Hypercomputation.info

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...

The other day I was skimming through Lee Smolin's The Trouble with Physics . On pages 317-138 one can read the following: In the context of quantum gravity, it resulted in a new approach to quantum cosmology, made by Fotini Markopoulou and her collaborators. Markopoulou emphasized that describing the exchange of information between different subsystems is the same as describing the causal structure that limits which system can influence each other. She thus found that a universe can be described as a quantum computer, with a dynamically generated logic. With all due respect, the idea that the universe is a computer was put forth by Konrad Zuse in his Rechnender Raum .  Furthemore, Zuse's ideas form in a way the basis of digital philosophy . Whether the universe is a computer or not is another discussion that I have addressed briefly in an older post.

SpiNNaker is a project to create a simulator of the human brain, The computer will consist of up to a million ARM cores to host a brain simulator. But as Steve Furber of the University of Manchester has correctly noted " [t]here are about 100 billion neurons with 1,000 trillion connections in the human brain. Even a machine with one million of the specialized ARM processor cores developed at Manchester would only allow modeling of about 1 percent of the human brain ." Nevertheless, I am sure such a project will provide some scientific knowledge.