3 ms·

You left out the part where the paper states that it's still an open problem whether hypercomputation is physically realisable. If some device can solve the Ha

You left out the part where the paper states that it's still an open problem whether hypercomputation is physically realisable. If some device can solve the Halting Problem, then it can solve every single unsolved mathematical conjecture that can be encoded as a Turing machine that halts if the conjecture is true (so about all of them?). This is an insanely bold claim, so please forgive the scepticism.

guiraldelli 7y ago
> This is an insanely bold claim, so please forgive the scepticism. I am interested in the concept of hyper-computation and I would like it to be physically constructable, but in the present moment I also see it as an intellectual construct only. Thus, I am as sceptical as you. :) If, someday, super-Turing devices will be built, I imagine it will (first) come as analog devices (e.g. Siegelmann's Analog Neural Networks [1,2]), not as biological ones. But this discussion is slightly off-topic, I guess. [1]: https://binds.cs.umass.edu/anna_cp.html https://binds.cs.umass.edu/anna_cp.html [2]: https://www.researchgate.net/profile/Arthur_Younger2/publication/278709409_Lecture_Notes_in_Computer_Science/links/56ec2ed408ae4b8b5e732fb0.pdf https://www.researchgate.net/profile/Arthur_Younger2/publica...
- antisemiotic 7y ago
  It was not my intention to argue that the entire concept will never fly (I'm nowhere near qualified for that), nor that it shouldn't be researched. It's just that the post by bollu that you've responded to specifically asked if this is physically possible, and the paper you linked quite clearly answers "we have no idea yet". Personally, I wouldn't be actually all that surprised if mathematics and computer science ended up solved some day by a system of chemical membranes, since, to put it extremely crudely, it was developed by systems of chemical membranes in the first place ;) That would raise some serious philosophical questions, though.

guiraldelli 7y ago

> This is an insanely bold claim, so please forgive the scepticism. I am interested in the concept of hyper-computation and I would like it to be physically constructable, but in the present moment I also see it as an intellectual construct only. Thus, I am as sceptical as you. :) If, someday, super-Turing devices will be built, I imagine it will (first) come as analog devices (e.g. Siegelmann's Analog Neural Networks [1,2]), not as biological ones. But this discussion is slightly off-topic, I guess. [1]: https://binds.cs.umass.edu/anna_cp.html https://binds.cs.umass.edu/anna_cp.html [2]: https://www.researchgate.net/profile/Arthur_Younger2/publication/278709409_Lecture_Notes_in_Computer_Science/links/56ec2ed408ae4b8b5e732fb0.pdf https://www.researchgate.net/profile/Arthur_Younger2/publica...

antisemiotic 7y ago
It was not my intention to argue that the entire concept will never fly (I'm nowhere near qualified for that), nor that it shouldn't be researched. It's just that the post by bollu that you've responded to specifically asked if this is physically possible, and the paper you linked quite clearly answers "we have no idea yet". Personally, I wouldn't be actually all that surprised if mathematics and computer science ended up solved some day by a system of chemical membranes, since, to put it extremely crudely, it was developed by systems of chemical membranes in the first place ;) That would raise some serious philosophical questions, though.