December 2010

A few months ago, I posted a graph and parametric equations for conchiglie rigati. Today I’m sharing a graph and equations for cavatappi. As before, I started with equations from Chris Tiee’s 2006 class notes for vector calculus.


Cavatappi Equations

Coming soon, a graph and equations for Möbius pasta.

Möbius Pasta

Roundup from the December Southwest Airlines Spirit magazine. (Which was thankfully captivating, there being no new SkyMall to which to turn.)


  • “Luxury” (as “Luxuy”, in large type on page 58)
  • “Remembrance” (as in “Pearl Harbor Rememberance Day,” page 126)

Arguable misspellingGoogleDamnit

  • “DAMMIT” (as “DAMNIT, page ??¹) 

Unexpected nonmisspelling

  • “memento” (as “memento”, page ??²)

Clichés (and other embarrassments) up the wazoo

Witness this small (trust me) sample from the literal surfeit in “Crowd Control,” a single article by Scott Steinberg, CEO of the “high-tech consulting firm TechSavvy Global,” who limited research suggests speaks and writes thus prolifically.³ The Spirit article wasn’t intended as humor or parody.

  • “bet the farm”
  • “field day”
  • “trust me”
  • au contraire
  • “dress for success”
  • “won’t be a cakewalk”
  • “make no mistake”
  • “weeding out the winners” [My personal favorite. –SK]
  • No matter how unique the idea, we’ll dress it for success.”
  • Even crappy concepts generate helpful response and criticism.”

Other funnies

I didn’t note the sources or page numbers of these other Spirit gems.

  • “(Though the Baltimore monument [to George Washington] is almost 400-feet shorter than the Washington monument in D.C., it’s actually 56 years older.)”
  • “reams of red tape” [A close second. –SK]
  • “When I watch Dr. Stern practice medicine, I am struck by how little it is like those medical shows on television. She doesn’t rush around with heart paddles and needles.”

¹ Despite the appearance of the jump line “Continued on page 108” on page 99, a dozen or so unnumbered pages (presumably including page 108) immediately and consecutively followed the page bearing the number 101. The first numbered page thereafter bore page number 114. “Page ??” refers to one of these unnumbered pages, though not always the same one.

² See previous footnote.

³ The quoted description of TechSavvy Global was copied from something on the internet. TechSavvy Global’s actual website rather roundly and soundly belies the description. (Remarkably, even the blue underlined email address on the home page is not a link.)

A theretofore charming day, spoiled in the blink of an eye, because I caught sight of the link “David Brooks: Obama’s Very Good Week” in the Times. Brooks isn’t known for sarcastic titles, and it’s been nobody’s good week in Washington. A $25,000,000,000 tax windfall (yes, 25 billion) for the richest 0.3% (yes, less than one third of one percent), and DADT, in particular.

I clicked, but I didn’t read the article. I’m trying hard not to read everything from start to finish that I know in advance will be crazymaking. I wasn’t about to backslide with the likes of Brooks, so I applied the How To Read a Ross Douthat Article approach.

The HTRaRDA approach is this: Type Control-End (preceded by SINGLE PAGE, if available) to reach the bottom of the article, and then read the last screenful. Do not pass Go! You will discover the offensive conclusion without wading through the invidious, lame, emetic screensful that invariably, insidiously, precede it.

Unfortunately, sometimes the insidious run-up extends into that last screenful, and it did today. It was impossible to ignore, because it included numbers.

Warning: The David Brooks quote below is a lie.

According to the most recent Gallup numbers, 67 percent of independents and 52 percent of Democrats support extending all the tax cuts.

Warning: The David Brooks quote above is a lie.

It was painful to follow up on this quote, but I’m still holding onto the belief that it would have been worse to have read Brooks in toto.

On December 1, Gallup reported that “Forty percent [of Americans] want Congress to maintain the tax cuts for everyone, while 44% support setting limits on how much of wealthy Americans’ income is eligible for the lower rates.” In particular, 18% of Democrats preferred keeping the tax cuts for everyone (when offered two alternatives: setting limits or letting the cuts expire entirely). Those can’t be the “most recent Gallup numbers” to which Brooks refers, because 18 doesn’t equal 52, even with rounding. (Maybe at the Times it does, but not on my blog.)

Here are the actual Gallup numbers to which Brooks refers. Over the past weekend, Gallup asked this question: “Suppose that on Election Day you could vote on key issues as well as candidates.  Please tell me whether you would vote for or against a law that would do each of the following.  Would you vote for or against a law that would extend the federal income tax cuts passed in 2001 and 2003 for all Americans for two years?” Fifty-two percent of the Democrats, 67% of independents, and 85% of Republicans surveyed said they would vote for such a law.¹

Quiz. Given three choices similar to those before Congress (A. extend cuts for all; B. extend cuts but only up to a dollar limit for the wealthy; C. let tax cuts expire), Democrat’s least preferred option is to extend all the tax cuts. (Breakdown: 18% answered A, 21% answered C, and 55% answered B). Is it fair to say that 52 percent of Democrats support extending all the tax cuts?

The correct answer is NO.

Kudos to Gallup for the careful and precise phrase to describe the option before Congress: “limits on how much of wealthy Americans’ income is eligible for the lower rates.”

Shame on Brooks for vulpigerating.

¹ I apologize for previously calling the Republican party the “Party of No.” I should have more precisely called them the “Party of No, except when it will make the rich richer.”

275_Colin-Davis-and-the-805552Sir Colin Davis led the New York Philharmonic Saturday evening in performances of Beethoven’s Symphony #2 and Mahler’s Des Knaben Wunderhorn, with soprano Dorothea Röschmann and tenor Ian Bostrich.

Beethoven’s Second is one of my favorites. Essential Beethoven, it dances and laughs like #7, it sings like #6, it marches like #5, yet without excess, ever elegant and confident. Sir Colin conducted, as he does, calmly, precisely, and without grandstanding, and the performance was delightful.

There’s no agreed-upon set and sequence for Mahler’s Wunderhorn songs, and they don’t comprise an integral song cycle or symphony. Nevertheless, Sir Colin and the Philharmonic made a good case for the choices and order they made.

During the Mahler, I was focused on the voices, so I have little to say about the orchestra beyond that they sounded fine, and perhaps they were outstanding.

media3e6745ff66dd9Tenor Ian Bostrich, although physically engaged with the songs, didn’t have enough vocal power. In his middle and lower registers, he was barely audible. The orchestra was holding back a bit, it seemed, and it didn’t help that Bostrich tended to project his voice down, not forward, something a man of his considerable height might be accustomed to doing in conversation. What I could hear was beautiful, and I’d like to hear him again, but in a recital and in a smaller hall.

As for Dorothea Röschmann’s soprano, there was nothing to criticize and everything to praise. She commanded sheer power, never harsh, and she delivered pure pianissimos, never unfocused, throughout her ample vocal range, each as the songs demanded, and she demonstrated flexibility as she shifted nimbly from one Wunderhorn “mood” to another.

Lob des hohen Verstandes (In praise of high intellect) is funny and sarcastic. (Synopsis: a donkey, because of his large ears, is chosen to judge a singing competition between a cuckoo and a nightingale. The cuckoo wins.) Here, Röschmann made an ass of herself in the best possible way, and she sang as beautifully as any nightingale has ever done. Das irdische Leben (The earthly life) is tragic. (Synopsis: Starving, crying child dies before the corn can be harvested and baked into bread.) Röschmann was haunting. In the peasant love ditty Wer hat dies Liedlein erdacht (Who thought up this little song?), the long, florid phrases spun forth like silver.

Run, don’t walk, to the Carnegie Hall box office for tickets to hear Röschmann sing Handel’s V’adoro, pupille and more in an April 3, 2011 recital with David Daniels.

Neither of last night’s works features a large orchestra, and the Philharmonic performed without several of its principals. Among the missing were Glenn Dicterow, Carter Brey, and Robert Langevin. Incidentally or not (and probably no fault of Sir Colin’s), the Philharmonic was not in top form. Some sections were as stunning as ever — the woodwinds, flutes in particular, were in fine form (save for the horns, who needlessly reminded us how difficult they are to play in tune), and the percussion were as well. As an ensemble, however, the orchestra wasn’t as tight as it can be.

Orchestral failings aside, Davis is, and was last night, a servant to music. This is the guy who can — no easy task — give us Berlioz without overdoing the grandiosity and sentimentality. It dawned on me hours after the concert that nothing seemed too fast or too slow. I don’t remember the last time I concurred with an entire concert’s-worth of tempos. As one critic said half a century ago, Colin Davis was the best English conductor since Sir Thomas Beecham, and it’s not clear England has yet produced his successor. It was a pleasure to watch him, still spry at the age of 83. May he treat us for many more years.

The major news organizations still can’t describe the tax cut proposals correctly.

Fact: The Democratic proposals that Senate Republicans killed today would have extended Bush tax cuts for all taxpayers (often called everyone, though poor people aren’t included).

Under the now-dead proposals, the tax cut extension would have been capped at $250,000 or $1,000,000 of income, but all taxpaying households would see lower taxes. The Bush tax cuts, which are about to expire, have no cap.

High-income taxpayers (often called rich people) would have received the biggest tax cut under these Democratic proposals. Republicans rejected the proposals because it’s not enough for them that the richest people receive the biggest tax cuts. The Republicans want the richest people to receive even bigger biggest tax cuts.

The Republicans also opposed the proposals because they were Democratic proposals. Also because they were proposals, and the Party of No opposes everything.

All this despite public sentiment that the Bush tax cuts should continue only for households earning less than $250,000, an idea no one is proposing.

As far as I can tell, no one has sought public opinion on the actual current proposals. I can’t understand or explain why CBS and other polling organizations continue to ask people about proposals that aren’t and have never been under consideration.

Here’s a sampling of today’s descriptions of the tax cut proposals, all of which are wrong, or at best misleading. The news outlets might as well say that the Democrats proposed extending the Bush tax cuts for White families.

CNN “The votes sought to extend the Bush tax cuts for families making under $250,000 and $1 million, respectively.”

Wall Street Journal “The Senate voted 53-36 to reject an attempt to initiate debate in the chamber on a measure that would have extended lower tax rates for individuals who earn less than $200,000 and couples earning less than $250,000.”

New York Times “The Senate on Saturday rejected President Obama’s proposal to extend the Bush-era tax breaks for all but the wealthiest taxpayers, sealing a triumph for Republicans who have long called for continuing the income tax cuts for everyone.”

Associated Press “Senate Republicans have blocked legislation allowing taxes to rise on Jan. 1 on people earning more than $1 million.”

Bloomberg “The U.S. Senate failed to advance a Democratic proposal to extend Bush-era income-tax cuts for families earning up to $250,000.”