= = = = = MEDIEVAL METROLOGY PART 3 = = = = =
Reading some medieval descriptions of weights and measures, noticed that one weight was prohibited by the king and cursed by the archbishop. It was called auncel or aunsell weight. The permitted or blessed balance was generally called the Roman balance. Why was one weight bad and the other good?
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The earlier statutes sometimes provided against the use in trade of particular kinds of instruments; an Act of Edward 3 in 1351 provided that auncel weight should be wholly put out, and that every person do buy and sell by the [Roman] balance, so that the balance be even.
In 1429 another Act was passed abolishing auncel weight, and providing that every city and town should have a common [Roman] balance with standard weights, at which the inhabitants might freely weigh without paying anything.
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The public balance is a good example of government serving honest people, in a time when most folks engaged in both selling and buying. After the Endarkenment such public measuring stations were rare.
Natural Law is EQUIPOISE. Natural Law tries to restore balance.
Natural Law celebrates differences in abilities and opportunities, and encourages everyone to contribute to the collective using their own abilities and opportunities. Peasants and lords were obligated to help the community. England had a HUGE variety of weights and measures and calendars and times, and some of the variety still survives. Each commodity and trade had its own measures, adapted for its own talents and skills.
The Endarkenment brought forceful standardization of life, most dramatically in France where EVERYTHING had to be metric. US copied France with our procrustean “self-evident” lies. 1776 brought standardized measures, calendars, money and spelling.
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Natural law hates cheating.
The Aunsell balance made cheating easy because weights were crowded together at one end of the sliding part, and far apart at the other. If customers were expecting linear, a sneaky seller could fool them. This isn’t intuitively obvious! I had to calculate and animate to see it. (Incidentally, this is the best way to teach math. Give the students a reason to need math, then it’s worth learning and doing.)
The two types of balance look similar, but differ in the way they determine the null point. Polistra and friends demonstrate both kinds.
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First the Blessed Roman:
Blessed Roman is still blessed after 2000 years. A familiar variant was used in labs and doctor’s offices until very recently. The fulcrum is permanently fixed. On the right is the unknown weight, the item to be weighed. On the left is a smaller standard weight movable on a long lever arm. (Most versions, ancient and modern, have one larger and one smaller movable weight, but I’m only showing the smaller for simplicity.) You put the unknown object in the tray on right, and slide the small weight back and forth until the balance is nulled. You then read the distance, which is usually calibrated in pounds. The calibration is linear.
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Now the Cursed Aunsell:
Cursed Aunsell has a movable fulcrum instead of a movable standard weight. At first it doesn’t seem like an important distinction. Why would the smaller numbers be crowded, enabling cheaters?
I had to run up the distinction mathematically to see why. I treated the distance of the moving weight as the input, and the unknown weight as the output, which is the way we normally use a balance. We move the movable weight and read its position, which tells us the weight of the desired object.
Each side of the equation is a torque, force times distance**.
For Roman: (abbreviating to keep the formula on one line)
StdWt x VarDist = UnknownWt x StdDist
Rearranging to get the unknown:
UnknownWt = VarDist * (StdWt/StdDist)
Output = Input x Constant, a basic linear form.
For Aunsell, the “standard” distance is no longer standard. It’s whatever remains on the right side of the fulcrum, so it’s actually TotalDistance – Varying Distance.
UnknownWt x VarDist = (TotalDist-VarDist) x StdWt.
Rearranging to get the unknown:
UnknownWt = (TotalDist-VarDist) x StdWt/VarDist
In the python code I stepped the distance from left weight to fulcrum linearly from 1 to 20, and then determined what unknown weight would null the balance. This is how we think of the weighing process. (In the code I chose arbitrary numbers for the standard parts to keep things in a reasonable range as the varying distance steps from 1 to 20.)
Graphing the two types:
Blessed Roman is linear. Cursed Aunsell is exponential. Near the center, a small move in distance corresponds to a GIANT change in weight, just as the old authors said.
Universal rule: Cheaters love exponential. Nature hates it.
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** Torque is the same thing as work in a physics sense. Natural Law attempts to balance work in a human sense. The Endarkenment separated work from money, so most transactions are purely abstract. When Wall Street is in control, real work has NEGATIVE value, like the Aunsell graph. Shares go up when humans are canceled out of the equation.
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Language note:
The Roman balance was often called a steelyard, named after the London market center of the Hanseatic League where it was used for weighing HEAVY stuff like loads of grain or entire carriages. The marketplace was Stalhof in German, which means stable yard. (Stall is the same in both languages.) But the HEAVY stuff led people to think of Stahl=steel, thus the translated form. Aunsell has no clear etymology. There were several speculative ideas but they don’t ring true.
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Previous in the series:
Polistra's Mill 