Monday, March 12, 2012

Snowdrops, Christmas Lights, Rush Limbaugh, and the Director Circle of an Ellipse

Our snowdrops bloomed on Sunday...the sun has been warming the earth. It was as good a day as any to take down the Christmas lights.

There are places where leaving your lights up until March would get you in trouble with the neighbors. In Vermont, we live and let live. I chaired my town's Planning Commission for a year; this is the group responsible for the town's zoning bylaws. One time, when we were debating the issue of junk cars in our town, a representative from the state government showed us a photo of a large junk car collection in the northern part of the state. This photo had been taken from space.

Anyway, speaking of space, I tend to take an astronomical view of things; I figure I'm not really late if the decorations come down before the vernal equinox.

***

I heard that Rush Limbaugh's sponsors are leaving in droves. People like Michael Kinsley, Andrew Sullivan, and Bill Maher have stressed that living in a country with free speech means that you're going to be made uncomfortable sometimes by what people say, and that you should fight speech with speech, not boycotts or campaigns.

The story here seems to confirm their fears.

I agree with Kinsley et al. about campaigns that would topple someone for stating their views. And I agree that if you don't like Rush, then you shouldn't listen to him, and you should counter what he says with better arguments and better rhetoric. If enough people stop listening to him, his advertisers will leave anyway.

But on the other hand, I also don't see how Rush Limbaugh's right to free speech obligates me to subsidize him. If we all have a duty to support Rush Limbaugh, then maybe Congress should pass a federal sales tax to keep his radio show running.

And what about people who aren't part of any "campaign"? If I decide on my own to send a tweet to ProFlowers saying I'm going to shop with their competitors as long as they advertise on Rush's show--not that I did, mind; I don't have a Twitter account--then I haven't been part of any campaign or attempt to "manipulate the system." So far, Kinsley, Sullivan, and Maher have argued against organized activity. What is the argument against individual consumer activism?

I suppose the argument is that consumer activism is good when it counters harmful actions--as when someone refuses to buy products from factory farming, out of a judgment that factory farming is a set of harmful actions. But consumer activism about speech acts gets into troubling territory.

Or maybe the argument is that the logical endpoint of individual consumer activism against media entertainers is a less vibrant media-tainment sector. If a small percentage of consumers, even without acting in concert, can spook advertisers through the power of social media, then we might not get to see people like Rush Limbaugh and Bill Maher.

That's the argument against tyranny of the minority. But despite what it says in the MediaMatters story linked to above, I don't think that's what's happening to Rush. I think what's happening to Rush is that a large percentage of consumers has finally decided  that paying his salary makes them feel dirty. It seems to me that an entertainer who enters into this particular territory has made his own bed.

Rush Limbaugh has a large audience--large enough, I suppose, to keep him in business even without sponsors. I imagine he could take his show to a subscription service on satellite radio. Or he could run for the Senate, or write a weekly newspaper column, or become a Republican speechwriter, or publish books. I'm not really worried about Rush Limbaugh's free speech rights. But I do wonder about the longevity of a business model founded on being an asshole.

Having said that, I'm impressed by the distinction I made earlier (if I do say so myself) between individual consumer activism about actions vs. individual consumer activism about speech acts. Perhaps with regard to the latter, we need moderation. So maybe the idea is that even if you would rather not listen to the KKK radio hour yourself, then even so, you shouldn't be worrying about whether companies you do business with are advertising there. Call it the "ignorance is bliss" theory. If it's true, then it would be yet another case of one of the paradoxes of democracy, that moderation is needed in order to enable the immoderate to flourish.

***

I was doodling the other day and "discovered" a nice property of ellipses. The puzzle I'd set for myself during some downtime (I think it was when my wife was outside taking down the Christmas lights) was to determine the locus of points from which an ellipse subtends 90 degrees. I did some algebra (here), and lo and behold, the locus is a circle! Here is an animation:


This property of ellipses gets forgotten and rediscovered periodically, at least to judge from this exchange on MathForum involving John Conway. Wikipedia knows about it. Here in case you're interested is a sketch of a proof from synthetic geometry, from a site with a wealth of geometry problems.

Given the equation of an ellipse and the equation of a line, my derivation simply demands that these simultaneous equations have a double root (for tangency), which determines two possible slopes, corresponding to the two tangents. Requiring these tangents be orthogonal leads to the equation of the circle. You can try this method with the parabola y = ax^2 to see how it works. (The algebra is less involved in this case.) If you do the parabola problem, you'll see why the circle in the above animation is called the director circle of the ellipse.





Friday, March 2, 2012

Some Solutions to the Quadruple Vowel Puzzle

There's nothing like a very long plane ride for getting work done. Here then are some answers so far to the quadruple vowel puzzle, including answers from the comments and answers from emails people have sent me. (N.B., occasionally I chose not to include a human solution if it "just didn't look as nice" as other solutions of equal or lesser length, or if it would have made the list seem too long. So the list is an editorial project to that extent.)

Also included below, in a few cases, are some notable answers from an online dictionary file available here (.txt file). An asterisk denotes what one might consider a "computer victory."

Word length isn't the only criterion one might use to judge the quality of a solution. For example, word frequency might be used to break ties. (On that view, SOMEONE is better than HONOREE.) Aesthetics might also enter into it; DOVECOTE is just a more beautiful solution than LOOSENED. One solver proposed a quality scale that involves linguistic concepts such as the number of morphemes in a word. Perhaps we can ask him to identify the "nicest" solutions according to that metric in the comments section.  Finally, one might argue that in the case of this puzzle, very long words are as good as very short ones, seeing as how piling letters atop one another gets harder and harder to do without adding a disqualifying vowel. (Finding such words is really CATCH-AS-CATCH-CAN...just ask any FENCINGMISTRESS or CANVAS-STRETCHER.)


In any case, the quality of the solutions was incredibly high.  Many or most of the words listed below were found by two or more solvers. Moreover, you'll see that there are few computer victories. Short words conforming to the given patterns are evidently rare, yet a small group of us found many of the best possibilities. Perhaps whenever we read, we are consciously or subconsciously attending to these rather "odd-looking" words and storing them away in our minds.

Thanks for playing!

--J



Solutions are presented in the following format: Humans first, then computer in a few cases. Each list is sorted by length, then sorted alphabetically within length (modulo clerical errors).

*1. BALACLAVA (9), CATAMARAN (9), JACARANDA (9). Notable computer answer:  MAHARAJA (8)

2. AERATE (6), ACREAGE (7), MANATEE (7), ANTENNAE (8), REAPPEAR (8)

3. AIRMAIL (7), MAINTAIN (8), MAINSAIL (8), BRAINIAC (8, slangy perhaps).

*4. BOATLOAD (8), MACAROON (8). Notable computer answers: AVOCADO (7), BAZOOKA (7)

5. ARUGULA (7), AUTUMNAL (8), AVUNCULAR (9),  UNFACTUAL (9).

6. ANYWAY (6), PAYDAY (6)

7. TEEPEE (6), ESTEEMED (8), EXCEEDED (8), REDEEMED (8).

8. DEITIES (7), ITEMIZE (7), IMBECILE (8), BELIEVING (9), DECEIVING (9), ILLEGIBLE (9), INSINCERE (9)

*9. HONOREE (7), DOVECOTE (8), LOOSENED (8), METRONOME (9), MONOTREME (9, jargony perhaps; anagram alert!). Notable computer answers: BOOTEE (6, if you can stomach that spelling), SOMEONE (7)

10. QUEUE (5), BURLESQUE (9), UNDERUSED (9), UNRETURNED (10). Notable computer answer: UKULELE (7)

11. BYE-BYE (6, if you can handle the hyphen), DYSENTERY (9). Notable computer answer: WHEYEY (6, archaic perhaps)

12. CIVILIZING (10), DIGITIZING (10), INFINITISM (10), NIHILISTIC (10), DIMINISHING (11)

13. COITION (7, jargony perhaps), OMISSION (8), POISONING (9), PROBIOTIC (9, used to be jargony but not really anymore), SOPORIFIC (9). Notable computer answer: OPINION (7)

*14. UNSUITING (9), FUTURISTIC (10), SUBSTITUTING (12), UNFULFILLING (12). Notable computer answers: JIUJITSU (8), RUBIDIUM (8, jargony perhaps), UMBILICUS (9, jargony perhaps)

15.YIPPILY (7, judgment call; "Well, it is how small dogs bark," argues the solver), WILLY-NILLY (10), NITTY-GRITTY (11). Notable computer answer: TYPIFYING (9)

16: VOODOO (6), COOKBOOK (8), FOOTSTOOL (9).

17: VOUDOU (6, unusual spelling), OUTPOUR (7), COUSCOUS (8), HUMOROUS (8), OUTBOUND (9), GLOBULOUS (9)

18. YO-YO (4), BOY-TOY (6, maybe a little neologistic), ROLY-POLY (8)

19. MUUMUU (6)

20. FUDDY-DUDDY (10), HURDY-GURDY (10), HURLY-BURLY (10)

21. For YYYY, one solver suggests 


SYZYGYLY (suh-zi-ji-lee): In such a manner as to cause three celestial bodies to align. "The supersitious began to panic as the planets moved ever more syzygyly across the heavens."
(Seeing as computers lack humor, we win this one.)

Previous word puzzles here, here, here, and here.