But we're talking about Snape, who is not dead as of the first Deathly Hallows movie.

While I don't agree with most of what GP said, wouldn't everything you said just be a factor of 'costs' that must be considered against the revenues gained from it? Your post reads more or less as "comparing revenue v. cost is short term thinking because you don't take into effect this and that cost" which... doesn't make much sense.

Clever, except that I can name at least four different methods of romaji, each of which have their own deep flaws and a lot of areas where they simply don't agree. This is how we got "Japan" out of "Nippon", after all.

Even if you do select a particular romaji method, you're still without a way to properly translate moras, pitch, and some of the subtly different sounds (like the "r" people so love to make fun of). Which brings us to the GPs point: there is no way to directly translate Japanese, but we have agreed on a handful of systems that we consider "good enough".

Who said I was doing anything more than a rebuke? It is clear that you don't understand the nature of real numbers, nor the nature of infinity. This left me with three choices: Be the one to try to teach you these fundamental concepts, don't comment at all, or take my time to poke some fun. By the way I derided constructionists at the end, I thought it would be clear that I was just being an ass.

Though, if you seriously do want some education, here's a few things to think about:
* 0.999... is not a process. It is simply a number.
* While it is just a number, 0.999... can be constructed from a process. Specifically, \sum_{i=0}^\infty 9/10^i.
* There is no analogous process for producing what you call "0.000..0001", nor does this concept mathematically make sense. The closest concept is lim_{n\rightarrow\infty} 1/10^n, but this is 0, not some mystical 0.000..0001.

The point is, as I've said multiple times already, a number is not a process. This is key to understanding why .999... and 1 are not distinct.

Another important thing to understand is that any numerical representation must have multiple representations for the same number. It is no stranger that .999...=1 than it is that 1 = 1.0 = 1.00...

Finally, one last thought to leave you with: you are proposing a number that would necessarily be the smallest possible positive real number. However, it would immediately follow that the real numbers would be countable, via an obvious bijection with the natural numbers (specifically, your 0.00...001 would match 1, 0.00...002 would be 2, and, in general, you would match n with 0.00...001 * n). However, it's already been proven to death that the real numbers are uncountable. Therefore your number cannot exist.

Honestly, though, when it comes to it, I can prove it rigorously many different ways, most of which you likely don't have the mathematical background for if you still believe .999... != 1, and you're going to continue to trust your intuition, thinking that we must be tricking you or something. Which is why I didn't even bother the first time around.

You're forgetting the second part of this: because NP-completeness proofs have formed a chain of reductions, finding an algorithm for one of them is the last step to finding an algorithm for all NP-complete problems that we have found (and any others we manage to reduce later).

It's actually much less complicated than that. The process you're proposing can't actually be done. Not only that, but 0.999999... is *not* a process; it simply is. I understand that infinity is hard to wrap your head around, but the first thing you need to understand is that there is simply no process here. That's one of the things that really pisses constructionists off, which just means it amuses me more.

And you're wrong in a very obvious way: 0.999.... is every bit as static and stable as 1, even if they were not equal (the same way that 0.333... is static and has a stable meaning). The fact that we are using an infinite number of digits to represent it in decimal does not change this fact. Numbers are not processes. If they were, then in order to cut .333... of a cake I'd need to go 3/10 from my first cut, then 3/100, then 3/1000, etc forever. You can do that if you want, but I''ll just go .333... from the outset and be done with it.

NOTE: Yes, I use a few simplifications and a lot of non-rigorous language. This should still be good enough to give the basic idea to people who don't study complexity.

Your first problem: NP does *not* mean "not polynomial" or even anything remotely like that. It means "non-deterministic polynomial time", which essentially means we can verify the answer in polynomial time. All P algorithms are inherently also NP. NP-complete problems, like 3-SAT, are problems such that it is easy (i.e. doable in polynomial time) to turn any other NP problem into them. That's why being able to solve an NP-complete problem in polynomial time means we can solve all NP problems in polynomial time. NP-hard is another class that only partially overlaps NP, and it means that the problem is at least as hard as the hardest problem in NP (i.e. it may or may not be in NP, but it's at least as hard as an NP-complete problem).

Note, there are many, many more complexity classes than just these, also. NP is just the set of yes/no problems that can be verified in polynomial time. One thing you'll note is that integer factorization isn't in NP. Or, more accurately, integer factorization as you usually think about it isn't in NP. The "decision version" (i.e. NP version) of the problem is, essentially, "Is there a non-trivial factor of a given number?" The analogous "function version" is much more what you probably consider to be integer factorization: "Is there a non-trivial factor? If so, give me one." Function problems exist in a different class: FNP, which has FP as the counterpart to P. However, FNP=FP if and only if NP=P.

And, just for your edumacation, a small sampling of other complexity classes:
* PSPACE (doesn't care about time; it's the set of problems that can be solved with polynomial _space_; note that we've already proven that the analogous "NPSPACE" is equivalent to PSPACE; we've also shown that NP is entirely contained within, but not equivalent to PSPACE)
* BQP (similar to P, except with quantum computers and a hint of uncertainty; in particular, it's the set of decision problems solvable on a quantum computer in polynomial time with the kicker that it allows for a limited probability of error; we don't know how this relates to NP, other than that all P problems are BQP)

There are many, many others, covering far more things than you can probably imagine without a background in complexity.

Anyway, that was a bit more teach-y than I had expected, but complexity is one of those topics that I adore too much to pass up such an opportunity.

Not that you aren't right to avoid pirated software, but I'd love to see your data on this. As it turns out, the pirate scene is big on reputation and cred, which can only be obtained with quick, clean releases. Anyone spreading malware with their cracks is basically done before they start.

I agree with you almost entirely, but there is a wide difference between "you should at least carefully consider what you are doing" and "we should eliminate all of culture".

That's where we get into some shady areas. For one, if it's an environmental difference, but only in the American population in 2008, it doesn't even come close to proving that men are better at it (although you might get away with the statement that, currently in the United States men are better at 3D perceptualisation, so long as the rest of the conditions I listed have been filled, but that's a vastly different statement). Similarly, an environmental distance, even in a worldwide study, from 1970 would be worthless now except as a historical view.

Secondly, if it shows to be a strictly environmental distance, especially one caused because of an environment negative towards women (such as constantly saying that women are bad at driving), then the continuation of jokes of women being bad at driving and the notion that science has proven it okay would be, not only mistaken, but also setting up a self-fulfilling prophecy that I'm not really okay with.

So, yes, the difference between environment or inheritance is a big deal here, even though your first sentence is strictly correct.

Unfortunately, my uni library doesn't seem to have a copy on hand. However, I do have access to just about every journal ever, so if you could just cite the studies that this book references, I'd love to check them out.

I'm amazed by how your brain leaped from "Do we want our culture to be degrading to women?" to "We should have no culture." Is that really what that post said to you?

Really now? Can you link me to a few unbiased studies the topic with statistically significant sample sizes and shows results of men having, not only higher scores, but statistically significantly higher scores? I assume, of course, that you also have available the justification for why we can trust the tests to be testing purely for 3d perceptualisation, without testing for additional unrelated factors (such as how well you can decipher difficult instructions, a common additional factor in such tests). And I also trust that these studies have properly isolated for sex, ensuring that additional factors such as training and practice in related skills or a lifetime of "you can do anything" vs. "oh, you're just a girl" have no bearing on the final results?

I'll be rather impressed if you can show me any such study. Now, I'll be the first to admit that not all people are created equal and that it is quite possible that people of different sexes and genders and races and sexual orientations have some amount of differences. However, I think you'll find that most of these studies in these topics are entirely inconclusive after you consider all of the factors surrounding them.

It's also worth noting the striking parallels to the number of 19th century studies "proving" that black people were strictly inferior to white people. Confirmation bias can prove anything, as it turns out.

Did you warn them when autocomplete wouldn't autocomplete pornographic searches? Because that's been happening for a while, and nobody cares.