Jackalope Tales

By The Metric Maven

Bulldog Edition

There are stories we tell ourselves to bring order to our world, and to define a culture within it. It is generally assumed that when scientific histories are written, they, unlike others, are thoroughly researched and checked against primary sources. Engineering and scientific discoveries have origin stories and the people involved become an important part of the narrative.

One interesting person and eponymous group is Pythagoras and the Pythagoreans. It is stated that Pythagoras was the first to prove the Pythagorean theorem. His group of ancient nerds were vegetarians, and also eschewed beans from their diet. Pythagoras had a strange birthmark on his thigh. I once read that Pythagoreans would not use metal to poke fires and after rising in the morning would smooth out the imprint they left in their bedclothes. Alberto A. Martinez in his book The Cult of Pythagoras: Math and Myths offers up a multitude of stories about the man and his followers.

According to Martinez, there is just one problem with the tale that Pythagoras proved the Pythagorean theorem: “… the story that Pythagoras found, proved, or celebrated the hypotenuse theorem dissolves into nothing.” There is no direct evidence of any kind that he had any interest in mathematics. Martinez studies contagious stories that have been passed down from century to century and embellished along the way. The author presents a table that summarizes the “game of telephone” that historians engage in:

The-Illusion-of-KnowlegePythagoreansIf Pythagoras wrote anything, his works were lost to antiquity. Gradually, like a tiny snowball rolling down a hill, layer after layer of detail began to accumulate on the tiny nugget of Cicero’s unsubstantiated assertion. According to Martinez, author Eric Temple Bell in his excellent and entertaining book Men of Mathematics is a prominent voice that added to this snowball of myth (and others).

Eric Temple Bell claimed: “Pythagoras then imported proof into mathematics. This is his greatest achievement. Before him geometry had been largely a collection of rules of thumb empirically arrived at without any clear indication of the rules, and without the slightest suspicion that all were deducible from a comparatively small number of postulates.” Bell wrote in an engaging way, but he echoed false anecdotes, adding imagined details and exaggerations.

The author offers another assertion about Pythagoras which has no primary source:

Diogenes Laertius said that Aristoxenus the musician claimed that Pythagoras was “the first person who introduced weights and measures among the Greeks.” (pg 205)

Martinez goes on to describe the slow creation of the tale of Archimedes’ death, and how it blossomed from an absence of information into a full-blown tale of his death at the hands of a Roman solder as he was drawing a mathematical proof in sand. This story of Archimedes’ death has been passed down and enhanced from Cicero, to Plutarch, to E.T. Bell in 1937, to Peter Beckmann in 1971, and Steven Hawking in 2005.

When I was in grade school, my class was asked to add the integer numbers from 1 to 100 and give the answer. I began thinking about how much paper it would take to do this, and wondered what we had done to deserve this type of punishment. Why was this assignment offered? Because it is erroneously believed that the mathematical genius Karl Friedrich Gauss, when he was a boy, had shown his mathematical promise by realizing that he could add 1 + 100 = 101, 99+2 =101, 98+3=101 and so on 50 times to make 101 x 50 or 5050 and quickly obtain the answer. It is said the boy offered up a general formula for the sum of integers from 1 to any end number. There is just one problem with this historical tale, it has no historical text or evidence to back it. It is a sort of scientific urban legend.

Recently The Atlantic, on June 6th, 2016 (2016-06-06), for reasons only they know, offered up two articles about the metric system. The first article is titled: Why the Metric System Hasn’t Failed in the U.S. And has an important place in education. Its author is Victoria Clayton. She interviews High School teacher Sally Mitchell who has been involved in metric promotion for some time. When Clayton queried her about why the US has not become metric:

Mitchell said. “And here’s the answer: We have, many years ago.” Well, yes and no. While many U.S. enterprises—from soft drinks and distilled spirits to cars, photographic equipment, pharmaceuticals, and even the U.S. military—are essentially metric, everyday use—Americans’ body-weight scales, recipes, and road signs, for example—hasn’t converted. And neither has the country’s educational system.

Clayton introduced a bit of healthy skepticism into Mitchell’s claim: “we have, many years ago” converted to the metric system, when it is clear to the most casual observer, we have not.

Next we read:

“I would say that the United States of America is at least 40 percent metric, perhaps even a little over 50 percent metric in practical terms,” said David Pearl, an Oregon government worker who, in his free time, is a self-appointed U.S. metric historian….”

This chestnut of 50% metric has been waved around probably for decades now, and there is not a single academic study, reference, or anything else, other than desired truthiness to back this claim up. I would like to know just how much metric is used in the US. I would like to see scholarly studies about metric usage that can be cited, and that offer up actual numbers. At this point I have no information that is substantial. I have my personal experience, and that can almost always be counted upon to be flawed.

A new tale with an old excuse is offered to explain the absence of metric in the US:

In the early days, the metric proponents lost elections and the customary—that is, pounds and inches—guys won. The issue continued to get tossed around, however. Then around the late 1870s, U.S. manufacturers of high-end machine tools effectively blocked the country’s metric conversion. By that time they were using a measurement system based on the inch and argued that retooling would be prohibitive.

This is new information to me. It was the outcome of 19th century elections and losses by pro-metric candidates that decided the fate of the metric system? I would very much like to see the source of this information or some primary sources upon which it is based. I don’t recall this information appearing in NIST historian Charles F. Treat’s A History of The Metric System Controversy in the US. This assertion would be an interesting new piece to the US non-metric puzzle, but probably not the smoking gun it seems to be offered as. Nineteenth-century pro-metric politician John Shafroth was re-elected and served as a US Representative, Senator, and was Governor of Colorado. In the twentieth century Clayborn Pell served six terms and opened the 1975 metric hearings.

John Bemelmans Marciano is brought in by the Atlantic to testify to the futility of any country adopting metric:

“I can’t overstate how much resistance there’s always been to metric in any country that adopted it,” Marciano said. “In Brazil, it caused a riot that went on for months. In France, it took decades and decades.” Yet, in the U.S., resistance seemed to prevail.

The article does address some actual problems that the US has experienced from its rejection of metric, such as medical dosage errors caused by teaspoon-tablespoon confusion. But the Atlantic once again calls on JBM’s “expertise” and his “extensive research”:

And Mitchell, the science teacher, says she’s witnessed firsthand that measurement bilingualism simply doesn’t work well in the classroom. “I think it’s just very confusing for kids.” She fears measurement confusion contributes to U.S. math and science woes. U.S. students have slid on their global ranking in science and math, according to the National Center for Education Statistics. In the most recent ranking, the U.S. was slotted between the Slovak Republic and Lithuania—just behind Russia. Still, there’s no evidence that Americans’ shaky embrace of metric accounts for math and science troubles. And Marciano, who spent three years researching his book, finds Mitchell’s argument preposterous—akin to saying humans can’t master two languages.

The comparison of measurement systems with human languages was the same red herring used by former NIST director Patrick Gallagher. It is the same narrative, the same story, the same myth repeated over and over in the press and by their celebrated persons. Why?—because it offers Americans a comforting truthiness. Clayton continues with another meme:

Why, then—if junior scientists applaud the effort, NIST supports it, and my kids and I had so much fun going metric in the kitchen—has a total switch to metric been such an epic battle with the public?

I have pointed out many times that the history of the metric system in the US seems to have very little to do with the public. The tale of the Metric Populist Uprising of the 1970s is but a comforting mythology. The 1975 Metric Hearings demonstrated that mandatory metrication of the US was never contemplated or enacted—period. Metric reform in the US never dies, it makes an evanescent appearance and then fades away.

The second essay offered up by The Atlantic is called Who’s Afraid of the Metric System? Stephen Mihm, an associate professor of history at the University of Georgia is interviewed about the metric system. Mihm indicates that it was makers of machine tools who thwarted the implementation of metric in the US. Mihm is said to be working on a book titled Mastering Modernity: Weights, Measures, and the Standardization of American Life. Early into the interview this exchange takes place:

Appelbaum: We’ve arrived at a hybrid system. Most American rulers show inches along one edge, centimeters along the other. Is it possible that the metric system will slowly displace English measurements, not by government fiat, but one inch at a time?

Mihm: Yes, that’s right. If history is any guide, government fiats don’t work when it comes to weights and measures. The undertow of history and custom is too strong (proponents of the metric system, for example, are often unaware that it took many decades for France to get its citizens to adopt it—there were many, many setbacks and a staggering amount of resistance).

The article has a quotation “pull out” of the phrase: “Government fiats don’t work when it comes to weights and measures.” in large type for readers just glancing at the essay to propagate the implied, accepted and sanctified cultural message and excuse. It is an embrace of inaction, and is used to justify its continuation. If history is any guide, the metric system is perhaps the most successful scientific idea in the history of technology. Currently, depending on how you count them, there are about 190 countries. Of them 187 have become metric. It is curious that only France is generally discussed and never Australia or New Zealand or dozens and dozens of countries without turmoil. The US introduced metric into the Philippines and it took but seven months.

I would challenge the professor to offer a single example of a nation that became metric using passive government inaction and relying instead on “technical Darwinism.” Australia became metric through legislation and government mandate requiring metric be used. Each industry could choose how they became metric, but metric was mandated. The statement that government fiats don’t work is a meme that is finely tuned for a resonance with a certain American mythology. As I point out in The 1000 Year Wait, it took Hindu-Arabic numerals about 1000 years to be adopted around the world without any government influence. The metric system swept the world in about 150 years with it.

The final exchange in the minute missive confirms another entrenched story about the metric system:

Appelbaum: Chafee’s call for the United States to adopt the metric system generated an immediate backlash. Why does a seemingly dry subject like metrology ignite such intense passions?

Mihm: National pride is at stake. The adoption of another country’s weights and measures—or in the case of the metric system, the rest of the world’s weights and measures—seems an infringement on national sovereignty. That the system in question has a long and distinguished history as a pet project of Francophile, cosmopolitan liberals probably doesn’t help make it appealing to American conservatives.

The implementation of the metric system may have been a “pet project” of France, but the system part of it originated in England. The articles presented in The Atlantic appear to act only to confirm inaccurate metric mythology that comforts status-quo Americans with embellished and fictional tales about the metric system. The metric research done for the Atlantic articles is a Megameter wide and a millimeter deep.

While stories of Archimedes Death, and the strange rites of the Pythagoreans have generated compelling historical myths, they are but the kind of Jackalope tales offered up inside of winter cabins, not for education, but simply for entertainment. The difference is that interlocutors inside of a Montana cabin in the 19th century knew they were spinning tall tales for entertainment and to test audience credulity. Many “historians” of the metric system, and the journalists who interview them, seem unable to realize they have engaged in the same activity, but without the realization they are simply playing telephone.


The Metric Maven has published a new 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.


Perception, Illusion and Measure

Sir William Fettes Douglas The Alchemist 19th cent.By The Metric Maven

My friend Ty introduced me to magic in my very late teens. The strange perception traps I encountered taught me some valuable lessons about the information presented to our eyes, and how it is interpreted by the brain. A vacuum of information causes the mind to devise fanciful interpretations. One day Ty purchased a small penlight and placed it into the front pocket of his jeans. The penlight had a momentary contact button on its back end. Ty then flashed the light and asked if I could see it through the cloth. Indeed I could barely see it, but when the room was darkened it was much easier.

Even though neither of us were in college at the time, we went to a fraternity party. Ty told me that he was going to tell one of the guys he knew, currently standing across the room, that if he whispered a number from one to ten into Ty’s ear, that person could walk across the room, and I would tell him the number as Ty remained in place. I stood there as the music blared and the person talking with Ty glanced at me with a skeptical countenance. As he walked across the room, Ty flashed the penlight in his pocket four times. When the participant asked what number he had given to Ty, I said “four.” His eyes became large. He went back to Ty, offered another number and walked back with his eyes on Ty, but apparently not on his pocket. I told him the new number, and he was shocked. A large crowd gathered around us, and with Ty only a meter or two away, several people whispered numbers into Ty’s ear, and each time he flashed the number. Not one person in the crowd noticed the flashes emanating from the cloth in his pocket. I was astonished, they were all looking for the wrong things in the wrong place, but the flashing seemed obvious to me, because I was looking for it.

At the corner of the basement where the party was held, was a bathroom. The skeptical crowd requested that Ty go into the tiny bathroom. A person would tell Ty a number and then leave the bathroom where Ty would remain sequestered, and then ask me to tell him the number. I started to freak out, but Ty remained calm. He claimed we could do it. I had sweat beginning to form on my brow as Ty leaned over slightly said “don’t worry I know you’ll figure it out.” He and the other person retreated to the small room. Then the participant emerged, carefully shutting the door behind him. As he walked across the room, I saw Ty flashing the penlight onto the floor through the crack at the bottom of the bathroom door. I counted “one, two…..” up to seven. No one in the crowd saw the large spot of light on the floor! There were probably 10-15 people standing in the room, intently watching me. When I announced that the number was seven, an exasperated gasp emanated from the group. “Ok, you must be a psychic!” one participant claimed.

He had no other hypothesis, and with this seemingly supernatural phenomena confronting the group, they assumed the explanation was that I had supernatural powers. Neither of us claimed these powers, we only claimed to be doing magic. Others in history would not be so forthright. Around the same time I was learning about magical illusion, I read Charles Mackay’s 19th century classic Extraordinary Popular Delusions and the Madness of Crowds. In his chapter on The Alchymists, one alchemical practitioner would brag that he had converted into gold “no less than fifty thousand pounds weight of quicksilver, lead and pewter into that metal.” (pg 117). The total amount of gold estimated to have been mined by humans is about 174 Gigagrams or about 174 000 Megagrams. The alchymist by himself would have added the not  unsubstantial amount of approximately 19 Megagrams. There was considerable concern that this claim was more than puffery, Macay points out:

In the year 1404 an act of parliament was passed declaring the making of gold and silver to be felony. Great alarm was felt at this time lest any alchymist should succeed in his projects, and perhaps bring ruin upon the state by furnishing boundless wealth to some designing tyrant, who would make use of it to enslave his country.” (page 129)

Mackay cites Alchymist after alcymist. The large number of witnessed “transmutations” were attributable to the use of devices which were designed to produce the illusion. In Charles Mackay’s words (pg 215):

The trick to which they oftenest had recourse was to use a double-bottomed crucible, the under surface being of iron or copper, and the upper one wax painted to resemble the same metal. Between the two they placed as much gold or silver dust as was necessary for their purpose. They then put in their lead, quicksilver, or other ingredients, and placed their pot upon the fire. Of course, when the experiment was concluded, they never failed to find a lump of gold at the bottom. The same result was produced in many other ways. Some of them used a hollow wand, filled with gold or silver dust, and stopped at the ends with wax or butter. With this they stirred the boiling metal in their crucibles, taking care to accompany the operation with many ceremonies, to divert attention from the real purpose of the maneuver. They also drilled holes in lumps of lead, into which they poured molten gold, and carefully closed the aperture with the original metal. ….

The number of exposed methods continues for another half-page. My familiarity with magical illusion recognized these as familiar tactics. My knowledge also gives me pause as I realize how easily I and others can be fooled into perceiving apparently supernatural occurrences.

All this information passed through my mind when I was re-reading L. Sprauge de Camp’s book The Ancient Engineers. The author describes an ancient work known as Mechanics. It is the world’s oldest known engineering textbook. Quoting de Camp (pg 123):

The author of the  Mechanics then goes back to the lever and discusses the geometry of the beam balance. He notes that dishonest merchants had discovered how to rig such a balance or scale to cheat their customers:

And thus dealers in purple [dye], in weighing it, use contrivances with intent to deceive, putting the cord out of center and pouring lead into one arm of the balance, or using the wood towards the root of a tree for the end towards which they want it to incline, or a knot, if there be one in the wood; for the part of the wood, where the root is, is heavier, and a knot is a kind of root.

This work is probably from around 300-400 B.C..

Sven states that Pat Naughtin once indicated that the history of measure is also a history of fraud. I’ve not been able to locate this quotation on his website, but Naughtin in large letters has always asserted:

ProHonesty-ProMetricThis aphorism has precipitated some snarky comments which state that it is an outrageous assertion that to not be pro-metric is to somehow promote dis-honesty. Those who have read my blogs from the beginning, will note that I have given examples of the contemporary use of pre-metric measures, such as those used with my utility bill, which might not be directly dishonest, but certainly obfuscate understanding without considerable unit conversion.

Derek Pollard of the UK Metric Association sent me a monograph entitled Metrical Miscellanea and Muddle a long time back. This work emphasizes the public’s concern for just and fair weights and measures as it has existed from the shadows of history to contemporary times. The book is written with a UK audience in mind, and therefore stresses the British experience with weights and measures.

The monograph has illustrations of a bismar, a sort of counterweighted scale that was in use for over one thousand years. It was renamed the auncel when introduced into England. It is quite easy to see how this device could readily be fitted for fraud.  On page 25 we read: “During the 1300s many laws were made in England that dealt with the control of fraud. These relate to the assaying of gold, the testing of liquors by aleconners and the checking of weights and measures.” In 1351 the auncel (bismar) was no longer allowed for the commercial measurement of weight. “its demise and the prohibition of this kind of instrument were due to the ease with which it could be used for fraudulent weighing.”

One of the oldest aphorisms I’ve heard in the US is “he’s got his thumb on the scale” to indicate that a person engaged in a particular business is shifty. This idea was prevalent enough in 1936 America that Norman Rockewell created an illustration, which was used as the cover of Metrical Miscellanea and Muddle.

NormanRockwellWhy do we use rulers and scales? Because our senses are not reliable for judging distance and mass. In my essay Seeing Is Not Measurement I have the example of center stripes on a roadway. We see these stripes everyday, but perceive their length as very much shorter than it actually is. In Precision: The Measure of all Things, Marcus du Sautoy has a number of masses with different volumes. People at an outdoor market consistently misjudge which mass is larger than which. Our Perception of mass is logarithmic and we only notice relative differences in mass. We had to create “artificial organs” to measure distance and mass, because our actual ones are rather poor at it. In one study, it appears that ownership can change distance perception:

People at an outdoor cafe were approached and asked to judge the distance to a soda can placed on the table within their reach. In one condition, the can had been given to the  participants—it  belonged  to  them—whereas  in  the  other condition, the can belonged to the experimenter. Participants perceived the can to be closer when it belonged to the experimenter—and had invaded their personal space—than when it was their own soda.

The metric system allows one to readily construct approximate standards which can be used to check quantities. One only needs to have a metric ruler (or a very well calibrated hand width); this can be used to construct a 100 mm cube, which is a liter. When filled with water it is very, very close to a Kilogram. The metric system is the most democratic system ever devised. The metric system (when used without the prefix cluster around unity) does not have the large number of unit step discontinuities found in the U.S. non-system of measures. The metric system is also a common system. The residents of 95% of the Earth use it,  which removes one more potential for fraud and confusion. Yes, Pat Naughtin was right, pro-metric is pro-honesty.


The Metric Maven has published a new 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.