Popped Secret

By The Metric Maven

Bulldog Edition

Popcorn is a very New World food. It is amazing that in ideal conditions the kernels of unpopped popcorn can be stored almost indefinitely. Corn was first domesticated in Mexico about 9000 years ago. As a young boy, I recall a friend showing me a popcorn pan with a hand-crank on the lid. We were watching an old movie and he wanted to make something special. My friend placed oil into the pan and heated it, he then tossed in a measured amount of popping corn. Normally, at that point one would  immediately put the lid on to keep from being splashed if it started popping immediately. He next tossed in some sugar. The handle was part of a wire sweeper that could push the corn around. This was done until the popcorn had finished popping, and for the first time I had popcorn with a sugar coating. At that age it seemed exotic. At that point in my life I gave no thought to how much extra energy was imparted by the introduction of sugar. The agitator was a nice addition. Generally when popping popcorn in a pan one would need to continuously shake the pan forward and backward to keep the popcorn from burning. Popping popcorn at home was an acquired skill. Popcorn balls (generally colored in some fashion) were often handed out at Halloween in my small town as a treat. The largest documented popcorn ball is 2.4 meters in diameter, 7.5 meters in circumference, with a mass of 1549 Kilograms (well over a Megagram). Popcorn was also strung on thread to decorate Christmas trees during the winter holiday season.

In China and Korea a sealed cast-iron canister with popcorn inside is used like a rotisserie  over a fire.  When a pressure gauge on the container reaches a threshold value, the canister is taken from the flame, a canvas sack placed over the top and the seal broken. With a large boom, the popcorn explodes all at once. It is then poured into the canvas bag.

The first popcorn was popped by hand (sometimes over an open fire), and  was later automated with steam powered mechanisms designed in the late 19th century. This new popcorn popper was introduced at the 1893 Colombian Exposition. When I was a boy we purchased sealed plastic bags of popcorn kernels with Jolly Time printed onto the transparent film. The big change in popcorn preparation came when General Mills obtained the first patent for bagged microwave popcorn in 1981. This made popping popcorn much more convenient and a surge in popcorn consumption followed. People also ceased to see popcorn kernels any longer as they now come in an opaque bag.

Microwave popcorn allows one to eat popcorn with a very consistent serving size in terms of mass and volume. This consistency would be great for those who are trying to monitor their food energy intake. When I first attempted to determine the energy content of popcorn I was very surprised at the low value. The serving size per bag is about 3 and the serving size is 1 cup popped or three cups. This works out to 90 Calories (377 KJ). My significant other (SO) immediately doubted this value. It had to be higher. In recent years it has been emphasized that we should go back to Olde English only nutrition labels. One can see this from the nutrition labels that Ye Olde English is still Kyng. Here is the nutrition label for Pop Secret’s Homestyle Microwave Popcorn:


So if the servings per bag is about three, and the serving size is two tablespoons unpopped, then it would be a total of 3*150 Calories or 450 Calories (1884 KJ). The fact that the serving size is given as 2 tablespoons unpopped and 1 cup popped seems to indicate an equivalence. So which is it? Ninety Calories per bag or 450 Calories per bag? This difference is a factor of five! The range given on the web for a single bag of Pop Secret Homestyle was from around 400-500 Calories or so. When I looked at the bag after popping, and used my 100 mm wide hand to measure it, the bag appeared to be somewhere around two liters in volume, but I had no idea how many cups that might be. I could immediately estimate the value in metric, but could not do the same with Ye Olde English.  My SO and myself then conducted an experiment, we popped a bag and measured it with a one cup measure. It turned out to be somewhere from about 10-12 cups of popped popcorn. It would seem that each bag contains about 6 tablespoons of unpopped popcorn, and 15 cups when popped, but the nutrition label does not say that.

When converted to metric the clarity has not increased much:

Nutrition Facts
Serving Size  15 mL unpopped  237 mL popped

Amount            15 mL     237 mL
Per Serving      Unpopped   Popped

Calories           150        30

So 15 mL of popcorn becomes about half of a 500 mL bottle of soda or water. Does that make sense or not? I was able to estimate the volume of a popped bag at about two liters or 2000 mL.  Given about 200 mL per serving 2 liters would be about ten servings or 300 Calories. Clearly the value would not be 90 Calories.

In my view this label has been designed to confuse. Who eats unpopped popcorn? Who even sees the unpopped popcorn in a sealed opaque paper bag? How would you estimate the unpopped amount when you can’t even see it! One would immediately look  at the label assume 3 cups per bag at 30 Calories per cup and compute 90 Calories total. There have been moves to go back to Ye Olde English from metric for US nutrition labels to make them more “understandable.” The Pop Secret label is unclear in metric and even more inaccessible in Ye Olde English. It could have been written:

Nutrition Facts

Calories per bag: 450

Servings per bag: 3

Calories per serving 150.

Calories per cup 30

Volume of bag: approximately 2500 mL

The nutrition label as it is originally formatted appears to be designed to mislead consumers into believing that microwave popcorn contains far less calories than it does. This in turn causes the person to consume more calories and hence more product while blowing their estimated food energy intake.

Profiting from measurement confusion and misinterpretation is often thought to be a thing of the past. It is clearly not—and never has been. I have a measuring scoop provided inside my laundry detergent box which has a volume twice that recommended for each wash. It has a line halfway up its side which is the recommended volume. People don’t notice the transparent line, or read the tiny instructions, and generally fill the scoop up to the top, using twice the recommended amount of soap. People who see the importance of implementing the metric system, and the teaching of basic numeracy as fringe issues in the United States, are but ignorant marks for our modern industrialized hucksters.

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Bad Astronomy and Bad Measures


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