No. The Halting Problem belongs to class UNDECIDABLE, not class NP-Hard. I admire your attempt at rationalizing it, but Alan Turing proved this to the world's satisfaction. If you wish to prove the Halting Problem does not belong to UNDECIDABLE then you're going to have an uphill road to hoe. If you still believe the Halting Problem belongs to NP-Hard, I would suggest you begin by correcting its Wikipedia article.)

Your argument involving an oracle that solves the Halting Problem is absurd because you're assuming the existence of hypercomputation -- and if such an oracle could exist, then we would simultaneously have P=NP and P != NP. Martin Davis has gone so far as to declare hypercomputation both "a myth" and "a nonexistent discipline." Those are strong words coming from one of the brightest lights in the field of computational theory and computational complexity.

It's a bedrock principle of logic that if you start from a false proposition anything can be proven. You assume the existence of an oracle that can solve the Halting Problem. This is a false proposition. Anything can be proven once you make oracular assumptions.

At this point I'm pretty sure you're trolling. The Halting Problem is UNDECIDABLE -- it exists in a complexity class considerably beyond what is normally thought of as 'NP-Hard'.

And if you don't understand my parenthetical remark, well... that should be taken as a sign that your computational theory is seriously lacking. The meaning is quite clear to someone who has a proper understanding of what complexity class NP-Hard is about.

Goodbye, troll.

No, even then your characterization of NP-Hard is incorrect.

"A class of problems is NP-Hard if being able to solve it in polynomial time..."

If you can solve it in polynomial time, then it's in P. Even under your revised definition, you're implicitly arguing that P=NP, because that's the only way you can solve an NP-Hard problem in polynomial time. (And even then, you would only be able to solve the NP-Complete subset of NP-Hard.)

Permit me to stand for a moment on my all-but-dissertation Ph.D. in theoretical computer science:

You're wrong.

Sorry, but the original poster was essentially correct. Your definition would make sense if it involved the existence of a polynomial-time transformation between an NP-Complete problem and the purported NP-Hard problem, but saying that "a solution to an NP-Hard problem allows for NP to be solved in polynomial time" is ... febrile. If an NP-Complete problem can be solved in polynomial time, then P=NP. Since we believe P != NP, your claim would mean NP-Hard problems would have no solutions, which would mean they would really belong to class UNDECIDABLE, and... etc. I don't think you meant to go there.

With respect to the OP's talk about direction, I understood that to be a layman's distinction between solution and verification. If that was the OP's intent then he's guilty of at most an infelicitous choice of words -- he's not "at best confused, and essentially wrong."

And even more compatible with the deaf. Zing!

(I kid, I kid. I lived for a couple of years near a church were bagpipers practiced and used to open the windows to hear them every Wednesday. I really miss that, even though they only ever practiced the same 3-4 songs.)

...and good industrial design. Our *five*...no... *Amongst* our weapons.... Amongst our weaponry...are such elements as customer support, quality.... I'll come in again.

Not since 2007, unfortunately.

http://www.youtube.com/watch?v=p0u8rI0JvaM

The only part of the above link that matters.

Heh. Reminds me of the time in high school when I had to play "Also Spake Zarathustra," which starts with several measures of a single low note and periodic timpani drumming before the rest of the band kicks in. The low, long note was to be played by the tubas, but I was the only one in our small band, so no stops for breath for eight slow measures.

The weeks of practice before the concert were a source of joy and mockery for the rest of the band as I had to train up my lung capacity to do it, and I usually ended up beet red from effectively holding my breath / trying to squeeze every last bit of it out of my body for over a minute. Even better, I had to try to stuff as much in air in my lungs as I could before the first note, so I was pretty red and semi-bugeyed from the beginning too. I felt like that guy at the end of "Big Trouble in Little China."

Good times.

At work, I can't really watch video, so could someone explain how a blind musician reads braille while playing the piano or most other instruments? Aren't both hands occupied?

(Please, no mods to me. Give them to the people who answer.)

I would guess that the right touchpad can emulate four buttons in the same way the left touchpad emulates a D-pad.

I think you have the wrong parallel. This is more like blaming someone whose brake lines get cut because they picked up the wrong girl at a bar for not checking their car out first before driving it every time. Or maybe it's more like blaming the parents of kids killed in school shootings for not home-schooling them and keeping them wrapped up in bulletproof vests whenever they go out.

We're not expected to have to defend ourselves against every determined attacker from every angle. That's part of why we have police and a court system -- to keep us from having to live in fear of anyone more skilled at offense than we are at defense. The very mark of rule of law is that don't blame those who acted in good faith for the acts of those who do not. Every time some self-centered prick blames the weak for being weaker than they are, they excuse the strong for being predatory. May you never be on the other end of that stick.

Who the hell are you to decide that? These women have been violated. He left at least one in tears. They have had their sense of security in their own home stripped from them. They will never be able to trust their computer again and use it in a way that the rest of us all get to take for granted. He has exerted a cruel power over their lives that will leave them harmed for years if not for life.

If you've never had your home invaded or never been raped and never have known anyone who has, you probably don't understand how long the effects of this will linger.

So, why is his suffering the only one that's valid? You seem all too dismissive of what he's done to those women in your sympathy for him. One might draw unfortunate conclusions about your values towards women if you keep dismissing sexual blackmail as just some childish prank that he deserves only to be mildly scolded for and told not to do it again.

Look, I would like a more reform-oriented judicial system, but we are not going to get there by treating people who did something like he did as harmless scamps. There needs to be punishment. There needs to be consequences. There also needs to be counseling, reformation, and an attempt to help him integrate back into society when he's done, but the lack thereof is no excuse to claim that he doesn't deserve the punishment for the very serious crime he has committed multiple times and with no indication that he'd stop if he hadn't been caught.