Category Archives: Centimeters or Millimeters

A Matter of Scale

Posted on by

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:

o-HUMAN-FOOTPRINT-570

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.

Don’t Assume What You Don’t Know

Posted on by

By The Metric Maven

Bulldog Edition

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

– Mark Twain

When I first learned about viruses, I found them terrifying. They were as terrifying as any plot in a science fiction novel. They were unimaginably small. The virus shown had a set of “legs” which it could use to attach itself to a cell. It would then inject material through the cell wall from a head that looked like a gem. The cell would then become a zombie and make more viruses until it exploded like a balloon popping and the new viruses were scattered everywhere to find new cells. What I took away from the grade school lesson was that viruses were so much smaller than bacteria, they were like comparing an m&m to a basketball.

During one Summer break in college I read One two three… infinity by George Gamov. The book was published in 1947, but remains a classic. In one section of the book, Gamov explains that bacteria like typhoid fever has an elongated body “about 3 microns (µ) long, and 1/2 µ across, whereas the bacteria of scarlet fever are spherically shaped cells about 2 microns in diameter” A footnote states: “A micron is one thousandth of a millimeter, or 0.0001 cm.” It would not be until 1960 that the micrometer would become an accepted term.

Gamov explains there are a number of diseases such as influenza “..or the so called mosaic-disease in the tobacco plant, where ordinary microscopic observations failed to discover any normal sized bacteria.” Clearly something existed which was transmitting disease, but what was it? “…it was necessary to assume that they were associated with some kind of hypothetical biological carriers, which received the name virus. The use of ultraviolet light and the development of the electron microscope allowed researchers to finally see viruses and describe their structure.”

Above I have reproduced the prose and type used by Gamov. You will note that he just uses the Greek letter µ to represent a micron, which is, of course, a micrometer or µm. Gamov continues:

Remembering that the diameter of one atom is about 0.0003 µ, we conclude that the particle of tobacco-mosaic virus measures only about fifty atoms across, and about a thousand atoms along the axis.

In modern terms:

Typhoid Fever Bacteria:  3000 nm x 500 nm
Scarlett Fever Bacteria: 2000 nm in diameter

Tobacco Mosaic Virus:  280 nm x 150 nm
Influenza Virus:  100 nm across.

Atomic diameter: 0.3 nm diameter

Excellent Graphic from New Scientist “Pandora Challenges the Meaning of Life” (2013-07-13) pg 10 all in nanometers — click to enlarge

Viruses are clearly much much smaller than bacteria, and much much harder to study. But then in 2003, an organism which first appeared to be bacteria, because a common test indicated it was, was instead discovered to be a virus. It was dubbed a Mimivirus or microbe-mimicking virus. This virus has a diameter of 750 nanometers. This is just plain gigantic. Suddenly researchers found “giant” viruses everywhere! Why was this? These viruses are really big—and we have much better microscopes and tools than existed in 1947, how could it be that only in the 21st century anyone identified them? An American Scientist article from 2011 entitled Giant Viruses explains:

Most giant viruses have only been discovered and characterized in the past few years. There are several reasons why these striking biological entities remained undetected for so long. Among the most consequential is that the classic tool for isolating virus particles is filtration through filters with pores of 200 nanometers. With viruses all but defined as replicating particles that occur in the filtrate of this treatment, giant viruses were undetected over generations of virology research. (Mimivirus disrupted this evasion tactic by being so large it was visible under a light microscope.)

It was assumed that viruses were smaller than 200 nanometers, so they were filtered out. No one even thought to look for them because it was something “what you know for sure that just ain’t so.” that precluded researchers from seeing this virus for over fifty years. In 2014 researchers resurrected a 30 000 year old virus from Siberian permafrost which is the largest thus far discovered. It is called pithovirus sibericum and measures 1500 nm in length and 500 nm in width, which approaches the dimensions of the Typhoid and Scarlett fever bacteria cited by Gamov.

In the 1980s, ground based British researchers in Antarctica noticed a large depletion of ozone above them. The numbers were so low, there was concern that the instrumentation was faulty. Satellite measurements did not reveal the ozone depletion which caused a considerable conundrum. The numbers were so low that according to folklore, the computer software had a lower limit and threw out the bad data. The story is difficult to pin down and a bit apocryphal, but it illustrates what I’ve seen in my own career.

When I was first creating computer models of antenna radiation using a computer method called FDTD, I calculated radiation patterns. There are two different values to calculate, one is large and the other smaller.  An antenna was fabricated, and measured based on my analysis. The large value was measured to be almost exactly the value expected. There was a confusion on my part when the analysis showed a clearly defined smaller valued radiation pattern, but the measurements indicated no antenna pattern was present. When I showed the person who had written the program for the measurement chamber this anomaly, he remarked “That’s so low, it’s meaningless, I just set the value to the bottom of the expected range.” I had to convince him to change the computer code so it would output the actual numbers, and to his surprise, the smaller data was far, far more accurate than he had imagined.

This brings me to a ubiquitous metric system fallacy that seems rooted in the heritage of our Ye Olde English Arbitrary Grouping of Weights and Measures or Ye Olde English. This fallacy Sven and myself call “The Implied Precision Fallacy.” It is the idea that one should decide what measurement units are to be used based on a prejudicial notion of what the magnitude is expected to be measured, and the expected measurement error. It also implies that if you measure further than this, you are implying you are measuring to that precision.

This fallacy may have its roots in the past, when the available precision of a measurement device or construction device (like a mill or lathe) might have limited how far down one could measure or fabricate to a given accuracy. If a person had a problem measuring or constructing to a particular precision and accuracy because of tooling limitations, one might be tempted to argue not to bother with places beyond what they thought was possible.

Unfortunately this argument could be turned around into a rationalization that if that’s the best one can do that’s the best one actually needs. I was told many times, by many school teachers to choose medieval units which reflect expected precision, and if I used smaller ones that this was very poor practice. It was overkill. The size of the units chosen would imply the precision of the measurement, so use as large of units as possible. As you see when the size of units are used a priori as an argument of precision, then they are a chosen limitation, and not a well informed limitation. They are in fact a guess.

I have run into many situations in my career where data looks like noise, and then using signal processing, useful information is obtained. The GPS signal you use to guide your car trips is well below the noise level at that frequency. It is like standing in the top row of a football stadium and trying to hold a conversation with a person with a person on the other side of the field also on the top row while the crowd cheers. Impossible—right? Well, perhaps not. Signal processing can do amazing things, but if you argue there is no way to make a measurement precise enough, you will not. It is a psychological self-imposed measurement limit, not a technical one.

This brings me to the measurement of people’s height and the mass of babies. I have been taken to task for arguing that height should be measured in mm, just like lengths are in the Australian construction industry. Some commentators argue that this is too much precision, that a person’s height changes so much that millimeters just have too much precision to have any meaning. There is no use taking measurements which are calibrated to millimeters, because we already know we don’t need them. This is a very platonic argument. It is also nonsense on a number of levels. First, the data itself should reveal where the precision no longer exists. If one can show that a certain set of digits on the right are randomly distributed, then one can obtain an implied measurement precision, but that is not the end of the story. Even digits which appear to be random may contain information which may be extracted. I’ve never seen a situation where measurements have been too precise, and led people to miss an effect, but I have seen situations where they have been masked by truncation. Measuring a person’s height as 1753 mm does not assault good technical practice, it is an example of it. One can always write this value as 1.75 meters immediately just by inspecting the millimeters, but one has taken a simple integer and needlessly introduced a decimal point. The two representations use the same number of symbols.

The grouping of three for numbers appears to be of great utility in our society. From one thousand (1,000) to one million (1,000,000) to one billion (1,000,000,000), these values have been designated in groups of threes long before I made my appearance on this planet.  The breaks in metric prefixes, are at the locations of the commas. In other countries only a space is used above four digits: 1000, 1 000 000, 1 000 000 000 (one can use a space with four digits also—it’s just not my preference).  This is also done in many US numerical analysis references.

Pat Naughtin, in his TEDx Melbourne  lecture on 2010-03-13 discussed a scale which measured the weight (mass) of babies. The baby would wriggle and it would require the device to take large numbers of measurements and statistically extract its mass. The precision and accuracy of this scale was to within a gram. The weight of a baby is supposed to increase with time. A decrease, even a very small one, could indicate a potential health issue.

Should the baby have an infection, accurate knowledge of its mass is important so a properly proportioned amount of medicine can be prescribed. Naughtin points out that yet again there is no measurement policy in this instance, and no one in charge of one. Naughtin argued there is a potential danger when babies are measured in Kilograms, and rounded to the nearest tenth of a Kilogram, which is the accepted practice in Australia. The use of a decimal point, and rounding, creates numbers which are decanted of information. The number is too close to unity for a clear understanding of changes in its magnitude. Using grams allows for one to eliminate fractions—decimal or otherwise—and compare simple integers.

Years ago when I lived in Montana, I encountered shade tree mechanics, small engine mechanics, construction contractors and others. One phrase which seemed to be ubiquitous was:

“He’s the kind of guy that will measure something with a micrometer, mark it with chalk and cut it with an axe.”

It showed a common understanding that over-precision does not hurt one, and a person who would throw it away is not good at his profession, be it mechanic, welder, contractor, or any other skilled vocation. The Australian construction industry has saved large amounts of money by measuring in millimeters. They have no need for a decimal point, and the numbers are simple. The argument that measuring a person’s height in millimeters, or a babies weight in grams is “too precise” is a cultural argument, not a technical one. Arguing that lots of people perform a measurement, or an authority like the EU or the medical profession has endorsed it is an argument from authority.

In my essay Metamorphosis and Millimeters, I point out that for thousands of years people had created bee hives which were made of clay. They had to be destroyed in order to obtain honey. It was only in the 19th Century that an American inventor had the temerity to question this dogma, and created the modern bee-hive. Common usage over a long period of time does not imply that common usage is optimum. This is a version of a technical Darwinism argument that is used by anti-metric people as a straw man cudgel. It has been increasing measurement precision (and accuracy) which has allowed the creation of a modern technical society and is at the forefront of scientific discovery. Arguing otherwise is arguing against all the benefits increased measurement accuracy has provided. There is no “common person’s measurements” and a separate set of “scientific people’s measurements” there are only precise measurements.

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.

Updated 2015-01-21