<p>There have been recent several conferences on the topic of infinitary computability, which have treated many topics in hypercomputation. </p>

<ul>
<li><a href="http://www.math.uni-bonn.de/people/logic/events/biwoc/index.html">Bonn International Workshop on Ordinal Computability (BIWOC) 2007</a>, see the program report there </li>
<li>Conference on <a href="http://nylogic.org/EMU/August2008">Effective Mathematics of the Uncountable (EMU) 2008</a></li>
<li>Conference on <a href="http://nylogic.org/EMU/August2009">Effective Mathematics of the Uncountable (EMU) 2009</a></li>
</ul>

<p>In addition, there have been special sessions on infinitary computability in many of the CiE conferences. </p>

CC BY-SA 3.0
2012-02-28T01:47:31.067Z
2012-02-28T01:47:31.067Z
JDH
<p>I don't think this is true. Searching <a href="http://arxiv.org/find/all/1/all%3a+hypercomputation/0/1/0/all/0/1" rel="nofollow">Arxiv for papers on hypercomputation</a> gets a bunch of hits. </p>

CC BY-SA 3.0
2012-01-01T09:57:07.667Z
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.
Martin Schwarz
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2012-01-06T13:14:01.260Z
I'm beginning to think that you're right, Joshua. Also, thanks for that link.
Velvet Ghost
CC BY-SA 3.0
2012-01-01T04:30:56.197Z
2012-01-02T07:11:50.227Z
2012-01-02T07:11:50.227Z
Joshua Herman
<p>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".</p>

<p>In any case, assuming that you are talking about <strong>computation of functions over natural numbers</strong> (and finite strings) (since I think it is clear that models for higher type computation is a very active area, e.g. <a href="http://cca-net.de/">CCA</a>) and <strong>models of computation not equivalent to computability defined by Turing machines</strong>, I don't think the claim is correct, for example see CiE'05 and CiE'11. Also see the <a href="https://en.wikipedia.org/wiki/Hypercomputation#Criticism">criticisms</a> made against the claim that hyper-computation is something new:</p>

<ul>
<li>Martin Davis, "<a href="http://research.cs.queensu.ca/home/akl/cisc879/papers/PAPERS_FROM_APPLIED_MATHEMATICS_AND_COMPUTATION/Special_Issue_on_Hypercomputation/davis%5B1%5D.pdf">Why there is no such discipline as hypercomputation</a>", 2006.</li>
<li>Martin Davis, "T<a href="http://www.maths.leeds.ac.uk/~pmt6sbc/docs/davis.myth.pdf">he Myth of Hypercomputation</a>", in "Alan Turing: Life and Legacy of a Great Thinker", 2004.</li>
</ul>

<p>If you are interested, there is also some discussion on <a href="http://www.cs.nyu.edu/mailman/listinfo/fom">FOM mailing list</a> starting by <a href="https://encrypted.google.com/search?q=site%3Acs.nyu.edu+fom+%22The+Myth+of+Hypercomputation%22&amp;nfpr=1">Timothy Chow's email</a> about Martin Davis' article.</p>

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2012-01-06T13:22:46.300Z
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](http://en.wikipedia.org/wiki/Real_computation).
Velvet Ghost
CC BY-SA 3.0
2012-01-06T13:32:35.067Z
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?
Velvet Ghost
CC BY-SA 3.0
2012-01-01T20:37:51.697Z
2012-01-01T22:37:28.850Z
2012-01-01T22:37:28.850Z
Kaveh
<p>I see a lot of research on <a href="https://en.wikipedia.org/wiki/Hypercomputation">hypercomputation</a> 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?</p>

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2012-01-01T19:55:41.553Z
3rd International Hypercomputation Workshop (HyperNet 11) http://www.hypercomputation.net/combinedpreprocs.pdf
Marzio De Biasi
CC BY-SA 3.0
2014-12-27T00:00:54.937Z
There weren't any black holes nearby to send a Turing machine into.
Andrej Bauer
<reference-request><computability><hypercomputation>
Why has hypercomputation research died down?
Velvet Ghost
# Why has hypercomputation research died down?

(Asked by: username_0 on 2012-01-01)

I see a lot of research on [hypercomputation](https://en.wikipedia.org/wiki/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?

**Tags:** reference-request, computability, hypercomputation
> **Comments:**
> **username_1**: 3rd International Hypercomputation Workshop (HyperNet 11) http://www.hypercomputation.net/combinedpreprocs.pdf  
> **username_2**: There weren't any black holes nearby to send a Turing machine into.  

---

## 3 answers

### Answer by username_6 on 2012-01-01. Score: 19 | Accepted answer

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](http://cca-net.de/)) 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](https://en.wikipedia.org/wiki/Hypercomputation#Criticism) made against the claim that hyper-computation is something new:

* Martin Davis, "[Why there is no such discipline as hypercomputation](http://research.cs.queensu.ca/home/akl/cisc879/papers/PAPERS_FROM_APPLIED_MATHEMATICS_AND_COMPUTATION/Special_Issue_on_Hypercomputation/davis%5B1%5D.pdf)", 2006.
* Martin Davis, "T[he Myth of Hypercomputation](http://www.maths.leeds.ac.uk/~pmt6sbc/docs/davis.myth.pdf)", in "Alan Turing: Life and Legacy of a Great Thinker", 2004.

If you are interested, there is also some discussion on [FOM mailing list](http://www.cs.nyu.edu/mailman/listinfo/fom) starting by [Timothy Chow's email](https://encrypted.google.com/search?q=site%3Acs.nyu.edu+fom+%22The+Myth+of+Hypercomputation%22&nfpr=1) about Martin Davis' article.

> **Comments:**
> **username_0**: 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](http://en.wikipedia.org/wiki/Real_computation).  
> **username_0**: 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?  

---

### Answer by username_3 on 2012-02-28. Score: 6

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](http://www.math.uni-bonn.de/people/logic/events/biwoc/index.html), see the program report there
* Conference on [Effective Mathematics of the Uncountable (EMU) 2008](http://nylogic.org/EMU/August2008)
* Conference on [Effective Mathematics of the Uncountable (EMU) 2009](http://nylogic.org/EMU/August2009)

In addition, there have been special sessions on infinitary computability in many of the CiE conferences.


---

### Answer by username_4 on 2012-01-01. Score: 2

I don't think this is true. Searching [Arxiv for papers on hypercomputation](http://arxiv.org/find/all/1/all%3a+hypercomputation/0/1/0/all/0/1) gets a bunch of hits.

> **Comments:**
> **username_5**: 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.  
> **username_0**: I'm beginning to think that you're right, Joshua. Also, thanks for that link.  

---

