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Comment Re:Tau is greater than pi (Score 1) 133

To anyone who knows what they are doing, both pi and tau are simply constants. Absorb either into some constant term, or carry it around with you wherever you go---it doesn't matter. Real engineers, mathematicians, scientists, etc can handle either constant without difficulty. The real advantage that tau has over pi is pedagogical. It is much easier to communicate the relation between angle measure and arc length with tau. Since trig functions deal with lengths more readily than area, it makes sense to teach people trigonometry using a constant that is more closely related to length.

Comment Re:Direct link to paper (Score 5, Informative) 279

This is not the paper described in the summary, but rather an older paper with some of the same authors. The paper referenced in the summary was published online yesterday in Nature Climate Change. I'm sorry that I can't give a direct link to a .pdf (yay for paywalls keeping all of the non-ivory tower plebs out! huzzah!), but for those with access, the paper can be found at Influence of high-latitude atmospheric circulation changes on summertime Arctic sea ice. For those without access to an academic library, the first author provides an email contact. One presumes that a polite request would yield the full text of the paper.

Comment Re:Somebody's on the Pearson payroll (Score 1) 363

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(for example, a 9th edition of Sullivan's Precalculus can be had for $30 or $40 if you don't mind being an edition out of date).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.

Comment Re:Same issues (Score 2) 157

*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.

Comment Re:Distance? (Score 1) 89

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.

Comment Re:11 rear enders (Score 1) 549

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.

Comment Re:Infinity (Score 1) 1067

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.

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