Mnemonic Metric Prefixes

By The Metric Maven

Integer Solar Orbit Day

Engraving of Kilroy on the WWII Memorial in Washington DC

Years ago, my friend Ty took an interest in how to remember information. He pointed out that often you will think of something you want to do or retrieve, leave the room where you made the decision, and by the time you arrive in the next room, have forgotten. Often you return to the the original room, and then suddenly can recall what you meant to retrieve or view. Ty asserted it was because you had associated the decision with the original room, and when you returned, the two things were attached in your mind and you immediately recalled why you left in the first place. Years ago, when I was a young boy, people would tie a string around their finger to remind them to remember an important piece of information.

When I was taking trigonometry in high school, the teacher indicated we should remember words and phrases to recall the definitions of the sine, cosine, and tangent of a right triangle. He offered:

The adjacent side of the triangle was closest to the angle, the opposite side was well, opposite of the angle, and the hypotenuse was the long side that was not the others. Silly Cold Tigers? and Oscar Had A Happy Old Aunt?—how ridiculous!—but decades later, I still remember this method of recalling the definitions of the basic trigonometric functions of a right triangle. He encouraged his students to make up their own, and indeed they came up with more memorable phrases that were the sort that teenage boys were more likely to remember.

A number of “metric advocates” have ridiculed my assertion that grade school children, middle school students, and high school pupils, should be instructed in the use of all the metric prefixes. In my view, all the prefixes means the eight magnifying and eight reducing prefixes separated by 1000. One of the most effective instructive methods for recalling information is the use of a mnemonic device. Here I propose a pair of these, one for the magnifying prefixes, and one for the reducing prefixes. The first mnemonic is presented in the table below for the magnifying prefixes:

The mnemonic phrase for the magnifying prefixes is: “Kilroy Might Get To Paris Escorting Zombies Yonder.” The first letter of each word corresponds to the prefix symbol. The first prefix is Kilo is suggested by the name Kilroy, but the rest of the prefixes all end with an “a.” This can be thought of as the prefixes “above” unity.

The second table for the reducing prefixes is:

The mnemonic phrase for the reducing prefixes is “Millie might not protest fetching another zesty yeti.” Again the first letter of each word corresponds to the prefix symbols except for micro. The student would have to spell out micro and then recall the μ symbol is used, rather than another m. The first word is again a name, Millie, which in this case contains the spelled out prefix. Again means we need to forget it, but realize the reducing prefixes all end with “o” and are “below” unity.

In both cases the phrase begins with a name, and involves that person compelling mythical creatures.

If students were taught these mnemonics from perhaps grade 6 or 7 onward, with metric prefix examples, like those found in The Dimensions of the Cosmos, by the time they graduated from high school, they could have the tools needed to recall the metric prefixes without a textbook, and be reminded to use them in their work.

I would be interested in any comments or suggestions readers might have about these proposed mnemonic devices that might improve them. The best way to promote their use would be for the US to become a mandatory metric nation, but as this country celebrates its reactionary nature with religious fervor, I’ll have to settle for whatever good these mnemonics might do without a change.

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The Presentation of Blank Space

(Greetings to the residents of Tokelau who have taken an interest in this website. We’d love to hear from you.)

By The Metric Maven

Over my career as an engineer, I slowly took more and more interest in the presentation of data and numbers. For small sets of data, tables are often preferable over graphs. Edward Tufte states:

Tables are preferable to graphics for many small data sets. A table is nearly always better than a dumb pie chart; the only worse design than a pie chart is several of them… [1]

When constructing a table, I have often needed to contemplate the presentation of numbers before I design it, and often need to review it afterward. The problem is not the numbers themselves, but with their presentation.

I’ve been exposed to graphic arts and printing for many decades, but when I was introduced to TeX I became much more interested in typesetting. Some typefaces are far more readable than others. The typeface known as comic sans is generally disparaged and has become something of a phenomenon. Helvetica is perhaps the most well-known typeface, and is ubiquitous. Some typefaces are known for their readability over long periods, but one very important aspect of creating a typeface and putting words on a page with it, is the spacing between letters (known as glyphs). The choice of spacing between glyphs in a manner which produces a visually pleasing result is known as kerning.

In my view, this applies to numerical presentation as much as it does to prose presentation using a typeface. It was also of concern to the founders of the metric system:

At the time of the creation of the metric system in France, financiers and businessmen were increasingly separating whole numbers in sets of three with commas between. This made them easier to read. The triad grouping was adopted, but the comma was thought to be inelegant and confusing. Laplace and Lagrange stated: “…, it is hoped that the use of a comma to separate groups of thousands will be abandoned, or that other means be used for this purpose.” Other means were adopted, which is the small space between groups of thousands. [2]

It has been my experience that introducing commas can really obscure information. For instance, in my essay The Expanding Universe, the table presented shows the expected size of the universe over time:

click to enlarge

I used full spaces to separate numerical triads in the table. The columns are easily seen in this case. Now here is the table with commas:

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The comma “separators” act to perceptually unite the string of numerical glyphs rather than separate them as a space does. In the first table one can clearly pick out each column that goes with each metric unit as shown at the bottom.

The modern international standard eschews commas and adopts spaces as desired from the beginning. The numbers are to be separated into triads, or groups of three. Mr. Reid, a physicist and teacher has a nice essay called Stop Putting Commas In Your Numbers. The amount of blank space separation is said to be a “thin space.” This is defined as a fifth of an em (or sometimes a sixth) for the Unicode Character THIN SPACE (U+2009). There is already a little waffling about the size of the space. Mr. Reid presents a helpful table that demonstrates his view:

click to enlarge

The BIPM has this to say:

…for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading.  Neither dots nor commas are inserted in the spaces between groups of three. However, when there are only four digits  before or after the decimal marker, it is customary not to use a space to isolate a single digit. The practice of grouping digits in this way is a matter of choice; it is not always followed  in certain specialized applications such as engineering drawings, financial statements, and scripts to be read by a computer.

This gets to the heart of this essay. I’ve always had difficulty deciding:

1) If, when there are four digits, would it would be best to use a thousands space separator, or not.

2) If I use a thousands space separator for a four digit number, how large should this space be to provide the most aesthetic presentation?

There does not seem to be a single definition of thin space, Merriam-Webster claims it is either a fourth em space, or fifth em space. Others say a sixth of an em space. In the end the choice may come down to kerning. In the TeX typesetting language, the \thinspace command is defined as a \kern .16667em or one-sixth of an em space.

It appears that the tables above, which have multiple groups of metric triads, a full space is aesthetic and the data is very accessible to the eye. It is when the data in a table does not go beyond five digits that I’ve been hard pressed to decide how to best display the data. Below I have taken the data for energy use in the US for 2016 and presented it with a full space, thin space and no space thousands separators:

– click to enlarge

The full space thousands separator data seems a bit awkward, with too much blank space seeming to slice the number so much they seem like separate values. The thin space amount of blank separation is probably the best in this situation. The four digit values still seem to be a single entity, but also work with the large numbers to provide separation. Using no space seems a bit disjointed, but in practice it is often difficult to provide a thinspace, so the alternative of using no spaces up to 9999 might be a good option.

The above table is in a random order of values. When it is ascending, the table can look quite different:

– click to enlarge

When presented this way, the thinspace column and the no space column have a similar aesthetic, and when it is not possible to use a thin space, no space for the four digit numbers looks good. The table can look different when the lines are removed between rows:

One might now prefer the full space column to the thinspace column. It would probably even be best to remove most of the rules as is often argued by some typographers.

Tufte would probably recommend a table like this:

In this case, one might like the fullspace column the best.

There is no real right and wrong way to do this, just more appealing and less appealing,  which is a very difficult value to measure. We each must find our balance between the aesthetics of numerical presentation and the clear presentation of information.

[1] Tufte Edward, The Visual Display of Quantitative Information, Graphics Press 1983 pg 178

[2] Bancroft Randy, The Dimensions of The Cosmos Outskirts Press, 2016 pg 9

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