Context and Units

By The Metric Maven

Bulldog Edition

The late Isaac Asimov once pointed out that people often use units alone to imply the magnitude of a dimension. A certain store is only minutes from your house, or a car missed another by inches and so on. Of course if the two cars were separated by 63 360 inches, they then also missed each other “by a mile.” The statement that two cars were separated by only inches as they passed each other is true, but they were not in any danger of colliding.  Using a unit without any numerical magnitude leaves one to comfortably assume a magnitude,  and trust that the person offering said unit is using it appropriately.

Years ago my father sent away for a set of cookware. The price was too good to be true, and the items that arrived were all about 25% of their expected size. I watched a consumer  advocate expose this rip-off on television. The advocate showed that using the cookware was not feasible and in one case the handle would become so hot it would burn anyone who simply used it to boil water. Many moons ago, it was apocryphally claimed that a raffle was held where the winner would get a sports car, such as a Corvette, as a prize. The winner did indeed receive a Corvette, but it was a  scale model worth only a few tens of dollars.

When really large numbers are expressed, such as those in astronomy, one generally ends up with concatenated pigfish such as billions of Kilometers. There are many examples of people who decide to use these large Olde English prefixes with incredibly small “everyday” units, in an attempt, I assume, to make the number something to which the average Jane and Joe can “relate.” As I’ve said before, large numbers are almost impossible to visualize, but with the metric system, their magnitudes can be categorized and metric worlds imagined.

I might ask, as a bit of a trivia question, if the Starship Enterprise, in the original Star Trek series, ever made a voyage that was more than a Zettameter? The answer is, probably yes, but not by much. The maximum extent of the Milky Way Galaxy is about 1000 Exameters or 1 Zettameter. TOS episode #51, titled By Any Other Name, has the Enterprise taken over by beings from the Andromeda Galaxy. The aliens were in the Milky Way looking for planets worth taking over or conquering. Their ship was destroyed and so the aliens duped the Enterprise crew into stopping by and then took over their ship. The alien beings, called Kelvans, modify the Enterprise so that it will only take 300 years to reach their place of origin. The distance to Andromeda is given in Wikipedia as about 2.5 million light-years. The use of light-years is bad enough, but using a Ye Olde English prefix modifier really helps to obscure the distance value. The distance, when written out, is 2 500 000 light-years which does not really help that much. We can calculate the Kelvans would be traveling about 8333 times the speed of light to reach Andromeda in “only” years—ok—300 years. How far is Andromeda from us? Well, in metric it’s about 23.7 Zettameters. The Andromeda Galaxy is about 220 000 light-years across, or about 2.1 Zettameters (2081 Exameters).

With our galaxy about 1 Zettameter in extent, we immediately see that Andromeda is about twice the size of our galaxy. The distance from us to Andromeda is about 24 times the extent of our Galaxy. Now that is rather close—and it’s getting closer—in fact it’s going to “collide” with The Milky Way in the future. But it’s only coming at us at the anemic rate of 600 Gigameters per hour. The distance from the Sun to Jupiter is 778 Gm. At this rate, it will “crash into us”  in about 4.5 billion years. Andromeda’s yearly rate of encroachment is a mere 5.25 Petameters, or 525 Petameters per century. A “light-year” is 9.46 Petameters, and therefore Andromeda is about 23 650 000 Petameters distant.  Andromeda is definitely taking its time getting here at its 5250 Petameters per 1000 year rate. When we use Zettameters  for galactic dimensions (or we could use Exameters and drop the decimal points) it is intuitive how far the two galaxies are separated, and their overall extent. Other appropriate prefixes provide clear context for a reader. Milliards and Milliards doesn’t cut it for astronomy.

We can never voyage more than 1000 Exameters (1 Zettameter) and remain within our galaxy. One could argue that when the Enterprise is on an imaginary voyage only Petameters in distance, it’s a nearby journey, and a voyage measured in Exameters, is a far away journey. Beyond 1000 Exameters, we are outside of our “Island Universe.”  Once again, we could be faced with a lack of magnitude causing confusion. If we accept as proper practice, that one does not go beyond 1000 for each metric prefix, when informally discussing magnitudes, we would expect that a 1 000 000 Petameter journey, would not be considered a “Petameter Voyage.” If we discovered otherwise, we would consider this an exaggeration, or in some cases even fraud.

click to enlarge

Zettameters and Exameters are not just for galaxies, there are other instances in astronomy where they can effectively be used. The May 2016 issue of Astronomy has an article[1] that discusses hourglass shaped lobes that extend for 25 000 light-years either side of our galaxy. Well, just how big are these lobes? A light year is 9.46 Petameters, and they extend about 240 Exameters above and below our galactic disc, with a maximum extent of about 500 Exameters (approximately half the maximum length of our galaxy). These structures are currently known as Fermi Bubbles. They could possibly be jets of material ejected by supermassive black holes found at the center of many galaxies, including our own. The Exameter sized bubble is composed of silicon and carbon atoms.

Recently, Astronomers have located unusual radio bursts “from beyond our galaxy.” These signals are called Fast Radio Bursts (FRB), and one of them, FRB 121102 is located in dwarf galaxy, dimmer than our own, over three billion light years away. But just how far is that?  It’s about 28 Yottameters! Remember our Universe has a diameter
of about 880 Yottameters. 28 Ym is a long way from Kansas.

The metric system is so well-suited for taming and categorizing astronomical distances, it’s a shame Astronomers refuse to use it in their work without Ye Olde English
prefixes, and generally after a light-year value has been alternatively presented. Perhaps Grade School and High School teachers could adopt the use of metric when expressing astronomical distances, and their students in turn might eventually become astronomers, and question why an infinitesimal yardstick the size of a light-year is used to measure the entire Universe. If you are an instructor, and have read this essay, please consider doing so.

[1] Kruesi, Liz “What’s Blowing Bubbles in The Milky Way?” Astronomy May 2016, pp 44-49.

Related essays:

Long Distance Voyager

The “Best Possible Unit Bar None”

The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.


5 thoughts on “Context and Units

  1. What’s andromeda’s actual yearly rate of encroachment? Either that figure is wrong or the century and millennium rates are wrong.

  2. We find it truly bizarre your worship of the metre, and of thousands.

  3. “Remember our Universe has a diameter of about 880 Yottameters.”

    Not true, the universe is infinite. The Big Bang was an explosion of space, not an explosion in space. Space and time were created everywhere in a single instance. The 880 Ym distance is not the diameter of the universe but of the observable universe. Due to the age of the universe and the speed of light, the farthest we can observe is 800 Ym, but the actual universe is actually much larger, an infinite amount larger.

  4. I actually find that the “light year” makes sense, since (a) the observable universe is only about 40 or 50 billion of them across (thus keeping the numbers sort of relatable), and (b) it gives a quick optimal bound on transport and communication in what still seems to be a strictly non-FTL universe.

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