Trivia question: where is the backup mirror now?

If you can identify a population of patients who are very likely to progress to a diagnosis without intervention and if there are useful treatments for these patients that can prevent suffering and large medical costs down the road, then it clearly will be worthwhile to diagnose and treat the condition early, even before there are visible symptoms.

The example of criteria for diabetes diagnosis is a good one. Type 2 diabetes is a progressive condition that often starts to develop long before a patient has obvious symptoms or uncontrolled blood sugar. Patients diagnosed wih "pre-diabetes" can often avoid becoming full-blown type 2 diabetics.

The trick is to use diagnostic tests intelligently and balance the risks and benefits. Advocating "don't introduce new tests" without explictly evaluating the costs and benefits of the new tests would be a horrible mistake. On the other hand, letting the vendors push the introduction of new tests without thorough evaluation would be equally bad.

The plan is to merge the state environment department into Energy, Minerals, and Natural Resources. Schmitt would then be in charge of enforcing the state's environmental regulations. Yep- he's the geologist who went to the moon.

It's worth pointing out that New Mexico is also the state who's governor has nominated note climate change denier Harrison Schmitt as secretary of Energy, Minerals, and Natural Resources.

Borgiapope's summary misses the point of both articles. In fact, the two authors are largely in agreement- it takes a well organized and disciplined group to organize change. Social media isn't enough by itself, although it might be useful as one tool among many in such an organization and it might be able to create an environment in which such an organization can flourish. If you accept these conclusions then you pretty much have to agree with Shirky that a policy focused on the short term exploitation of social media to effect quick change isn't the smartest strategy for US foreign policy. I don't think that Gladwell would disagree with that at all.

Somehow "s (symbol for is far less than) N" got trimmed to "sN" in my posting above.

For anyone who's interested in what these guys have done- the WHPCF'09 paper by Bekas and Fedulova (and going back a bit further, their 2007 paper by Bekas et al.) give the details.

In many statistical problems we end up with the problem of finding the diagonal entries of the inverse of a known symmetric and positive definite matrix A. For example, in linear regression the variances for the fitted parameters are found on the diagonal of inv(X'*X). When this matrix A is very large, the computation can be very expensive, since it requires O(N^3) time by conventional methods (Compute the Cholesky factorization of A and then use the Cholesky factors to solve for N right hand sides.)

Bekas et al. have developed a Monte Carlo approach that can give good (e.g. 2-3 digits of accuracy) estimates of the diagonal entries in inv(A) by using an interative method to approximately solve systems of linear equations involving A. The approximate iterative solutions take roughly O(N^2) time, and there are s of these systems to solve, where sN. Thus the computational complexity is lowered from O(N^3) to roughly O(N^2). Furthermore, you can solve these s systems of equations in parallel. Going one step further, you can do a lot of the computation in single precision, so it can be done on GPGPU's and other machines that don't do double precision floating point efficiently.

I have to agree that much of the open source material that's available is either not very well done or more commonly the author has recovered the copyright on a published book after it went out of print and then released it into the wild.

On the other hand, I've been through the process of publishing a textbook with one of the mainline commercial publishers, and frankly I can't see where they added any value- the copy editor was a grad student in English who had trouble editing the text because she couldn't figure out which technical terms were nouns and which were verbs, the type setters took our perfectly servicable LaTeX and broke things (like splitting the "dx" at the end of an integral over two lines!), and the subcontractor who made the CD-Rom for the book produced it with a file system that only supported 8.3 filenames after agreeing that it should have Joliet and Rockridge extensions for longer file names.

Many of the books suggested here are really more about the history of mathematics with a small dose of mathematical explanation added. Some books in this category are better than others, but nearly all of them provide such a shallow explanation of the underlying mathematics that students really can't learn much mathematics from them, even if they do pick up some interesting biographical and historical information. It's sad that the publishers have churned out so many of them in recent years.

Several posters have also mentioned books in the "introduction to proof based mathematics" genre. This is certainly an important topic, but many of these books are a bit too advanced for most high school students.

Another important category that I haven't seen mentioned are books on problem solving techniques for mathematics competitions. In this category, I'd strongly recommend "The Art Of Problem Solving" by Richard Rusczyk.

Most of the professional societies that publish journals use the profits from journal publishing to cross subsidize annual meetings. In many cases journal profits also help to pay for unnecessarily large staffs at the society headquarters.

In my experience, the societies that are most dependent on journal subscriptions to fund the operations of the society are the ones that are most opposed to open access, allowing the posting of online preprints, and so forth- they've got the most to lose.

LaTeX with the associated tools (BibTex, makeindex, etc.) worked very well for a textbook that I coauthored. It was also the publishers prefered format, although they sent our LaTeX source out to a commercial type setter who proceeded to mangle the mathematics in unimaginable ways. Who knew that when an integral ends in "dx", the "d" and the "x" should be on the same line?

I've had a number of conversations with intelligent young people who've told me that they're looking for a career that will put them into a position where they aren't subject to competition from around the world. Viewed from this angle, science and engineering are dumb choices. Rather, if you want to study something that will lead to a job that can't be outsourced, you should look towards business (management or sales), medical fields (such as nursing), or the skilled building trades (welding, plumbing, electrician, etc.) It's no surprise that there's lots of interest in those fields.

As long as our immigration laws slow down the influx of foreign competition in the labor market, and as long as some jobs can easily be outsourced while other jobs cannot, there will be a strong incentive for young people to specialize in those jobs that can't be outsourced.

Of course, outsourcing is happening in lots of fields now, including law (paralegals doing routine work over the internet) and medicine (radiologists interpreting X-ray images over the internet.) However, it will likely be decades before this process of globalization is complete.