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:


This 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.


Why 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.

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.

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

8 thoughts on “Perception, Illusion and Measure

  1. Maven:
    Re the comment following the implication “pro-honesty —> pro-metric”, namely:
    “This aphorism has precipitated some snarky comments which [sic] state that it is an outrageous assertion that to not be pro-metric is to somehow promote dis-honesty”
    Some of those unfortunately snarky comments may just have logic on their side because the contrapositive of the statement must also be true, which is what you apparently have above and which is something I am confident Mr. Naughtin did not quite mean.

    • David, sweetie, ten deep breaths:

      It’s an old forensic trick, popular among dilettante debaters with no idea what debate is: take a general statement, frame it as a universal, point out that this leads to absurdity, and look smug. The problem lies not in any supposed contrapositive, but in the underlying sweeping generalization: in this case, that being pro-honesty implies being pro-metric. If you really want to be schoolmarmish about this, there are several latin names for the fallacy: dicto simpliciter is just one. Try it in Wikipedia.

      Come to think of it, this is probably better classified as a classic straw man, since “pro-honesty — pro-metric” could as easily imply distinction as equation: one could conceivably be one and not the other. It would be difficult, but not impossible. Personally, I think it unlikely that it ever occurred to Naughtin that there was a dilemma lurking here.

      However analyzed, it all sounds pretty snarky to me. So why the need to defend such Dogberrys as having logic on their side?

      • Sven:

        Such was just an observation, which was primarily the result of the Maven writing he was unable to find the content/context were Mr. N made the “implication”.

        And yes, such Dogberrys do have a strange type of logic on their side as USC is sort of logically equivalent to a world of malapropisms…

        [BTW, I am looking at this following comment, don’t follow it, but think maybe in a Presidential debate a questioner should ask an SI-related question, which of course is extremely unlikely but would be extremely interesting as T and C tend to frequently deliberately take opposite positions (and so the first one answering such a question may just also determine how the second would respond!).]

  2. “Sven states that Pat Naughtin once indicated that the history of measure is also a history of fraud.”

    That is a recurring theme – beginning circa 5000 BCE Mesopotamia, following right through to current times – in Pat Naughtin’s “Metrication Timeline” at (PDF, 1.1 Mb).

    “Many previous measuring methods were profoundly dishonest and many of these are still in use.”
    ~~~~~ Pat Naughtin ~~~~~

    [Sorry if the following is off-topic or inappropriate — delete it if you wish.]

    I figured out why a statement like “The residents of 95% of the Earth use it…” bothers me every time I see one. It is a use of Argumentum Ad Populum, the logical fallacy of appeal to the people. In short form, “If many people believe it, it must be so.” It is popular, along with other fallacies like appeals to consequences, emotion, nature, tradition, et cetera ad nauseum, with the anti-metric supporters of the anarchy of archaic measurement units.

    I know the argument about the reduced confusion between folk that comes with using S.I., and sometimes it is an appropriate point to make, but it is not a primary concern for most people, and some people perceive “95%…..” as a bullying argument from intimidation. It weakens pro-metric argument by saying “Our gang is bigger than your gang.”, to which most people, including me, say, “So what?!”. It is not a matter of numbers (of adherents — metric math is *much* easier), it is a matter of what is better.

    I’ve used the metric system for over forty years because it is *good* — my work goes easier, faster and more accurately with it. How many people use it is no more meaningful than arguments like, “It’s French, it must be bad.”, or “It’s not what my grandfather used.”. With a few exceptions, “95%…..” is distracting and irrelevant. Using it is good for our opponents, bad for us.

    • I generally bring up the 95% of the world uses metric as a counterpoint to the provincial view that the rest of the world should adopt “our system.” Frank Mankiewicz, not long before he died, asserted this on reddit, and then quickly tried to walk it back to “everyone should use both” in a global economy. The impracticality of rest the world adopting a medieval non-system less modern than British Imperial should be obvious at this point.

      Secondly, the people who argue that it is too “expensive” to become metric in the US seem impervious to the idea that remaining in this minority costs our economy and ourselves. We are the only country where it is mandatory from a practical standpoint to have both Olde English “standard” and metric tools circulate within our economy. It is a self-imposed waste of resources. This situation is directly attributable to the fact that we are in the 5% population minority when it comes to the use of Olde English units, and what little is left of our manufacturing economy is also generally non-metric and in the minority. This is a recipe for decline.

      I agree that the number of people who adopt an idea does not necessarily have any relevance to its truth, practicality or rationality. Nor do I subscribe to the idea that 1000 fools are smarter than 1, but in the case of the metric system, it appears to me that we have 153 (or so) rational countries and 1 fool. Considering the irrational and nationalistic nature of humans (in my view), I see it as miraculous that 95% of the world had the good sense to adopt a single measurement system. It might be the only idea utilized by this many people. I cannot control how people interpret this simple demographic information when I offer it, but I will continue to offer it.



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