My family loves the Little House on the Prairie books. We read them aloud to our three oldest children and we’re in the process of reading them with our fourth child. We just read the chapter describing when the entire Ingalls family came down with malaria, or “fever ‘n’ ague” as they called it.

The family had settled near a creek that was infested with mosquitoes. All the settlers around the creek bottoms came down with malaria, though at the time (circa 1870) they did not know the disease was transmitted by mosquitoes. One of the settlers, Mrs. Scott, believed that malaria was caused by eating the watermelons that grew in the creek bottoms. She had empirical evidence: everyone who had eaten the melons contracted malaria. Charles Ingalls thought that was ridiculous. After he recovered from his attack of malaria, he went down to the creek and brought back a huge watermelon and ate it. His reasoning was that “Everybody knows that fever ‘n’ ague comes from breathing the night air.”

It’s easy to laugh at Mrs. Scott and Mr. Ingalls. What ignorant, superstitious people. But they were no more ignorant than their contemporaries, and both had good reasons for their beliefs. Mrs. Scott had observational data on her side. Ingalls was relying on the accepted wisdom of his day. (After all, “malaria” means “bad air.”)

People used to believe all kinds of things that are absurd now, particularly in regard to medicine. But they were also right about many things that are hard to enumerate now because we take them for granted. Stories of conventional wisdom being correct are not interesting, unless there was some challenge to that wisdom. The easiest examples of folk wisdom to recall may be the instances in which science initially contradicted folk wisdom but later confirmed it. For example, we have come back to believing that breast milk is best for babies and that a moderate amount of sunshine is good for you.

Mike Croucher wrote a post the other day explaining why he’s going to buy an iPad. He said that one of the objections to the iPad he’d heard was

Apple are evil because they take away control of how we use their devices.

I teased Mike that I would never say “Apple are evil.” On this side of the Atlantic we’d say “Apple is evil.” But in the UK it is accepted usage to say “Apple are evil.”

“Apple” is a collective noun when used to refer to Apple Inc. British English treats collective nouns as plural, but American English treats them as singular. Although the British usage sounds odd to my American ears, it makes sense just as much sense as the American convention. You could argue for plural verbs because corporations are made of individual people, or you could argue for singular verbs because the corporations act as a single entity. See Grammar Girl’s tip on collective nouns for more background.

By the way, I don’t believe Apple is evil. They’re just a company, no more or less virtuous than most other companies.

I have five Twitter accounts that send out one tip per day, including a new one I just added last week.

Regular expressions

@RegexTip started over today. It’s a cycle of tips for learning regular expressions. It sticks to the regular expression features common to Python, Perl, C#, and many other programming languages. This account posts Monday through Friday.

Keyboard shortcuts

@SansMouse gives one tip a day on using Windows without a mouse. By practicing one keyboard shortcut a day, you can get into the habit of using your mouse less and your keyboard more. This cycle of tips started over January 29 with the most common and most widely useful shortcuts. I’m also sprinkling in a few extra tips that are less well known. This account also posts Monday through Friday.

Math

I have three mathematical accounts. These post seven days a week.

@AlgebraFact, just started February 2. It will be a mixture of linear algebra, number theory, group theory, etc.

@ProbFact gives one fact per day from probability. Usually these facts are theorems, but sometimes they include a note on history or applications.

@AnalysisFact gives facts from real and complex analysis. The topics range from elementary to advanced.

What if I don’t use Twitter?

You can visit the page for a Twitter account just like any other web page. And every Twitter account has an RSS feed link allowing you to subscribe just as you would subscribe to a blog.

How do you write these?

I write up content for these accounts in bulk. I may sit down on a Saturday and come up with several weeks worth of tips. Then I use HootSuite to schedule the tips weeks in advance. Sometimes I’ll post something spontaneously, such as link to something relevant, but most of the work is done in advance. I use my personal Twitter account for live interaction.

I ran across a long rant from Steve Yegge this evening about junior programmers. In a nutshell, Yegge says they like to play around with metadata rather than getting real work done.

Here’s an insightful observation Yegge makes along the way.

And Haskell, OCaml and their ilk … try to force people to model everything. Programmers hate that. These languages will never, ever enjoy any substantial commercial success, for the exact same reason the Semantic Web is a failure. You can’t force people to provide metadata for everything they do. They’ll hate you.

What is the Carnival of Mathematics? Math bloggers submit articles they have written recently and each month a host writes a post linking to the submitted posts. The sister carnival, Math Teachers at Play, focuses on math education and on math up through high school level. For a more thorough description of the two carnivals and some FAQs, please see Mike Croucher’s article What is a Maths Carnival?

I’m taking a turn hosting this month. Tradition dictates that the host begin with some trivia about the number of the post. As this is the 62nd Carnival of Mathematics, here are a few facts about 62.

62 is the only number whose cube (238328) consists of 3 digits each occurring 2 times.

Louis Pasteur developed the first rabies vaccination at age 62.

And now onto the posts.

Math and science teacher Cory Poole sends in a video that he created along with his partners and students. The video features a 64-foot Sierpenski triangle about of 12,000 tortilla chips. Read more about the story of the video. Also, here are the bloopers from making the video.

St. Swithun’s day is a sort of British analog of America’s Groundhog Day. If it rains on St. Swithun’s day, it is supposed to rain for the next 40 days. Is there some truth to the legend? See Jon McLoone‘s article Mathematica Tests the St. Swithun’s Day Proverb posted at Wolfram Blog.

Did you know that sine and cosine are equal for all x? Heather (Xi) submitted a pseudo-proof in A=B implies that 1=1, therefore? by her colleague TwoPi at 360. (If there is ever a 360th Carnival of Mathematics, Heather should host it.)

Update: The 360 blog has agreed to host the 360th Carnival of Mathematics, tentatively scheduled for December 1, 2034. (Mike, I hope it’s OK that I scheduled this date without consulting you. ;))

Annarita Ruberto from Matem@ticaMente presents the article “How heavy the fish?” The original post was written in Italian, and here is Google’s translation of the page into English.

You can keep up with Carnival of Mathematics news on Twitter by following @CarnivalOfMath. You may also be interested in daily math facts on Twitter from @ProbFact (probability), @AnalysisFact (real and complex analysis), and @AlgebraFact (algebra and number theory).

A few days ago I wrote a post on finding parameters so that a probability distribution satisfies two percentile conditions. Since then I’ve written Python code to carry out the calculations described in that article and the accompanying technical report.

Parameterizations are the bane of statistical software. One of the most common errors is to assume that one software package uses the same parameterization as another package. For example, some packages specify the exponential distribution in terms of the mean but others use the rate.

Python’s SciPy library has a somewhat unusual approach to parameterization with some advantages. SciPy makes every continuous distribution a location-scale family, even those distributions that typically do not have a location or scale parameter. This eliminates, for example, the question of whether an exponential distribution is parameterized by its mean or its rate. There is no mean or rate parameter per se. But there is a scale parameter, which happens to also be the mean.

Some methods on distribution classes have unusual names. For example, the inverse CDF function, often called the quantile function, is ppf for “percentile point function.” The complementary CDF function, or CCDF, is called sf for “survival function.” (Survival function is not an unusual name, though my preference would have been ccdf since that would make the API more symmetric.)

Discrete distributions in SciPy do not have a scale parameter. Also instead of a pdf method the discrete distributions have a pmf method; continuous functions have a probability density function but discrete methods have a probability mass function.

One surprise with SciPy distributions is that the SciPy implementation of the lognormal distribution does not correspond to the definition I’m more familiar with unless the location is 0. In order to be consistent with other continuous distributions, SciPy shifts the PDF argument x whereas I believe it is more common to shift log(x). This isn’t just a difference in parameterization. It actually amounts to different distributions.

For more details, see these notes on distributions in SciPy. See also these notes on distributions in R and in Mathematica for comparison.

Little programs are delightful to write in isolation, but the process of maintaining large-scale software is always miserable. … Technologists wish every program behaved like a brand-new, playful little program, and will use any available psychological strategy to avoid thinking about computers realistically.

… every one of the great industrial disasters of the past twenty years — Chernobyl, the Exxon Valdez, Bhopal, Three Mile Island — occurred in the middle of the night. For the most part, those in charge had worked very long hours and built up considerable sleep debt.

There’s a new Python podcast: A little bit of Python with Michael Foord, Brett Cannon, Jesse Noller, Steve Holden, and Andrew Kuchling.

So far I’ve found the first episode most interesting. It discusses the “moratorium”, the plan to give Python library authors time catch up with Python 3 before extending the core language further. This sounds like a very smart move.

Last year I wrote a little 10-page booklet called PowerShell Day 1. It covers many of the things I wish I had known when I started using PowerShell.

How do I configure PowerShell?

How do I make PowerShell launch faster?

How do I get documentation?

Why did PowerShell make some of the design decisions they did?

Once I’ve written some useful functions and scripts, where do I put them?

Where can I find more PowerShell resources?

Now I’ve started updating the booklet to reflect changes in PowerShell version 2.0. I haven’t had a lot of experience with version 2.0 and would appreciate your help updating the booklet. I have put a link to an alpha version of the update for version 2.0 on the download page.