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@Chronos (can't reply for some reason, so I'm just replying to my own post and tagging you) Its true that LQG is not known a natural schema to implement hyper-computation. However, since we don't well understand the time-dynamics of twistors ( how these operators may interact non-linearly through time), i don't see any a-priori reason why it is not a possible scheme for super-computation (you could make a good counter- response based on occam's razor, which I'd grant). Look, lots of thereotical CS folks get disturbed by the idea of hyper-computation/super-turing machines, but in truth Turing machines are a toy model in comparison to true physics; as such, it doesn't take a whole lot more to get something more powerful; Siegelmann and colleagues have shown that real weighted, analog recurrent nets have super-turing abilities [1] [2]. While Aaronson and other raise good questions about physical realizability of such systems, a good thing to keep in mind is that these discussions often take place at computational 'limit' cases, eg solving intractable PSPACE problems, which may not be as relevant to more pedestrian problems solvable by biological systems. Central point: dynamically evolving systems iteratively exploring through (from) in-consistent systems towards more and more consistent ones have many of the same compelling qualities we would call 'super-turing'. Also see the lit on evolving turning machines. Finally, while I don't agree with the magnitude your Pauling analogy, I certainly agree with you statement that Penrose is out of his depth here. While I do not , presently, buy his argument that quantum effects are necessary to realize consciousness, I remain open to the idea until we know more about BOTH physics and computation. [1] http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00263
[2] http://www.kurzweilai.net/super-turing-machine-learns-and-ev... |