Monthly Archives: February 2008

Orthogonal polynomials

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

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Posted in Math

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

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Posted in Math

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

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Posted in Business, Software development

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

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Posted in Computing

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

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Posted in Business

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.

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Posted in Uncategorized

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.

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Posted in Creativity

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

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Posted in Math

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

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Posted in Clinical trials, Statistics

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

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Posted in Statistics

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

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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

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Posted in Math

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

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Posted in Computing

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

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Posted in Creativity, Software development