I noticed that today is both Metrology Day and Bee Day, so I’ll remix closely related items that fit both themes at once.
= = = = = MEDIEVAL METROLOGY PART 1 = = = = =
This year I’m focusing on the medieval way of thinking as illuminated by Sherri Olson.
Medieval villages embodied Natural Law.
The Almighty has created this world as a trial and test for man; every person has therefore been made to depend on others for his living. No one in this world can live independently as regards his needs and requirements. A person of the highest rank turns to the most ordinary to fulfill them. In other words, every single person has an important role to play, without which this world cannot continue.
This role depends upon his abilities, intelligence and inclinations as well as upon his means and resources, which vary from person to person. In fact, it is because of this variation that a society comes into being. Consequently, laborers and workers, artisans and craftsmen, tillers and peasants are as indispensable as scholars and thinkers, savants and sages, leaders and rulers. Every individual is an integral component of the society and contributes to its formation according to his abilities.
By creating various classes of people, the Almighty is testing whether the big and the small, the high and the low create a society based on co-operation and respect or create disorder in the world by disregarding the role each person has been ordained to play.
= = = = = END REVIEW.
Each village had a single collective purpose of growing food. The momentary purposes of villagers changed all the time as needs and talents and seasons changed, in the same way that our brains create momentary groupings to serve each purpose. Natural Law enforced the ideals by balancing departures from ideal. Thieves and trespassers had to pay back in money or work, beaters were beaten. Jail and physical punishments like whipping and stocks were available but rarely used. The constant maintenance of dynamic stability kept things in line most of the time.
There were very few permanent offices or permanent jobs. Government happened in court sessions, usually monthly, where everyone attended and participated in various ways. The goal of the court session was broad consensus, not precise numerical conformity. Oddballs were welcomed as long as their odd ways worked in different styles toward the common goal. Decisions were made by juries which existed for the day of the court session then disappeared. Anyone could end up as a juror.
Juries are the ONLY remnant of Natural Law governance, and we do everything possible to squeeze them out of their remaining power. Instead of making all decisions, juries only decide 2% of criminal and civil cases.
Villages had permanent metrologists devoted to the most important measurements of food and water. The size and quality of crops needed to be monitored, and the amount and quality of ale needed to be monitored. Ale was the main liquid input, hydrating and lubricating civilization all at once.
Polistra is the village brewer, boiling up a batch for sale.
Ale tasters or ale conners were the Bureau of Standards. Brewers had to send for a taster before selling the current batch. The taster measured the batch for quantity and tasted it for quality. At each court session the brewers were required to calibrate their pots. Tasters took center stage as each brewer brought her measuring pots forward to be checked for size. A brewer who measured wrong, or failed to send for the taster, or diluted the ale after the taster had checked it, was in trouble.
In 1364 a brewer called Alice unabashedly cheated her customers by selling them ridiculously false amounts of ale. She added 1.5 inches of pitch to the bottom of an unsealed quart measure thus making it so false that “even her six quarts didn’t add up to a gallon”.
Prices were also controlled. In 1470 Dublin laws said: “It is ordained that the brewsters shall sell to their customers a dozen of their best ale for 2 shillings.”
Happystar, the taster, is checking the quantity in the pot with his ruler. He will also check the dispensing tankards in the background.
Medieval rulers were simply ruled sticks with no numbers. Most commercial accounting was done with tally sticks, also notched and numberless. When society relies less on written language it also relies less on written numbers. In fact numbers interfere with most uses of a short ruler. You need to subtract the starting point from the ending point, which can be confusing. If you’re concerned with counting the intervals, the subtraction is correct. If you’re concerned with counting the individual marks, you need to add 1. With no numbers you can’t get confused. You’re always counting one way or the other. No abstract math needed.
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= = = = = = VECTOR MEASUREMENT PART 1 OF 2 = = = = =
Following from the Medieval Metrology series last month.
Medieval land measures were vector, not rectangular. The base unit was time and work, not distance and weight. With land as with money, the base was one day of work or one completed task. The linear aspect was secondary and loose, varying with local conditions, but the one-task standard was absolute.
Land was divided among tenants by the length and width of furrows plowed by an ox team in one day, defined as one acre.
One rod was the length of the rod used to spur on an ox team. A furlong or furrow-long was taken as 40 rods or 660 feet.
The rod became a standard in surveying, the ultimate vector measure. Cars are horses, and a team length persists as a car length. The average full-size car is about one rod long.
The rood is an area of 1 furlong by 1 rod, or 10890 square feet. The four parts outlined by white here are roods. An acre is four roods or 43560 square feet. The number 43560 always puzzled me until I learned this history. It’s not a perfect square because the acre wasn’t meant to be square!
= = = = =
Larger and more permanent land divisions were recorded in vector form as metes and bounds, a system that lasted well into the 1900s.
Bees use metes and bounds, so it’s a basic part of animal sensory systems.
Careful observers have decoded the honeybee’s waggle dance. It’s a vector message. The dancer is telling her hivemates about a good source of honey. She repeatedly forms a figure-8 pattern, with the message in the middle. (Human messages, from business letters to telegrams to web packets ahd html pages, follow the same pattern with standard header and footer bracketing the variable message.)
The direction of the dance is relative to the main honeycomb wall of the hive. The angle between the central motion line and the wall represents the vector of the food source relative to the sun.
Transposing the viewed dance to a position on the bee’s internal compass is complex, but using the memorized template can be hardwired in an insect with compound eyes that cover most of the compass. The template is assigned to one radial set of lenses, and the bee keeps the sun centered on that group of lenses.
The distance component of the vector is conveyed by the number of waggles in each central run.
This reminds me of the glial abacus that keeps track of numbers in short-term memory. Astrocyte cells serve as a kind of scorecard or abacus outside of the neurons. The neurons click up the astrocytes, and when the number of raised beads reaches a threshold the neurons tell the body to stop swimming or flying.
Let’s try to imagine how this feels to a forager bee watching the dance.
Polistra has a hive near the mill…
Looking downward inside the hive we see one scout telling one forager about her find:
The forager observes the direction of the dance with respect to the hive. I’m showing a sun next to the forager to represent the sun template in her mind.
Taking the important part in slow motion:
Each waggle ticks up the beads of her astrocyte abacus. For a simple animation we’ll assume she’s a Babylon Bee who counts in base 60. For each of these five waggles she brings in one 12-bead astrocyte. The total of all the counters tells her how many wingflaps she needs. (Obviously the real multiple of wingflaps per waggle would be far more than 12.)
She then launches out of the hive and turns until the actual sun matches the template position supplied by the dance. As she flies, each wingflap clicks down a bead. When the astrocytes have all reached threshold, she’s there.
= = = = =
Computer graphics continue metes and bounds. My courseware engine, designed to be easily readable and editable, draws lines of a specified length at a specified angle, like a waggle dance. LOC marks the point of beginning as an XY pair, then the list of angle-length SHAPE pairs draws the boundaries of the area. In this example the area is the Middle Temporal Gyrus, important in auditory processing, nicely resembling a farm field. After the last named SHAPE, the bound returns automatically to the point of beginning.
ITEM ZONE BROD21L LOC 164 296 SHAPE 74 25 M SHAPE 6 19 M SHAPE -16 34 M SHAPE -29 30 M SHAPE 0 10 M SHAPE -11 44 M SHAPE -18 15 M SHAPE -35 20 M SHAPE -68 10 M SHAPE -116 26 M SHAPE 140 28 M SHAPE 167 26 M SHAPE -158 5 M SHAPE 171 35 M SHAPE 145 15 M SHAPE 167 22 M SHAPE 179 8 M
The resulting zone:
SVG, used on the web**, is another metes and bounds system. Start here, go to next location, go to next location. My waggle pairs translate to this sequence of bounds:
path d= "M164.0 296.0 L170.9 320.0 L189.8 322.0 L222.5 312.6 L248.7 298.1 L258.7 298.1 L301.9 289.7 L316.2 285.1 L332.5 273.6 L336.3 264.3 L324.9 241.0 L303.4 259.0 L278.1 264.8 L273.5 262.9 L238.9 268.4 L226.6 277.0 L205.2 282.0 L197.2 282.1 Z"
M marks the point of beginning, as an XY pair of screen pixels. Each L bound gives the destination of a line segment as an XY pair. Z automatically returns to the point of beginning, closing the bound.
Sequences in traditional metes and bounds do the same, with a mix of directions, identifiable locations, and XY pairs defined by the Township-Range system.
Thence westerly to the north quarter corner of Section 4, T1N, R70W; thence northwesterly to a point marked by an iron stake; thence N 45° W to a large oak tree; thence northeasterly to the point of beginning.
Continued in Part 2 on surveying.
= = = = =
** Techy note: Per Wikipedia, SVG was initially developed in 1998, at the same time when I first developed my courseware authoring system. Parallel ideas in different forms. But SVG wasn’t commonly available until 2010 when all browsers enabled it. When I switched from Windows EXE to online in 2014, I found that SVG couldn’t do many of the tricks my system could do. I had to dumb it down to make it compatible. Globalism ALWAYS dumbs things down.
Polistra's Mill 