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:

click to enlarge

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


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.

perf6.000x9.000.indd

6 thoughts on “The Presentation of Blank Space

  1. You quote an example from Mr. Reid, with correct/incorrect columns. It contains two columns of numbers where the decimal places are not aligned. Am I wrong to find this troubling?

    I generally prefer to justify to the decimal point, rather than the absolute right or left of the text area. How far I pad with 0’s depends on the associated margin of error or, for presumed-perfect calculations, the roundoff point.

    For instance, if I were to display some results I had calculated, let’s say just two of them, shown to a larger precision here:

    1.500013
    1.571428

    And my margin of error, or degree of confidence, dictates that only two decimal places are reliable/noteworthy, I might display this:

    1.50
    1.57

    This is meant to indicate that the ‘0’ on 1.50 can be safely assumed, whereas 1.5 might imply being rounded off from 1.54. Similarly, to three places:

    1.500
    1.571

    You get the idea. I would generally never prefer to clip rightmost zeroes unless they are absolutely guaranteed, e.g. if I were listing the results of calculating 3/2 and 11/7:

    1.5
    1.571

    Leaving off the trailing digits subtly indicates that the number is exact. It’s sort of the complement of adding an ellipsis to indicate that the given number is not exact, which is something no one actually seems to do in practice. Ideally, the above example should be written with both hints:

    1.5
    1.571…

    Interesting to find someone else so interested in these things. I found you by looking to see who else thought Milligrade would be preferable to Centigrade/Celsuis. I think SI made a mistake with that one, especially since its supposed lack of precision (are decimals really too hard?) is the primary ammunition used by most anti-metric folks in the USA.

  2. I wonder what Michael Alley would say. Let us (me) ask him!

  3. For the USA I would use a comma for thousands – and for larger numbers thin space.

    But – if the rest of the world might see it (which is the case most of the time now ) Just thin spaces everywhere..

    I also agree with Felice above – there is an implied precision claimed by using more decimal places. If I see a number with 3 places – I assume they know it to +/- .001.

    This is often not the case! Particularly in medicine where you will see numbers without error bars that are greatly exaggerating what they know!

    If we don’t know the error-bar – we really don’t know much. We should extend this to noting precision..

  4. In regard to how we in science and engineering write, I am all for changes that improve clarity, as long as precision is not sacrificed. The thin spaces, when used to separate numerical triads in tables, accomplishes that goal. One challenge is that for many readers in the U.S., the convention will be new, and most people (especially folks in engineering and science) resist change in the way they communicate.

    That is not to say that you should not press forward. Rather, you should not surprised with resistance when you do press.

    Once concern that I about clarity would be for numbers with tenths, hundredths, and so forth. I agree with Felice that such numbers are more clearly understood when they are aligned on the period. Such cases would be for measurements in which the number of significant digits varies.

    • Yes Michael, I’ve encountered nothing but resistance from my fellow engineers and scientists, but I will continue to persist—at least for a while. I was once accused of making-up the idea of spaces for triad separation.

      MM

Comments are closed.