21–30 of 34 posts
I remember a TED talk on the failed attempts to find cases in which nature solves a NP-complete problem. Paper must be an interesting read.
Related: http://www.wired.com/2010/01/slime-mold-grows-network-just-l...
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…
How is killing yourself a correct solution to anything, and what is "n" in your equation? Humans are experience integrators with the rather interesting (and unique) opportunity to "emit" the useful integrations that make it easier (or possible) for others to perform a similar integration. We do it on a personal level with children and friends; and on an impersonal level with books and papers.
Its a not-entirely-serious riff on the Anthropic Principle [1] and maybe the "Quantum Suicide" thought experiment. It's clear to me that the meaning in the article is not that killing yourself solves life problems.
[1] https://en.wikipedia.org/wiki/Anthropic_principle
[2] https://en.wikipedia.org/wiki/Quantum_suicide_and_immortalit...
"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.
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…
By running the validation "in parallel", do you mean running it in each of the possible quantum "many worlds" in which validation takes place? 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 underlyin…
I keep pointing out to people I can't make their beers (including glass) disappear while we're talking at a table. That this universe doesn't allow me to hack it (and presumably keeps others from hacking it) is a nice feature.
Earlier quoted context omitted.
How is killing yourself a correct solution to anything, and what is "n" in your equation? Humans are experience integrators with the rather interesting (and unique) opportunity to "emit" the useful integrations that make it easier (or possible) for others to perform a similar integration. We do it on a personal level with children and friends; and on an impersonal level with books and papers.
I'm not sure if you read the paper. Aaronson writes: "given a formula ϕ, guess a random assignment x, then kill yourself if x does not satisfy ϕ." In other words, the only universes in which you find yourself existing (alive) are ones in which you are in possession of a solution to ϕ, which you obtained easily by guessing. Its a not-entirely-serious riff on the Anthropic Principle [1] and maybe the "Quantum Suicide"…
Earlier quoted context omitted.
By running the validation "in parallel", do you mean running it in each of the possible quantum "many worlds" in which validation takes place? 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 underlyin…
I'm leaning toward the parallel universe hypothesis as well, except I'm thinking it's more like there are part-time processes that run in parallel, do their work, then exit after they come to some type of consensus of state. It would end up looking something like a bunch of containers running a game on your computer, processing all the other player's moves, arriving at consensus, sending that consensus to a central '…
Earlier quoted context omitted.
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.
We already have commoditised math solvers for any number of (relatively) trivial problems. What we haven't automated is mathematical creativity , which is a completely different class of problem.
Creativity is an anthropomorphic, abstract concept, a way of describing human ways to find solutions. What really matters is the proofs.
"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.
Right, it is automated. we are the machine that automates it.
"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.
There is zero reason to believe that human level mathematical creativity is computationally significantly more expensive than normal day to day thinking.
But appropriately accounted for, I think it is.
The relevant metric would be, "what do I have to increase in order to get more [interesting, new] theorems proved?" Is it as easy has having mathematicians work more hours? Having more people start working on them?
Intuitively, it is not so easy -- each insights need exponentially more work as time progresses. An exponentially-small fraction of humans is capable of producing novel results, and so on.
This, I think, is what Aaronson is getting at: if P = NP, if proving is as easy as verifying, then coming up with hard mathematical insights should be as easy as following a cookbook, or any other routine, mundane mental task.
But that doesn't seem to describe the world we live in, where getting mathematical insights has rapidly diminishing returns per unit resource invested.