Gauss & The Metric System

When I was in High School, I had the momentary thought that I might have some talent for mathematics. This delusion passed immediately, but I’ve done my best to understand as much about the subject as possible. I did have my mathematical heroes to whom I looked up in admiration. In the pantheon of great mathematicians, Carl Friedrich Gauss was Zeus. He was the man who loved numbers from his youth onward. Isaac Asimov stated: “He was virtually mad over numbers.” He created the method of least squares, which enabled Gauss, still in his early twenties, to compute Ceres orbit from a few extant observations. He developed mathematics that allowed for the discovery of Neptune. Isaac Asimov points out in his Isaac Asimov’s Biographical Encyclopedia of Science and Technology:

While still in the University he also demonstrated a method for constructing an equilateral polygon of 17 sides (a 17-gon) using only a straight edge and compass. Here was a construction all the Ancient Greeks had missed.

Gauss proved the fundamental theorem of algebra, and the fundamental theorem of arithmetic. He invented the Heliotrope which used the sun to produce accurate land surveys. The device was used into the late 1980s when it was replaced by GPS. He created the first observatory to measure terrestrial magnetism, and calculated the location of the magnetic poles from geomagnetic observations. In 1833 he constructed an electric telegraph as Joseph Henry was doing the same in the US. At age 62 he taught himself Russian.

Gauss is responsible for the development of the normal distribution or “Gaussian Curve” (bell curve) that describes many natural processes. This was celebrated on a German 10 Mark note, an example of which I proudly own:

My 10 Mark Bank Note

When I arrived at my Midwestern university to study engineering, I enjoyed looking at the paper clad doors of the professors and graduate students. I saw one with a theorem that I’ve completely forgotten the professor was quite proud of creating. There are Mean Nerds, and one wrote anonymously on the paper, “if this was really important Gauss or Euler would have already discovered it.” Ouch! Early on in College, I was told that centimeter-gram-seconds (cgs) units were “Gaussian.” This was not very important as we were using MKS or essentially what is now SI in engineering school.

I never gave it a second thought until years later my metric studies brought me to read and listen to Pat Naughtin, who implored people to use millimeters and not centimeters. His arguments all seemed very sound, but in the back of my mind I remembered cgs and sweat began to form at my temples. Gauss? How could he not see the obvious advantage of millimeters over centimeters? This was of much more concern to me than any nonexistent “error” Mechain or Delambre might have introduced. It was a debate point I did not want to disclose. It provided a gloomy low-level angst in my psyche. How on Earth could Gauss have been pro-centimeter?

Over the years I became more and more convinced the British under the auspices of the British Association for the Advancement of Science (BAS) were behind the c in cgs. I was certain they were using centimeters as a virtual inch to maintain a vestigial version of their precious imperial measures somehow. A unit with a magnitude near the size of an inch must be preserved for Queen and Country. But in my view, it’s just not cricket. I didn’t have any documentation to reinforce this suspicion, and my evidence was circumstantial. But how could it be that Gauss would go along with this terrible choice? After all they are called “Gaussian units.”

With the recent re-definition of the Kilogram, I found my answer: “he didn’t.” While reading through the new SI Brochure, I found these two nuggets of information on the history of the metric system:

So Gauss, used millimeters!—-and as I suspected the notion of centimeters was apparently introduced by the BAS. Gauss had been dead since 1855! My relief was existential as I no longer had to furtively worry about a question I might be asked, but never was. Gauss used millimeters, and the apparent intellectual blemish simply did not exist. He used a millimeter-gram-second system–mmgs!. In the future, when I’m asked, “who other than you thinks we should use millimeters?”, I can reply without hesitation: Isaac Asimov, Herbert Arthur Klein, Pat Naughtin, and Carl Friedrich Gauss.

Related essays:

Familiarity Versus Simplicity

Building a Metric Shed

Who Says!?

Metamorphosis and Millimeters


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.

Project Hail Mary

I worked in aerospace for about 8 years, and in commercial engineering for about 15 years. The last company I worked for was packed-up and divided between China and India. I found myself accidentally becoming an engineering consultant. I expected to do this for perhaps 2 or 3 years at most, and then take a full-time position. It has been 14 years. When I found myself setting up my lab, it was a bit like how Thomas Paine described the potential of the young United States: “We have it in our power to begin the world over again.”

I decided there must be a person or persons somewhere that had studied and investigated the best way to use the metric system. The person I found by internet search was Pat Naughtin. He had wisdom and experience, but I had provincial American certainty in my unexamined views. Fortunately, I had Sven, and also the ability to change my view when the information I have changes. I very soon understood the utility of millimeters, and the Olde English distraction of centimeters. Cultural inertia in the US provides a ready barrier to adopting intellectual change—even when it is clearly superior after dispassionate examination.

It has been decades since I last worked in aerospace. I know a couple of engineers who worked in commercial, and moved to aerospace after our commercial company off-shored. I had lunch with them, and when I mentioned a dimension in millimeters, one of the pair jokingly said “what’s a millimeter?” Thirty years after I had worked in aerospace, and had metric drawings rejected, aerospace still uses inches, foot-pounds, and other non-SI measures, when the non-US world uses metric.

As I’ve pointed out in the past, the use of Ye Olde English (Imperial is New English) measures has colored our view of how to most efficiently implement a measurement system. The compulsion to translate the new system into the same familiar measures seems irresistible. Inches are a familiar size of pre-metric measure, so we’ll have a centimeter. This does two things psychologically, it first validates the current measurement prejudice, and second it diminishes the importance of adopting the metric system at all. A number of European countries adopted the metric system in the 19th century, and adopted an “Imperialized” view of metric usage, embracing the centimeter, deciliters, and such. When I question the use of centimeters there is often a visceral reaction: “lots of people use centimeters, they’re perfectly fine.” This is very strange, as it is the same non-argument Americans use about inches, feet, and so on. It was only the later adoption of metric in places like Australia, New Zealand, South Africa and others that allowed for more introspection, and a more rational adoption of efficient metric practices.

The instinctive reaction is to look for the commonality in measures, and equate the Anglo-Saxon compromise inch with centimeters. This was certainly the case in aerospace. It was seldom that metric was used in a discussion, but when it was you can be sure it was with Olde English interpretation in mind. Thirty years have passed, and for the last 14 I’ve tried to implement as much simplified metric as possible. Has any measurement change occurred in aerospace since my absence?

This year, 2021, Andy Weir published his new novel Project Hail Mary. I almost never read fiction anymore, but the gushing over this novel caused me to purchase a copy. Before I say anymore, this novel is the best piece of science fiction I’ve seen in decades. This is hard science fiction. Science is constantly used to move the plot along. There are no large dog-fights between space ships. No buxom space women. If you like SCIENCE in your science fiction, this is the book for you. I highly recommend it. It is like a combination of Isaac Asimov’s The Gods Themselves, The Currents of Space, Micheal Creighton’s The Andromeda Strain, and well, many other classic works of science fiction. This book is truly unique in today’s science fiction zeitgeist. I’m going to do my best not to introduce any spoilers, so forgive some of the vague discussion that follows.

It appears Andy Weir worked in government labs, and commercial companies for much of his career as a computer programmer. The use of metric throughout Project Hail Mary is consistent with the same pidgin metric I recall from my days in aerospace, and much of my commercial experience. Amazingly, early in the novel, metric usage is important to the plot, which is refreshing, but it also would could have been more nuanced if the author had a more expanded view of metric usage. His usage is consistent with the same metric usage I experienced in aerospace 30 years ago—nothing appears to have changed. I find no fault with Andy Weir, he is offering me a touchstone of the metric ossification that exists in 2021.
Most readers will never notice.

Andy Weir uses the term imperial for pre-metric measures and does not make distinction between Ye Olde English, and New English measures. I don’t fault him for this, as it is part of the word-of-mouth tradition in the US, rather than education based on investigatory work. I suffered from it myself. Microns are constantly in use, but I don’t recall a single micrometer within the text. There is a constant back-and-forth of pre-metric and metric units. The book is a centimeter smorgasbord with millimeters seldom encountered. The irresistible cultural force to phase-lock onto a unit that preserves pre-metric usages is a powerful one. The separation of what could be all millimeters into centimeters and millimeters is seen as normal:

“The solar disc is 27 centimeters on-screen and the sunspots are 3 millimeters. And they moved half their width (1.5 millimeters) in ten minutes…..”

Andy Weir has an understanding of how non-metric use is detrimental for American engineers and scientists:

“The tunnel is about 20 feet long. Or 7 meters. Man, being an American scientist sucks sometimes. You think in random, unpredictable units based on what situation you’re in.”

There is a point in Project Hail Mary where the definition of units becomes of importance, and centimeters are chosen. There is a place where a measurement error is of great importance to the plot, but as I said—no spoilers. Finally there is this:

“Yes, inches. When I’m stressed out, I revert to imperial units. It’s hard to be an American, okay?”

It is a sort of echo of Naughtin’s 1st Law: Dual-Scale Instruments are Evil. One reverts back to what one has used since grade-school. The educational system decides what “comfortable” measurement units are when you are young, and it makes it more difficult to “get a feel” for new units in an ocean of “imperial.”

Project Hail Mary gave me a touchstone into how metric is used in industry. Andy Weir has a very, very, promising future as a science fiction writer. I’m very hopeful that with all the use of measurement found in his novel, that he takes some time to look into modern metric usage, and perhaps integrate it into future work.


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.