= = = = = = 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!
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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.
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, and forms a template for where the sun should be when she’s flying.
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.
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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 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
SVG, used on the web**, is like the official metes and bounds. 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.
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** 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 