Friday, December 30, 2011

Merry Christmas

Did Santa disappoint this year? Just how good do you have to be in order to get what you've always wanted? Is a generalization of the Law of Cosines applicable to pentagons really too much to ask for? Well, whether you wanted it or not, here it is. I doodled it today during my morning coffee.

As you'll recall, the Law of Cosines gives one side of a triangle in terms of the other two sides and the opposite angle. (See Wikipedia here, and why not give them five bucks while you're at it?) So as I sat down with my coffee, I decided there ought to be a Law of Cosines that gives the unknown side of a pentagon in terms of the other four sides and the "opposite angles" (i.e., the three angles of which the unknown side is not a part).
First I treated u, v, w and x as vectors with appropriate orientations; then I computed t-squared as the inner product of u + v + w + x with itself. This led easily to the desired relation, which has some nice rhythms in it pointing to the general case (click to enlarge):
Here is an example problem:
I find t = 1.3826 or so. See how useful the formula is? I don't know how I ever got by in theoretical physics without it.

 As an extra stocking stuffer, the simpler Law for quadrilaterals:
Note, these formulas also work for non-simple polygons (closed polygonal chains with self-intersections; see Wikipedia here and you'll have another chance to give them five bucks).

By the way, I donated $10 to Wikipedia myself today. Merry Christmas, Jimmy Wales!

Monday, September 12, 2011

Richard P. (Rip) Zimba, 1926-2011

On September 2, 2011, Mr. Richard P. (Rip) Zimba, of North Bennington, Vermont, died in his sleep of natural causes. He was 84 years old.

Rip was born in his parents’ farmhouse in 1926, on land that would later become part of the city of Dearborn Heights, Michigan. An entrepreneur from an early age, Rip sold strawberries during the Great Depression as “The Strawberry Kid.” After working as a machinist during the 1940s, he founded his own business, Rip’s Drive-In restaurant, a suburban Detroit landmark located at the corner of Joy Road and Inkster Road in Dearborn Heights. At the drive-in, Rip worked alongside his wife, Dorothy (Dot) Zimba. The two remained happily married until Dorothy’s passing in 2009.

Rip’s Drive-In was known for its welcoming atmosphere and excellent donuts. Rip and Dorothy were also known for their charity, providing meals and support to the needy and serving free food to volunteers during the annual “Detroit Goodfellows” fundraising campaign. Raised a Catholic, Rip regularly attended Quaker meetings later in life and took university courses in Peace and Conflict Studies.

Rip lived most of his life just a few hundred yards from the place of his birth, and he retained a farmer’s pragmatism and connection to the land. Each year he used his father’s Ford tractor to cultivate what remained of his family’s farmland, raising corn, tomatoes, lettuce, raspberries, and other crops. And yet he was anything but provincial. He was actively interested in world affairs and knowledgeable about world languages and cultures. He traveled widely, including to Central America, Italy, England, Morocco, and Turkey.

After Rip’s Drive-In closed in the mid-1980s, Rip worked as a machinist for Master Automatic, Inc., where his strong work ethic made him a valued employee for many years. Advancing symptoms of Parkinson’s disease led to his retirement, and in 2007 he relocated from Michigan to Vermont, where he received kind and attentive care at Prospect Nursing Home in North Bennington until his passing.

Rip will be lovingly remembered by his children: Ms. Intissar Greene, Mesa, Arizona; Ms. Jilly Dybka, Kingston Springs, Tennessee; and Dr. Jason Zimba, Pownal, Vermont; by his stepsons, Mr. David Bailey, Novi, Michigan, and Mr. Wayne Bailey, Southgate, Michigan; by his grandchildren, Miss Abigail Zimba, Pownal, Vermont, and Miss Claire Zimba, Pownal, Vermont; by his sisters, Mrs. Marie O’Connor, Webberville, Michigan, and Ms. Virginia Zimba, East Lansing, Michigan; by his brother, Mr. Leo Zimba, Dearborn Heights, Michigan; and by his many nieces, nephews, and cousins.

Sunday, May 8, 2011

For My Wife on Mother's Day

When we got back from the desert green trumpets were blowing from the earth green flags were planted in the earth bouquets were exploding from wand-tips today your smaller daughter counted one, two, three, nine tulips

Tuesday, March 1, 2011

Spot the error

From the bio of syndicated columnist Jonah Goldberg:
Jonah Goldberg is one of the most prominent young conservative journalists on the scene today. His column, syndicated by Tribune Media Services, offers shrewd analysis on a wide range of subjects, from political philosophy and economic trends to popular culture, with an entertaining writing style that speaks to a whole new generation. With keen wit and hard-hitting insight, Goldberg brings a fresh perspective to the typical right-left debate, by rejecting party lines, talking points and stale clich├ęs.

Tuesday, February 22, 2011

On the Pleasures of Constraints

When I was interviewing for faculty positions back in 2004, I visited several liberal arts colleges across the country. Some were ranked higher than others, some had better labs than others, but one college stood out from the rest as markedly more vibrant: Bennington College. Something different was going on at Bennington, and I could feel it in the festive intensity of the faculty and students.

Sometimes I think Bennington's vitality is due to its visual and performing artists, both student and faculty. These folks certainly pack a wallop. The sculptors, painters, and other artists on the faculty were always announcing gallery openings in big cities and having their work featured in museum programs. The dancers were always going to or from their studios in New York City, or being written up in the New York Times. All of this inspired me to fulfill the college's ideal of faculty members as "teacher-practitioners." Without the artists' example, I think it would have been easy for a theoretical physicist in a rural college to go to seed.

The student-artists were an inspiration too. For one thing, they were often the people in my physics laboratory who had actual skills - they could use lathes, drill presses, welders, and a lot of other tools that nobody in their right mind would let me use by myself. Together we made some pretty cool apparatus. The artists also had an effect on my classroom presentation of physics and math. When teaching Newton's laws to dancers, the implications for the body and for locomotion become at least as interesting as the implications for spaceships. (You can get a sense of this from the occasional blog post here and here.)


The arts faculty were curious about my work, and they often invited me into their classrooms to share my research, or discuss some of the parallels between physics, math, music and art. For example, there was a drawing class in which the students made 100 drawings throughout the semester, each in response to a set of constraints imposed by the teacher. (A drawing might be required to use only vertical lines, for example.) So I paid a visit to the studio one day and gave some remarks about the role that constraints play in math and games. The handout from that day, called "On the Pleasures of Constraints," is here.

On another occasion, I spent an hour in a dance studio talking force and motion with faculty member Susan Sgorbati and a pair of dancers who were rehearsing one of her pieces. When I got there and started looking around, I saw all this floor just asking to be walked on. Pretty soon I found myself moving and grabbing hold of people - doing the explaining with my body. That was the day when the thought first occurred to me that locomotion is a series of controlled collisions with the earth (and that, consequently, the floor is a partner in every dance - an idea, by the way, that means mechanizing the dancers, not enlivening the floor). After that, even my regular classroom teaching was fairly kinetic.

Sometimes the artists at Bennington pulled me out of my comfort zone and out of my shell. One student asked me to act in her video art project. It was a deep and powerful piece, and I was terrified that I'd ruin it for her. But I heard I was actually OK, and I enjoyed doing it! (Though I was a little disturbed by how easily I could get angry at a lens. Like I was a pigeon or something.)

Then there was the sculptor on the faculty who suckered me into making this puppy and showing it in the college art gallery.

I wrote about the making of the sculpture here. Soon afterwards, I wrote about the show's after party, where I spoke with a student artist whose next project would have astronomical relevance. The artist, now graduated, was Charlotte X.C. Sullivan, whose latest work can be seen here.

These experiences probably helped me to take a few risks with my lecture for the College's 75th anniversary, a portion of which can be seen in, um, a literary magazine called The Charles River Journal.

***

Bennington has always made the arts central to a liberal education, ever since its founding. And design and the arts remain central in the new vision of the liberal arts being spearheaded by college President Elizabeth Coleman. Bennington's newest building is being dedicated to this vision later this year. It's called the Center for the Advancement of Public Action. I had a tour of the building and construction site a few weeks ago. As befits the college and its artistic heritage, the Center is an architectural masterwork by Tod Williams and Billie Tsien. It is staggeringly beautiful inside and out. The exterior, faced with reclaimed Vermont marble, hearkens back to the origins of democracy in Greece - and in America. (Many buildings in Washington, D.C., contain Vermont marble, including the exterior columns and walls of the Jefferson Memorial.) The surprisingly spacious interior is fit for various purposes, and is gorgeously made of wood, tile, and stone. The building is a beautiful instantiation of the idea that the arts have a serious role to play in fostering thoughtful action in a liberal education.

Wednesday, January 26, 2011

Numbers Don't Lie (but Michele Bachmann Does)

In her rebuttal to last night's State of the Union Address, Minnesota congresswoman and entertaining crank Michele Bachmann showed the following graph:


If you look beneath the graph's horizontal scale, you'll see that these data are actually monthly unemployment rates for October of each year. (The graph doesn't show annual employment, as one might have expected from a year-by-year display.)

Presumably the reason for picking October is that
it allowed Bachmann to highlight the 10.1% spike in unemployment that occurred in October of 2009. (The annual unemployment figure for that year was a less dramatic 9.3%.)

Noreen Malone at Slate has noted the lack of labels for the even years, which helps to create a sense of separation between the two administrations. But personally, I can't see that the data support such a clean separation. Here is what you get when you look month by month:


I was also amused to notice that in Bachmann's graph, President Bush's bars were squeezed to the left of his yearly slots, while Obama's bars were squeezed to the right of his yearly slots. The effect of this was to enlarge the gap of white space between the red bars and the blue bars - again enhancing the sense of separation between the two administrations. With a regular pattern of small gaps to the left, and a regular pattern of small gaps to the right, the large gap "does the work" of distinguishing between the two presidents. Nice of her team to save us the trouble.

Recently I laughed out loud when I saw Chris Matthews losing it while interviewing Tea Party strategist Sal Russo about a speech Bachmann had given, in which she suggested that the Founders worked tirelessly to eliminate slavery. Bachmann had said:

But we also know that the very Founders that wrote those documents worked tirelessly until slavery was no more in the United States.

Matthews went ballistic about this apparent attempt to whitewash the story of the founding of the nation. The Constitution was ratified around 1788, and slavery was abolished around 1865; so given that 1865 - 1788 = 77, it's pretty hard to imagine that the Founders "worked tirelessly until slavery was no more in the United States." Many have suggested that Bachmann is ignorant of history; maybe she's just ignorant of subtraction.

Bachmann's speech posed another math puzzle:
Do you realize it's been 21 generations that America has survived?
As soon as I heard this, I started scratching my head because I normally think of a generation as being about 25 years long - and 21 times 25 is going to be something like 500 years. Yet I had always thought of America as being more like two hundred and some years old.

Could Bachmann be referring to Columbus? The fuller quote is:

Do you realize it's been 21 generations that America has survived? For 21 [generations], we've passed the torch of liberty from one generation successfully to the next.

It's hard to believe this refers to Columbus, who as I understand it was an Italian. But then again, I don't know what the alternative is. Wasn't "the torch of liberty" lit sometime around 1776? If so, then (2011 - 1776)/21 = 11 or thereabouts...and a generation can't be 11 years long.

So I don't know if she's fuzzy on history or fuzzy on math. She's certainly fuzzy on something.

Sources: I found annual unemployment numbers at http://www.bls.gov/cps/prev_yrs.htm. For monthly numbers, I used the query tool at http://data.bls.gov/pdq/querytool.jsp?survey=ln to find the following (paste into Word and use the Convert Text to Table command):

Year,Jan,Feb,Mar,Apr,May,Jun,Jul,Aug,Sep,Oct,Nov,Dec
2000,4,4.1,4,3.8,4,4,4,4.1,3.9,3.9,3.9,3.9
2001,4.2,4.2,4.3,4.4,4.3,4.5,4.6,4.9,5,5.3,5.5,5.7
2002,5.7,5.7,5.7,5.9,5.8,5.8,5.8,5.7,5.7,5.7,5.9,6
2003,5.8,5.9,5.9,6,6.1,6.3,6.2,6.1,6.1,6,5.8,5.7
2004,5.7,5.6,5.8,5.6,5.6,5.6,5.5,5.4,5.4,5.5,5.4,5.4
2005,5.3,5.4,5.2,5.2,5.1,5,5,4.9,5,5,5,4.9
2006,4.7,4.8,4.7,4.7,4.6,4.6,4.7,4.7,4.5,4.4,4.5,4.4
2007,4.6,4.5,4.4,4.5,4.4,4.6,4.7,4.6,4.7,4.7,4.7,5
2008,5,4.8,5.1,4.9,5.4,5.6,5.8,6.1,6.2,6.6,6.8,7.3
2009,7.8,8.2,8.6,8.9,9.4,9.5,9.5,9.7,9.8,10.1,9.9,9.9
2010,9.7,9.7,9.7,9.8,9.6,9.5,9.5,9.6,9.6,9.7,9.8,9.4

Monday, January 10, 2011

Word Puzzle, Word Problem

1. A word puzzle:

"Downshifting" a word means replacing its initial letter with the immediately preceding letter of the alphabet. For example, to downshift the word BOIL, replace the B with an A to obtain AOIL. (Unfortunately, AOIL is not a word.)

Some words are "downshiftable," meaning that when you downshift them, you obtain a new word. For example, TIP is downshiftable, because it downshifts to SIP.

In fact, SIP is itself downshiftable, because it downshifts to RIP.

But unfortunately, RIP is not downshiftable, because QIP is not a word.

Altogether then, we might say that TIP was downshiftable twice: TIP -> SIP -> RIP.

Can you find a word that is downshiftable three or more times?


The best word I could think of before I fell asleep last night was 3x downshiftable. When I woke up this morning, I wrote a program to see if my computer could do any better. It found six words that were 3x downshiftable (mine was in the list), as well as a single 4x downshiftable word! Happy hunting.

Fine print: In case you were wondering what to do with words that begin with A, let's agree that A always downshifts to Z, as in AERO -> ZERO. (Not that AERO is a legitimate word, it's just the best example I could think of to illustrate the concept.)


2. A word problem. This one is for math-major types (solution here).

John picked up a notebook and saw that there was a positive real number written on each page. The product of all the numbers was e^(S/e), where S was the sum of all the numbers. Prove that S is not an integer, and find the average of the numbers in the notebook.

Friday, January 7, 2011

Achtung!

Seen today on Google News:


BBC caught the error quickly; if you click the link, here is what you see:


Since we're doing journalism again today, I'll end by linking to something funny I read that relates to my earlier post about science journalism.