Take It With 64.798 91 Milligrams of Salt

Grains-of-SaltBy The Metric Maven

Bulldog Edition

I have often made a point that a pound of feathers weighs more than a pound of gold, and that an ounce of feathers weighs less than an ounce of gold. This is because A troy pound is equal to 0.822 857 1 avoirdupois pounds. Feathers are weighed in avoirdupois pounds and gold is measured with troy when using medieval units. The Troy pound is divided into 12 ounces and the avoirdupois pound is divided into 16 ounces.

At one time I made the incorrect assumption that because the troy pound is defined as 5760 grains and the avoirdupois pound is 7000 that the value of a troy grain and avoirdupois grain were different. To my surprise, the common weight definition for pounds in Ye Olde English is the grain. The same grain is used to define the 5760 grains of a troy pound and the 7000 grains of an avoirdupois pound.

Recently I was watching an episode of the 1960’s mini-series The Prisoner. A discussion took place concerning how much of a drug had been given to the main character and what should be done when the effects were not as predicted:

Number 86: “I gave him eight grains of mitol. Suspicion, doubt, these are factors of aggression. The drug should preclude all such reactions.”

Number 2: “….go to him now repeat the dose.”

Number 86: “Now? But sixteen grains of mitol is quite impossible.”

Number-86The values are all in grains. What struck me as I thought about this exchange is the concern that some literary Lilliputians have that our clichés will suffer at the hands of a metric switch-over. The one phrase I don’t recall being discussed in this context is: “you better take that with a grain of salt.” It means that one should view a statement with some skepticism. The origin of the phrase is a bit apocryphal and is possibly from a Latin phrase. I realized that I had never interpreted the phrase “properly” until I saw that old episode of The Prisoner. The invention of the microscope around 1610 or so soon allowed humans to look at individual “grains” of salt. These grains vary, but a reasonable estimate is about 60 micrograms per salt crystal “grain.” I always took the meaning of taking something with a grain of salt as adding in an infinitesimal amount of salt to make it more palatable. When I thought of the phrase I thought of the microscopic salt crystals of NaCl and not the approximately 1000 of them that make up the Ye Olde English unit called the grain. when I think of a grain of sand I don’t think of 64.798 91 milligrams of sand, I think of a single particle of sand, which is on the order of 15 milligrams.

The grain as a unit is so unfamiliar to Americans as to be intellectually invisible. One has to remind people that some aspirin in the US are also labeled in grains, and if one asked how many grains are in an ounce they would not realize that it is 473.5 grains for an avoirdupois ounce and 480 in a troy ounce. The grain is as devoid of meaning for the average person as is a coomb.

The grain was defined in 1572 long before our modern notion of mass was developed. The pound was not uniquely defined as a mass or a force, and because of its pre-scientific heritage it continues to act as a barrier to a scientific understanding of our world by the average person, and often educated engineers and scientists. When we stand on a bathroom scale and read off the value in pounds, it is often assumed to be a mass. But the word pound is used interchangeably for weight or the force gravity exerted on the mass of the object. We in the US still say pounds per square inch when discussing pressure, which in terms of mass does not seem to make any sense. An object with mass is a three dimensional object and not a two dimensional area. Using the identical name pound for pound-mass and pound-force traps citizens in the US into a medieval view of the world. It also traps engineers and scientists.

Recently I was watching an episode of the highly enjoyable program Impossible Engineering. It dealt with the design of the World’s Biggest Cruise Ship. In the program Physicist Dr. Andrew Steele sets out to demonstrate the amount of drag or opposing force that different hull shapes of boats produce, as first mathematically expressed by engineer William Froude (1810-1879) in the 19th century. Dr. Steele attached a spring scale using rope to each example and then described the amount of force (hydrodynamic drag) they each exert. The value is read from the scale in Kilograms (mass) and not in newtons (force). Dr. Steele is British, which produces a sort of double irony. When a person is conditioned to see pounds as both mass and force, it is a short step for an average person, or a PhD, to substitute Kilograms for newtons and blur the modern distinction. The retention of medieval units brings along their pre-scientific baggage in a world where the public understanding of science is of existential importance.

When you see scientific explanations on popular television programs, remember to take them with a grain of salt.


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.

Blowed-up Real Good

Blowed-Up-Real-GoodBy The Metric Maven

Bulldog Edition

I very much like to check-out Phil Plait’s Bad Astronomy blog. His measurement presentation causes me to generally wince, but its topics are often rather interesting. On 2016-02-20 he wrote about the Largest Fireball Since Chelyabinsk falling over the Atlantic Ocean. The object appears to have possibly exploded (or just burned up) about 30 Kilometers above the ocean surface. Plait assures us there is no cause for alarm; this was a small meteorite. He states:

For comparison, the Chelyabinsk explosion, which was strong enough to shatter windows and injure more than 1,000 people (due to flying glass), had an equivalent yield of 500,000 tons of TNT, 40 times the energy of this more recent impact.

Plait provides a link to the NASA/JPL Near-Earth Object Fireball page, and presents a cropped graphic from the site:

NASA-ClippedI was quite pleased to see NASA using international dating for the entries. It all is nice and ISO 8601. The total radiated energy from the meteor is given in joules. It is presented in scientific notation with an exponent to the tenth power. Here is a larger section of the NASA table with the data for the new meteorite in the first row at the top:

Blowed-Up-NASAThe total energy radiated from the meteor as it cruises through Earth’s atmosphere is about 685.3 x 1010 joules. Why an exponent of ten? We can see as we go down the list that all of the examples have this same multiplier. When presenting data, scientific notation is not good for numerical comparison. One could choose a metric prefix and have 6.85 Terajoules instead. As the values are typically smaller than this, one could switch to Gigajoules and write it as 6853 GJ. In my view presenting comparison data with scientific notation hinders intuitive understanding. I know that some computer languages have a setting that parses the exponents so they are presented in engineering notation by steps of 1000.[1] The exponent for all of the values given in the table can be expressed in Gigajoules. Below is a table with the recent meteorite and the Chelyabinsk radiated energies:


When Expressed in Gigajoules it is apparent just how much larger the radiated energy of the 2013 Chelyabinsk meteor was when compared to the recent one thought to have have exploded over the Atlantic Ocean.

When presenting the calculated total impact energy, NASA gets their Dr. Strangelove on and uses kilotonnes of TNT. As I’ve pointed, out the tonne is nothing more than the introduction of medieval measures into the metric system and should be eschewed. Worst of all, a tonne is a Megagram, and when you use a Kilo- prefix it produces a KiloMegagram. The last column is KiloMegagrams of TNT when actually expressed without hidden metric notation. It should be Gigagrams of TNT, but then metric is not NASA’s strong suit. The metric system has a well-defined unit of energy, the joule; the same one that was used with radiated energy.

One kilotonne of explosive is equal to 4.814 Terajoules. It appears that using Gigajoules is probably still a viable choice for presentation of the Calculated Explosive Energy:


In my view the change from joules to kilotonnes of TNT was just an anemic attempt at a “gee whiz” expression without making an actual comparison. An atomic bomb using nuclear fission ranges from about 4 000 Gigajoules to about 80 000 Gigajoules. The 2016-02-06 meteorite is in this range. The largest Hydrogen bomb exploded released an energy of about 210 000 000 Gigajoules. One can see the Chelyabinsk explosion of 2013 is about 23 times larger than a typical fission bomb, but is overwhelmed when compared to the amount of energy released by the largest hydrogen bomb.

How data is presented matters. I wish someone in a position to enforce change within NASA would create a position called a “numerical editor,” something like what in book publishing is called a copy editor, but concerned specifically with the presentation of numeric data for consistency and clarity. I leave you with a graph I’ve presented before. It shows that sometimes NASA presents data in an effective manner, they just need to make it consistent:

Asteroids-Joules[1] Fortran 90/95 for Scientists and Engineers Stephen J. Chapman McGraw Hill 1998 pp 534-535