A Matter of Scale

By The Metric Maven

Years ago, my friend Ty introduced me to the world of magical illusion. It was during this time I realized that seeing may be believing, but believing what you see is not guaranteed to be reality. For instance, one evening I attended the Indiana State Fair. I had played basketball in high school and took immediate interest in the free throw area. I had seen many of these before at carnivals, and they all had some modification of the basketball basket to make it much harder to make a free throw. The width (diameter) of a regulation basketball hoop is large enough for two basketballs to pass through it at the same time. Often, this diameter will be reduced, or a second rim will be installed to reduce the probability one will make a free throw. These modifications are usually very obvious.

That evening, I held up the regulation basketball in front of me, and used it to judge the width of the basketball goal.  It looked like two basketballs would fit. I was assured by the person manning the booth that the goal was regulation width. The other variable was the distance to the basket. I could not see the side view of the basket as there were canvas drapes on either side. I paced off the distance as best as I could and it seemed approximately the right distance.

I tried to shoot and it was short, I shot again and it was still way short. On my third and last try the basketball rattled out in a  very strange manner. I knew something was wrong, but didn’t know what. I walked around and studied the situation. Finally I was able to just peek between the seams in the canvas. The basketball goal was an oval!  From the free throw line, its width appeared to be regulation, but a basketball would barely fit through the goal from front to back. It would be almost impossible to ever make a shot. Another person realized what was happening, became angry, and started yelling at the operator. I began laughing, and walked up to him and said “learning how this worked is worth $5.00.” Before I had figured out the illusion, I was sure something was confusing my perception, because for a few years my friend Ty and myself performed magical illusions at parties we attended and elsewhere. I had learned not to trust my perception—especially at a carnival or fair.

I recall the first time I saw an engineering photograph with a ruler in the foreground. I thought it was genius. The scale is right there to provide an accurate and exact scale for the photograph. I believed (and still do) that design photographs should have scales in them.

Assuming a car is about 15 feet long isn’t the woman closer to 100-150 ft tall?

I ran across the above photograph, which has a person with the Eiffel Tower, when I was researching the Eiffel Tower for another essay. The person appears to tower over the tower. One immediately realizes that the photograph probably shows a person that is close to the camera, with the landmark in the distance, which makes him look larger than the tower. The problem is not because of the absence of an official scale, but that two contradictory ones, one which is approximate, and one which is rather accurate and known, compete for your perception. This is more formally known as forced perspective. The Eiffel Tower is often known elsewhere in the world as the 300 meter tower. The man standing next to it is probably about 1500 millimeters tall. Is the tower a miniature?, along with the background?—or is the tower far away?—or is the man actually a giant! We cannot be completely certain. Well, we can be fairly certain that a person who is over 300 meters tall would probably be structurally  and biologically unsound, and in need a serious amount of food each day, so we can scratch the giant alternative. The addition of a ruler type scale in photographs can help, but it can only do so much.

Often engineering photographs will have coins or other familiar objects to act as approximate scale references. I’ve seen South African coins used, as well as Euros, and US currency. I have no immediate idea of the size of the non-US coins. That’s why I’ve always been a fan of a nice photo documentation ruler. I see them in archeological photographs, paleontology photographs and elsewhere in engineering and science. The targets and alternating stripes on the rulers used in engineering and scientific photographs have always held an unexpected fascination for me. What I’ve found somewhat surprising, is the apparent lack of standardization of photographic documentation scales. What first made me think about this was when I recently viewed a photograph from a collection by the 19th Century photographer Timothy O’Sullivan. The photograph of interest is reproduced below:

An earlier visitor: Nearly 150 years ago, photographer O’Sullivan came across this evidence of a visitor to the West that preceded his own expedition by another 150 years – A Spanish inscription from 1726. This close-up view of the inscription carved in the sandstone at Inscription Rock (El Morro National Monument), New Mexico reads, in English: “By this place passed Ensign Don Joseph de Payba Basconzelos, in the year in which he held the Council of the Kingdom at his expense, on the 18th of February, in the year 1726” (click on image to enlarge)

When I first looked at the scale in the photo, I thought “it has to be inches,” but the numbers and graduations seemed just too closely spaced, they looked somewhat like centimeters. The photograph was taken in 1875, so it’s not impossible it could be metric, but in all likelihood it is in inches, but how to know?  Sven noted that the length is 36—somethings, which could well be a yard. It is also possible that in the early days of metric a 36 cm rule might have made sense to people of that time. The rule is only graduated in even numbers, and with 2.54 cm to an inch it gives one pause—no that doesn’t make sense. The handwriting could be of any size and the form of the letters used is not consistent. The plant in the foreground is unfamiliar and not useful for scale. Clearly the photographer knew the units on the scale, but posterity is less certain. If the scale is 36 inches, then the width of the yardstick is about 2.31 inches or 58.7 mm, which seems reasonable. If the scale simply had inches written on it, or a yard, or both, that would help.

When I began doing my own engineering consulting, I decided I wanted to use photo documentation rulers (PDR) when taking photos of my designs and other devices. It caused me to observe PDR’s in a more careful manner than I previously had. In a recent PBS Nova I noted this PDR:

Human finger ring found by archeologists made of jet

In this case, the labeling actually causes some confusion. Are the alternating stripes each 5 cm in length?—or is the entire scale 5 cm and each stripe 1 cm? As this is a ring, one can be fairly sure it is the latter, as a 20 mm inner diameter makes sense. The idea of putting the photographic documentation ruler there in the first place is to remove the need for context. I decided the scale of the PDR based on knowledge of the object. Clearly this is not a good scale label. It is very common for metric PDRs to have 1 cm length stripes. Unfortunately many PDRs which are for sale have centimeter numbering, but use mm for an alphabetical designation. This is the same problem one finds with US rulers.

Centimeter numerical graduations with mm label

The inch version has no alphabetical designation. One would have to infer its units by the context of the subdivisions, as they appear fractional:

The inch PDR has no inch label. It assumes you know the units, possibly from the way the divisions are implemented.

Rather than accepting  the ways I’ve generally seen PDRs designed, I very much like the idea of using 10 mm length stripes on PDRs. I would also like the numerical designations to match so that the scale has divisions which are 5, 10, 15 and so on. A label which states mm would be adequate to make certain one understands the numbers and labels are consistent. A further advantage is that one would not confuse a centimeter scale with an inch version which one would also expect to have 1, 2, 3 and so on as numerical designations.  Below is a scale used by the Allegany County Coroner’s Office which clearly shows millimeters, but lacks alternating black and white stripes. Clearly one can tell it is a mm only scale.

In my search I found a few—very few options for the type of photo documentation rulers I’ve described. One I commonly use in my work is also used as the mast head graphic for this blog. I also use an L shaped PDR which was purchased from SIRCHIE. Forensics Source is another vendor that has some mm only PDRs.

Recently archaeologists in Denmark uncovered footprints on a Danish island which are over 5000 years old. This photograph appeared with the article:


The large scales I own have orange and white alternating stripes, which are each one hundred millimeters (a decimeter) in length. The ten millimeter stripes used for the ring example previously discussed were confusing even though it had 5 cm written on the scale. In this case we see a handwritten 40 on the scale. Once again we end up estimating the length of the “documentation scale” and guess its unit by noting that an adult male human foot is around 250-300 mm, but could it be a woman’s foot, a child’s foot?–a hobbit’s foot?

When I watch television programs such as Forensic Files, I see metric, millimeter, centimeter, dual-scale, and inches only PDRs, but one one night I saw this:

It appears to be an adhesive scale with inches in an outlined typeface, and boldface feet. You can see it goes from 1 to 11 (like Spinal Tap) and then a bold 1 appears meaning one foot. The second one which follows is a new inch after the foot designation. Only in the United States would one see a scale with feet and inches without any alphabetical markings to clarify the matter. This is forensic evidence?—I expect better.

In my view, long ago US law enforcement, coroners and others should have standardized. It is my contention that the best standard would be to use millimeter only scales, with 10 mm calibration stripes, and numerical millimeter designations. The stripe lengths would still be consistent with the old cm versions, but the numerical designations would not be confused for centimeters or inches. The exchange of evidence between US jurisdictions and foreign countries would never entail any conversions if this was done, be it shoe prints, tire prints, or other evidence. Complexity only provides opportunities for error. This is yet again another symptom of the fact we have never had a government coordinated mandatory metric switch-over in the United States. This measurement autopsy is not pretty, but unlike a biological one, we can resurrect and bring the body of measurements in the US to complete health, but this cannot be done in isolation. Without government intervention, and business cooperation, it may never happen, much to our detriment.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

2 thoughts on “A Matter of Scale

  1. I was hoping you would list a good source for PDRs. I have taken pictures with metric rules and found it unsatisfactory – the metal with black markings photographs poorly unless the angle and lighting are perfect.

    A guy with a print shop could probably come up with a good solution and corner the PDR market. Looks like Amazon has a few – perhaps I will create a PDF of one and post it here when I have time.

    • You could probably improve on this one, but someone has already done one. Click on the image to download the pdf.

      I would prefer it without the inches and also not such fine (0.5 mm) graduations, at least on the 30 cm ruler. I measured it against a more accurate rule. It prints pretty close on my printer (be sure to select 100% in print dialog).

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