## Comment Re:At what point? (Score 2) 77

You might be willing to compromise on this for the sake of practicality, but I am not.

What is there to compromise if I don't share you veneration of dead bone?

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You might be willing to compromise on this for the sake of practicality, but I am not.

What is there to compromise if I don't share you veneration of dead bone?

His manners have made the universe a more pleasant place for me to live, so, on balance, I'd call it a win for the AC.

You mean something like the Sieve of Eratosthenes?

You mean 2, right? I mean, it is the only even prime number, which makes it rather odd among primes...

The problem isn't really the textbooks---the books themselves are often relatively cheap (for example, a 9th edition of Sullivan's Precalculus can be had for $30 or $40 if you don't mind being an edition out of date). The problem is that students are also required to buy access to the publisher's website in order to do their homework. One alternative is to hire advanced undergraduates to grade papers, or (better yet) hire more expensive graduate students, or even (heaven forbid) tenure track lecturers to teach smaller sections and/or grade papers. There is basically no money to do that, so it isn't going to happen. Another alternative is to use something like MAA's WeBWorK for homework. This might be quite feasible in the future as WeBWorK is improved (or another, better free, open source system comes along), and my department is doing as much as it can via WeBWorK, but the system is still not all there---there are simply things that, as bad as it is, MathXL can do much better than WeBWorK.

This might be evidence of my own lack of creativity, but I just don't see many other alternatives, and none of them are going to be any cheaper at the end of the day.

*Mathematics* isn't science. It is more properly a branch of philosophy that happens to be really, really useful for the sciences. The difference is that sciences are empirical---ideally, scientists observe the world, form explanations of their observations, then test those explanations with further observations. Mathematics is not empirical---mathematicians start from a set of fundamental assumptions, then use logic to deduce the consequences of those assumptions.

From the summary, it seems that the criticism is that economists are behaving more like mathematicians than like scientists---that is, they are making assumptions about how the world works, then using logic to determine the consequences of those assumptions. Instead, they should be making observations, then using the tools of mathematics analyze data taken from the real world and test their explanations.

I don't know about that. A couple of back-of-the-envelope computations make me think that 10 years is not a long enough timeframe to make such a camera anywhere near common. Consider, for instance, the 3 ton weight. Suppose that technology develops such that an equivalent sensor halves in weight every year. Ten years then represents halving the weight 10 times, giving a weight of approximately 6 lbs. That definitely isn't iPhone weight, and comes from a pretty optimistic assumption about how quickly the technology will develop. The computation, for completeness: (3 tons) / 2^10) ~= 5.9 lbs

Or we could look at pixel counts. The summary claims that the camera will capture 3.2 gigapixel images. Apple claims that the iPhone 6 has a 8 mega pixel camera. So the telescope camera will capture 400 times as much data. Assuming that the iPhone camera doubles its pixel count every year, it would take almost 9 years to get to 3.2 gigapixels. Even if we assume that the iPhone is used to take panoramas, where a panorama can have up to about 2^3 the pixel count of a non-panorama (again, see Apple's claims), this represents 6 years of doubling every year, which is, again, pretty optimistic.

Long story short: yes, technology marches forward, but this is likely to be a pretty impressive instrument even 10-15 years in the future.

I would still consider "fraud" to be an edge case.

Change (1) to "Following too close for the given conditions," and both (3) and (4) are dealt with. If conditions are such that your stopping distance will be increased, you are responsible for leaving a correspondingly larger amount of space between yourself and the car in front of you. There is, perhaps, an edge case in freeway driving: someone changes lanes in front of you, then slams on their brakes, but that isn't really relevant to approaching a stop sign.

2001 called!? Did you warn them about the airplanes?

You're not the boss of me!

Well, I think that it could be argued that the *fundamental* theorem of algebra is more fundamental (that's the rule that, when vastly oversimplified, states that polynomials have roots). That being said, the identity that you propose is, as pointed out by the GP, an identity derived from properties of multiplication. It is not really all that fundamental, and one of the hypotheses of the identity is that x is not zero.

In the one-point compactification of the real (or complex) numbers, it makes sense to assign the value infinity to x/0. This is both meaningful and has value (particularly in complex analysis). That being said, the original question is asinine. It betrays a fundamental misunderstanding of both mathematics and programming.

Yes... because the defining characteristic of a geek is the desire and ability to much about with hardware. Obviously.

I have a theory that it's impossible to prove anything, but I can't prove it.