This one fails because indefinite integrals don't give you functions, but equivalence classes of functions, all of which differ by a constant. That is why in calculus class you wrote Integral[x dx]=x^2/2 +C. So there are two solutions. The first is that you say that both sides are in the same equivalence class. The second is that you get out of equivalence class land by turning all the integrals into definite integrals on some interval [a,b]. If you do this, you get

1 |_a^b +Integral_a ^b tan x dx = Integral_a^b tan x dx

where 1|_a^b means that we evaluate the function 1 at the points b and a, and we take the difference. 1[b]-1[a]=1-1=0, and so both sides simplify to Integral_a^b tan x dx

Except that there is a lot more to do on facebook than status updates (e.g. looking at other people's status updates, playing games, and slowly eroding your privacy in ways you can't even fathom). The number of status updates on FB is NOT the number of searches people do. For the marketing people, a better metric would be "amount of time spent on the site", which is proportional to how much time you spend look at adds. For direct search comparison purposes, status updates is not a good stand in.

So maybe there are only 2% as many status updates as there are google searches, but what about page views or time spent? They say there are "lies, damned, lies, and statistics" because there are lots of different statistics that let you "prove" all sorts of competing points. Don't be that guy who compares apples to oranges. Facebook might not be as big as google by any reasonable measure, but this is not a reasonable way to compare.

No, transfinite means "beyond finite". As in infinite. There are techniques for working with "infinite numbers" (more correctly called ordinals or ordinal numbers), and these techniques usually have the adjective transfinite, like transfinite induction. To make things more complicated, even if one ordinal number is bigger than another, they can still have the same size (or cardinality), but since this was probably a troll, I've said too much.

Yes, this time, but how do you think that the world changes with technology? Sometimes, we find better ways of doing things, and with a fair bit of luck, those better ways become the popular ways, and then become the tried and true ways. Things that survive the test of time tend to be good, but you shouldn't conflate "good" with "better than the new thing". I mean, if not for technology finding better ways to do things, you would be forced to peddle your sarcastic remarks at the local bar, where you risk being punched in the face. Are the old ways really that much better?

Yeah, though it's a common problem that reporting on science is overblown and inaccurate. Scientists make subtle claims, and reporters will simplify and exaggerate them. Whether this is through ignorance, a desire to make things more palatable for their readers, or a desire to make the article more punchy and widely circulated, I cannot say, though the further it goes through the news cycle, the worse it gets. This is a large reason why people don't trust science: when you oversell your case, people can tell.

Relevant comic:
http://www.phdcomics.com/comics/archive.php?comicid=1174

Well, if we're going based on anecdotal evidence, I've been an AT&T customer since they merged with Cingular, and while I can't remember how the network was when I was living in New England, since I moved to Chicago, I haven't had a call over 20 minutes that didn't get dropped at least once. I don't have an iPhone, just a regular non-smartphone, so it's not just NY and it's not just iPhones.

(as for why I am still a customer when they suck so hard if I don't have an iPhone, a family member gets a discounted family plan through work, and everybody else in the family has an iPhone, but I would change carriers if there were not extenuating circumstances.)

No, it only creates fear for those of us who think about how they act. If you've ever spent time on facebook, it's painfully clear that many people have no fear about what they do or say and then commit to their permanent public record. Unless, of course, they are just too afraid to be thinking about what they are doing when they post?

Belief systems in and of themselves may not constitute knowledge, but they are definitely something that one can be knowledgeable about. Given the number of people who subscribe to some of the most popular belief systems, and the fact that one cannot go far without interacting with a person who subscribes to one of these systems, it is genuinely useful to know about how these systems work, how they are similar, how they are different, and what they are really all about.

If people were more informed about religion, both their own and others, maybe the level of discourse after 9/11 would have been better than "Kill the Muslims, they hate us for our freedom!"

Of course, there is a difference between teaching religion and teaching about religion, and it is difficult for some people to teach this kind of thing evenhandedly. Small changes in language could set people off, e.g., "Christians believe that Jesus was the son of God, sent to give us salvation" vs. "Jesus was the son of God, sent to give us salvation". And then there is the issue that, if someone has strong religious beliefs one way, they will not take kindly to the perception that their children are being indoctrinated in another belief system.

If astrology was a widely held belief that affected the way laws were passed and who we went to war with, if people were apt to get into big arguments over astrology, and if a working knowledge of astrology was required for someone to understand many of the big arguments in our society, I would advocate that they teach a little bit about astrology in school too. Just make sure to teach it in a way that says "this is what astrology is" and not "this is what is true about the world." The danger is not in explaining a religion, it is in espousing one.

No, because getting a warrant now with too limited a scope might prevent them from ever getting admissible evidence for the other crimes, they are sending in non-federal agents to prevent a miscarriage of justice stemming from a legal technicality. Like how some big investigations go on for years before any overt action is taken, because a bust without enough admissible evidence is just a waste of time and money. But feel free to oversimplify things however you would like.

No, things have not changed as much as I would like. We're not living in a utopia. Not all of Obama's campaign promises have been met. The government isn't ceding all the ill gotten power it's grabbed in the last few years, it hasn't made itself transparent, and it's hard to say how far things will go in the right direction. However, it is quite disingenuous to say that nothing has changed and that things are not better than they were before.

So let's compromise: The more things change, the more they stay the same.

(And it might be off topic to say so, but this isn't a power grab. At issue here is whether information in a file you already have a warrant for is off limits because you went in specifically looking for different information. People bitched and moaned about how stupid it was that patents were being granted for doing business things *on a computer* when there was nothing essentially new, why turn around and say that they way warrants work should change when they refer to things *on a computer*?)

Well, a large number of people did vote for McCain with Palin on the ticket (and it would be statistically unlikely if not one of them reads slashdot), but I think it proves your point. I certainly wouldn't have voted for Obama if I had believed he was a secret muslim, white hating, crazy pastor having, kenyan socialist out to destroy America. Maybe.

Is it really fair to compare people who went to universities to people who went to vocational college to focus on writing great software? Wouldn't it be better to compare them to people who went to vocational college to write regular software?

Of course, I don't know exactly what is taught at a vocational college, but my guess is that it revolves more around programming than computer science, and that is the difference. If you know how to program, and you know all about the standard libraries, than you can accomplish quite a lot. However, what you don't cover in a CS program is likely going to be picked up quickly on the job, while the theoretical underpinnings of a good CS degree will not just be picked up by someone who doesn't already have them.

Depending on the job, it might not make a difference at all. If you don't need fancy algorithms and data structures, if you're not doing OS coding, if everything is straight forward to implement, or if you never have to do anything that isn't already well covered by standard libraries, then going to a vocational school is probably great preparation. However, if that's not the case, then there are things you need to learn (either in or out of school).

It really does depend on the job, though. A man who knows how to design cogs and create vast machines of his own with them isn't going to have an advantage over a man who can just put cogs together following a diagram if the job is as part of an assembly line. So I would say, there are blue collar programming gigs, and there are white collar ones. For a blue collar one, either education level works fine, and are perhaps equivalent. For a white collar one, that's no longer the case.

So having something to export is bad because lobbying will yield laws preventing imports? Subsidies are different than tariffs or import bans.

In part due to OPEC, and in part due to speculation, gas prices soared not too long ago. As worldwide demand for oil increases, we are only going to have more problems. And the cost doesn't have to skyrocket unpredictably for it to cause major problems. A steady increase of 10% over inflation each year could easily cause problems faster than we can deal with it. In fact, it could be argued that we see the need for these technologies right now, but consumers don't buy what is in their best long term interests, they buy what is cheapest right now, and that creates an economic incentive for companies to do what is cheapest right now. The way U.S. capitalism is structured, most companies seem to do what is in the best interests of short to medium term profits. Subsidies are required to get the country to act in it's long term best interests.

Yes, subsidies can cause unintended side effects, and bad subsidies (e.g., subsidies for corn ethanol) would be disastrous. I can understand being wary. However, blindly saying "subsidies bad, free market good!" is likely to lead to equally bad results too.

Yes, and no. Yes, there are inefficiencies associated with subsidizing anything, and so, in the short term, there is an economic penalty for it. However, in the long run, there are many advantages. There are political issues relating to oil shortages, there are real economic gains to being a leader in new forms of energy (e.g., we can sell it to others), and since the money is going to be spent on the research and development eventually anyway, using subsidies and doing it now offers a few other perks: We aren't in a dire need to implement the first working thing on a wide scale if there are better things in the pipeline, we are diverting resources we have now instead of being forced to spend those we don't have later, we're creating jobs to get us through a bit of a rough patch, and keeping the middle class in the middle class (as opposed to waiting till they cannot afford anything resembling their current lifestyle) does a lot for both the country's morale and future economic prosperity. So maybe by some metrics, things would work out better if we let the market take care of everything, but there are other advantages which make this route at least as attractive, if not tangibly better.