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You don't think it's exciting that we can show that we can show that routing FedEx trucks, scheduling university final exams, and finding mathematical proofs ar
by davmre 15y ago
You don't think it's exciting that we can show that we can show that routing FedEx trucks, scheduling university final exams, and finding mathematical proofs are, in a very strong mathematical sense, the exact same problem (NP-Completeness)? That if someone at FedEx could came up with an efficient way of finding the shortest paths for their trucks to follow, they would in the process have broken all modern cryptography and solved all open questions in mathematics?
You don't think it's interesting that it's provably impossible to predict in general what will happen if you follow a set of instructions, even if you have the entire set of instructions sitting in front of you (Rice's theorem)? This is the only plausible path I've ever heard towards recovering a notion of free will in a deterministic universe: even if you know the entire state of the universe and the rules by which it operates, it's still mathematically impossible to predict the future in any way more efficient than just sitting back and letting it unfold.
And you don't think it's important that we can prove that finding Nash equilibria in large games is computationally difficult, and that the amount of computation required grows much faster than the number of the players in the game (http://www.cs.berkeley.edu/~christos/papers/cacmDGP-2.pdf http://www.cs.berkeley.edu/~christos/papers/cacmDGP-2.pdf)? You think the fact that it's literally impossible for large markets to compute optimal solutions doesn't have profound economic and political implications?
If all this stuff is really as uninteresting to you as the details of your plumbing, then good for you, I guess. Maybe this is just the wrong site for this sort of stuff; maybe the audience here is self-selected to be all the people who thought their CS theory classes were so boring that they dropped out and founded startups instead. But I'm in the same camp as Scott Aaronson: I think there are a lot of people out there who would be just as fascinated by the profound questions, results, and paradoxes of CS as they are by quantum mechanics and relativity, if these ideas were given the same level of exposure. Theoretical physics is both a much older and much larger field than theoretical CS, so it's not surprising that it's managed to come up with many more charismatic and insightful popularizers. That doesn't mean that CS is any less interesting or exciting.
- hugh3 15y agoOh, don't get me wrong, I find that interesting... but then again I find everything kinda interesting. I'm actually kinda keen to see the aforementioned plumbing documentary. I was merely speaking in the voice of "member of the general public" up there who probably can't be persuaded to find all this stuff as interesting as whiz-bang relativity/quantum mechanics/cosmology. Note that it's only the most whiz-bang bits of physics which capture the imagination of the general public too -- try explaining solid state physics or optics to the general public and watch their eyes glaze over.
- anamax 15y ago> You don't think it's exciting that we can show that we can show that routing FedEx trucks, scheduling university final exams, and finding mathematical proofs are, in a very strong mathematical sense, the exact same problem (NP-Completeness)? I think that it's exciting, but it's not generally exiting. > That if someone at FedEx could came up with an efficient way of finding the shortest paths for their trucks to follow, they would in the process have broken all modern cryptography Slow down there there cowboy. Polynomial time is not enough. You need a reasonable constant factor and a small-enough degree. To put it another way, N2 is too slow at Google-scale. (Actually, N lg N is too slow for some of their problems.)