thus, one needs to reformulate them: This sort of reformulation was first attempted by Konrad Zuse [18, 19] in the 1960’s. Since then, increasingly sophisticated attempts have been made by Edward Fredkin [3] and Stephen Wolfram [17]. In contrast, Roger Penrose [9, 10] has speculated that the universe might not be computable, but efforts to find experimental evidence for this assertion have not succee...

I have been thinking for many years why economists usually fail to make any reliable predictions. And when one does make some reliable predictions, then she is considered phenomenal! But if economics is to be considered a science, then it should be able to make reliable predictions, otherwise it is completely worthless. First of all economics is a social science . Thus, in order  to make trustworthy predictions, one must ensure that an economic system is computable and, why not, deterministic . Economics systems consist of agents (ordinary people) that interact and create the world we see around us. But how can be so sure that the behavior of these agents is computable? In fact we are not and, furthermore, we shouldn't! One of the basic ideas of hypercomputation is that the human mind, ergo our agents, has capabilities computational, hypercomputational, and paracomputational (i.e., abilities that lie outside computation as we presently know it). In different words, eco...