Hypercomputation.info

Recently, I read a review by Colin McGinn of Ray Kurzweil's How to Create a Mind: The Secret of Human Thought Revealed . According to McGinn, the book reveals, at last, the secret of human thought which is pattern recognition! Kurzweil argues that one needs to build a machine that recognizes patterns in order to create a mind. Personally, I find this idea extremely naive because pattern recognition is just one of mind's many functions. On the other side, McGinn says that "the brain is causally connected to the mind and the mind contains and processes information", which seems bizarre. I always thought that the brain induces the mind but this statement implies that the brain and the mind are two separate entities. What is even more bizarre are reviews of the book like this: Ray Kurzweil's understanding of the brain and artificial intelligence will dramatically impact every aspect of our lives, every industry on Earth, and how we think about our future. If y...

Florent Franchette presented an interesting problem in his " Oracle Hypermachines Faced with the Verification Problem ". Franchette argues that a physical oracle machine cannot be used to prove that physical hypercomputers exist simply because we cannot verify the results computed by the machine. However, an answer to what can be computed by a form of oracle Turing machine is described in " Computational complexity with experiments as oracles " (see also " Computational complexity with experiments as oracles. II. Upper bounds "). Roughly, their oracle machine, which is called an analog-digital Turing machine, is an ordinary Turing machine coupled to an abstract physical experiment. The authors of these papers prove that this machines have computational power that goes beyond the Church-Turing barrier. Now, if one proves that a machine is actually a hypercomputer, then I think there is no need to verify results computed. After all, we trust the results com...