ZimBlog

Merry Christmas

2011-12-30T17:09:00.000-05:00

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!

Richard P. (Rip) Zimba, 1926-2011

2011-09-12T13:31:00.000-05:00

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.

For My Wife on Mother's Day

2011-05-08T03:36:00.000-05:00

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

Spot the error

2011-03-01T15:05:00.000-05:00

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 clichés.

On the Pleasures of Constraints

2011-02-22T10:55:00.000-05:00

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.

Numbers Don't Lie (but Michele Bachmann Does)

2011-01-26T14:16:00.007-05:00

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

Word Puzzle, Word Problem

2011-01-10T11:49:00.000-05:00

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.

Achtung!

2011-01-07T12:44:00.000-05:00

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.

A couple of puzzles

2010-12-27T18:57:00.000-05:00

Since we just had a geometric puzzle, let's go numerical this time:

1. A probability puzzle

By the time the movie started, there were 91 men and 121 women in the theater. If the first moviegoer to enter the theater was a man wearing glasses, and the second was a woman not wearing glasses, then what is the probability that equal percentages of men and women in the theater were wearing glasses?

Solution here.

2. Fun(?) with fractions

I saw a survey in the newspaper once in which 33% of the people surveyed said "no" to something, while 67% said "yes." Whenever I see something like that, I always think, "Huh - I wonder if they only asked three people."

Well, suppose you saw it reported that 34% of people surveyed answered "no" to something, while 66% said "yes." What is the smallest number of people who could have participated in this survey? Assume that the people reporting these results have rounded their figures to the nearest whole percentage point.

Solution here.

***

I'll end with a graph that shows what the solution to puzzle #2 would be for any possible pair of percentages adding to 100%. Don't study the graph too carefully if you are going to solve the puzzle yourself!

Merry Christmas! (Solution to the Optimization Game)

2010-12-21T00:07:00.001-05:00

December 21st! Well, it's winter, and once again America turns its collective thoughts to the Winter Biathlon.

Hah - just kidding.

But I confess I was thinking of the winter biathlon the other day, the reason being that it's an optimization problem of sorts. Winter biathlon is the sport in which an athlete's score depends on speed (cross-country skiing) as well as accuracy (rifle marksmanship). So, just as in other optimization problems, you won't do your best by maximizing over each variable separately. If you ski too fast, your heart rate will spike and your marksmanship will suffer; but skiing too slowly, or taking too much time with your aim, will hurt your skiing time as well. An optimum approach balances competing factors.

The same is true for the optimization game I posted a while back. Recall that in order to play the game, you choose four distinct points on the unit circle. Your score is the area of your quadrilateral, plus the area of the largest triangle that may be formed by deleting one of your points.

Supposing for a moment that you wanted to maximize the area of the quadrilateral, then you would choose four points to form a square, for a score of 3. But this would mean settling for a fairly small triangle (area 1). Alternatively, if you wanted to maximize the area of the triangle, then you would choose three of the points to form an equilateral triangle; but this would mean settling for a fairly small quadrilateral. So, just as in the winter biathlon, the optimum approach requires that we sacrifice a little of the quadrilateral score and a little of the triangle score for the good of the sum.

My own intuitive solution to the area puzzle was as follows. Begin with a square, oriented as a diamond (with points at the four cardinal points North, South, East and West). Given four points in this configuration, the score is 3. Now imagine grabbing hold of the points at East and West, and nudging them both slightly northward. Will the score increase or decrease?

* Because the original square was a maximal-area quadrilateral, when you nudge the two points northward, the area of the quadrilateral will not change, to first order. (We say that the area is "stationary.")

* Meanwhile, the area of the triangle based at the south pole will increase to first order, because the altitude of the triangle will increase to first order, while the base remains unchanged to first order. (The tangent to the circle is vertical at the East and West cardinal points.)

* So altogether, when we nudge the East and West points slightly northward, our score increases, to first order. Hence, this nudging is a good way to improve on the square configuration.

* Of course, if we nudge the points too far toward the north pole, then our score will suffer, because ultimately the score approaches zero as the points reach the north pole. Thus, there is a local optimum configuration, in the shape of a kite, that improves upon the square configuration.

A little geometry, together with some first-semester calculus, suffices to find the optimal shape in this family:

This shape scores about 3.1488, or to be exact

Anyway, this is as much thinking as I did before posting the puzzle. I was confident that the kite was best, but I didn't want to prove it because I hoped it would be at least theoretically possible for someone to beat my score. But I'm afraid that the intuitive solution presented above turns out to be the best. A sketch for a workmanlike proof follows.

In the meantime, Merry Christmas all! Best wishes for a healthy and happy 2011.

*****

Consider any four distinct points on the unit circle. Label the points P,A,B,C as follows: first choose a point so that the remaining three points form a triangle of maximal area in the configuration; label the chosen point B. Then label the points adjacent to B by A and C in such a way that A,B,C are traversed counter-clockwise around the circle. Label the remaining point P. If necessary, rotate the configuration so that P has coordinates (1,0) - here shown at the south pole - understanding the unit circle to be x^2 + y^2 = 1. Then points A,B,C have coordinates given respectively by (cos a, sin a), (cos b, sin b), (cos c, sin c), where 0 < a < b < c < 2 pi:

By construction, triangle PAC is a triangle of maximal area in the configuration, so the score for the configuration can be expressed as twice the area of triangle PAC plus the area of triangle CBA. Using vector cross products, the score can be expressed in terms of a,b,c as

2S = 2 sin(a) - 2 sin(c) - sin(a-c) + sin(c-b) + sin(b-a).

At this point, it is a relatively straightforward exercise in third-semester calculus to show that the optimal configuration, unique up to rigid motions of the circle, is the kite we arrived at by intuition.

I am for you, and you are for me, not only for our own sake, but for others’ sakes

2010-12-13T22:53:00.000-05:00

I came across an article in Slate today written by an old acquaintance of mine, the constitutional scholar Kenji Yoshino. The topic of Yoshino's piece is a newly published scholarly paper entitled "What Is Marriage?" which argues that the state need not, and indeed should not, recognize same-sex marriage. You can find the paper here. In his piece for Slate, Yoshino argues that the authors' position actually does more to cheapen the idea of marriage than to protect it. This made me curious to read the paper itself. (Warning: there is frank language in what follows.)

The paper begins by arguing that

some sexual relationships are instances of a distinctive kind of relationship - call it real marriage - that has its own value and structure, whether the state recognizes it or not, and is not changed by laws based on a false conception of it.

The authors then set out to discover what this real marriage is. The major premise is this:

As many people acknowledge, marriage involves: first, a comprehensive union of spouses; second, a special link to children; and third, norms of permanence, monogamy, and exclusivity.

This sounds reasonable, at least to me. But I started scratching my head when the authors began to develop these principles. Here is the implication they draw from the principle that marriage necessarily involves a comprehensive union of spouses:

Because our bodies are truly aspects of us as persons, any union of two people that did not involve organic bodily union would not be comprehensive—it would leave out an important part of each person’s being.

I think what they are trying to say is what Whitman said when he wrote "Yet all were lacking, if sex were lacking." One can agree with this, it seems to me, and still deny that anything has been proved in this part of the paper. The authors have merely clarified their own favored meaning for the term "comprehensive." Others might consider a union "comprehensive" if it involves profound and lasting feelings of love and trust. (The authors consider such people "revisionists.")

The authors' point is also confusing because it fails to attend to time. It cannot be uncommon for married couples in their fifties, or even in their forties, to all but set aside their 'organic bodily unionizing.' We still consider them really married. Perhaps the conclusion the authors wanted to draw was that "any union of two people that did not, at some point in the union's history, occasionally involve organic bodily union, would not be comprehensive." (Or is real marriage a time-dependent concept, like some kind of indicator light on the headboard that illuminates when you're having sex?)

The authors continue:

This necessity of bodily union can be seen most clearly by imagining the alternatives. Suppose that Michael and Michelle build their relationship not on sexual exclusivity, but on tennis exclusivity. They pledge to play tennis with each other, and only with each other, until death do them part. Are they thereby married? No. Substitute for tennis any nonsexual activity at all, and they still aren’t married: Sexual exclusivity—exclusivity with respect to a specific kind of bodily union—is required.

I find this confusing, because the authors were supposed to be talking about comprehensiveness (the first principle), yet they've helped themselves to exclusivity (the third principle). And they also seem to be confusing necessity with sufficiency. What I mean by that is, exclusivity with respect to a specific kind of bodily union is required...OK, say for a moment that we agree with that. But does exclusivity with respect to a specific kind of bodily union suffice? Presumably not - there is that second principle yet to attend to, the one about the "special link to children." Yet if exclusivity with respect to a specific kind of bodily union is not sufficient, then why are we denigrating tennis as not being sufficient? Perhaps we should be asking whether tennis is necessary to be married? Tennis with the kids, maybe? By now I'm confused enough to believe anything.

Then we get to the good parts. Assuming I have parsed all of the euphemisms correctly, I think the authors next argue that 'organic bodily union' only occurs when a woman accepts a man's penis into her vagina. ("organic bodily unity is achieved when a man and woman coordinate to perform an act of the kind that causes conception.") Interesting. Let's recap the argument then:

1. A real marriage requires a penis to enter a vagina. (At least once? On date nights? The authors are unclear.)

2. Mathematically then, it follows that a real marriage requires an odd number of penises and an odd number of vaginas.

3. But in a typical same-sex relationship, there are an even number of penises or an even number of vaginas.

4. Therefore, same-sex relationships cannot be real marriages. QED

The paper goes on for quite a while, and frankly I got tired of reading it. But it seems as if the main argument is really the one about penises entering vaginas. Thinking about penises entering vaginas, say the authors, helps us to make sense of real marriage as a harmonious complex of organic bodily unions, special links to children, and norms of permanence and exclusivity.

OK - if you say so. Or not. Again, I'm not sure what has been proved in this paper. It seems to be a great, big, superheated version of a bumper sticker I saw once: "God Made Adam and Eve, Not Adam and Steve!" Anyway, I'm reminded of another work of philosophy I read not long ago: Frankfurt's On Bullshit.

Science Reporting and Evidence-Based Journalism

2010-11-30T12:25:00.003-05:00

I tore an article out of The American Scholar about a year ago and crumpled it into my pocket to think about later. The pages turned up again this weekend when my wife was sorting through one of the rat’s nests of loose papers I maintain around the house. The article is an extract of a speech by a Washington Post reporter named David Brown. The speech is available here:

http://www.theamericanscholar.org/science-reporting-and-evidence-based-journalism/

Brown talks about ways in which science journalism could be a lot better than it is today. He argues that science journalism, done better, could be a model for improving journalism as a whole. The implication is that our democracy could certainly use some better journalism.

You'd probably be using your time more wisely if you were to read the speech instead of reading this blog post, but I'll carry on for a moment under the assumption that you have time for both.

According to Brown, the most important thing science journalism has that makes it a good model for journalism as a whole is evidence. When you read a story, says Brown, "[N]otice how much space is devoted to describing the evidence for what is purportedly new in this news, and how much is devoted to someone telling you what to think about it. Ask yourself whether there is enough information in the story to permit you to reach your own opinion about its newsworthiness. I think you’ll be surprised. If there isn’t enough information to give you, the reader, a fighting chance to decide for yourself whether something is important, then somebody isn’t doing his or her job."

I decided to apply this test to a short piece of science reporting, which I reproduce here in its entirety:

Lithium, Water, and Suicide

Lithium is a staple prescription for bipolar depression and suicidal tendencies. But it is also a naturally occurring element, with traces found in most of the world's drinking water, and that raises a question: Do levels of lithium in tap water correlate with suicide rates? A recent study by a team of Japanese doctors says yes.

Published May 1 in the British Journal of Psychiatry, the study reported that in 18 municipalities in southwest Japan, towns with relatively low levels of lithium saw higher suicide rates than towns with relatively high levels. The lithium content ranged from 0.7 to 59 micrograms, much lower than the 200 to 400 milligrams usually prescribed to bipolar patients (and much, much lower than the toxicity threshold). Nevertheless, the researchers speculated that even very low levels of lithium can have a cumulative, prophylactic effect on mood swings that might induce suicidal thoughts, completely separate from the effect large doses have on mood disorders. The implication, says lead researcher Takeshi Terao in response to an e-mail inquiry, is that "adding lithium to drinking water may be useful to prevent suicide."

But even Terao admits that further study is needed. Among other concerns, not enough is known about the long-term effects of even low levels of lithium, according to Dr. Allan H. Young, the director of the Institute of Mental Health at the University of British Columbia. Still, given the immense social costs of suicide, the team in Japan concluded in a follow-up paper that adding lithium to drinking water offers "an easy, cheap and substantial strategy for worldwide suicide prevention."

Although this article is better than most in that it includes several pieces of numerical information, it still leaves us pretty hungry for the one piece of information we need: namely, how big was the observed effect?

Reporters might not always realize that publication in a prestigious journal is no guarantee that the study in question matters. Sometimes the study only proves a theoretical point. Sure, maybe the study offers convincing evidence that eating more X will raise your risk of getting Y. But what if it only raises the risk from one in a million to one in a thousand? This is hardly newsworthy. Yet it might very well get published in the newspapers anyway. The headline? "Eating X Makes You A Thousand Times More Likely to Get Y!"

Brown makes this same point when he says,

Science stories, and especially medical stories, have a really good shot of getting out on Page 1. They are inherently interesting and they appeal to what might be termed, somewhat cynically, as the narcissism of the reader. But that often isn’t enough to get them on the front page. To get there, the story must emphasize novelty, potency, and certainty in a way that, as a general rule, rarely exists in a piece of scientific research. That truth is why so many medical stories only mention the [relative] magnitude of change that occurs with a new diagnostic test or treatment, and not the absolute change it brings about.

To be fair, reporters are not entirely to blame. They don't manufacture all of the buzz. The research university itself, ever conscious of building its brand, might even be suggesting the overblown headline in its own press release. More fundamentally, a scientific journal article is itself a rarified form of reporting, and the scientist's job security depends no less than the journalist's upon having something sensational to report. The scientist certainly has no incentive to downplay his own results - not in the research writeup itself, nor later when the reporter calls for a quote.

In any event, by withholding the evidence about the magnitude of the effect observed, "Lithium, Water, and Suicide" fails Brown's basic test of science journalism. It doesn't give us the information we need to decide whether the research in question matters or not. The closest the reporter gets to the notion of effect size or importance is the final "kicker" that adding lithium to drinking water offers "an easy, cheap and substantial strategy for worldwide suicide prevention." But that quote by itself isn't evidence.

I liked Brown's speech, but I think that giving a speech about how science journalism should be better is not actually going to make it any better. Or anyway, so I thought when I read "Lithium, Water, and Suicide." That's because it was in the same issue of The American Scholar in which Brown's speech itself appeared.

Postscript

In case you're curious to find out more about the lithium research, the article is available online. Also, in a later issue of the journal, there is some interesting discussion of the shortcomings of the study. The authors do not dispute the shortcomings, rightly pointing out that the study was meant to be suggestive, and that a lot of work remains to be done before the link between suicide and lithium in tap water can be taken as established. (Note in particular that lithium intake from food is not negligible in comparison with lithium intake from tap water.) And even if the link were established as a matter of basic science, a host of other questions arise when we consider adding lithium to tap water as a public health strategy.

I wanted to find out the rationale for the statement that lithium offers an "easy, cheap and substantial strategy for worldwide suicide prevention," so I did a little digging. If you Google this phrase, you'll see what a buzz the lithium story created a year ago. It even made it onto the 9th annual New York Times "Year in Ideas" list. What you won't find so easily is the follow-up scientific paper that contains this phrase. But I finally tracked it down and paid $31.50 for a copy. The citation is Terao et al., "Even very low but sustained lithium intake can prevent suicide in the general population?" Medical Hypotheses 73 (2009), 811-812.

The striking thing about this paper is that it does little better than the American Scholar article did in explaining the absolute magnitude of the effect in question. Yes, it quotes the slope of the regression line in the original research. But the raw data for that regression were massaged in various ways, and the y-axis of the regression model is a confusing measure called "suicide standardized mortality ratio." So we are never actually told how many suicides might be prevented each year based on a given treatment model. We never find out what that model would cost to implement. We never find out what the public health benefit would be in terms of years of life saved or lost wages regained. Even order of magnitude estimates would have helped. But as it is, if we want to decide for ourselves whether the results matter, then there's almost nothing to go on. And after all, if the scientists themselves aren't providing the necessary information, then how can we expect the reporters to give it to us?

OK - Just One More

2010-09-19T21:12:00.000-05:00

I added a third animation to my previous post.

In My Ample Spare Time

2010-09-18T11:47:00.001-05:00

These two animations might bring back a few memories for my former students....

     Click for first animation

     Click for second animation

     Click for third animation

(Higher-resolution .mov files available on request.)

Rare photos from the 1930s and '40s

2010-08-08T11:13:00.018-05:00

Some news outlets are publicizing a rare collection of color photographs from the Depression-era Farm Security Administration (think Dorothea Lange). A breathtaking series of photographs is here. Below, a few that I grabbed quickly.

An optimization game

2010-07-30T11:23:00.008-05:00

Here's a game I thought of the other day while driving in my car:

Choose four distinct points on a circle of radius 1 in such a way as to maximize your score. Your score is the area of your quadrilateral plus the area of the largest triangle that may be formed by deleting one of your points.

As a warm-up, you might show that if you choose the points to form a square, then your score is 3.

My high score is shown below. Can you beat it?

(Numerically, this is between 3.14880129427 and 3.14880129428.)

The Fortune-Tellers

2010-01-18T23:11:00.010-05:00

I asked a fortune-teller my future. In answer she said: "The next fortune-teller you ask will mislead you."

I asked a second fortune-teller my future. She answered: "The next fortune-teller you ask will tell you true."

A third answered me this: "The next fortune-teller you ask will lead you astray."

The fourth would not read my future, but said: "The first fortune-teller you sought answered false."

Ginger Beef

2010-01-13T13:07:00.024-05:00

They say supermarkets are a good place to meet people, and I've certainly found that to be true. When people see you trundling down the aisle with two little redheads in tow, they're liable to drop their rutabagas and march right over. Shopping takes a little longer than it used to, but obviously I love it. Why shouldn't everybody dote on them like their daddy does?

But I wish I had a nickel for every time somebody has said, "Did you know redheads are going extinct?" Then at least I'd have enough money to do what I'm about to do, which is to offer a $100 Reward for the first person who sends me a reputable scholarly publication that draws such a conclusion. I don't think any such research exists.

Mail contest entries to jzimba@gmail.com. Offer void where prohibited; I will be the final authority as to the meaning of the terms "reputable", "scholarly", "publication", and "draws such a conclusion."

According to How Stuff Works, the coming extinction of redheads is a myth that goes around the web periodically. But that hasn't stopped everybody from quoting myth as fact. (See here for example.)

***

The other thing people often tell me is that redheads feel pain more acutely than other people do. This is more than a myth. "Increased Sensitivity to Thermal Pain and Reduced Subcutaneous Lidocaine Efficacy in Redheads" (Liem et al., Anesthesiology, 102(3), 509-514, March 2005) was a study of 30 female redheads and 30 brunettes. The redheads reported pain from cold temperatures at about 43 degrees Fahrenheit, whereas brunettes reported pain at a significantly (and significantly) lower temperature, about 32 degrees Fahrenheit. (Some data here.)

Interesting results, although my own elder daughter seems pretty impervious to the cold.

And I'd say the little one seems pretty robust too.
Subject reported feelings of euphoria upon application of the stimulus.

The Bottom Line

2010-01-06T11:03:00.004-05:00

FYI

2009-12-11T17:10:00.002-05:00

For anyone who wants to know, I have just deactivated my Facebook account. I didn't use Facebook very much, so this is just a move to simplify.

y = x - (x - y): a Consequence Thereof

2009-11-01T18:37:00.039-05:00

Last year I discovered a trick for helping myself to fall asleep at night. When I lie down in bed, I close my eyes and think about ways to prove the Pythagorean theorem. Usually I'm asleep in no time! It's very peaceful, watching those little triangles float past my mind's eye, like so many tricorn sheep leaping a stone wall.

The first two of these narcotic proofs turned out to exist already (as I noted here and here). Amusingly enough, however, the third seems to be new. Claims of novelty are never certain when it comes to the Pythagorean theorem, but in any case, you can see the proof at Forum Geometricorum, an open-access, peer-reviewed geometry journal with a recreational slant.

The idea for the proof is to use the subtraction formulas for sine and cosine to derive the trigonometric identity cos^2(x) + sin^2(x) = 1. From this identity the Pythagorean theorem follows immediately.

There are some details involved, but here is the crux of the argument. Given any x with 0 < x < 90, let y be any number with 0 < y < x < 90. Then x, y, and x-y are all strictly between 0 and 90 degrees, so we may straightforwardly apply the subtraction formulas cos(a-b) = cos(a)cos(b) + sin(a)sin(b) and sin(a-b) = sin(a)cos(b) - sin(b)cos(a). We note that:

cos(y) = cos(x-(x-y)) = cos(x)cos(x-y) + sin(x)sin(x-y) = cos(x)[cos(x)cos(y) + sin(x)sin(y)] + sin(x)[sin(x)cos(y) - sin(y)cos(x)] = cos(y)[cos^2(x) + sin^2(x)].

Hence cos^2(x) + sin^2(x) = 1. QED.

Strangely, it does not seem to have been recognized before that the identity cos^2(x) + sin^2(x) = 1 can be derived independently of the Pythagorean theorem using the subtraction formulas. (Of course, to be certain of this, one would have to comb through three centuries' worth of trigonometry textbooks!)

A note on the proof can be found at the recreational math website cut-the-knot.

***

The algebraic manipulation used above can also be represented diagrammatically using triangles; this yields a more traditional style proof, as shown here. The recursion that is apparent in the algebraic argument gets rendered diagrammatically by nesting a little proof of the subtraction formulas inside a bigger proof of the subtraction formulas.

I'm not sure whether I think of the diagrammatic version and the trigonometric version as being distinct. The style of reasoning is quite different in the two cases, although the two arguments are of course direct transcriptions of one another in some sense.

In any case, it is interesting to note that because the y parameter is arbitrary, the diagram is in a sense "flexible" - it can be drawn in infinitely many ways for any given initial right triangle. In that sense the basic argument spawns infinitely many proofs of the Pythagorean theorem. I made a movie in which each frame represents one of these proofs; you can see it on YouTube or here.

Dorothy Jean Zimba, 1931-2009

2009-11-01T17:40:00.004-05:00

On October 28, 2009, Mrs. Dorothy Jean Zimba, of North Bennington, Vermont, died in her sleep of natural causes. She was 77 years old.

Dorothy was born in Chattanooga, Tennessee, in 1931. In her first marriage, to Mr. Ray Bailey of Chattanooga, she had two sons. Later she married Mr. Richard Zimba of Dearborn Heights, Michigan; the couple had three children together and remained happily married until the end of Dorothy's life. For decades, husband and wife worked alongside one another in the family business, Rip's Drive-In, a suburban Detroit landmark during its time.

A gifted storyteller with a lively laugh, Dorothy was admired for her outgoing personality and incisive intelligence. She was a crossword prodigy and a formidable opponent in card games of all kinds. Her hobbies included needlework, gardening, collecting antiques, and painting landscapes and still lifes.

Dorothy's health began to decline in 2007, and at that time she relocated from Michigan to Vermont with her husband. She resided at Watson House and Prospect House in North Bennington, facilities in which she received kind and attentive care until her passing. Dorothy will be lovingly remembered by her husband, Richard; by her five children: Mr. David Bailey, Issaquah, Washington; Mr. Wayne Bailey, Southgate, Michigan; Ms. Intissar Greene, Mesa, Arizona; Ms. Jilly Dybka, Kingston Springs, Tennessee; and Dr. Jason Zimba, Pownal, Vermont; by her five grandchildren: Sgt. Erik Bailey, Camp Liberty, Iraq; Mr. Robert Bailey, Monroe, Michigan; Mr. Jonathan Bailey, Issaquah, Washington; Miss Abigail Zimba, Pownal, Vermont; and Miss Claire Elizabeth-Jean Zimba, Pownal, Vermont; by her two great-grandchildren, Miss Madalyn Bailey, Monroe, Michigan, and Miss Joanna Bailey, Monroe, Michigan; by her sister, Mrs. Patsy Ramsey, Ringold, Georgia; by her two nephews, Mr. Chris Ramsey, Tampa, Florida, and Mr. Barry Ramsey, Ringold, Georgia; by her grandniece, Ms. Valerie Ramsey, Tampa, Florida; by her great-grandniece, Miss Caitlyn Ramsey, Tampa, Florida; and by her many cousins.

The 'Get a Life' Principle

2009-07-28T16:47:00.010-05:00

Like a lot of people with more important things to worry about, I've been paying rapt attention to the spectacle of the so-called "Birther Movement." For my money, getting the full experience requires going to the source, such as www.obamacrimes.com. On this site, attorney Phillip Berg writes:

The Obama candidacy is the biggest ‘HOAX’ perpetrated on the citizens of the United States in 230 years, since our nation was established. Obama must be legally removed from office.

I believe that 15 to 20 million people are aware of the Obama 'HOAX,' and we must make 75 to 100 million people aware.

(Screaming uppercase in the original; ditto for the scare quotes.)

Alas, Berg might actually be correct when he estimates that 15 to 20 million people agree with him. I base this observation on the fact that in a 1999 Gallup poll, fully six percent of Americans expressed a belief that the 1969 moon landing was faked by the government. I’d like to see this as a glass 94% full. But what it would appear to indicate is that if all of the Americans who dispute the truth of the moon landing were to get together and form their own U.S. state, it would likely be the fifth largest state in the union, outranking Illinois (take that, Obama). So I’m thinking that in terms of his numbers, Berg is probably in the right ballpark. (Though "being in the right ballpark" hardly seems an appropriate metaphor for this situation.)

Another interesting site is www.obamacitizenshipfacts.org. On this page we are treated to a quote by Thomas Jefferson:

To restore ... harmony, ... to render us again one people acting as one nation should be the object of every man really a patriot.

(I guess they are taking the long way around to harmony, by seeking the removal of the President.)

A small 1994 study by Rutgers sociologist Ted Goertzel found that among the subjects studied,

Belief in Conspiracies was significantly correlated (r = .43) with a three-item scale of "Anomia" (alpha = .49) made up of items taken from the General Social Survey of 1990. These items measured the belief that the situation of the average person is getting worse, that it is hardly fair to bring a child into today's world, and that most public officials are not interested in the average man.

The Belief in Conspiracies scale was also significantly correlated (r = .21) with the item "thinking about the next 12 months, how likely do you think it is that you will lose your job or be laid off."

Volkan (1985) suggests that during periods of insecurity and discontent people often feel a need for a tangible enemy on which to externalize their angry feelings. Conspiracy theories may help in this process by providing a tangible enemy to blame for problems which otherwise seem too abstract and impersonal.

***

As the name implies, ObamaCitizenshipFacts.org is full of FACTS. Conspiracy theorists love facts – and they love FACTS even more. In FACT, in a 1999 scholarly article on conspiracy theories, philosopher B.L. Keeley stressed the importance to the conspiracy theorist of certain very special facts, which Keeley called "errant data":

The chief tool of the conspiracy theorist is what I shall call errant data.

Errant data come in two classes: (a) unaccounted-for data and (b) contradictory data. Unaccounted for data do not contradict the received account, but are data that fall through the net of the received explanation. ... For example, ... the fact that no BATF employees were in the building at the time of the [Oklahoma City] explosion [is] unaccounted-for data with respect to the received account of the bombing. Contradictory data are data that, if true, would contradict the received account. McVeigh's manifest idiocy in fleeing the scene of the bombing in a car without license plates is a contradictory datum with respect to the official account of him as a conspiratorial ringleader capable of planning and carrying out such a terrorist operation.

***

It may be that there are certain propositions which simply do not reward one's sustained attention. Take, for example, the proposition "Your mother and your father were both faithful to each other during all the years of their marriage." To adopt a position of serious doubt on this question, and then, in such a frame of mind, to scour the family archives for bits and pieces of errant data, would not bring you any closer to the truth – it would only drive you crazy. Along similar lines, philosopher Lee Basham would counsel us to avoid conspiracy theories in order to preserve ourselves from harm:

A more solid ground for the rejection of conspiracy theories is simply pragmatic. There is nothing you can do. While it would be speculative (but reasonable) to conclude that this is why many people dismiss conspiracy theory, it is a considerable reason why we should. The futile pursuit of malevolent conspiracy theory sours or at least distracts us from what is good and valuable in life.

Later in the article Basham writes:

Any number of conspiracies might be worming their way through our world order. Now what? The 'get a life' principle kicks in with a vengeance.

Keeley has additional advice:

...[We] should be careful not to over-rationalize the world or the people that live in it. Rejecting conspiratorial thinking entails accepting the meaningless nature of the human world. Just as with the physical world, where hurricanes, tornadoes, and other "acts of God" just happen, the same is true of the social world. Some people just do things. They assassinate world leaders, act on poorly thought out ideologies, and leave clues at the scene of the crime. Too strong a belief in the rationality of people in general, or of the world, will lead us to seek purposive explanations where none exists.

It would be easy to view conspiracy theorists as irrational. But as Keeley points out, their beliefs sometimes depend on an extreme faith in the rationality of others; and their dogged pursuit of errant data is in some ways a model of sober detection, similar to the work of journalists, detectives, and scientists. Keeley says something similar when he writes,

I suggest that there is nothing straightforwardly analytic that allows us to distinguish between good and bad conspiracy theories. We seem to be confronted with a spectrum of cases, ranging from the reliable to the highly implausible. The best we can do is track the evaluation of given theories over time and come to some consensus as to when belief in the theory entails more skepticism than we can stomach. Also, I suspect that much of the intuitive "problem" with conspiracy theories is a problem with the theorists themselves, and not a feature of the theories they produce. Perhaps the problem is a psychological one of not recognizing when to stop searching for hidden causes.

It’s hard to read a website like ObamaCitizenshipFacts.org or ObamaCrimes.com without becoming slightly concerned about the psychological well-being of conspiracy theorists. There is an obsessive quality to the undertaking, of course, but also a hint of something unmoored. I think of those theories of paranoid schizophrenia, according to which many sufferers from this disease may lack a "theory of mind."

[M]any patients are unable to represent or imagine the actions or intentions of other people. They lack a "theory of mind." Persecutory delusions may form because the paranoid patient cannot imagine someone else's perspective or psychological experience. Instead, idiosyncratic and ultimately sinister speculations are manufactured about the motives and intentions that govern the social world.

And now at the end of this exercise, I’m sensing that the sanity or insanity of the birthers is itself a proposition that doesn’t reward sustained attention. And the artifacts produced by people like Philip Berg on ObamaCrimes.com finally speak to me of pain. At the top of this page, we read:

12/09/08 – My brother, Norman Barry Berg, just passed away. My brother meant so much to me. I gave the attached Eulogy in loving memory of him at his funeral. I go forth in my efforts to find the truth of Obama in memory of my brother.

I guess it is time to start practicing the ‘get a life’ principle myself.

I Say, The Thing is Done

2009-05-08T13:55:00.010-05:00

In the early days of this blog, I had some things to say about physics teaching and physics textbooks (here and here, for example). Then I got pretty quiet, because I was working hard on a book of my own - and it's finally here!

The title is Force and Motion: An Illustrated Guide to Newton's Laws (Johns Hopkins University Press, 2009). To find the book on Amazon, you can click here. To order instructor's examination copies, you can click here.

I should say that although this is a textbook, I did my best to ignore the conventions of the genre and write for human beings. Much of the story is told with diagrams, and even a casual reader might be tempted to try a problem or two; many of the problems ask you only to sketch, and there are answers in the back. (Physicists, don't be alarmed: the equations are all in there. Indeed, in some ways this book exceeds the usual ambitions of an introductory course.)

My thought is that the book could be a primary text for a suitably focused course in a liberal arts college, or a course at the high school level. It's also concise enough (70,000 words) to be a supplemental text for a university-level survey course - to help students who are having trouble or who just want to dig deeper into the essential material. A friend of mine who is a returning student at Cal State Hayward had a good experience using a rough draft of the book in this way.

A third goal is to put the book in front of current and future teachers of physics at the high school and college levels.

***

The title of this post refers to my own book of course, but it's also an allusion to the original textbook on Newton's Laws: the Principia of Isaac Newton himself. One of the things I always enjoyed about reading the Principia was the style in which its mathematical proofs were written. Often there would come a moment when, having arranged all his pieces on the chessboard, Newton would imperiously announce checkmate: I say, the thing is done. The last two or three sentences would then play out the inevitable conclusion as the components of the strategy clicked into place. You can see examples on this page of the Principia.

***

I could say a lot about how my book differs from traditional presentations of Newton's Laws, but I'll save that for a separate post. Right now I want to celebrate being #5 on today's Amazon ranking of books about dynamics! (Friends and family, I owe you one.)

Majorana Representations and Platonic Solids

2009-03-28T08:25:00.006-05:00

A few years ago, I was asked to contribute a paper to a book celebrating the centenary of the birth of Ettore Majorana (1906-1938), a gifted Italian theoretical physicist who died during World War II in mysterious circumstances. I got this call because in my graduate work under Sir Roger Penrose (see here for example), I had used Majorana's representation of quantum spin states to investigate the conceptual foundations of quantum theory. (Roger had effectively rediscovered the Majorana representation just prior to my arrival at Oxford.)

I agreed to contribute a paper to Majorana centenary, but I didn't have any suitable projects in the pipeline. So, while driving down to New York one night along the Taconic - the setting for more than one productive daydream - I started thinking about spin states. Reflecting on a particular variety of spin states called "coherent" spin states, I wondered "how far from coherent" a state could get. It immediately occurred to me to look at (inverse) Majorana representations of Platonic solids. These states would, in a sense, be the opposite of the familiar coherent spin states of quantum theory, and so I gave them the name "anticoherent" spin states.

Following this chain of reasoning leads to some geometric curiosities, including a basis for complex five-dimensional space consisting of five states whose Majorana representations form a dodecahedron's worth of interlocking tetrahedra! The resulting paper is available online here (see especially the figures at the end). It was my honor to receive the 2006 Majorana Prize for it, as part of the centennial celebration of Majorana's legacy in contemporary theoretical physics.

These anticoherent states were such beautiful little objects that I felt sure they must have some physical importance. After all, coherent states are often said to be "as classical as possible," so perhaps the anticoherent states would be useful for exhibiting exotic quantum phenomena such as one encounters in quantum information theory. In the paper, I alluded to a couple of potential physical implications, but I'm not an expert on quantum information theory so I couldn't say much. But I was happy to see recently that some physicists who do know a thing or two have found some interesting physical properties of the anticoherent states! See Kolenderski and Demkowicz-Dobrzanski, "Optimal state for keeping reference frames aligned and the platonic solids," Phys. Rev. A 78, 052333 (2008), available here (subscription required).