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Canonical: https://semiotic.nteract.io/examples/where-you-draw-the-line
Where You Draw the Line
An explorable explanation of the modifiable areal unit problem
Nothing beneath the boundary changes. The answer does.
Cedar Bend is a constructed city with a fixed heat field and a fixed population. Group it one way and its districts tell one story. Move a border and the policy answer can move with it.
fixture CB-1B137C1149 fixed microcells28 fixed days
01
Take away the map.
A map is a line with more directions in which to draw a cut.
Divide this unchanged field into , then move the orange rule.
fieldunchanged
weightunchanged
stateone line moved
raw high58%
assigned high79%
+21% from grouping alone
The rug is fixed population weight. The teal curve is the same continuous heat score before and after every drag.
Each interval wash and every weight-rug mark is a Semiotic scene node. The orange rule is the direct control layered on frame geometry.
02
Put geography back.
Geography makes the cuts look official. It does not make the averaging disappear.
With , 2 of 6 districts are high. They assign 40% of Cedar Bend residents to high-heat districts.
Same city. Same six districts. Two defensible ward plans:
6 districts, 53% raw high, and 40% assigned high.
fieldunchanged
weightunchanged
state6 compact districts
raw high53%
assigned high40%
-13% from grouping alone
fixed raw heat field movable district boundary district average meets threshold
The River and Avenue plans move only the partition. The fixed field moves from 40% to 72% assigned high: a 32-point change.
This is a `StreamGeoFrame`: it projects a local GeoJSON city support, renders each fixed microcell as a geographic point, and keeps its geographic hover and accessible table.
03
Thresholds turn drift into decisions.
A threshold is not MAUP. It makes partition sensitivity categorical.
Call a district high when its average is at least
64.8
global weighted mean, unchanged by borders53%
raw population above the decision rule40%
population assigned to high districtsThe threshold stayed put. One district average crossed it. A small continuous move became a yes-or-no label.
04
Time gives the boundary another direction.
A week is a partition, not a law of nature.
Average the same city into beginning on day 5.
6 districts, 64% raw high, and 82% assigned high.
Day 13: the slice changes. The city does not.
One city, cut into 7-day windows
day 1 calendar: 55% assigned highthis calendar: 61% (+6 points)
Starting on day 1 assigns 55% of population-time to high blocks. Starting on day 5 assigns 61%. The heat did not change; the reporting calendar did.
fieldunchanged
weightunchanged
state7-day windows, phase 5
raw high58%
assigned high61%
+3% from grouping alone
Spatial borders make vertical walls through the conceptual stack. Reporting windows make horizontal planes. Both decide which values are averaged together.
The bars are a bounded `TemporalHistogram`; its annotation layer carries the current playhead and the draggable reporting-window boundary.
05
The range is part of the result.
Aggregation is useful. A result that survives only one plausible border is brittle.
Across 29 compact versions of this 6-district plan, the assigned-high share runs from 42% to 70% between the 10th and 90th percentiles.
Show the support. State the finest data available, the population weight, and the outer extent.
Show the rule. Report the aggregation, threshold, and whether labels belong to people or units.
Show alternatives. Test more than one defensible scale and zoning, then report the range.
Nothing beneath the boundary changed. The answer did.
Inspect the construction
Cedar Bend is deterministic. The geography is `StreamGeoFrame` over a local GeoJSON city support; the calendar is `TemporalHistogram`; the line and sensitivity field use `XYCustomChart` scene-node layouts. Border handles and explanatory annotations are SVG overlays on the corresponding frame geometry.
This explainer concerns aggregate sensitivity. It does not license individual inference from district averages, and it does not claim that every partition is equally defensible.