The Presentation of Blank Space

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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:

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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:

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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.


Kilowatt My Ride

By The Metric Maven

The first manifestation of my interest in both art and engineering was when I first saw some of the crazy models of Kustom Kars created by Ed “Big Daddy” Roth. I had obtained a small plastic Rat Fink from a novelty dispenser, and in my single digit youth experienced a fascination with metallic sheen, so I spray painted the small plastic image with gold paint. I witnessed the last few years of the American Graffiti era in the US. On Saturday nights in my small town, I watched a string of cars cruising down main from a second story window. Myself and others would identify each car cruising main street, each had a customized low pitched rumble emanating from their engines. They pointed out cars like a ’57 Chevy Nomad, ’68 Camaro with moons along with three digit integers for each engine displacement. The bigger the number the better. There was the 289, 350, 383, 442, 396 and 454, which all became familiar. The Beach Boys had a song called 409, which a news segment assured me was a fictitious engine displacement number. One evening I saw a late 1950s Chevrolet Impala with a 409 on its side. I thought it was a joke. I knew the person driving it, and asked if it was real. He said “everyone seems to ask me that.” He pulled out the oil dipstick and it read 409 SS. Never had a single number of measurement seemed so romantic. I should have realized The Beach Boys would know more about cars than a TV reporter. In 409, the Beach Boys make a direct metaphor with a horse, as the refrain goes: “Giddy up giddy up 409”

There was not much mention of horsepower, but one would hear values from 300-400 when engines were discussed. It wasn’t something that was readily measured. The time in the quarter mile, or who had beaten whom in late night racing, was the metric used by those who still cruised Front Street. The first and second Arab oil embargoes of the 1970s brought the era of muscle cars to an end for the average teenager. The 1970s was the era when US cars began to become metric.
Only in recent years did I begin to realize that all those three digit engine displacement numbers had all become two digits with a decimal point. When I drive along the streets of my metropolis I see numbers like 3.7 L or sometimes numbers over five liters, which I know is a serious amount of engine displacement.

Engine displacement in cubic inches was a proxy for the power output of a car engine in the 1960s-1970s, a 289 was not going to be as powerful as a 396, but they were not direct power descriptions. They were also strictly tied to Otto gasoline engines. Another type of engine introduced in that era, the Wankel engine by Mazda, was not. It did not have a set of pistons, but instead a stator and rotor, which caused a mismatch between its displacement and that of Otto engines. The Mazda had a 10A engine (10 suggesting 1 Liter). In races this caused considerable confusion, and often the displacement quoted for Wankel engines was doubled. The old “reliable” three digit displacement in cubic inches was not consistent, even for gasoline powered cars.

Dodge Demon

The Kustom Kar Kulture of the 1960s and 1970s has been preserved, but is no longer a mainstream activity of modern youth. The nostalgia for these cars is epitomized in the television series Counting Cars. They are almost exclusively cars from before 1980 and exclusively non-metric. But time has moved on, hot cars remain, but have morphed. My friend, Dr. Sunshine, has a friend, Good Randy, an extreme car enthusiast, who keeps him up on current car culture. Dr. Sunshine one day showed me an image of a car on his smartphone, and asked if I could identify it. I had no idea, other than it looked pretty cool. It is the Dodge Demon, and it is currently the most powerful production car ever created. Rumors were flying that it would have 1000 horsepower or a mere 746 Kilowatt. My mind reeled at the amount of energy flow involved. I made an off-hand comment about how electric motors are much more powerful than mechanical engines. Dr. Sunshine pointed out that in car races electric cars are not allowed, specifically Teslas, which they disparagingly call “the world’s fastest golf cart.” He told me the Tesla has a “ludicrous mode,” where the car is able to go from 0 to 100 Km/hr in 2.8 seconds. I smiled and said that in this case “Maxwell beats Newton.”

Three digit engine displacement has been a problematic proxy for energy output when comparing Otto and Wankel engines, and now electric motors. Electric motors outperform engines,  but don’t have a displacement value, as they are not heat engines. The obvious metric, in a metric age, would be watts. Energy in the metric system is measured in joules. The amount of energy flow is in joules per second, which is defined as a watt. The use of watts provides a measure that is common for all vehicles, steam powered, gasoline powered, diesel powered, natural gas powered, or electric powered. The way to get a feeling for the energy output of vehicles is to compare them with known historic and contemporary vehicles directly and unsegregated. The appropriate prefix would generally be Kilowatts, but to maintain integers (Naughtin’s Laws) I’m going to produce the table using watts:

I suspect that persons in their 20s, 30s and possibly 40s do not have any feeling for a 289 engine versus a 454, as all modern cars have liters on their sides. (My 1959 Volkswagen Beetle had around 1200 mL (cc) written on its rear lid or 1.2 L.) If they have any feeling for the displacement of engines as a proxy, it would probably be in terms of liters. That proxy disappears with electric cars. In my imagination, it would be interesting to see 131 KW on the side of a Toyota Rav 4, and 215 KW on the side of a passing Tesla 2.5 Sport. The Toroidion would have 1000 KW or possibly 1 MW depending on the desires of marketing. The expected values would be from 25 to 1000 KW for cars in general. Looking at the table we can see that my 1959 chartreuse Volkswagen Beetle had about ten times less power than my friend Rick’s 1968 Plymouth Road Runner.

Of course, the power output alone doesn’t given any feeling for the amount of acceleration one can expect. A fast car in the era of Muscle Cars was around 12 seconds or so for a quarter-mile as I recall. A quarter-mile is about 400 meters, so this could be changed to 400 meters. Humans have run the 400 meters since the first modern Olympics in 1896. The current 400 meter world record is 43.03 seconds for a human, so a fast street legal car would take about 12 seconds or so to cover the same distance. The Dodge Demon has the production car record with 9.56 seconds. The Demon is about four times faster in the 400 meters than a human can run. The Tesla Model S takes 10.44 seconds. The world’s fastest horse ran 400 meters in 20.57 seconds. So a horse can run 400 meters about twice as fast as a human. The fastest production car with a heat engine is about twice as fast as the fastest horse.

I won’t hold my breath waiting to see a Jeep Wrangler with 354 KW in chrome letters, a new three letter power designation value, that is actually equal to power, but a person can always dream. Mike Joy sent me an ad from Australia that gave me at least a little hope for the future:

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essay:

One Hundred is Everywhere!

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.