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February 27th, 2011 (Permalink)


Crocs Can Pose a Danger on Escalators

Gators, too!

February 25th, 2011 (Permalink)

Blurb Watch: The Eagle

An ad for the new movie The Eagle uses a familiar trick: it shows four stars, followed by the obligatory exclamation point, and attributed to Keith Uhlich of Time Out New York. What it doesn't show is that Time Out New York uses a five star rating system.


February 17th, 2011 (Permalink)

New Books: The Doublespeak Dictionary & The Panic Virus

February 16th, 2011 (Permalink)

If it bleeds, it leads.

Here's a Slate article on the fear of crime:

Even as crime rates have gone down around the country over the last 20 years, our fear of crime hasn't changed much at all. Between 1990 and 2009, the national violent-crime rate was halved, while property crime dropped to 60 percent of its previous rate, according to the National Archive of Criminal Justice Data. But almost every year since 1989, most Americans have told pollsters they believe crime is getting worse.

Why does the perception of crime, as revealed by public opinion polls, not correspond to the reality?

Part of the reason is that most people can't measure the crime rate accurately based on their own experience. While you may be twice as safe statistically speaking, the odds of getting assaulted at any given moment have merely gone from very small to extraordinarily small.

As a result, most of our sense of the crime rate is based not on statistics but on news reports, and perhaps even on fictional portrayals of crime. The rate of crime reporting does not necessarily drop when the crime rate does, and the more sensational the crime is the more coverage it will get.

One possible reason fear of crime remains high is that powerful people have an incentive to ring the alarms anyway. … Media play up only the most horrifying deeds. The result is a skewed perception of how dangerous the world is.

In addition, the old idea that "man bites dog" is news means that as crime becomes rarer it actually becomes more newsworthy! So, if anything we're likely to see more crime news as the crime rate drops. Crimes that formerly were too common to be reported will be uncommon enough to become news, that is, they will go from the "dog bites man" category to the "man bites dog" one. Unless crime is totally eliminated―which is, of course, extremely unlikely―crime reporting will always be with us. So, if our estimate of the crime rate is based on how often we hear about crime in the media, and not on crime statistics, we can expect to see exactly what the polls are showing.

Fallacy: The Anecdotal Fallacy

Source: Christopher Beam, "Head Case", Slate, 2/11/2011

February 6th, 2011 (Permalink)


The following claim occurred in a wire story about the possibility that the Super Bowl would attract under-age prostitutes:

Up to 300,000 girls between 11 and 17 are lured into the U.S. sex industry annually, according to a 2007 report sponsored by the Department of Justice and written by the nonprofit group Shared Hope International.

Is this a plausible claim? Don't just assume that because it's in a news report that it must be true. How can you test it in some way just using what you know and a "back-of-the-envelope calculation" (BOTEC)? Before looking at "the back of the envelope", do your best to check the claim for plausibility.

See the Back of the Envelope

Source: Mickey Goodman, "Super Bowl a magnet for under-age sex trade", Reuters, 1/31/2011

February 4th, 2011 (Permalink)

The Puzzle of the Absent-Minded Professors

Four professors, including one named Anderson, were attending the same conference, and each hung up a hat and coat on a coatrack just inside the door of the conference room. Unfortunately, when leaving, each professor managed to take a hat and coat belonging to another, so that none ended up with their own garments. Not only that, but each took a hat that belonged to one colleague, and a coat that belonged to a different one. Afterwards, one of the four, Professor Church, investigated and summed up what was known about the mix-up:

I didn't take Professor Davidson's coat. Professor Belknap took the hat that belonged to the professor whose coat was taken by Professor Davidson, whose hat was taken by the one―which wasn't me!―who took Professor Belknap's coat.

Can you determine who took whose hat and coat so that the garments can be returned to their rightful owners?


The Back of the Envelope: First off, notice that the claim is hedged by the phrase "up to", which means that all that is literally claimed is that no more than 300,000 girls become prostitutes in America annually. However, let's assume that 300,000 is correct. How can we translate that large number into terms that are easier to evaluate?

One way to make sense of large numbers is to translate them into percentages. In this case, we can ask the question: what percentage is 300,000 of the total number of girls between 11 and 17 in the United States? If you're like me, you don't know off-hand how many girls of that age there are in the U.S. However, you may know that the total population of the U.S. is a little over 300 million. Can we estimate the number of girls in question from the total population? We can if we can figure out what proportion of the total population girls 11 to 17 represent.

Given an average lifespan of about 70 years, the seven years from 11 to 17 represent one-tenth of that span. Assuming an approximately equal distribution of the population at each age, then about 10% of the population will be between the ages of 11 and 17 at any given time. Of course, we are only interested in girls, who are almost half of the population of that age, so those girls will represent roughly 5% of the total population. Thus, there should be about 15 million girls between the ages of 11 and 17 in the United States at this moment, and 300,000 is about 2% of that number.

So, is this a plausible percentage? Is it believable that 1 in 50 girls in the U.S. between the ages of 11 and 17 become prostitutes? Unlike some previous BOTECs we've done, it isn't incredible, but it seems implausibly high to me. Of course, prostitution―especially, under-age prostitution―is an underground activity and inherently difficult to count. But that's all the more reason to be skeptical about the number.

Solution to the Puzzle of the Absent-Minded Professors:

The first step in solving this puzzle is to break Professor Church's statement up into four separate clues:

  1. Prof. Church did not take Prof. Davidson's coat.
  2. Prof. Belknap took the hat that belonged to the professor whose coat was taken by Prof. Davidson.
  3. Prof. Davidson's hat was taken by the one who took Prof. Belknap's coat.
  4. Prof. Church did not take Prof. Belknap's coat.

From clues 1 and 4, we can conclude that Prof. Church took Prof. Anderson's coat, because we know that Church didn't take his or her own coat.

Clue 2 tells us that some unknown professor―let's call him or her Prof. X―had his or her hat and coat taken by Prof. Belknap and Prof. Davidson, respectively. Now, Prof. X cannot be either Belknap or Davidson, since none of the professors took their own garments. So, X is either Anderson or Church; however, X cannot be Anderson, since we already know that Church―not Davidson―took Anderson's coat. Therefore, X is Church.

Clue 3 says that another unknown professor―let's call him or her Prof. Y―took Prof. Davidson's hat and Prof. Belknap's coat. Again, Y cannot be either Davidson or Belknap, since no one took their own hat or coat. So, Y is either Anderson or Church; but we know that Church took Anderson's coat, not Belknap's. So, Y is Anderson.

Thus, we know that Church took Anderson's coat, Davidson took Church's, and Anderson took Belknap's. By a process of elimination, we can conclude that Belknap took Davidson's coat. We also know that Belknap took Church's hat, while Anderson took Davidson's. That leaves Anderson's and Belknap's hats unaccounted for, and Church and Davidson hatless. However, we already know that Church took Anderson's coat, so he or she can't also have taken Anderson's hat. Therefore, Prof. Church must have taken Prof. Belknap's hat, which leaves Prof. Anderson's hat for Prof. Davidson.

To sum up:

Professor Hat Coat
Anderson Davidson Belknap
Belknap Church Davidson
Church Belknap Anderson
Davidson Anderson Church

Source: J. A. H. Hunter & Joseph S. Madachy, Mathematical Diversions (1975). The puzzle is based on one from page 108.

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