I once had a conversation with a department head at Caltech who told me that, thanks to their endowments, they could easily afford to charge a much smaller tuition, and that like 70% of their students were given fairly good financial packages, but if they lowered their base price and charged less than other universities, people would assume that they were of lesser quality. Since the value of a degree (not of an education) is in how other people view it, cutting their prices would be a great detriment to their graduates.

As long as the system is in place, and as long as there are more people who want to go to good schools than those schools can accommodate, it is in their best interests to keep their sticker prices high. They only have reason to show you the price you will pay if nobody is considering them because they are too expensive.

Of course you have to allow people to say things you disagree with to be able to call it free speech. But we don't allow people to shout "Fire!" in a crowded theater when there is none, and threats of bodily harm can construe assault. It is clear that society appreciates that speech has power and consequences, and the question is, where do we draw the line on what should be allowed in the name of free speech versus what should be disallowed for the sake of a calm and peaceable society?

Should we allow to call for the assassination of abortion doctors? What about when the people who listen to them actually commit murder? Should there be culpability?

What about verbal bullying? If someone kills themselves because you repeatedly put them down, do you not bear some responsibility, even if you didn't pull the trigger?

Of course, in both these cases, the blame can't be placed entirely with the speaker, as others had to decide what to do with the words (nor should placing any blame on the speaker be seen as a lessening of the blame on the actor), but when words have a direct impact on whether someone lives or dies, I don't think it is as easy to dismiss them as just words. Of course, it is much harder to judge intent of words, it is harder to judge what the reasonable expectation of the consequences of words should be, and it may well be that there is no way to prosecute this kind of speech without creating a system that is rife for abuse and which undesirably suppresses other kinds of free speech, but the issue isn't so clear cut that it can be put to rest by a few choice quotes.

An iPhone may not be a necessity, but if you ALREADY HAVE ONE and you drop AT&T as your carrier, you are essentially throwing away money and converting it to an iPod. If this was about what carrier to choose if you were just starting out, or if smart phones didn't exist and all cell phones were roughly equivalent, you might have a point. As it stands, I honestly have no clue how what you are saying is relevant.

Maybe there are other phone companies, but I'm pretty sure that horribly unfair contracts are the norm (with terms like required arbitration and that the terms of the contract can be changed at any time without notice). Additionally, without jail breaking (which might be undone the next software upgrade), you can't switch if you are an iPhone user. To say "just use someone else, competition solves everything" is a bit glib and shortsighted, if not downright disingenuous.

Why do people think that CO2 = bad? There is a natural carbon cycle. CO2 goes into the air, plants breath it in and breath out O2 while turning the carbon into sugar. Animals eat the plants (and other animals) and use the bonds in molecules containing carbon as a storage for energy. As they use the energy, the carbon goes back into the atmosphere. When things are in relative equilibrium, everything is fine.

The problem with fossil fuels is that there used to be a lot more carbon in the atmosphere, which was absorbed by plants which died and took the carbon with them. When we burn fossil fuels, we are re-releasing this carbon into the atmosphere, changing the balance of things. Except for deforestation and burning of fossil fuels, most other CO2 related activities don't actually change the overall amount of carbon in play. There is no need to be alarmist about this.

I'm afraid I have to disagree with you.

First, the distribution of the primes is not an observation, it's a proven mathematical fact that took many smart people a long time to fully establish.

Second, knowing the distribution of the primes has direct applications to things like the security of encryption methods (if large primes were significantly more sparse than they are, then factoring numbers which are the product of two large primes would be much easier than it is).

But the difference in the distribution of the primes versus the distribution of their leading digits is akin to a shoe manufacturer knowing how many shoes of each size to make versus a shoe manufacturer knowing the distribution of the third digit of the number of atoms in the human foot. Yes, they are both observations of a sort, but only one of them has useful information.

Actually, the result is more that the prime numbers don't obey Benford's law, but obey a generalized version of it having to do with the specifics of the distribution of prime numbers. However, a list of numbers doesn't have to be random to obey Benford's law.

The reason the discovery isn't useful is because, while there is use in knowing the distribution of the primes, there is little use in knowing the probabilities of the leading digits of primes. The only application I could think of is if someone gave you a list that they claimed to be all the primes up to 10^100, and you wanted a quick sanity check on whether it might be it. Of course, adding 1 to every number would make nothing (but 2) prime and change almost none of the leading digits.

But in any case, since numbers on income tax statements or stock prices are not required to be prime numbers, and since the leading digit of a number has very little mathematical use, there is little in terms of applications of this observation, mathematical or otherwise.

You say this as if it is a mystery why a company would feel this way. But regardless of whether IT is as expendable as some companies may treat it, I think it is important to understand why things are the way they are.

To any large company, there are essentially two parts. First, there is the part of the company devoted to whatever the company sells. This will include engineering and design, product, sales and marketing, and perhaps some portion of management.

On there other side, there is the part of the company that is there so that the company runs smoothly. This is the part of the company that is there to facilitate and support the first part of the company. IT is in this group (in a non-IT company), as are janitorial staff, a certain other amount of management, and other random departments which might vary from company to company.

There is, of course, some overlap between the two sides. For example, while you might consider the running of the website an IT role, it is also essential to sales. Still, viewing a company as having the two sides is helpful for understanding why companies see IT the way they do.

When money is tight, and a person needs to decide where to cut money, they cut the things they deem less important to their survival. They can refuse to buy a new stereo or new underwear, but they can't refuse to buy any more food.

Similarly, when money is tight and a company needs to decide what to cut, they get rid of what they deem to be the least important to their survival. From upper management's point of view, they see what the impact of laying off staff in their core business will be, and will be less likely to view management as just support. However, it is harder for them to see why they can't just halve their IT staff or janitorial staff. Maybe the floors will get vacuumed less often or it will take slightly longer to deploy Windows 7, but the company will still do what it does roughly as well as it currently does, right? (That is not to say that IT isn't crucial to a company's success, just that it is much harder for upper management to appreciate the relative worth of IT staff).

It's much harder to appreciate exactly how expendable support staff is, but it isn't that hard to see why management would view support staff as more expendable than others.

Benford's law works by the observation that, when numbers come up in certain real world contexts, the fluctuations you get in numbers should be proportional to the numbers themselves. Phrased differently, variations tend to be relative, not absolute. Because of this, if you have a very large range of random numbers from many real world measurements, then you would expect the number between t and t*(1.0001) not to vary too much for small changes in t. Let us try to use this observation very coarsely. Among the numbers with 6 digits, the number that look like 1xxxxxx (those between 100000 and 200000) should be about the same the number between 200000 and 400000. The same thing happens with the numbers with 5 digits or 7 digits or n digits (assuming that you have a wide range of random numbers, and the numbers are the kind that come from certain sorts of real world measurements). Additionally, you can get distributions for the first two digits, the first three digits, etc.

This observation doesn't depend on the base that you're working with.

Now, with the prime numbers, they have a distribution that is different from a lot of real world measurement data. The number of primes between n and n+d is approximately d/ln(n), where ln is the log with base e and d is small compared to n. So the number of primes between 500000 and 600000 is about 100000/ln(500000), and the number of primes between 500000 and 600000 is about 100000/ln(600000). By using this, and being slightly more careful, one can determine fairly easily the distribution of the leading terms of the prime numbers.

This is not a hard result. I would say that any professional mathematician who knew about the basic distribution of the primes could derive the distribution of the leading digis of the prime numbers fairly easily if anybody actually asked them to. The reason nobody mentioned this before is that nobody actually cares. While Benford's law does have applications to fraud detection, this new result does not. It's one of those things that makes people say "ooh, a pattern!" but which is just an easy and somewhat mundane corollary to a well known theorem.

A spider monkey inspired car horn set for space? A webkit inspired grapling hook set for space? Oh, the joy of open source browsers.

Yes, it is conceivable that standing up to Amazon will cause them to back down. They might feel that this is a fight they won't win and that isn't worth the bad press. Then again, they might not. Best case scenario is that the site owner (who might just be running the site as a hobby, and who may currently be in a less than stellar financial situation) spends a few hundred dollars and kills his relationship with Amazon, which he might view as important given the content of the website. Still, no legal precedent is set.

Worst case scenario is that Amazon views this as a legitimate matter that is too important to drop, it goes to trial, he is out thousands of dollars and a lot of time, and even if he wins, he has still lost. Additionally, I think you far overestimate how much publicity this will get. Odds are good that, even if the mainstream media picks up the story, it will only be a brief blurb. Most people who hear it won't care, and many who do will go, "Oh wow, that's a nice ebook reader!" While slashdot probably has a higher percentage of people would would buy portable ebook readers than in the general public, a boycott by all slashdot/digg/reddit/etc readers would still probably not persuade amazon to stop, if they are that concerned about piracy and the device really is a loss leader.

I would love to see him fight and win. I hate bullies, I hate people who abuse the system, and I feel that one should be able to use hardware however one sees fit. However, I honestly cannot fault him for choosing not to fight. If you want to teach them a lesson, go ahead and pick a fight. But remember, not everybody has the luxury of being able to stand on their principles (and even fewer still have the luxury of standing on yours).

Just because you run and hide from a pack of wolves doesn't mean you are a sheep. While you might wish them to martyr themselves for your principles, if they don't have the resources to fight, or if a win would not accomplish anything for anybody else, why shouldn't they act in their own best interests?