The Pendulum Swings

Posted by jns on January 30, 2008

Sometimes I’m just reading, minding my own business, when the oddest things smack me squarely in the forehead. For instance:

As believers in faith and ritual over science, perhaps it’s not surprising that they [Evangelical Christians, as it turns out] failed to heed the basic laws of physics.

Most people understand that when a pendulum is pushed too far in one direction, it will eventually, inexorably swing back just as far to the opposite side. This is the natural order of things, and it tends to apply across the board — even to that bulwark of chaos theory, politics.

[Chez Pazienza, "Losing Their Religion", Huffington Post, 30 January 2008]

Whatever is this person talking about and where did s/he get the crazy notions about “the basic laws of physics” on display in these few sentences? (It seems about as nonsensical to me as people who use “literally” to mean “really, really metaphorically”.)

Based on the laws of physics, I believe that a pendulum is a physical object that swings back and forth, often used to keep time. I also believe that if it’s pushed far enough in one direction is will eventually break or, at the very least, enter a non-linear mode of oscillations. In my book, it is in the nature of pendula, even when swung a little in one direction, to swing in the other direction, and then back again in the original direction.

It is this oscillatory nature of the pendulum that is referred to in the metaphorical pendulum of politics and public opinion. Perhaps our author is thinking of a spring that, when squeezed, or stretched, in one direction will spring back just as far in the opposite direction?

As for politics being the bulwark of chaos theory — WTF? Someday, perhaps when we have more time, we’ll talk about some interesting history and results in chaos studies, but I don’t think politics will get mentioned, alas.

A pendulum is a fascinating thing, of course. Its use in clocks as a timing governor^* is traced to Galileo’s observation that the period of oscillation depends only on the length of the pendulum and not on the amplitude of its swing. The period (“T”) depends only on the length (“L”) of the pendulum and the acceleration due to gravity (“g”–a constant number):

Now, this is really an approximation with some assumptions like a) the pendulum has all its weight at the swinging end; and b) the amplitude of the swing isn’t too big. But it’s really a very good approximation, good enough for very precise horological instruments.

This equation tells us a couple of interesting things. One is that, because of the square-root sign over the length, if you want to double (multiply by 2) the period of a pendulum you must increase its length by 4; likewise, for half the period make the length one-fourth the original.

This also tells us that tall-case clocks tend to be much the same size. Generally speaking, they are constructed to house a pendulum with a two-second period, i.e., a pendulum that takes precisely one second to swing either way, or one second per tick, one second per tock. The length of such a pendulum is very nearly 1 meter.

At our house we also have a mantel clock that is, not surprisingly, a little under 12 inches tall because it has a pendulum with a period of 1 second, i.e., one second for a complete back-and-forth swing; such a pendulum has a length of about 0.25 meters, or one-quarter the tall-case clock’s pendulum.

Many tall-case clocks that I’ve seen have a pendulum whose rod is actually made from a flat array of a number of small rods, usually in alternating colors. This is a merely decorative vestige of the “gridiron pendulum” invented by master horologist John Harrison in 1720. The pendulum is constructed of two types of metal arranged so that the thermal expansion of one type of metal is compensated for by the thermal expansion of the other. (It’s easiest to look at an illustration, which is discussed here.)
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^* The pendulum, coupled with an escapement mechanism, is what allows a pendulum clock to tick off uniform intervals in time.

Sing a Song of Science

Posted by jns on January 16, 2008

As so often happens, this began innocently enough.

It all started on Monday, when a friend of mine sent me a YouTube link, claiming that he had found the prefect theme song for Ars Hermeneutica’s Sun Truck project. Indeed he may have done. The song was called “Why the Sun Shines?”. Fans of the group called “They Might Be Giants” will find the song familiar, because TMBG appear to have performed the song frequently, and many versions and performance recordings exist. This one is my favorite so far.

Then, in an amazing bit of thought convergence, on Tuesday night, another friend announced that he had found the perfect theme song for the Sun Truck project!

“Oh?” I asked, innocently enough. “Does it begin with the line ‘The sun is a mass of incandescent gas…’?”

He was a bit deflated, but only a bit. Being a big fan of very alternative music, his version was a mash-up called “Shining Sun Flash”, put together from Moog Machine’s “Jumpin’ Jack Flash,” Tom Glazer’s “Why Does The Sun Shine?,” and Earth Wind & Fire’s “Shining Star”. It comes from an online album of extraterrestrially themed music called “Sounds for the Space Set“.

This did get us some more information about the song, though, the suggestion that it was originally performed by one Tom Glazer. I decided to do a little follow up to verify that and maybe look into getting permission to use the song with the Sun Truck project.

Well, a little follow up turned into the beginning of a whole project about science songs, a worthwhile topic in itself. I’ve only scratched the surface.

The song “Why Does the Sun Shine?” was indeed first performed by folk-singer Tom Glazer. The song first appearance was as part of a six-LP set of recordings known collectively as the “Singing Science Records” — or, “Ballads for the Age of Science” (Wikipedia entries for Glazer or Zaret differ on this fact).

That 6-LP series contained dozens of songs on science written by Hy Zaret^* (lyrics) and Lou Singer (music), produced by Zaret in the late 1950s and early 1960s. The albums,

• Space Songs
• Energy & Motion Songs
• Experiment Songs
• Nature Songs
• More Nature Songs

were packed with songs that had titles like:

• Planet Minuet
• Ultra Violet And Infra Red
• It’s A Magnet
• Warm Fronts, Cold Fronts
• Why Do Leaves Change Their Color
• How Does A Cow Make Milk

and, of course, “Why Does the Sun Shine?”. Two of the albums were performed by Tom Glazer.

I was delighted to find that all of the songs on all of the (long out of print) albums are preserved and available online, at the “Singing Science Records” page of Jef Poskanzer.

The song “Why Does the Sun Shine?” appears to have a unique cultural status. Before this week I was blissfully ignorant of its existence, but plenty of other people have enjoyed it for years. Not only that, but it has enough status that its lyrics, for reasons that are not entirely clear to me, appear on a web page served by the National Institutes of Health. At least it saves me the trouble of reproducing them here, although they fail to mention that the couplets following the ellipses are done in interrupted voice-over. But you’ll notice that if you listen to one of the recordings available.

Now, that didn’t quite exhaust the subject for me. While I was searching for information about Tom Glazer and the origins of this particular song, I turned up several fascinating articles, web pages, and databases devoted to the topic of science songs. Hey, I have to put the links somewhere!

• The New York Times article referenced in the note below, is about a young musician named Timothy Sellers who, along with his band Artichoke, had (at that time) been working on a project to record 26 songs he wrote celebrating the lives of historic scientists, one for each letter of the alphabet. At the time of the article they had just released “26 Scientists: Volume 1, Anning to Malthus”. I admit that I haven’t yet heard any of the songs.

Science songwriting is a little-known avocation indulged in by many working scientists; in many cases their results deserve to remain little known. One sees occasional efforts shared, for example, in the pages of Physics Today. Having found several source-pages for these delightful treasures, I didn’t want to lose track of them again.

• New Scientist, on 28 June 2007, published a delightful article by Gaia Vince called “Top 10: Science Pop Songs“; along with all the appended comments, it’s a good survey of the state of the art, such as it is.
• Walter Smith, of Haverford College, has compiled and annotated a magnificent bibliography of Physics Songs as part of the project he calls PhysicsSongs.org.
• Greg Crowther, who is on the faulty at the University of Washington, apparently likes to write and perform his own science songs.
• But not only does he make his own, Greg Crowther maintains MASSIVE (“Math And Science Song Information, Viewable Everywhere”), a database of science and math songs.

There, perhaps that will keep us busy for awhile. I fear that I’m not through with this topic.

Oh dear, it seems that I even forgot to mention Tom Lehrer!
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^* There is an interesting side-controversy here about the true author of the songs, or rather, about the real Hy Zaret. The name Hy Zaret is associated with the song “Unchained Melody“, which he wrote. We’re told may be the most recorded song of the 20th century. No doubt because of its popularity, there is a person named William Stirrat who claims that he wrote the song “Unchained Melody” using the pseudonym Hy Zaret.

Wikipedia assures us that Stirrat is an impostor, but the page for Zaret notes that the false claim has gotten around. In particular, I myself quickly found that the false information had gotten as far as the New York Times, where one finds this mention:

Around the same time [late 1950s], William Stirrat, an electronics engineer, co-produced six albums of science songs for children (“Why Does the Sun Shine?” and “Vibration”). Mr. Stirrat, whose songwriting nom de plume was Hy Zaret, was better known as the person who wrote the lyrics to “Unchained Melody.”

[Michael Erard, "When You Wish Upon an Atom: The Songs of Science", New York Times, 17 May 2005.]