It’s all about the units

Oh come on now! Has the journalist who wrote this story about how much the earth moved been watching THAT much Star Wars?

And just in case it's not clear what I'm talking about in Star Wars (I'll get to the newer post in a second) it's when Han Solo is bragging to Obiwan Kenobi about how fast the Millenium Falcon is. Obiwan had, in essence, asked "So how fast is it?" And Han answered (again paraphrasing a tiny bit) "It made the Kessel Run in less than 12 parsecs. It's fast enough for you, old man."

Well, that was all I got to see during that screening because they threw me out of the theatre. I mean, I had to stand up and scream "WHAT?!! A parsec is a unit of distance, not a speed or a time interval." You'd think the audience would have welcomed the observation but noooo.

Anyway, when's the last time you asked someone if their car was fast and they answered, "Hey, I made the In-N-Out burger run in less than 2 miles." Never, that's when. Sheesh. (And yes, I know they've since worked feverishly to come up with a lame explanation of why it might have somehow made some sense. Not buying it. The answer is that Lucas simply blew it. Of course, he blew it a lot less with that than with entire movies later in his life (The Phantom Menace comes to mind) but you get the point.

So, what am I on about now? Just this Yahoo report of how the Chile earthquake may have "shortened days on Earth!" If you read it, you'll find the interesting line:

"… also found that it should have moved Earth's figure axis by about 3 inches (8 cm or 27 milliarcseconds)."

Yoicks! How fascinating! Because I know that inches is a unit of length and seconds of arc is an angle. These are not the same. Not even close. When I tell someone seeking directions to go to that sign up ahead and then turn 90 degrees to the right it's going to be a whole lot more helpful than saying to go there and turn 2 yards to your right. And when buying pants I'd rather tell them my inseam is 32 inches, not 17 degrees. (I wonder what kind of pants 17 degrees would result in?)

So, having read it, I figured the science guys knew what they were talking about and it was the Yahoo scribe who couldn't quite grasp the details. So I thought for a sec and concluded that probably the science guy had said the ONLY thing that made sense, namely that the angle of an axis had shifted. But how to explain that to the Yahoo scribe? I know, the science guy probably thought, I'll put it in physical terms by saying that a shift of 27 milliarcseconds would mean that a point previously HERE on the surface of the earth would now be THERE. Just like what I've drawn below. A is the angle they're talking about (drawn WAY bigger than reality) and the two red dots show the shift on the Earth's surface.

 

So let's do the math. There are 360 degrees in a circle. Each degree has 60 minutes and each minute has 60 seconds. That's right, there are 1,296,000 seconds in a circle. So if you evenly divided an entire pumpkin pie into 1,296,000 slices, each slice would have an angle (at the sharp end) of one second. (Yes, they confusingly decided to use seconds to denote an angular measurement AND a time measurement. At least they added "arc" to it.)

A milliarcsecond is one thousandth of an arcsecond. So there are over a billion of these in a circle. That's pretty sharp.

Well, now it's easy. The circumference of the Earth is 24,800 miles. So what's 24,800 divided by 1,296,000,000? It's 0.0000191 miles. 5,280 feet in a mile so 0.1 feet. 12 inches in a foot so 1.2 inches. The total angle is 27 milliarcseconds so let's multiply by 27 to get 2.7 feet. WHAT?! But, but, they said it was only three inches! Did I do something wrong? How depressing. Hold on, just waaaait one second. If we read further in that piece we find:

"Strong earthquakes have altered Earth's days and its axis in the past. The 9.1 Sumatran earthquake in 2004, which set off a deadly tsunami, should have shortened Earth's days by 6.8 microseconds and shifted its axis by about 2.76 inches (7 cm, or 2.32 milliarcseconds)."

So earlier they'd said 3 inches and 27 milliarcseconds and now they're saying 2.76 inches and 2.32 milliarcseconds. See the problem? The inches are almost the same but the angle measurements are off by ten times. 27 as opposed to 2.32. What do I conclude? That not only did these Yahoo scribes confuse themselves with lengths and angles, but they also got the angle WRONG. It wasn't 27 milliarcseconds, it was 2.7 milliarcseconds. Because if we now use 2.7 instead of 27 we get a motion shift on the Earth's surface not of 2.7 feet but of 3.3 inches! YAY! 

So once again we see two things. First: Math is Fun! It lets us understand the world around us. Second: Reporters aren't so great with their listening and remembering skills. And finally (bit of a corollary on the last one): Don't trust what you read. Not now, not ever. Check it three ways from Sunday before you believe it. Because, and I can't stress this enough, it's SO likely to be wrong. (Man, I sure hope I didn't overlook some typos in this one …)

 

- And that's today's word from the bird