Steve Kass

December 8, 2012. The Pittsburgh Tribune-Review reported that Loughrey told police he had emptied the magazine of his 9-millimeter Taurus handgun, and he didn’t know there was a bullet in the chamber. The gun discharged and his son was struck in the chest.

February 13, 2012. Authorities in St. Petersburg, Fla. say the daughter of a pastor was accidentally killed at church Sunday when a gun went off. Investigators say a man was showing his gun to another church member interested in buying it, but didn’t know there was a bullet in the chamber. The gun went off and fired through a wall at Grace Connection Church, striking 20-year-old Hannah Kelley in the head.

December 11, 2009. Asked by the judge why he pulled the trigger, Airman Hernandez said, "I trusted him; I’d seen him doing it earlier that night, and I trusted him. Even though I saw him load (the gun), I didn’t know there was a bullet in the chamber."

December 31, 2006. He didn’t know there was a bullet in the chamber of his .45-caliber semiautomatic handgun when investigators say he pointed the weapon at his friend’s head.

September 8, 2006. “It was my fault,” Robert Christie told the neighbors, according to a sheriff’s report. “I didn’t know there was a bullet in the chamber.”

October 16, 1998. “She was chiding him in her discussion with a friend,” Givens told Wagner. “He didn’t know there was a bullet in the chamber and pulled the trigger.”

September 9, 1994. Steinberg said Cruz recklessly pointed the gun at his brother after ejecting the clip and didn’t know there was a bullet in the chamber.

February 15, 1988. Defense lawyers claim that Matthews didn’t know there was a bullet in the chamber of the .380-caliber handgun.

March 10, 1971. He told police he had removed the ammunition clip from the pistol and didn’t know there was a bullet in the chamber when he pointed the gun at the girl.

David Petraeus. A Brilliant Career With a Meteoric Rise and an Abrupt Fall

Tony Watt, Scottish footballer. Dream night against Barca caps meteoric rise for Watt

Justin Welby. New Archbishop of Canterbury: Justin Welby, the meteoric rise of an ‘astonished’ former oil trader

Eben Etzebeth. Young Etzebeth’s meteoric rise

Four rose, one fell. VIEW SLIDE SHOW DOWNLOAD ALL

* See “METEORIC RISE” at Michael Quinion’s excellent site, World Wide Words.

I’m a mathematics teacher, and I have some arithmetic problems for you to solve.

1. Mitt drives to the beach and back.

Q. Mitt Romney drives 50 miles from his home one of his homes to the beach and back one summer, with or without a dog on the roof. He averages 50 miles an hour on the way out, and he averages 10 miles an hour on the way back. What was Mitt’s average speed on the road?

A. It was 16-2/3 mph¹, but Mitt’s campaign insists he’s no slowpoke and that he averaged 30 mph. (They also say the trip explains his tan.)

2. “Going Dutch” with Mitt.

Q. You and Mitt Romney have lunch together at Chick-fil-A. The bill is $15, and he only has a $10 bill, so he pays 2/3 of the bill. Later, you have dinner together at the country club, and the bill is $300. He puts in $100, and this time you pay 2/3 of the bill. Are you even-Steven?

A. Of course not, but Mitt says you are, because he paid 1/3 once and 2/3 once.

3. Mitt Sees Red.

Q. In the four squares below, about what percentage of the area overall is red?

A. About 10%. Certainly way less than half. Mitt disagrees. He says the percentage of red is over 75%, and he surprises you by providing actual details instead of saying he has a secret calculation that solves the problem and comes out the way he wants it to. He says there are three 100% red squares and one 5% red square, for an average of 305%/4 or about 76%. Ann tells you to stop giving him a hard time.

Earlier today, the Romney campaign website posted a letter from PriceWaterhouseCoopers “PWC” LLP summarizing the Romneys’ tax returns for the years 1990-2009. The carefully-worded letter² states that

The average of the annual “effective federal personal income tax rates” as computed based on the returns as prepared during the period is 20.20%.

PWC computed each year’s “effective federal personal income tax rate” as instructed by the Romneys.

As you requested, we compute each annual “effective federal personal income tax rate” as total taxes owed divided by adjusted gross income as shown on the federal income tax returns as prepared.

First of all, the Romneys’ “adjusted gross income” (AGI) may be less than what most of us think of as simply “what the Romneys made.” For example, the expenses of carrying on a trade or business (such as dressage) can be deducted from total income. The Romneys’ tax rate on their total income is lower than that on their adjusted gross income. Maybe a little, maybe a lot.

More importantly, however, is how Mitt and Ann instructed PWC to compute a number they could call an “average.”

Despite appearances, no one has said that the Romneys paid 20.20% of their adjusted gross income in federal income taxes during the period 1990 – 2009. They probably paid less.

The 20.20% figure is not the Romney’s federal income tax rate for income they earned during the period 1990 – 2009. It’s the average of 20 separate annual rates. Mathematically, it’s a weighted average of their annual rates.

If you think the average of 20 annual rates is the same as the 20-year average annual rate, you’re wrong. By that flawed logic, Mitt averaged 30 mph, you and he are even-Steven for splitting meals, and the colored squares in the picture above are 75% red. Go away.

Further blurring the issue, the campaign today also posted a letter from Brad Malt, the “trustee of the Romney’s [sic] blind trust,” about Mitt’s taxes. Malt tries to say that PWC calculated something that it didn’t calculate.

Regarding the PWC letter covering the Romneys’  tax filings over 20 years, from 1990 – 2009:

Over the entire 20-year period, the average annual effective federal tax rate was 20.20%.

Malt omitted two short and crucial words: of the. PWC did not say that Romneys’ average annual effective federal tax rate was 20.20%. They said that if you average the 20 separate effective rates on their 20 federal tax returns, you get 20.20%. It’s a silly thing to calculate, but it’s what the Romneys told them (and presumably paid them) to do.

The Romneys’ overall tax rate might have been lower than 20.20%. It might have been higher, too, but given the outrage over the relatively low rates they pay compared to working Americans, if it were higher, he’d have said so. And Mitt won’t release his tax returns. We can only assume the worst.

If you value the truth, vote for Barack Obama on November 6, 2012.

¹ Let’s figure it out. Mitt drove a total of 100 miles. It took him 1 hour (50 miles at 50 mph) to drive the first half of the trip and 5 hours (50 miles at 10 mph) to drive the second half. He drove a total of 100 miles in 6 hours, so his average speed was 16-2/3 miles per hour.

² The letter is signed personally, in blue, by PriceWaterhouseCoopers LLP, because why wouldn’t they sign it? Corporations are people.

[This will be brief and sloppy, since I should be packing, not blogging. With luck, there will be an update later this month/year/decade, but don’t hold your breath.]

Today went like this:

5:00 a.m. Wake up a good four hours before my usual wakey-uppy time, because in order to get to the Marvin Hamlisch Memorial Choir rehearsal, I had to catch the 6:21 train.

7:45 a.m. – 1:00 p.m. Rehearse for and sing at Marvin’s funeral. While it isn’t the subject of this post, highlights of the event were a) President Bill Clinton, b) John Updike’s Perfection Wasted, a sucker punch if there ever was one, and c) Terre Blair Hamlisch’s heartbreakingly stunning eulogy to her late husband.

12:45 – 2:30 p.m. Lunch at Serafina on 61st (a martini and a plate of paglia e fieno) with fellow singers Andy, Darcy, and the just-married Baninos. Disappointingly, although we were all dressed in black, no one asked “Who died?” Only in New York.

3:45 – 8:03 p.m. Procrastinate.

8:04 p.m. See Dr. Rubidium’s provocative and pithy tweet,

“People, eggs are bad for you AGAIN. jezebel.com/5934776/your-b… … via @Jezebel #untiltheyrenot”

“Your Breakfast Is Trying to Murder You: Eggs Are Almost as Bad for You as Cigarettes,” Jezebel crowed.

Well, I love me my eggs, and egg slander is up there with salt slander and sugar slander as a high crime against food. Eggs give Cheez-Its a run for the money as the perfect food, and this had to be wrong.

Here’s the hard-boiled truth. The latest research on eggs and heart disease is flawed. Eggs are not going to kill you.

Jezebel and other news outlets have jumped on Egg yolk consumption and carotid plaque, a paper recently published in the journal Atherosclerosis, which claims that a person’s carotid plaque increases exponentially with their egg yolk consumption. (This paper is referred to below as EWKY, for Eggs Will Kill You.)

Most likely there is no exponential relationship at all. But if you believe the authors’ statistics, perhaps you will believe what I can prove by an identical analysis:

The length of objects, measured in centimeters, grows exponentially with length measured in inches.

Of course, this is ridiculous. The length of an object in centimeters is exactly 2.54 times its length in inches. The relationship is linear, not exponential. After you finish reading this post, I hope you’ll realize that the egg slander in Atherosclerosis is also ridiculous.

The “exponential” dependence of plaque on egg yolk consumption is an artifact of skewed data.

I created a data set with the same distribution as the EWKY data to investigate a hypothetical relationship between inches and centimeters, using the same flawed way the authors of EWKY analyzed the relationship between egg yolk consumption and plaque.

Briefly, the authors of EWKY treated “quintile”  as a scale variable, which it is not.

Here are the histograms of my data and the EWKY data. Pretty much the same.

And here are error bar charts of my data and the EWKY data. Both appear to show a clearly non-linear relationship.

The error bar chart from EWKY is the sole justification for the claim of an exponential cigarette-like relationship to plaque:

(My error bars are much shorter because the correlation between inches and centimeters is perfect. While the relationship between egg-yolk years and plaque is not, it’s nevertheless not exponential.)

There are other statistical gaffes in EWKY, but I don’t have time to delve into them. I’ll mention the worst very quickly.

First, most of the EWKY analysis compares lifetime egg yolk consumption to plaque. Lifetime anything consumption is a proxy for age, and atherosclerosis is strongly age-dependent. Nowhere do the authors of EWKY provide convincing evidence that the relationship between egg yolk consumption and plaque is anything but an artifact of the proxy for age.

Furthermore, the authors pay no heed to the always-important question of effect size. They provide a single analysis that shows a statistically significant relationship between the non-age-proxy measurement of egg yolk consumption per week (as opposed to over a lifetime) and plaque that’s independent of age:

The difference in plaque area between the <2 eggs/week group and the 3 or more eggs group (an arbitrary split, and ignoring the several hundred subjects who ate from 2 to 2.99 eggs/week) is about 1/20 of a standard deviation, otherwise known as squat. The fact that p < 0.0001 after adjustment for age is irrelevant, because with such a large sample, significance might appear for an even smaller effect (micro-squat).

Gotta run, gotta pack. Thanks for listening.

[Note added 2012/07/26 4:42PM EDT: The Spider-Man designs appear on only one side of each Amazing Spider-Man Cheez-It. Crackers were arranged design-side up.]

My friendly neighborhood Shop-Rite is carrying more and more varieties of Cheez-Its lately, but it didn’t take long to decide on The Amazing Spider-Man Cheez-Its. The top reasons?  1. Serving size is a sum of consecutive squares. 2. Flavor is not Monterey Jack. 3. Spider-Man, Spider-Man!

The Amazing Spider-Man Cheez-It is not the perfect food, but it’s closer to it than Cheez-It BIG Monterey Jack. Spideys taste almost like the original, but they’re a little too hard and crunchy. I can’t imagine eating an entire box in one sitting.

The Amazing Spider-Man Cheez-Its are slightly less uniform in size and shape than regular Cheez-Its or Cheez-Its BIG. The crackers chosen for these figures are a more uniform sample than one would expect in a random serving.

Another Steve on the internet has written more about The Amazing Spider-Man Cheez-Its, so I’ll just wrap up with two more arrangements. You should definitely head over to the other Steve’s blog when you’re done here.

Yes, you read it right: white people are more likely to marry other good people.

Just kidding!

Now that I have your attention, though, I hope you thought I was out of my mind. I may be, but for the record, I’m absolutely not saying that white people are good (and that non-white people aren’t). And geez, if I wanted to say that (which I don’t), I’d say it directly, not with underhanded rhetoric.

In the title, I wrote “white people . . . other good people.” That doesn’t even make sense, really.¹ It’s like talking about your other Range Rover when you only have one.

What did I mean by other good people when I hadn’t mentioned any particularly good people in the first place? Or had I?

Now read what David Brooks wrote earlier this week in the Opinion section of the New York Times:

Affluent, intelligent people are now more likely to marry other energetic, intelligent people.

Brooks mentioned “other energetic, intelligent people,” but he hadn’t mentioned any energetic, intelligent people in the first place; he’d only mentioned affluent, intelligent people.

Maybe Brooks didn’t notice his slip, because to him, the affluent people are the energetic people. Or maybe he intended to say flat out that poor people are lazy — which I think he believes — but he knew it would have been crude to say.

Even worse, saying that poor people are lazy, even if you believe it, wouldn’t have been “gentlemanly conduct.” Gentlemanly conduct is a thing the “best of the WASP elites” had, according to Brooks (in the same article). The WASP elites (and some Catholics) also thought the poor were lazy. They weren’t. They aren’t.

Why are 30 million Americans poor? To many the answer would be obvious: They are poor because they are lazy, or lack initiative, or prefer welfare to work.

Wrong, . . .

  — Jack Rosenthal, The New York Times, November 16, 1969.

¹ I’m not sure I’ve explained this clearly, so here’s an extended try. The construction “<adjective> people . . . other <adjective> people,” refers to some <adjective> people and then some additional <adjective> people of the same kind. For example: Tall people often date other tall people. Loud people sometimes even disturb other loud people. Clumsy people occasionally bump into other clumsy people.

On the other hand, to say “<adjective> people . . . other <different adjective> people” is a mistake, a ruse, or a (not necessarily good) joke. For example: Dumb people often marry other blondes. Homosexuals are more likely to marry other sailors.

As you know from my last and first How Do You Arrange Your Cheez-Its? post, not only are Sunshine Cheez-Its the perfect food, the serving size of Cheez-Its is 27 crackers, a perfect cube. As the name suggests, Cheez-It BIG crackers are bigger¹ than Cheez-Its, and a serving contains fewer crackers — 14 instead of 27. While 14 is not a perfect cube, it is the sum of consecutive perfect squares, which is nearly as wonderful.

Figure 1. One serving of Cheez-Its BIG arranged as a pyramid.  14 = 9 + 4 + 1

Figure 2. One serving of Cheez-Its BIG arranged like a pyramid. 14 = 8 + 3 + 2 + 1

Figure 3. One serving of Cheez-Its BIG arranged unlike a pyramid. 14 = (2 + 3 + 2 + 3 + 2) + 2

Unfortunately, Cheez-Its BIG, the Monterey Jack variety (which I purchased by mistake) is not the perfect food, and I can only recommend it for arranging, not for snacking.

Figure 4. The author (center) ascending a Pyramid not made of Cheez-Its BIG.

¹ “Twice the Size!*”, the front of the box declares.²

² The asterisk leads to a footnote, in smaller type: “*Than Original Cheez-It® Crackers volume.” My rough measurements confirm this. One Cheez-It BIG is about 35% larger than a Cheez-It in each of its larger dimensions, and about 10% thicker.

Updated June 5, 2012. (Scroll to the end for the update.)

This week’s Numberplay is about a locker room full of, well, lockers – 100 of them, to be exact. The lockers are closed until a janitor (let’s call her Portia) visits the room and opens them all. Then Portia visits the room again and closes every other locker. Later on, she visits the room a third time, opening or closing every third one. And so on, for 100 visits in all.

Head over to the Times, then come back here and enjoy the pictures.

Picture #1. The 100 lockers of the puzzle are represented as a row of tiny squares – red squares for closed doors, green for open. The squares in the top row (all green) show the lockers all open after Portia’s first visit to the locker room.

The second row of squares, alternating green and red, show the lockers after her second visit, and so on.

If you squint at the patterns across the top, I think you can see Portia’s face.

Picture #2. After Portia’s first visit to the locker room, all 100 lockers are open. After her second visit, 50 are open and 50 are closed. Ninety-eight visits later, ten lockers are open. (Just which of the lockers are open in the end is the beautiful result of the puzzle, which you’ll find more easily in the comments to this week’s puzzle than you will by trying to count the tiny squares in the picture here.)

You might wonder – I did anyway – how the number of open lockers changes between Portia’s second and hundredth visit. Here’s a graph.

What a delightfully curious graph! The number of open lockers wanders seemingly aimlessly about the low 50s for a while. It briefly threatens to stay put at 54, then glides down with a few small bumps to a final value of 10.

Intrepid readers can find the Excel spreadsheet I created these pictures from here.

Thanks to Gary Antonick for sharing this great puzzle, which was suggested by Volodymyr Ivanchenko.

Updated June 5, 2012. Back at Numberplay, Gary suggested looking for the number of open lockers sequence at the Online Encyclopedia of Integer Sequences. I didn’t find anything, and I suspect that’s because this puzzle gives different sequences for each initial number of lockers.

So, I put together a SQL Server 2012 script (and posted it at SQL Fiddle here) to generate data for this “number of open lockers” graph for locker rooms with other than 100 lockers.

The graph gets even more interesting when there are more lockers.

From Public Document No. 34 of the Commonwealth of Massachusetts, “Annual Report of the Department of Public Health for the Year ended November 30, 1928,” which can be found here:

It was the last sentence that drew me to this page. Manny was my grandfather, and my mother grew up at the (Lakeville State) Sanatorium. (See RUTGER.)

Once here, though, it was impossible not to puzzle over the several averages in the report that were given to seven-digit precision. For example, 193.9426, the daily average number of patients for the year. In the late 1920s, computing 70,983/366 to seven places wasn’t a snap like it is now. More likely, it required some cranking, punching, or scribbling.

My minimally-informed guess? That the Massachusetts Department of Public Health had one of the early motor-driven calculators, like the Marchand above (center). It’s hard for me to imagine a reason to compute seven digits of precision when fewer would suffice unless it was very little extra work to get the extra digits.

Then again, maybe I’m wrong and the reality was more romantic, and there was a clerk who loved little more than long division. I suppose we’ll never know.

During the 13-year period (1995-2007) for which public data is available, 141 babies were born in Los Angeles County and named Unique. Two were boys.

A great many baby names were more unusual than Unique, including Z (boy, 2007), Q (boy, 2005), Abcde (girl, 2005), Awesome (boy, 2007), Yourhighness (girl, 2007), Queenelizabeth (girl, 2005), Unknown (boy, 2005), and Y (boy, 2007).

Data source: Los Angeles County Department of Public Health [link]

Update (May 5, 2012)

I updated this post last year when I discovered the Social Security Administration’s baby-name database, but it turns out there was more there than I realized. In his Breakfast Experiment™ of this morning, Language Log’s Mark Liberman mentioned this richer source of SSA name data.

As was the case for the SSA data I found last year (in the earlier update, which appears below), there’s no data for baby names that are unique (or almost so). But in recent years, Unique is not unique, so there’s more to report. The chart below summarizes the latest SSA data I have for Unique boys and girls.

Update (June 24, 2011)

The Social Security Administration provides a basic query interface to its national baby-name database. Based on Social Security card applications for births that occurred in the United States, Unique was a common enough girl’s name to make the annual top 1,000 list nine times between 1996 and 2009.

Both the Los Angeles and national figures suggest that as a baby name, Unique is becoming less common.