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Heuristically. There is no reason to suspect we solve the halting problem or even any restricted variant. In fact, there is no reason to suspect we solve any p

by sago 7y ago

Heuristically. There is no reason to suspect we solve the halting problem or even any restricted variant. In fact, there is no reason to suspect we solve any problem of even modest computational complexity for anything but the tiniest domains. It is 'not taken seriously' because the only evidence seems to be handwaving and philosophical argument (perhaps with a dollop of quantum weirdness, a la Penrose). There are a number of models of hypercomputation. Finding any with a physical basis that might credibly match neurobiology is highly dubious. It is not even clear that any of them have any physical basis.

bitL 7y ago
Berkeley already uses electricity for finding instant solutions to quadratic optimization problems[1], why do we restrict ourselves to some primitive digital mode in humans? In addition, we already know neurons do some form of protein-based computation, alongside to what looks like spiking/timing-based electric computation. Some neurons can be 1 meter long as well, interfacing with many parts of brain. Can we rule out some super clever electric potential optimization or even something better isn't going on in the background? I am not saying Penrose is right that brain can compute BQP and is using collapses of quantum gravity to solve halting problem, but why can't we keep open mind about it? Hypercomputation is a cool theoretical device, again the models are way too primitive for now and likely any finding in nature would have super complicated mapping to the current theory. But hey, there might be some graduate student with an idea already... [1] http://www.mpc.berkeley.edu/research/analog-optimization http://www.mpc.berkeley.edu/research/analog-optimization
- yters 7y ago
  Exactly. Turing himself left the door open to such ideas with his notion of the oracle machine. It seems odd that we have narrowed the range of possible explanations so dramatically. There are many more oracle machines and even higher order machines on the Turing hierarchy than there are Turing machines.

by sago 7y ago

bitL 7y ago

Berkeley already uses electricity for finding instant solutions to quadratic optimization problems[1], why do we restrict ourselves to some primitive digital mode in humans? In addition, we already know neurons do some form of protein-based computation, alongside to what looks like spiking/timing-based electric computation. Some neurons can be 1 meter long as well, interfacing with many parts of brain. Can we rule out some super clever electric potential optimization or even something better isn't going on in the background? I am not saying Penrose is right that brain can compute BQP and is using collapses of quantum gravity to solve halting problem, but why can't we keep open mind about it? Hypercomputation is a cool theoretical device, again the models are way too primitive for now and likely any finding in nature would have super complicated mapping to the current theory. But hey, there might be some graduate student with an idea already... [1] http://www.mpc.berkeley.edu/research/analog-optimization http://www.mpc.berkeley.edu/research/analog-optimization

yters 7y ago
Exactly. Turing himself left the door open to such ideas with his notion of the oracle machine. It seems odd that we have narrowed the range of possible explanations so dramatically. There are many more oracle machines and even higher order machines on the Turing hierarchy than there are Turing machines.