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Jurors in Albany City Court last week had a dilemma on their hands. Is a 75-gram bag of marijuana greater than or less than two ounces?

According to this story in today’s Albany Times-Union, the six jurors on the case used the measurements on the bottom of a box of crackers and a jar of peanuts to calculate the conversion factor between ounces and grams.

“We were stumped, and I said, ‘Wait a minute, maybe we can figure this out from these food packages,’ ” No. 3 said. “The crackers listed 1 pound and in parentheses was the number of grams and it was some high mid-400 number. The peanut container, however, said 10 ounces, 28.3 grams per ounce, “so that’s easy math,” he said.

It’s great that the jurors took the time to get it right. If the jurors had collectively decided that the math was too difficult and elected to convict on the lower charge out of laziness, I’d be seething as I write this post.

On the other hand, it’s unfortunate that of the six jurors in the room, only one had the mathematical thought required to realize he could calculate the conversion factor between grams and ounces.

And what about the court? The insistence of No. 3 that he could use the ten-ounce number but not the 400+-gram number because the smaller number was “easy math” implies that they didn’t even have a calculator to work with. Everyone should be able to do this on paper, but — no calculator? Come on.

What irks me the most about this story is that it exists in the first place. Apparently now you can get an article in the region’s most prominent newspaper for successfully performing a unit conversion. That this story was published only continues to subtly reinforce the message that becoming fluent in mathematics is a Herculean feat that only clever people like juror No. 3 can attain.

(Tip-of-the-triple-beam-balance to All Over Albany for the link to the story.)

Today’s xkcd is, like most of Randall Munroe’s comics, genius.

Converting to Metric

The jokes are, of course, funny. But Munroe makes a really good point here in his top-center “key to converting to metric”. Students never get a really good sense of what metric is because of how it’s presented. Just about every teacher says something to the effect of, “This is an inch, this is a foot, this is a pound. There are centimeters and meters and kilograms too, but you’ll just about never use them.”

We’ve all seen it in textbooks. There will be a passage like this: “The average weight of an American man is 175 pounds (79.379 kilograms).”

A metric conversion, when it’s given, is a complete afterthought. It’s presented with a ridiculously high number of significant figures, fresh from the calculator of the editor responsible for making sure the book sells well in Canada too.

What does this say to students? Everyone loves 175 pounds! Who would really give their weight as 79.379 kg anyway? Screw the metric system!

Even favoring English units over metric, my former students, surprisingly, didn’t really know how heavy a pound is or how far 100 feet is. Math teachers spend so much time teaching students that there is one correct answer that they forget how important estimation is in real life. So we might as well work on drilling centimeters and kilograms into their brains while they’re still open to anything.

Metric isn’t about conversions, it’s just another way of seeing things. It’s a slightly different language, one that the entire rest of the world is comfortable with.

Americans have a world-famous sense of entitlement. Our rabid adherence to meaningless tradition generally leads us to avoid that which is easy, sensical, or superior, in favor of that which is more complex or vastly more expensive. (How many Sacagawea dollars have you seen around lately?)

Despite all this, America really does use metric when it counts. Scientists use the metric system pretty much always. Engineers use metric as much as possible, though they’ll still pull out a twelve-inch ruler when working with old toolsets or equipment. Does it matter that speed limit signs say “50 mph” instead of “80 km/h”? Probably not.

But despite the economic downturn, globalization is still happening. Something as apparently inconsequential as our preferred system of measurement is important so that we can remain conversant with the rest of the world. It’s important for our students and us to become not just familiar with metric, but comfortable with it. Not just as a means to convert numbers from one language to another, but as a way for all of us to speak the same numerical language.

The International Earth Rotations and Reference Systems Service has announced a leap second will be inserted into the calendar immediately before the stroke of midnight on January 1, 2009.

If you’re a real geek and are sitting at your PC rather than partying on New Year’s Eve, run the date command once per second around midnight London-time. The time as reported would progress like this:

Wed Dec 31 23:59:56 UTC 2008
Wed Dec 31 23:59:57 UTC 2008
Wed Dec 31 23:59:58 UTC 2008
Wed Dec 31 23:59:59 UTC 2008
Wed Dec 31 23:59:60 UTC 2008 (?!)
Thu Jan 1 00:00:00 UTC 2009
Thu Jan 1 00:00:01 UTC 2009
Thu Jan 1 00:00:02 UTC 2009

Why?!

A leap second is inserted into the calendar whenever the time as measured by a collection of atomic clocks (UTC) and the time as measured from the stars (UT1) differs by more than 0.9 seconds. If there is a difference, a second (or two, in extreme cases) can be added or subtracted from our “official” time. This brings our clock time (called TAI) as close as possible to the Earth’s rotation, while still maintaining a regular clock-tick second.

The U. S. Naval Observatory is the official time-keeping entity of the United States. They currently host 34 cesium clocks and 14 hydrogen-maser clocks that together provide an exceptionally stable second. The USNO Time Service Department hosts a wonderful reference for all things time. In particular, their summary systems of time is a good (if not confusing) overview of the different time scales.

There are a few standards for leap seconds. Leap seconds are only added at two points each year — the last second of June 30 or December 31. They’re announced at least a few months ahead of the leap second — this allows plenty of time to alert those who really do need to worry about this stuff. Leap seconds occur simultaneously at all points around the world. Because UTC is based on Greenwich mean time, the leap second will occur then. (For those of us on the east coast of the United States, five hours behind GMT, the leap second will occur at 18:59:60 EST on December 31, 2008.)

Most clocks aren’t precise enough to care. Your bedroom alarm clock probably deviates UTC by more than one second, unless you’re a complete time pedant (or you’re just really lucky). Being off by one additional second (or one fewer second, depending on whether your clock is slow or fast) isn’t going to make any considerable difference.

Some clocks do care. The GPS system’s clocks started at zero at midnight UTC on January 6, 1980. There have been fourteen leap seconds since this date, and so the GPS system runs fourteen seconds faster than UTC. After the next New Year’s party, GPS will be an even quarter-minute faster than UTC.  The lesson?  Don’t synch your atomic clock to your GPS receiver.

If you have one of those fancy-dancy radio-based atomic clocks and you happen to be standing near it at midnight, I’d love to see if at 23:59:59 UTC it hangs for two seconds instead of one.  If you get video of this I’ll give you a dollar.

Thanks, Tom, for the heads up on the upcoming leap second.

Scientists and nonscientists throughout much of the civilized world use a standard set of units called the Système Internationale, or SI for short. You probably know it by its more common colloquial name, the metric system.

The metric system is comprised of a series of base units upon which all other units are derived. The most important of these base units are the meter (length), kilogram (mass), second (time), kelvin (temperature), and ampere (electric current). There are also other derived units that are created from combinations of the base units. For example, a velocity is measured in terms of a distance traveled divided by the total time of the trip. The derived unit is distance divided by time, or meters divided by seconds (which we usually write m/s and pronounce meters per second).

In order for measurement to be as accurate as possible, the units must be defined as accurately as possible.

How might you define a unit of “one foot”? You might say that a foot is twelve inches or one-third of a yard or 1/5280 of a mile. But these aren’t definitions: these are merely conversion factors, to convert from one unit to another. Go ahead: try to come up with a definition for the meter that depends on a fixed unit that will be constant for all time. Bet you can’t do it.

Various standards of nature have been adopted to define the base units. Over time, artifacts have been replaced with actual physical definitions. A meter was first defined as one ten-millionth of the distance between the north Pole and the Equator (as measured through Paris, France). Next the meter was defined as the distance between two lines on a metal stick in a vault. It was finally redefined in 1983 as the distance that light travels in 1/299,792,458 s. Of course, this requires a definition for the second, but thankfully we have a similarly confusing yet still physically accurate definition there too.

The kilogram is another story. It’s 2007 (last time I checked) and there’s still no physical definition for the kilogram. The current kilogram is a cylinder made from a platinum-iridium alloy sitting in a vault in Paris. Actually, there are quite a few of these kilograms in vaults around the world, and every couple years they all get together for a big reunion. They’re compared against one another, cleaned and cared for, and recalibrated as best as possible.

This isn’t optimal because our base unit, the kilogram, could change if too much dust gets in the air in the vault or even someone drops it! Ultimately, there needs to be a way to fix the kilogram in terms of naturally-occurring phenomena, not arbitrary human-chosen artifacts.

This is actually a really hard problem.

News was released this week to change this. Australian scientists of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) are proposing to produce perfect spheres of silicon which will both serve as artifacts and fix the definition of the kilogram. In essence, the kilogram will be defined as the number of silicon atoms in such a sphere.

Why even produce an artifact? Why not just define that a kilogram is an exact number of silicon atoms, and leave it at that? I’m not sure. I suspect that after 100+ years of having an artifact kilogram, the scientific community has grown to depend on such an artifact. Regardless, this is at least a positive step, and the scientific community will eventually wean itself from the artifact kilogram.

This is an actual letter written by Connie M. Meskimen of Hot Springs, Arkansas, published in the Arkansas Democrat-Gazette on April 16, 2007.

You may have noticed that March of this year was particularly hot. As a matter of fact, I understand that it was the hottest March since the beginning of the last century. All of the trees were fully leafed out and legions of bugs and snakes were crawling around during a time in Arkansas when, on a normal year, we might see a snowflake or two. This should come as no surprise to any reasonable person. As you know, Daylight Saving Time started almost a month early this year. You would think that members of Congress would have considered the warming effect that an extra hour of daylight would have on our climate. Or did they?

Perhaps this is another plot by a liberal Congress to make us believe that global warming is a real threat. Perhaps next time there should be serious studies performed before Congress passes laws with such far-reaching effects.

CONNIE M. MESKIMEN / Hot Springs

I’m hoping that Ms. Meskimen is getting her share of ribbing from her friends and colleagues, and it is not my goal to soil her good name on the Internet by continuing to poke fun at her. I’m sure plenty of future blog posters will do that anyway once they get their meathooks on this little story. Here at Physics is Phun we (okay, I) aim to educate the general populace, so I won’t mention the extent to which Ms. Meskimen is a complete dolt.

Daylight Saving Time has a long and varied history in this country. The idea was supposedly started by Benjamin Franklin, but the article in which he suggested the French shift their clocks was satirical. The concept really wasn’t even necessary in the United States until the existence of the transcontinental railroads. Until then, each city with a clock kept its own time based on the exact moment when the sun reached the zenith, the highest point in the sky. Once the means existed for people to travel distances far enough to notice these tiny differences, the ideas of standard time and time zones were born.

Much to the chagrin of Ms. Meskimen, daylight saving time does NOT add any daylight to the day. The Earth rotates at the same rate no matter what our clocks say. The published sunrise and sunset times for a location are those times at which the Sun would appear to cross the horizon (if the horizon were visible). The day length is the same for all points sharing the same latitude line across the entire Earth.

An honorable mention in the Hall of Shame voting goes to the Arkansas Democrat-Gazette for publishing this letter in the first place. I don’t know how many letters to the editor the Arkansas Democrat-Gazette receives, but they must be really hurting to publish something like this. Or that means that no one at the paper detected anything wrong with Ms. Meskimen’s argument, which is what I suspected happened.

Thanks to An American in Distress for this one. If you don’t trust me (or her), the original scanned newspaper clipping is here.