Old Days

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By The Metric Maven

I read a “fun fact” recently, that stated because metal expands when heated, the Eiffel Tower is actually 150-170 mm taller in the Summer than in the Winter. This fact reminded me of an old physics textbook, New Practical Physics by Black and Davis (1929 edition) that I’ve had for sometime but never really inspected. The section at the front on the metric system has an interesting graphic:

The authors of the book show a comparison of English and metric, with inches divided into tenths. This is interesting, because the general usage in the US (even in
High School or College physics classes) employs a common yardstick where inches are divided into fractions. It is very interesting that the textbook authors note both centimeters and millimeters are on the metric rule in their illustration. They seem to be falsely equate inches and tenths with centimeters and millimeters to provide a non-existent continuity between metric and Ye Olde English. Centimeters are the only labeled graduations, and it seems they do not contemplate using millimeters alone as an option. As I’ve said in the past, centimeters are so identified with inches in the US they are the default small metric unit, and a poor choice.

Black and Davis note that US currency is decimalized, but:

Our system of weights and measures, on the other hand, is not a decimal system, and is very inconvenient. Nevertheless, since the pound, foot, quart, gallon,
and bushel are still in general use in the United States and Great Britain, we must be familiar with them.

The basics of the metric system are touched upon and the definition of the:

Meter and yard. The meter is the distance between two lines on a metal bar (Fig. 2)

which is preserved in the vaults of the International Bureau of Weights and Measures near Paris.

Since the length of this metal bar changes a little with temperature, the distance is measured at the temperature of melting ice. A very accurate copy of the bar is deposited in the United States Bureau of Standards in Washington, D.C., and this copy is the legal meter of the United States.

In the United States the yard is legally defined as 3600/3937 of a meter.

My Father’s friend Mark was looking through a surveying kit, owned by his father, that appears to be from the 1930s, and found this interesting ruler:

Click to enlarge

One side has temperature correction for Lufkin steel measuring tapes. The difference for the 50 foot length is given on the left side and expanded for a 100 foot length on the right hand side. The wooden ruler itself is graduated in tenths of inches. I have no idea how prevalent rulers with 1/10th inch graduations were, but I suspect they were about as rare as they are now.

The back side:

Click to enlarge

Has hundredths of a foot, and is marked in tenths of a foot with integers. Below it is a scale with 1/16ths of an inch (of course millimeters would be 1/25). The value of a chain is a foot, divided into tenths and hundredths.

A footnote at the beginning of the textbook reminds us:

It was originally intended that the meter should be equal to one ten-millionth part of the distance from the equator to either pole of the earth, but it is impossible to reproduce an accurate copy of the meter on the basis of this definition. Later measurements have shown that the “mean polar quadrant” of the earth is about 10,002.100 meters.

First the Earth was used, and it had considerable difficulties as a standard, then metal bars, that needed to be measured at a precise temperature. Now the current definition is in terms of the speed of light in a vacuum, and is very, very accurate and reproducible. We still have some issues with better usage and simplification, but before that, we have to adopt the metric system exclusively in the US.

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Related essay:

The Chain Gang

The Americans Who Defined The Meter

The Metric Maven has published a 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.


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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The Metric Maven has published a 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.