By The Metric Maven

When I look back at my years of academic study, the academic institutions I attended seemed to view measures as something of secondary concern—or tertiary—at best. There is a strange irony that engineers and scientists can ascend academic educational levels from BS to PhD, and then become post-graduates, without ever attending a course contemplating or reflecting on how to best express numerical data. Data presentation is either thought to be beneath consideration, or simply knowledge acquired through osmosis.  Some of these academics then become popular science writers and presenters, without measurement expression introspection laying a glove on their consciousness.

Recently, Klystron provided a link to an article in Wired explaining why balloon castles go air-born when they encounter winds. The line from the article that jumped out was this:

We already have the speed to use: 25 mph, or about 37 feet per second. The density of air is 0.04 kilograms per cubic foot. (I’ll use kilograms for masses and pounds for forces and weights to avoid confusion.)

The author of this article, Brendon Cole, writes 0.04 kilograms instead of 40 grams and then mixes in Ye Olde English feet to create a single expression for density. Kilograms per cubic foot? WTF? Pigfish is introduced without reservation or thought. The author then decides to use Kilograms for mass and pounds for forces! The common pound is generally thought of as the avoirdupois pound, which is generally thought of as a mass. When referring to pound force, it is written as lbf. But 1 lbf = 32.17 ft*lbm/(s*s) where lbm is pound mass and lbf is again pound force. Clearly this is less confusing than simply using newtons?—really?

When I see such piss-poor mixed-up scientific expression in science writing I wonder if I’m the only one who notices. This person apparently gets financial compensation for this writing and cred as a “science writer.”

The density of air in Denver Colorado on a pleasant day is around 1000 grams per cubic meter, or about one Kilogram per cubic meter. Air density varies depending on temperature and pressure. Cole’s value when converted to metric is a very reasonable 1413 grams per cubic meter. Helium has a density of about 170 grams per cubic meter and, because of its much lower density, is clearly useful for filling balloons that will float upward. Cole chooses 0.04 Kilograms per cubic foot?—to make his calculations more accessible?

The fashionable term for today’s “science writers” is “science communicators” which I like, because compared with traditional science writers such as Isaac Asimov, L. Sprauge de Camp, Arthur C. Clarke and such, they don’t seem like they are serious about expressing science in a clear and cogent manner or prepared to do so. This is especially true when it comes to the presentation of numerical information.

Phil Plait is an astronomer and has also been involved in scientific skepticism during his career. As I’ve pointed out in the past, scientific skeptics can embrace a form of technical hubris when their use of the metric system or data presentation is questioned. Plait is the author of the book Bad Astronomy, and blogs at Slate. I find his topics and writing engaging and enjoyable, but his presentation of numerical information is at best ad hoc and devoid of introspection.

Chapter 3 of Plait’s 2002 book Bad Astronomy is titled “Idiom’s Delight: Bad Astronomy in Everyday Language.” It begins:

One of the reasons I loved astronomy when I was a kid was because of the big numbers involved. Even the nearest astronomical object, the Moon, was 400,000 kilometers away. I would cloister myself in my room with a pencil and paper, and painstakingly convert that number into all kinds of different units like feet, inches, centimeters, and millimeters. ….

The fun really was in the big numbers. Unfortunately, the numbers get too big too fast. Venus, the nearest planet to the Earth, never gets closer than 42 million kilometers from us. The sun is 150,000,000 (150 million) kilometers away on an average day, and Pluto is about 6,000,000,000 (6 billion) kilometers away. The nearest star that we know of, Proxima Centauri, is a whopping 40,000,000,000,000 (40 trillion) kilometers away! Try converting that to centimeters. You’ll need a lot of zeros.

Phil Plait does not seem to have any concern with using Olde English concatenated prefixing such as 40 trillion kilometers. I have written an essay that illustrates an elegant way large numbers in astronomy may be expressed and categorized using only metric prefixes. Solar System distances from the Sun to the planets are generally in the Gigameter range. The distance from the Earth to the moon is 400 Megameters according to Plait’s essay. The distance around the Earth is 40 Megameters, so one can immediately see the distance from the Earth to the Moon is about 10 times the distance around the Earth. The Earth is 150 000 Megameters from the Sun (or 150 Gigameters), Pluto is 6 000 000 Megameters from the Sun (or 6000 Gigameters). The nearest star, Proxima Centauri is in the Petameter range, or 6 000 000 Megameters distant. Why on Earth would anyone want to convert this value to centimeters!

He then offers a way out out of the centimeter difficulty:

There is a way around using such unwieldy numbers. Compare these two measurements: (1) I am 17,780,000,000 Angstroms tall. (2) I am 1.78 meters tall. Clearly (2) is a much better way to express my height. An Angstrom is a truly dinky unit: 100 million of them would fit across a single centimeter. Angstroms are used to measure the sizes of atoms and wavelengths of light, and they are too awkward to use for anything else.

American scientists always turn to centimeters as their go-to “scientific” pseudo-inch. Long time readers know I have a low opinion of centimeters. If you are a new reader, see, this, this and this or read Pat Naughtin’s epistle on centimeters or millimeters, or watch his video. The use of the Angstrom as a unit of measure places Plait squarely with non-SI usage, and on the side of unnecessary complication and confusion. If he kept with modern practice, he would have written his height as 1 778 000 000 nanometers versus 1.78 meters tall. Plait does not offer 1778 millimeters as a height, he rounds to the nearest centimeter without giving it a second thought. The pseudo-inch is very entrenched. His essay could have been about an optimum choice of metric prefixes and their simplicity, but Plait has not been prodded by his academic experience or elsewhere to even contemplate how he expresses numbers. It is examples like this that cause me to chuckle, and sometimes laugh out loud when I’m told that “US scientists use the metric system.” They use a strange mixture of cgs, mks and Ye Olde English.

Once the Bad Astronomer has established that angstroms are “too awkward to use for anything else” He carries on with his view of the situation:

The point is that you can make things easy on yourself if you change your unit to something appropriate for the distances involved. In astronomy there aren’t too many units that big! But there is one that’s pretty convenient. Light!……..

Plait then offers an enraptured colloquy that the Moon is 1.3 light-seconds from Earth, the Sun is 8 light-minutes from Earth and Proxima Centauri is 4.2 light-years. Then this:

The light-year is the standard yardstick for astronomers. The problem is that pesky word “year.” If you’re not familiar with the term, you might think it’s a time unit like an hour or day. Worse, since it’s an astronomical term, people think it’s a really long time, like it’s a lot of years. It isn’t. It’s a distance

The use of light-year by astronomers is simply confusing inside-speak. I’m going to defend the pesky word “year” in this situation. I have studied electromagnetism and its propagation for my entire multi-decade career. Light is an electromagnetic wave; it travels at 300 Megameters per second in a vacuum. The speed of light is the speed limit for sending information along wires and through interstellar space. Einstein was clear about this. The speed limit of the universe is 300 Mm/s or 1 080 000 Mm/h. The term light-year, light-hour or light-second make much more sense when thought of in terms of time. When we look at the farthest reaches of the Universe, we are looking back in time. The more powerful a telescope is, the further back in time it allows us to see. The Voyager spacecraft is about 19 light-hours from us. It takes 19 hours for a signal sent from Earth to be received by the probe. It then takes 19 hours to make the return trip. Light (electromagnetic waves) are the only way information is conveyed around the universe. Well, until gravity waves were detected, but they also travel at the speed of light. When, in 1604, Kepler saw the supernova which bears his name,  the stellar explosion which produced it had occurred about 20 000 years earlier. Expressing 20 000 light-years as a distance suppresses the more important interpretation in terms of time. Phil’s view:

I can picture some advertising executive meeting with his team, telling them that saying their product is “years more advanced than the competition” just doesn’t cut it. One member of the ad team timidly raises a hand and says, “How about if we say ‘light-years’ instead?”

It sounds good, I’ll admit. But it’s wrong. And more bad astronomy is born.

The subtitle of Phil Plait’s book Bad Astronomy is: “Misconceptions and Misuses Revealed, from Astrology to the Moon Landing `Hoax’.” Scientific skepticism involves questioning our most basic concepts, but scientists, like most people, often don’t. In this situation Phil Plait defends astronomical tradition over introspection. Could he for just one moment, think about the fact that perhaps the word “year” is equal to the word light in light-year, and time might be a better interpretation than distance. Isaac Asimov pointed out that as a unit the light-year is so small, that a sphere with a one light-year radius will not encompass our nearest star. Might not questioning or thinking about the assumptions and units astronomy uses to relate distance and time be an example of bad astronomy?—or simply ossified astronomy? The introduction of parsecs, light-years, AUs and such have an implied assumption for the reader that they are indispensable to Astronomers, and so they are units that the reader must learn to deal with despite an unfamiliarity with them. Scientific communicators and astronomers could use the metric system, which is the scientific standard of the world, but instead popular science writers embrace astronomical argot. Megameters, Gigameters, Petameters and such are too much of an intellectual imposition for delicate US readers, but parsecs, AUs and light-years are acceptable?

The chapter on measure ends with quantum dimensions:

In reality, a quantum leap is a teeny-tiny jump. The distances are fantastically small, measured in billionths of a centimeter or less.

So you might conclude that an ad bragging about a product being a quantum leap over other products is silly, since it means it’s ahead by only 0.00000000001 centimeters!

You might be surprised to find out that I have no problem with this phrase. I don’t think it’s bad at all! The actual distance jumped may be small, but only on our scale. To an electron it truly is a quantum leap, …..

I can only hope that when Phil Plait said that quantum leaps are “measured in billionths of a centimeter” he did not actually mean any scientific instrument would display such “units.” In my view this phrase is part of the problem. A billionth of a centimeter is 100 femtometers or 100 x 10-15 meters. This is five metric triads or 15 orders of magnitude smaller than a meter. He also reflexively chooses the pseudo-inch, aka the centimeter, as the base for his illustration.

An electron has a dimension on the order of 3 femtometers. Electrons shift between energy levels in atoms and not across exact locations. One can’t really say exactly “where an electron is” around a given nucleus. It is inside a sort of “probability cloud.” We can use a value called the maximum radial probability distance as a benchmark. It lets us “pretend” we have a solid location for the position of an electron. The classic Bohr radius for an electron in a hydrogen atom is about 53 000 femtometers from its single proton nucleus. When expressed this way, one can see that a 3 femtometer electron, which is 53 000 femtometers from its nucleus, is positioned at a very long distance in terms of its dimension. In the case of a hydrogen atom, the maximum probability electron radii for the first three energy levels are 53 000 fm (1S), 281 000 fm (2s) and 689 000 fm (3s). The distance from the 1s to 2s subshell is 165 000 femtometers. This is very large distance for an electron to traverse compared with its own 3 femtometer dimension.

The essay Plait wrote could have helped to educate the public and reinforce the use of the metric system for his professional audience. When I have asked why the metric system is not used in American science writing, I generally get an excuse that the author must write using units the general public understands. Strangely, this often involves centimeters. If the purpose of science writing is to qualitatively inform and entertain only, perhaps this would make sense, but to educate is part of informing an audience. Readers of popular science magazines are interested in the acquisition of new knowledge, why would the metric system be too large an imposition for this self-selected audience?

I meant for this essay to cull examples from numerous articles found in diverse publications, but the contents of Phil Plait’s Bad Astronomy chapter impelled me to follow it to its end and this essay expanded precipitously. The problem is not Phil Plait, it’s the entire pantheon of modern “science communicators.” They are a cohort of public intellectuals that praise numeracy and then dismiss the metric system. Phil Plait, Neil de Grasse Tyson, and Bill Nye are perhaps the best known examples. From a measurement expression standpoint, current science writing in the US is abysmal overall. Henri Petroski’s essay on paperweights in the July-August 2016 issue of American Scientist is a primer on how awful fractions are for expressing magnitudes. New Scientist, Scientific American, Discover, Astronomy and other popular magazines I read all are tone-deaf when it comes to using the metric system, yet claim to be performing a symphony of science. It’s time they tuned their instruments.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essays:

The “Best Possible Unit Bar None”

Long Distance Voyager

The Expanding Universe

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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.

1. My theoretical physicist partner says that “Physics is about measuring.” If so, then indeed bad measures are bad for science.

2. “Plait does not offer 1778 millimeters as a height, he rounds to the nearest centimeter without giving it a second thought.”

Clearly, he did not measure his height directly in metric; he just soft converted exactly 5 ft 10 in.

3. Han Solo: “You’ve never heard of the Millennium Falcon? It’s the ship that made the Kessel Run in less than twelve parsecs.”
I now see how Han was wrong, it’s like saying:
“I can chug this beer in less than twelve liters!”
Seriously I could tell people that and they would say:
“Whoah that’s fast!”
Maybe that’s why Obi Wan rolled his eyes when Han boasted.

Great essay Mavin, keep up the amazing work!