After way too many years since I initially wrote it, I recently published a paper on the physical church-turing thesis in BJPS. The paper argues that computation properly so called must be usable by an observer such as human beings to generate desired values of a function. When this point is made explicit, it becomes fairly clear that all the schemes recently proposed for hypercomputation (= the computation of Turing-uncomputable functions) are not genuine computational devices because they are not usable in the required sense. Maybe someday someone will come up with a usable scheme for hypercomputation, and that would be really cool. But I’m not holding my breath.
Incidentally, this published paper is a much revised version of the paper by the same name that is still posted on my website (I hope to remedy that by updating my website in the not too distant future). A yet older version of the paper on my website was rather summarily dismissed by Apostolos Syropolous in an old blog post from a few years ago. I probably deserved Syropolous’s dismissal given that I summarily dismissed his book on hypercomputation in an even older blog post. I am sorry for not doing justice to his book at the time. I do hope that my published paper advances our understanding of some issues surrounding physical computation, including the possibility of hypercomputation. As such, it constituites a more adequate response to Syropolous’s book (and blog post).