This morning I posted some notes on orthogonal polynomials and Gaussian quadrature. “Orthogonal” just means perpendicular. So how can two polynomials be perpendicular to each other? In geometry, two vectors are perpendicular if and only if their dot product of…
Monthly Archives: February 2008
First post with new address
I moved my blog this weekend from the limited version of WordPress provided by my web hosting company to self-hosted WordPress. Please let me know if you have any problems with this new version.
Posted in Uncategorized
Honeybee genealogy
Male honeybees are born from unfertilized eggs. Female honeybees are born from fertilized eggs. Therefore males have only a mother, but females have both a mother and a father. Take a male honeybee and graph his ancestors. Let B(n) be…
Enterprising software
Cyndi Mitchell in a talk from Rails Conf points out how “enterprise” in the phrase “enterprise software” has taken on the opposite of its customary meaning. If you call a person enterprising, you have in mind someone who takes risks and accomplishes…
Introduction to Mac for Windows developers
Here are a couple podcasts introducing Windows developers to software development on the Macintosh. Scott Hanselman: What’s it like for Mac Developers, an nterview with Steven Frank .NET Rocks: Miguel de Icaza and Geoff Norton on Mono, mostly about .NET development…
How to avoid being outsourced or open sourced
Kevin Kelly has a post entitled Better than Free that lists eight things people will pay a premium for, even while closely related things are free or cheap: Immediacy Personalization Interpretation Authenticity Accessibility Embodiment Patronage Findability Daniel Pink has a…
Merry-go-round water pump
I ran across this on Guy Kawasaki’s blog, what he calls “the cleverest idea I’ve seen in years.” It’s a water pump for developing areas that works by having children play on in. Here’s a video from National Geographic demonstrating the pump.
Complexity and unity
Here’s a quote from Gene Edward Veith to chew on. A work is beautiful to the extent that it displays at the same time both complexity and unity. From “Acquired taste”, World Magazine, February 9/16, 2008.
Chebyshev polynomials
I posted a four-page set of notes on Chebyshev polynomials on my web site this morning. These polynomials have many elegant properties that are simple to prove. They’re also useful in applications. Mr. Chebyshev may have the honor of the…
False positives for medical papers
My previous two posts have been about false research conclusions and false positives in medical tests. The two are closely related. With medical testing, the prevalence of the disease in the population at large matters greatly when deciding how much…
False positives for medical tests
The most commonly given example of Bayes theorem is testing for rare diseases. The results are not intuitive. If a disease is rare, then your probability of having the disease given a positive test result remains low. For example, suppose…
Most published research results are false
John Ioannidis wrote an article in Chance magazine a couple years ago with the provocative title Why Most Published Research Findings are False. [Update: Here’s a link to the PLoS article reprinted by Chance. And here are some notes on…
Tagged with: Biostatistics, Probability and Statistics
Posted in Clinical trials, Science, Statistics
Posted in Clinical trials, Science, Statistics
Proofs of false statements
Mark Dominus brought up an interesting question last month: have there been major screw-ups in mathematics? He defines a “major screw-up” to be a flawed proof of an incorrect statement that was accepted for a significant period of time. He…
A bigger clipboard
Imagine you find a paragraph on the web that you want to email to a friend. You copy the paragraph. Then you think you should send a link to full article, so you copy that too. You start composing your email and you type…
Footnote to interruption post
In my post yesterday about interruptions I quoted Mary Czerwinski from Microsoft Research. She told me afterward that two of the applications mentioned in the interview have been released. They are publically available from the Microsoft Research download site. GroupBar…
