I see a lot of research on hypercomputation in the 1990's, but in more recent years there seems to be little work on the topic. Is it true that research in this area has died down? If so, what could be the reasons for it? Was this area convincingly shown to be unpromising?
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6$\begingroup$ 3rd International Hypercomputation Workshop (HyperNet 11) hypercomputation.net/combinedpreprocs.pdf $\endgroup$– Marzio De BiasiCommented Jan 1, 2012 at 19:55
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$\begingroup$ Velvet Ghost asked: > is it true that the Bekenstein Bound refutes...? Well, there's a good case for that since it limits the information in a volume of space as a consequence of Murphy's Law. $\endgroup$– user30490Commented Dec 25, 2014 at 20:17
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1$\begingroup$ There weren't any black holes nearby to send a Turing machine into. $\endgroup$– Andrej BauerCommented Dec 27, 2014 at 0:00
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3 Answers
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It would be better if you specified what you mean exactly by hyper-computation and gave evidence for why you think it has "died down".
In any case, assuming that you are talking about computation of functions over natural numbers (and finite strings) (since I think it is clear that models for higher type computation is a very active area, e.g. CCA) and models of computation not equivalent to computability defined by Turing machines, I don't think the claim is correct, for example see CiE'05 and CiE'11. Also see the criticisms made against the claim that hyper-computation is something new:
- Martin Davis, "Why there is no such discipline as hypercomputation", 2006.
- Martin Davis, "The Myth of Hypercomputation", in "Alan Turing: Life and Legacy of a Great Thinker", 2004.
If you are interested, there is also some discussion on FOM mailing list starting by Timothy Chow's email about Martin Davis' article.
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$\begingroup$ Thanks a lot for that very informative reply. To be honest, my only acquaintance with hypercomputation is through Siegelmann's work on the computational power of neural nets back in the mid 1990's - and her proof that a particular neural net (the analog recurrent NN) is hypercomputational. The key to it's hypercomputational power is it's analog nature - it can have weights which are REAL numbers. So I was referring to the subfield of hypercomputation known as Real Computation. $\endgroup$ Commented Jan 6, 2012 at 13:22
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$\begingroup$ I had read Martin Davis' articles previously, and they were what started to make me think that hypercomputation was out of fashion. Btw... is it true that the Bekenstein Bound refutes any possibility of analog computation in this universe? $\endgroup$ Commented Jan 6, 2012 at 13:32
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There have been recent several conferences on the topic of infinitary computability, which have treated many topics in hypercomputation.
- Bonn International Workshop on Ordinal Computability (BIWOC) 2007, see the program report there
- Conference on Effective Mathematics of the Uncountable (EMU) 2008
- Conference on Effective Mathematics of the Uncountable (EMU) 2009
In addition, there have been special sessions on infinitary computability in many of the CiE conferences.
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I don't think this is true. Searching Arxiv for papers on hypercomputation gets a bunch of hits.
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9$\begingroup$ Hypercomputation refers to models of computation that are more powerful than Turing computability (see e.g. Wikipedia), whereas both, PostBQP=PP and P_CTC=PSPACE, are certainly computable. $\endgroup$ Commented Jan 1, 2012 at 9:57
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$\begingroup$ I'm beginning to think that you're right, Joshua. Also, thanks for that link. $\endgroup$ Commented Jan 6, 2012 at 13:14