But he, and you, are missing the entire point of flu vaccines. Yes, a healthy person does not personally need a flu vaccine to prevent them from dying; however, there are many people--mostly the very young and very old--who cannot get flu vaccines due to other health concerns and for whom the flu could be fatal. The reason to get a flu vaccine is not to protect yourself, it's to protect your grandparents & your newborn nephew.

The proof is actually rather technical, but the general idea is as follows:

A problem is in NP iff solutions to said problem can be verified in polynomial time. That is, there is a Turing Machine that when given an instance of the problem and a proposed solution will run in polynomial time and spit out a yes or no; we'll call this machine the Verifier.

Since we are trying to show that solving 3-SAT in poly time solves any NP problem in poly time, let's start by picking any old NP problem, and call it's verifier machine V. Let's also pick some particular instance of the problem that we're interested in. To answer our question, we essentially need to answer the question "Is there any input to V that will cause it to give a 'yes'". The hugely technical part of the Cook-Levin theorem is that the preceding sentence can actually be coded as an instance of 3-SAT with polynomial-many (in the length of your problem instance) clauses; this is done by introducing variables to trace each step of the computation of V to make sure it agrees with what V is supposed to do and then having extra variables for the inputs of the proposed solution. Thus, if you can answer this 3-SAT problem in polynomial time (as you surely can if you claim to have an algorithm that can answer ANY 3-SAT problem in poly-time), then you have answered the original question from your other NP problem in poly time as well.

Despite what is taught in most CS classes, constants do in fact matter. If I give you an algorithm for breaking RSA that runs in time n^(2^1000000000000000000), it's essentially useless as the the number of clock cycles to decrypt even a 2 bit key exceeds the number of nanoseconds that have passed since the beginning of the universe. My algorithm is polynomial, but who cares?

Discrete log is also in NP--I can verify your proposed solution by simply exponentiating it, which is a very fast operation when working in modular arithmetic. In fact, any reasonably normal asymmetrical encryption algorithm pretty much has to be in NP since you can verify a proposed private key for any public key by simply encrypting and decrypting something, both of which should be polynomial time or else the system is probably too slow to be useful anyways.

You might want to check your math there. Comcast currently caps at 250GB per month, so unless you're streaming 4+ movies per day, you really shouldn't have trouble. You can say whatever you want about the appropriateness of bandwidth caps in general, but the truth is that 250GB is a LOT to pull in one month; in particular, you can download at 100k/s continuously for the entire month and still stay under the cap...

Hashing is so fast as to be a truly negligible part of the time required to perform a brute-force attack. At worst, it maybe makes it take twice as long, which in the world of password cracking is completely irrelevant (just think, if it takes 2 days without hashing, is there much of a difference if it goes up to 4 days?). The parent's post is 100% correct in that restricting your keys to only a certain subset of the alphabet has the same effect as simply using shorter keys in the first place. For example, if I tell you that passwords are no more than 8 characters and only consist of lower case letters a-z, then there are only as many combinations as using a 37 bit key in the first place. Hashing my character password up to 128 bits doesn't actually do anything to increase the strength; if it did, we would just hash everything and anything up to $LARGE_NUMBER-bits and call it a day.

Yikes. I guess I gave the guy way too much credit.

True, the number of trapezoids is not an active area of research, but the idea of picking which points to evaluate a function at in order to approximate its integral in some nice way is in fact active. For example, Gaussian Quadrature methods can be used to exactly calculate integrals of some classes of functions by simply evaluating them at certain points and weighting appropriately and there are questions as to which classes of functions can be approximated in this way and more specifically what the points/weights should be. After some further digging, I clearly gave this paper way too much credit and it does in fact appear to be just the trapezoid rule, but the general point I was trying to make--that numerical integration is not as trivial as some people seem to think--is still valid.

First, does anyone have a link to the actual article? TFS only seems to include an abstract. Second, this was published in 1994. Third, while it may simply seem that the author is rediscovering integration, the field of numerical integration is actually a rather rich one. It's all well and good to say "take an antiderivate and evaluate at the endpoints", but for a function that is found experimentally this is essentially nonsense. While the submitter here claims that this article is simply rediscovering the trapezoid rule, there's actually no such evidence given in the Abstract--algorithms for determining how big of rectangles/trapezoids/etc to use in your calculations is actually an active area of research (albeit usually for the multidimensional case) and it is possible that this researcher did actually discover a better algorithm for deciding how to do the numerical approximations.

The sad part is that many students and their families are talked into sending in dozens of applications to schools that they really have no chance at getting into. At $50-$100 each, application costs in the thousands of dollars are becoming more and more the norm. What's worse, many schools apply a simple GPA/SAT based gross-cut filter and won't even look at some of these applications; in essence, these students and their families have spent $50 to have a computer think for 1ms and then spit back a "no."

I love Chrome's snappiness, but until they change their plugin/extension architecture so that AdBlock can block mid-video Flash ads, Firefox is still the winner in my book. Also: 7.0? Really? Not just 6.1?

My issue is not with their overall process, which I agree is better than most shows. The issue is that when they don't have enough time/money/perseverence to try another route, they go ahead and show that same "Busted" logo and pretend as if their one experiment was proof-positive that the myth was entirely infeasible. As any real scientist will tell you, it's much easier to prove something is possible (just do it!) than it is to prove that something can't be done. Researchers will spend entire careers trying to find ways of doing something new, and even if they fail after 50 years, the correct conclusion is NOT that it's impossible to do, only that nobody's tried the right thing yet.

If the goal is to promote science education, Mythbusters seems like the LAST place to do it. Seriously, this is a show that will try one particular way of doing things, fail at it, and then conclude that the original "myth" is busted based on their one experiment. I would have a lot more respect for the show if their only possible conclusions were "confirmed" and "inconclusive"

Really? I know this is what Bruce Schneier advocates, but to me this means that having your wallet stolen means all of sudden your bank passwords are gone too. Given how much more likely it is to be robbed outside your home than it is to have someone break into your home, this seems completely backwards to me. You would call someone crazy for taping their PIN to the front of their ATM card, but putting all your passwords in your wallet is just about the same thing.

No, it's not. Moving the sun with respect to the parabola and surrounding sidewalks is the same as moving the parabola AND SURROUNDING SIDEWALKS with respect to the sun. One of the beautiful things about parabolic reflectors is that regardless of what angle of light you shine at them, the light ALWAYS comes out parallel to the axis of the parabola. Always.