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"But another reason we believe P≠NP is that otherwise mathematical creativity could be automated!" I have a problem with this. Just because the thought is unpleasant does not make it true or false. Besides, perhaps this is the very difference between automation and intelligence, perhaps the point at which you can ask this of a computer is the point at which you should no longer consider it a computer.
I posted this link because (a) it seemed like a good survey of the subject, and (b) I felt like I almost understood most of it. Does anyone have any suggestions for accessible further reading at the intersection of computer science and physics?
His Philosophy-Complexity paper is also fantastic, in case you have not read it already: http://www.scottaaronson.com/papers/philos.pdf It has also been discussed most recently here: https://news.ycombinator.com/item?id=9061744
Aaronson's talk on Computational Complexity and the Anthropic Principle [1] also looks interesting.
"But another reason we believe P≠NP is that otherwise mathematical creativity could be automated!" I have a problem with this. Just because the thought is unpleasant does not make it true or false. Besides, perhaps this is the very difference between automation and intelligence, perhaps the point at which you can ask this of a computer is the point at which you should no longer consider it a computer.
"But another reason we believe P≠NP is that otherwise mathematical creativity could be automated!" I have a problem with this. Just because the thought is unpleasant does not make it true or false. Besides, perhaps this is the very difference between automation and intelligence, perhaps the point at which you can ask this of a computer is the point at which you should no longer consider it a computer.
Sure, it is certainly possible that mathematics can be automated, but mathematics is also over 2000 years old. We are not much closer to automating it than the Greeks were. P=NP does not only break the Complexity theory (which is a relatively new invention), it also has profound consequences to all of human reasoning.
What we haven't automated is mathematical creativity, which is a completely different class of problem.
If you enjoyed this I highly recommend both his book, "Quantum Computing Since Democritus", and blog ( http://www.scottaaronson.com/blog/ ). Tagline of the blog is "If you take just one piece of information from this blog: Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once."
On the point of anthropic computing: it is important to note that you have not accomplished any _improvement_ to your condition by killing yourself; before as after, you had found a correct solution with probability 2^-n. Anthropic computing is just "fancy guessing". What is interesting about it to me is that the "true computational nature of reality" must be such that sufficient computation is available for you to r…
If so, aren't you implicitly assuming that these other parallel worlds somehow draw on a shared pool of computing resource? This might be true [1], but equally there may not be a "behind the scenes" of reality at all.
[1] How would we know? Run a timing attack on the underlying compute infrastructure?
If you enjoyed this I highly recommend both his book, "Quantum Computing Since Democritus", and blog ( http://www.scottaaronson.com/blog/ ). Tagline of the blog is "If you take just one piece of information from this blog: Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once."
On the point of anthropic computing: it is important to note that you have not accomplished any _improvement_ to your condition by killing yourself; before as after, you had found a correct solution with probability 2^-n. Anthropic computing is just "fancy guessing". What is interesting about it to me is that the "true computational nature of reality" must be such that sufficient computation is available for you to r…