Today’s eLetter from the folks at Fine Cooking began “Baked Pasta 259,200 Ways. We did the math.” As you can imagine, I did the Baked Pasta Recipe Maker math, too. I figure it’s 16,128,000 ways, or about 60 times the number Fine Cooking found when they did the math. Here’s the calculation. The recipe maker walked me through the following steps:

• Choose one or two of four Flavor Bases
• Chose one of three Sauces
• Choose two or three of nine Sauce Enhancers
• Choose one of eight Pastas
• Choose zero, one, or two of five Vegetables
• Choose two or three of six Cheeses

Assuming no choice combinations are forbidden (the recipe maker doesn’t appear to prevent you from adding olives and sherry vinegar to sausage and chicken in pink sauce, for example), you find total number of different ways to make a choice at every step by multiplying together the numbers of choices at each step.

It’s easy to count the number of ways to “choose this many of those Things.” If this many is k, and those Things are n in number, the number of ways to choose k of the n things is “n choose k,” sometimes written as C(n,k). These numbers can all be found in Pascal’s triangle. As it’s shown here, C(n,k) is in the row labeled with the n value, under the column labeled with the k value. Here’s how to use the triangle to find the value of C(9,3):

• To choose one or two of the four Flavor Bases, there are C(4,1) = 4 ways to choose one plus C(4,2) = 6 ways to choose two, for a total of 10 ways to choose this item.
• To choose one of the three Sauces, there are C(3,1) = 3 ways.
• To choose two or three of the nine Sauce Enhancers, there are C(9,2) = 36 ways to choose two plus C(9,3) = 84 ways to choose three, for a total of 120 ways.
• There are C(8,1) = 8 ways to choose a pasta.
• There are C(5,0) + C(5,1) + C(5,2) ways to choose up to two vegetables, or 1 + 5 + 10 = 16 ways.
• There are C(6,2) + C(6,3) to choose the Cheeses, or 15 + 20 = 35 ways

Multiplying these numbers of choices for each step yields 10·3·120·8·16·35 = 16,128,000 ways, about 60 times as many as Fine Cooking found when they did the math. Counting ways isn’t standard recipe math, and I’d like to note that Fine Cooking’s math is generally fine when it comes to ounces, grams, cups, servings, and calories.

Contralateral prophylactic mastectomy lowers post-mastectomy five-year death rate by 30%

The five-year death rate after mastectomy was 11.5% for women who had both breasts removed. It was 16.3% for those who only had the cancerous breast removed. Adding a contralateral prophylactic mastectomy to the original surgery therefore reduced the five-year death rate from 16.3% to 11.5%. Almost a third fewer mastectomy patients died within 5 years when the had chosen to remove the second (healthy) breast, compared to mastectomy patients who had not chosen to remove the second breast. The bilateral mastectomy decreased the 5-year death rate by 29.4%.

This strikes me as a significant benefit. Suppose I have breast cancer and need a mastectomy. I can choose a single mastectomy and have a one-in-6 chance of dying in five years, or I can choose a double mastectomy and have a one-in-9 chance of dying in five years. One-in-9 sounds quite a bit better to me. If 100,000 women with unilateral cancer need mastectomies, performing 100,000 double mastectomies instead of 100,000 unilateral mastectomies will reduce the number of deaths in the first five years from 16,300 to 11,500. About 4,800 fewer women will die within five years.

Contralateral prophylactic mastectomy benefits only 5% of mastectomy patients.

The reporting of this study takes a very different viewpoint. It compares the survival rate, not the death rate, and notes that the bilateral prophylactic mastectomy increases the survival rate from 83.7% to 88.5%, “a difference of less than 5%.” Five percent sounds like a small number, but 5,000 lives saved sounds like a large number.

Point of view

Both statements (lowers by 30%; benefits only 5%) are the same. Only the intent to communicate is different. Whether prophylactic mastectomy is good practice depends not only on the change in five-year survival rate, and I don’t have more information.. For example, how does a double mastectomy (which for 95,000 of the women will not change the five-year death rate outcome) affect a woman’s well-being and general health over time? What is the cost to save these 5,000 lives, and how will the disparity of death rates change more than five years after surgery?

Good news

There is a good piece of news in the study: The study data identified a subgroup of women for whom double mastectomy had an even greater benefit: women 50 and younger with early stage estrogen receptor negative cancer. Removing the second breast had no benefit for women 60 and older, and the benefit for women in their 50s was uncertain, presumably because of the small number of bilateral mastectomies in the sample.

The journalists writing about this study generally downplayed the benefits. It would have been better for them to downplay the benefits on most of the women, but hype the discovery that there is a subgroup of women who might get a substantial benefit from this procedure. If you read the study, or find better summaries of it, you may find that this study can help patients and doctors make wise treatment choices (contralateral mastectomy sometimes among them). With luck and more studies like this, prophylactic mastectomies might in the future go only to those women whom they might help. With even more luck, we’ll improve our diagnosis and prevention of breast cancer and the number of mastectomies will go down.

Silly me for thinking the Math Wars ended when Mathland bit the dust a couple of years ago. Last May, according to this month’s Scientific American, the Seattle School Board adopted the “Discovering Mathematics series, a reform-math high school text that uses student investigations as a means of discovering math principles—such as using toothpick models to derive recursive sequences.”

I looked at it for as long as my stomach could bear — at least at the one chapter that’s available online as a .pdf file here. It’s wretched. Wrong. Not only wrong like in I-don’t-like-it wrong (which it also is), but falselike wrong. And bad, stupid, dumb, and foolish, among other things. It would take me too long to point out all the things wrong in just the first few pages. (I won’t lie. There were some good things, but not many.)

I don’t think the students who wouldn’t have gotten much out of mathematics curricula in the ‘60s will do any better with this. For the students who want to learn mathematics, unfortunately, school will be even more of a waste than it used to be. They should do their best (especially if they go to public school in Seattle) to learn mathematics from the Internet, which is not nearly so wrong as Discovering Mathematics. With luck, any poor grades they get in stupid reform math courses won’t count against them, and if College Board caves and reforms the SAT to correlate with grades in stupid reform math courses, there will hopefully still be pressure for them to keep the AP and SAT II tests. If everything falls apart, kids that like math can drop out of school, learn from the Internet, then make a living tutoring the hapless victims of the new reform math.

Oh, and if you ever see an elevator whose “control panel displays ‘0’ for the floor number,” when it’s at the basement, please take a photo and send it to me.

Before 1985 (3 known cases, all listed below)

• 1965: Nuclear confusion. “Although [An Inquiry into Enoughness, by Daniel Lang] produces no solutions, his ‘inquiry into’ provides a vivid and troubling portrait of the nuclear confusion we live in.”
• 1979: The Supreme Court and the U.S. “He has drawn on his legal and personal experience to present a rich and troubling portrait of the court and the country.”
• 1984: The Kid’s father. “And in addition to being musical and sexy and light-hearted, ‘Purple Rain’ also is dark and depressing, presenting a troubling portrait of the Kid’s father, who beats his wife and has thereby traumatized his son into seeking refuge in his own music and private lair.”

1986-1994 (approx. 70 cases, examples listed below)

• 1986: Rural American rot. “[Sean Penn] again proves himself the best actor of his generation in ‘At Close Range,’ a powerful, uneven, troubling portrait of rural American rot.”
• 1987: Sexism and racism. “The play [Darrah Cloud’s The Stick Wife] is termed ‘an expressionistic comedy’ and is an imaginative yet troubling portrait of sexism and racism.”
• 1987: Ronald Reagan. “As the Iran-contra hearings fade off into the sunset, they leave behind a troubling portrait of a president who was strangely victimized both by his best and worst impulses.”
• 1989: St. Paul (Minnesota). “Demographics and statistics paint a troubling portrait of St. Paul as it enters the next decade:”
• 1989: Man’s alienation from nature. “Yet a consistent theme of ecological obsession pervades [The Pixies’ Doolittle]; the result is a troubling portrait of man’s alienation from nature”
• 1990: America’s Children. “A federal commission Thursday painted a troubling portrait of America’s children, saying that too many are reaching adulthood ‘unhealthy, illiterate, unemployable and lacking both moral direction and a vision of a secure future.’”
• 1991: The Albanian People. “Mr. Kadare thus accommodates his former Government’s nationalist ideology, yet at the same time draws a nuanced, troubling portrait of the Albanian people.”
• 1992: Courtney Love. “A profile of Love in the September issue of Vanity Fair offers a troubling portrait of the lead singer for Los Angeles band Hole and her rock-star husband, who grew up in Aberdeen.”
• 1992: Ross Perot. “[…] a troubling portrait emerges of the independent presidential candidate.”
• 1993: Elizabeth Holtzman. “In a report released yesterday after a reluctant Ms. Holtzman gave her assent, the department paints a troubling portrait of a public official so driven and distracted by ambition that, at best, she put politics ahead of her office’s responsibilities.”
• 1994: The Holocaust. “Director Marcel Ophuls’ 1988 Oscar winner is a troubling portrait of unimaginable evil.”
• 1994: Portland (Maine). “Portland confronts a troubling portrait of itself in this week’s US News and World Report.”

1995-2004 (over 100 cases, examples listed below)

• 1997: Timothy Leary. “The book’s final pages, a gathering of testimony by the many friends who surrounded Leary in his last days, offer a troubling portrait of a complex, driven man, always on stage, outwardly upbeat but secretly torn by anger, bitterness and a pervasive sense of loneliness.”
• 1998: New Line Cinema. “It paints a troubling portrait of a 31-year-old pioneering film company that carved out a niche with films like A Nightmare On Elm Street.”
• 1998: Jack Kerouac. “Recounted without the context given in earlier biographies and the larger humanity of Kerouac’s work, the story is left as gossip, to sully further an already troubling portrait.”
• 1999: Saddleback College. “The accrediting panel painted a far more troubling portrait of Saddleback College.”
• 2000: Contemporary America. “Black and White is volatile and messy, but it’s also uncommonly rich in ideas, and it leaves you with a deeply troubling portrait of contemporary America”
• 2001: Jesus Christ. “The most radical and, for orthodox Christians, troubling portrait is the one drawn by the Jesus Seminar, a Santa Rosa, Calif.-based group of about 50 non-denominational scholars who investigate scriptural accounts of what Jesus said and did during his life.”
• 2001: Edgardo Alfonzo. “Mets manager Bobby Valentine offered a slightly more troubling portrait of Alfonzo, who has battled various minor back ailments throughout his career.”
• 2001: Domesticity. “Whereas Seurat’s ‘Sunday’ shows a whole panoply of Parisian society enjoying itself in public, Signac’s ‘Sunday’ is a more intimate and ultimately more troubling portrait of domesticity.”
• 2001: Jarius Phillips and Marquita McCord (persons accused in a Virginia rape case). “Through it all, a troubling portrait arose of Phillips, McCord and the crimes with which they had been charged.”
• 2002: Paul Shanley. “Despite the release of hundreds of pages of documents that paint a troubling portrait of the Rev. Paul R. Shanley and his relationship with the Boston Diocese, the Ford Family wants more.”
• 2004: Hester Prynne. “She paints a vivid, troubling portrait of a woman who has fallen through the cracks.”
• 2004: Social inattentiveness to an underclass. “Without labouring the point, this skilfully assembled film [José Padilha’s Bus 174] makes the authorities’ bungling of the situation on the bus seem symptomatic of wider institutional failures; what emerges is a troubling portrait of social inattentiveness to an underclass that looks so much more desperate with its City of God ghetto glamour stripped away.”

2005-date (over 100 cases, examples listed below)

• 2005: The professional baseball locker room. “The ensuing congressional investigation turned up a troubling portrait of a locker room in which such substances were passed and injected by some players.”
• 2006: Bush’s handling of the Iraq occupation. “While the book is studded with familiar administration sound bites about the importance of deposing Mr. Hussein, it paints a troubling portrait of the administration’s handling of the occupation.”
• 2006: Student life at the U.S. Naval Academy. “But though much has improved since women first arrived — and many female graduates express great loyalty to the storied 161-year-old institution — a complex and sometimes troubling portrait of student life emerges from three recent studies sponsored by the Defense Department.”
• 2007: Robert Hawkins. “A troubling portrait emerged Thursday of the disturbed teen who turned a cheerful shopping center into a killing field in a bid to gain fame as he ended his life.”
• 2007: Seung-Hui Cho. “Investigators revealed details Tuesday about Cho that painted a troubling portrait of young man waiting to explode.”
• 2008: A fictional Jewish Neo-Nazi. “Written and directed by Henry Bean, ‘Noise,’ which Mr. Bean has called partly autobiographical, is the second part of a projected ‘fanatic trilogy’ that began with ‘The Believer,’ a deep, troubling portrait of a Jewish neo-Nazi.”
• 2009: Nidal Malik Hasan. “Emerging portrait troubling: Suspect’s name linked to radical postings on Web”
• 2010: The FBI’s investigation of the Oklahoma City bombing: “When it is examined, a troubling portrait emerges of an agency eager to tailor its investigation for the purposes of prosecuting a criminal case, rather than doggedly seeking out the truth.”
• 2010: Joseph Stack. “Troubling Portrait Emerges of Pilot Who Crashed Into Texas Building”

Recently, some portraits have been emerging but not identified as troubling, though they might be. The significance of these reports is unknown.

• 2009: Richard Poplawski. “The emerging portrait of Richard Poplawski: a white-supremacist radical”
• 2010: Dr. Amy Bishop. “The emerging portrait of neurobiologist and murder suspect Amy Bishop shows a disconnect between how she saw herself and her life and the actual reality of her experience.”

The earliest troubling portrait (1916) was hypothetical. A fictional character in The Girl Philippa suggested the possibility that one could be painted. He said, “I see. A man could paint a troubling portrait of her — a sermon on canvas.”

Earlier this evening, I wanted a word like “otherwise” that didn’t highlight a contrast. For example, suppose El Patagón Goloso’s dorade was the best I’d ever eaten, and the rest of the meal was also excellent. After a description of the dorade, “otherwise” doesn’t work. “Otherwise, the meal was excellent” suggests that something (whatever was previously mentioned) about the meal was not excellent. The only solutions seem to me too long or a bit awkward: “In all other respects, however, the meal was excellent.” or “The meal was otherwise excellent as well.”

Stuck without a word, I made one up: “alsowise.” I think it’s useful, not only as an answer to the analogy AND:BUT::?:OTHERWISE.

Barry Petchesky sicized “miniscule” in a recent and alsowise fine Deadspin article on Paul Shirley’s Haiti fumble. Despite the fact that—as Barry put it—“Deadspin has long been [the] go-to source for professional athlete penis,” and despite the fact that Barry was on Jeopardy! last year, somehow I didn’t know Deadspin from Adam or Barry from Steve. I’m glad Barry captured my attention, and I’m happily spending this evening with him at home. Thanks, Barry!

Related forms:
sicization: the act of sicizing
sicizy: / ˈsɪ sɪ zi/ a rhetorical device, specifically, the use of sicization in order to deprecate or ridicule

I hope you’ll join me next week, when the word of the day will be intertelligible.

Really. The New York Times said so. Our founding fathers wrote in their diaries about this weekend’s storm. Awefomenefs.

This snowstorm was bigger than the U.S. Civil War, bigger than the moon landing, and bigger than Lady Gaga and Elton being on stage together last week! Geo. and Th. didn’t write about those other things, right? I mean, I spent most of the summer of ‘69 reading and would’ve seen something about the moon landing being in those guys’ diaries, I think. Yeah, Nixon was president, but still, we’d know, right?

Here’s the Times quote:

The National Weather Service said the blizzard did not challenge Washington’s 28-inch record, set in January 1922, a snowfall that collapsed the roof of the Knickerbocker Theater, killing 98 people and injuring 158. Nor did it rival the three-foot snowfall of 1772, long before record-keeping began, although it was noted in the diaries of George Washington and Thomas Jefferson.

Unless I missed something in Bits about time machines, I’m pretty darn sure the Times is wrong. Maybe they meant to write something like

The National Weather Service said the blizzard did not challenge Washington’s 28-inch record, set in January 1922, a snowfall that collapsed the roof of the Knickerbocker Theater, killing 98 people and injuring 158. Nor did it rival the three-foot snowfall of 1772, long before record-keeping began, although it that was noted in the diaries of George Washington and Thomas Jefferson.

or

The National Weather Service said the blizzard did not challenge Washington’s 28-inch record, set in January 1922, a snowfall that collapsed the roof of the Knickerbocker Theater, killing 98 people and injuring 158. Nor did it rival the three-foot snowfall of 1772, which occurred long before record-keeping began and was noted in the diaries of George Washington and Thomas Jefferson.

Or maybe they meant this for an audio-only story, where it would be possible to say “Nor did it rival the three-foot snowfall of 1772, long before record-keeping began, although IT was noted in the diaries of George Washington and Thomas Jefferson,” (still sloppy, but talk is a whole nother language from written) because if you say “it” very emphatically, you can intimidate it and make it change its antecedent.

And maybe I understood what they meant, too. But writers should write as precisely as possible; they shouldn’t write in the spirit of nearest-neighbor error-correcting codes and assume it’s fine to publish written nonsense assuming the reader will subconsciously refer to a Hamming distance ruler and an unabridged vector space of things that make sense and infer the right thing.

Any errors, whether regarding pronomial antecedents or otherwise, are my responsibility.