Hypercomputation.info

In a recent paper  entitled " Bounds on Spectral Dispersion from Fermi-Detected Gamma Ray Bursts ",  Robert J. Nemiroff and his colleagues use scientific data to disprove the idea that space-time is "foamy" at the Planck scale. Apparently, this is really bad news for the aficionados of digital physics, phoilosophy, etc. 

The Active Element Machine is a new model of computation invented by  Michael Stephen Fiske . The model can use a random bit source from the environment to generate an arbitrary real number in the unit interval.  In addition, by using the same randomness, the machine can decide any language L ⊆ {0,1} * . In other words, this machine has capabilities that transcend the capabilities of the Turing machine.

It seems that some people do not understand the connection between hypercomputation and what Mark Burgin calls super-recursive algorithms. According to Burgin, "super-recursive algorithms are algorithms that control hypercomputation." In different words, a method that describes a task that produces a result not computable by a Turing machine is a super-recursive algorithm (or a hyperalgorithm, as I like to call them).

Roughly speaking, Turing has proved that it is not possible to tell whether a computer program will terminate or not. Recently, William Gasarch posted an article to the arXiv in which he shows how one can prove program termination. Gasarch does not disprove Turing, but " discuss various ways to prove that [a] program terminates".

Gentian Kasa has posted to the arXiv a good summary of hypercomputation. His summary is actually his MSc thesis and it is entitled " Hypercomputation: Towards an extension of the classical notion of Computability? " It is quite encouraging to see students work on hypercomputation despite the unfair criticism.

According to EETimes Europe , Princeton researchers claim quantum computing breakthrough . In particular, they "have developed a technique to read spintronic information off electrons, a potential step on the road to quantum computing." The importance of this development is that it opens the road to quantum computers  with millions of qubits.

Today I discovered yet another proof of the Church-Turing thesis (CTT)! In particular, Ramón Casares in his Proof of Church's Thesis proves the CTT using another more "general" thesis: Persons’ syntax engine is a Finite Universal Turing Machine.  A finite Turing machine is one that has a tape of finite length. Any person has a syntactical capability, that is the ability to speak a language and a syntax engine is a machine with a syntactical capability. So the question is whether there are machines that can really understand languages? Obviously, it is one think to dully manipulate symbols and another to understand the meaning associated to symbols. After all, this was nicely demonstrated with the Chinese Room Argument (in essence, this argument is a "proof" that intelligence cannot be equated with symbol manipulation, and, obviously, it is not an argument "against the possibility of true artificial intelligence"). Now the problem with this proo...

The First International Conference on Logic and Relativity: honoring István Németi's 70th birthday took place in Budapest, last September. The theme of the conference was the connection between logic and relativity theory. Obviously, since Németi initiated what is now called relativistic computing , a number of speakers presented work that falls in this research area. Unfortunately, for a number of good reasons, it was not possible to attend the event, so I cannot give a report of it. Nevertheless, when skimming through the web pages, one can easily see that the event was very interesting. I just hope more events like this will take place.

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...