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. [click to continue...]
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.
The doctor says 10% of patients respond within 30 days of treatment and 80% respond within 90 days of treatment. Now go turn that into a probability distribution. That’s a common task in Bayesian statistics, capturing expert opinion in a mathematical form to create a prior distribution.
Things would be easier if you could ask subject matter experts to express their opinions in statistical terms. You could ask “If you were to represent your belief as a gamma distribution, what would the shape and scale parameters be?” But that’s ridiculous. Even if they understood the question, it’s unlikely they’d give an accurate answer. It’s easier to think in terms of percentiles.
Asking for mean and variance are not much better than asking for shape and scale, especially for a non-symmetric distribution such as a survival curve. Anyone who knows what variance is probably thinks about it in terms of a normal distribution. Asking for mean and variance encourages someone to think about a symmetric distribution.
So once you have specified a couple percentiles, such as the example this post started with, can you find parameters that meet these requirements? If you can’t meet both requirements, how close can you come to satisfying them? Does it depend on how far apart the percentiles are? The answers to these questions depend on the distribution family. Obviously you can’t satisfy two requirements with a one-parameter distribution in general. If you have two requirements and two parameters, at least it’s feasible that both can be satisfied.
If you have a random variable X whose distribution depends on two parameters, when can you find parameter values so that Prob(X ≤ x1) = p1 and Prob(X ≤ x2) = p2? For starters, if x1 is less than x2 then p1 must be less than p2. For example, the probability of a variable being less than 5 cannot be bigger than the probability of being less than 6. For some common distributions, the only requirement is this requirement that the x’s and p’s be in a consistent order.
For a location-scale family, such as the normal or Cauchy distributions, you can always find a location and scale parameter to satisfy two percentile conditions. In fact, there’s a simple expression for the parameters. The location parameter is given by
and the scale parameter is given by
where F(x) is the CDF of the distribution representative with location 0 and scale 1.
The shape and scale parameters of a Weibull distribution can also be found in closed form. For a gamma distribution, parameters to satisfy the percentile requirements always exist. The parameters are easy to determine numerically but there is no simple expression for them.
Universal time (UTC) is the same as Greenwich Mean Time (GMT), give or take a second. It’s essentially the time in Greenwich, England except it ignores Daylight Savings Time.
The abbreviation UTC is an odd compromise. The French wanted to use the abbreviation TUC (temps universel coordonné) and the English wanted to use CUT (coordinated universal time). The compromise was UTC, which doesn’t actually abbreviate anything.
Sometimes a ‘Z’ is appended to a time to indicate it is expressed in UTC. The NATO phonetic alphabet code for ‘Z’ is ZULU, and so UTC is sometimes called “Zulu Time.”
It’s useful to know how your time zone relates to UTC. (You can look it up here.) For example, I live in the US Central time zone. Central Standard Time (CST) is UTC-6, i.e. we’re 6 hours behind Greenwich. Knowing your time relative to UTC makes international communication easier. It also helps you read computer time stamps since these almost always use UTC.
One of the advantages of UTC is that it avoids Daylight Savings Time. DST is surprisingly complicated when you look at it in detail. Some countries observe DST and some do not. Countries that do observe DST may begin and end DST on different dates, and those dates can change from year to year. And inside countries that observe DST some regions are exceptions. For example, the United States generally observes DST, but Arizona does not. Actually, it’s even more complicated: The Navajo Nation inside Arizona does observe DST.
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