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.