ILGISA 2026 · Monday 10:30 · River H

Polygons from
First Principles

How χGRIDs extend the UN's 2025 settlement methodology to neighborhood-scale geographies.

QR: What Is Chicago?miccheck.media/what-is-chicago
QR: chiGRIDs on GitHubgithub.com/HarryBrisson/chiGRIDs
Five questions

What we will answer in thirty minutes

Chicago first, then Peoria and Illinois. The last slide answers all five in one line each.

Why I care

I measure wellbeing in cities, everywhere

Every week, Mic Check asks people how their lives are going: 18,855 answers from 121 countries and 133 metros since May 2024.

  • Nielsen, measurement 2011–2021 · what counts as a view, a listen, an exposure
  • Mic Check, a survey engine 2021 – present · the same questions, answered city by city, weighted by geography
  • Ward Wise / Penlight 2024 – present · Chicago measured by ward, neighborhood and square mile

To compare cities, I first have to decide what a city is. That question is personal, and it is why this work exists.

Mic Check global happiness board
Why I care

My own board has to choose a Chicago

City Wellbeing board, city-defined
city-defined · each city's own ZIP frame
City Wellbeing board, UN-defined
UN-defined · plus a sample from the dense ring
Life evaluation, 0–10cityUN
Houstonn 139 → 188#1 · 6.62± 0.43#2 · 6.56± 0.36
Chicagon 1,119 → 1,491#2 · 6.58± 0.13#1 · 6.59± 0.11
Fremontn 61 → 161#3 · 6.55± 0.57#4 · 6.38± 0.33
Los Angelesn 143 → 243#4 · 6.40± 0.37#3 · 6.40± 0.29
New York Cityn 144 → 194#5 · 6.23± 0.36#5 · 6.31± 0.31

Flip one switch and the order changes. The intervals overlap, so neither order is a finding. The finding is that the ranking depends on the boundary, and a reader cannot tell which one they are seeing unless the number says so. This UN-defined view is live today on Mic Check's board; offering it in Ward Wise's Penlight is the next step.

1 · Who draws the lines?

Chicago: 77 frozen areas, 50 moving wards

Community areas beside wards
  • 1920s: the University of Chicago's Social Science Research Committee, led by Ernest Burgess, cut the city into 75 community areas for publishing the 1930 census.
  • The boundaries were frozen on purpose, so that each decade's numbers could be compared with the last.
  • 1956: O'Hare became area 76 after the airport was annexed.
  • 1980: Edgewater split from Uptown, area 77. No change since.
  • The 50 wards are redrawn after every census, so a ward number never means the same place twice.
1 · Who draws the lines?

Every official line has an author

“Nobody can recompute this line. Anyone can download it.”What Is Chicago?, on the city limits
2 · What do the lines cost us?

Five Chicagos, five authors, one decade

DefinitionAuthorPeople (2020)km²ZIPs
City of ChicagoCity Council, by ordinance2,744,50059956
UN urban centre (2025)UN DESA, from the JRC grid3,683,95193298
Older GHSL rule (2023)Joint Research Centre5,533,6872,231174
Census urban areaCensus Bureau, from blocks8,669,0506,148301
Metro area (CBSA)OMB, from commuting flows9,447,37318,186362

2020 residents inside each boundary, from the Census PL 94-171 block counts; a ZIP counts when at least half its residents live inside. Source: the explainer's data bundle (built 2026-09-08). Mic Check samples Chicago by ZIP: the city-defined board draws from the first row's 56 ZIPs, and a ring sample over 48 more extends it to the UN centre.

2 · What do the lines cost us?

Comparability: the UN changed its ruler

The 2018 edition carried the Census urbanized area forward to about 8.9 million. The 2025 edition applies one rule to the whole planet: Chicago is 3,683,385, ranked 125. Same city, same decade; only the definition moved. The same rule drawn over local units elsewhere:

Paris · communes

Paris · communes · 274 units cover 100% of the centre's 9.4M; 1% of their residents sit outside it

Tokyo · municipalities

Tokyo · municipalities · 144 units cover 100% of the centre's 33.2M; 2% of their residents sit outside it

Jakarta · kota / kabupaten

Jakarta · kota / kabupaten · 17 units cover 93% of the centre's 41.9M; 6% of their residents sit outside it

3 · Is there a rule instead?

Four first principles

  1. Start from a lattice, not from borders. Equal cells over the whole surface; city limits, counties and ZIPs play no part.
  2. One public rule. Thresholds anyone can read: a density, a size, a neighbourhood vote.
  3. Regenerable by anyone. Public data and a published recipe in, the same polygons out, cell for cell.
  4. Versioned. When the rule changes, the old polygons stay citable and the change is one clause you can name.
3 · The UN rule on Chicago · Step one of six

Step one: ignore every border.

Step one: ignore every border.

The rule starts from a grid of one-kilometre squares laid over the whole planet, with an estimate of how many people live in each square. City limits, county lines and zip codes play no part.

The grid is drawn in an equal-area world projection, which is why it sits at a slight tilt over Chicago. Hover a square to read its population.

Live: miccheck.media/what-is-chicago#beat=grid

3 · The UN rule on Chicago · Step two of six

Step two: keep only the dense squares.

Step two: keep only the dense squares.

A square counts as dense if it holds at least 1,500 people per square kilometre of land. Water does not count toward the area, so a lakefront square with a sliver of shore can pass on a few hundred residents. Everything else goes dark.

Live: miccheck.media/what-is-chicago#beat=dense

3 · The UN rule on Chicago · Step three of six

Step three: dense squares must touch side to side.

Step three: dense squares must touch side to side.

Dense squares that share an edge belong to the same cluster. Squares that only meet at a corner do not. Watch the connection spread from the Loop and stop wherever the chain breaks.

If corners counted, the Loop's cluster would pick up another 1.5 million people.

Live: miccheck.media/what-is-chicago#beat=connect

3 · The UN rule on Chicago · Step four of six

Step four: a cluster needs 50,000 people.

Step four: a cluster needs 50,000 people.

There are 301 dense clusters in the region. Most are a few squares around a town centre. The bar rises to 50,000 and everything under it drops out. 16 clusters survive. They are the seeds of the urban centres.

Live: miccheck.media/what-is-chicago#beat=size

3 · The UN rule on Chicago · Step five of six

Step five: fill the small holes.

Step five: fill the small holes.

Parks, rail yards, cemeteries and factory land leave gaps inside a cluster. Any enclosed gap smaller than 15 square kilometres is filled in. Nothing larger is.

44 holes in the region, 74 squares in all.

Live: miccheck.media/what-is-chicago#beat=holes

3 · The UN rule on Chicago · Step six of six

Step six: smooth the edges by majority vote.

Step six: smooth the edges by majority vote.

Each square just outside a centre looks at its 3-by-3 neighbourhood. Water squares abstain. If at least half of the voters are inside, the square joins. The vote repeats until nothing changes: 14 rounds for the Chicago region.

Live: miccheck.media/what-is-chicago#beat=smooth

3 · The UN rule on Chicago

The result: 932 km², 3,683,385 people

The result

Every break in the chain of dense squares became a border. Replaying the rule on the public grid reproduces the UN's boundary exactly: 932 of 932 cells match. The neighbours, each its own city to the UN:

  1. Hammond301,148
  2. Arlington Heights298,081
  3. Elmhurst223,924
  4. Schaumburg218,625
  5. Aurora190,074
  6. Waukegan112,414
  7. Wheaton108,584
  8. Downers Grove84,702
  9. Elgin80,255
  10. Joliet79,086
  11. Tinley Park58,362
  12. Lake in the Hills58,273
  13. Round Lake Beach52,986

13 neighbouring centres, 1,866,514 people between them. 2025 grid populations.

4 · Peoria

To the UN, Peoria is a town

144,315people in Peoria's urban cluster on the 2025 grid (160 km²); 144,549 on the 2023 grid
47,875in its one dense core under the 2023 rule: 2,125 short of the 50,000 an urban centre needs
20,057 + 13,391the same core under the 2025 rule, split in two with the built-up clause gone. No urban centre; the UN's city table skips Peoria
Peoria 2025 urban cluster
Peoria 2023 dense core
4 · Illinois

Illinois under the rule: cities and towns

CityUN 2025 urban centreJRC 2023 urban centreCity limits 2020Metro area 2020
Peoria nonelargest dense core 20,057 nonelargest dense core 47,875 113,150124 km² 368,789Peoria, IL
Springfield nonelargest dense core 13,878 nonelargest dense core 44,311 114,394158 km² 208,636Springfield, IL
Rockford 86,647 150,998 148,655167 km² 338,788Rockford, IL
Champaign 79,407 87,759 88,30259 km² 236,075Champaign-Urbana, IL
Bloomington 58,461 78,345 78,68070 km² 170,956Bloomington, IL

Urban centres: contiguous 1 km cells of class 30 on each published grid, replayed from the rasters (tools/peoria_stills.py). City limits: Census 2020 PL 94-171 geoheader, summary level 160, Illinois. Metro: U.S. Census Bureau, Population Estimates Program, Vintage 2023 CBSA table, April 1 2020 estimates base, 2023 OMB delineations.

4 · Comparables

Peoria's peers: three honest lists that do not agree

By city-proper populationPeoria city, Illinois · 113,174

  1. Broken Arrow, Oklahoma113,553
  2. Lansing, Michigan112,661
  3. Lakeland, Florida112,629
  4. High Point, North Carolina114,161
  5. Gresham, Oregon114,249

By metro areaPeoria, IL · 368,789

  1. Atlantic City-Hammonton, NJ369,798
  2. Ann Arbor, MI372,258
  3. Hickory-Lenoir-Morganton, NC365,270
  4. Naples-Marco Island, FL375,760
  5. Ocala, FL375,904

By UN settlement, USPeoria, Illinois · 144,315 · tier: town

  1. Deltona, Florida156,006
  2. Tuscaloosa, Alabama125,962
  3. Harlingen, Texas119,381
  4. Winter Haven, Florida146,841
  5. Waco, Texas166,057

Across all 97 Illinois settlements, the city-limits and metro lists share 12 names with the settlement list. Every settlement's lists: miccheck.media/parallel-peorias.

4 · One clause

One clause, and fourteen centres become one

The 2023 rule

The grid is built by the European Commission's Joint Research Centre, and its own 2023 release used the same six steps with one extra clause: a square also counts as urban if at least half of its land is built up, even when few people live there. That clause admits airports, rail yards, factories, malls and freight terminals, and those squares sit exactly in the gaps between Chicago and its neighbours.

Chicago's peers under one rule, 2025 urban centres (UN MTUC table)

CentrePeoplekm²
Chicago3.68M932
Barcelona3.98M454
Berlin3.56M686
Sydney4.15M1,317
Melbourne3.64M1,357
Athína (Athens)3.10M404
Busan3.26M361
Washington, D.C.3.27M1,186
San Francisco3.16M915
Houston3.96M1,583
5 · Neighborhood scale

The gap: there is no rule below the city

  • The UN rule stops at the urban centre. Inside it, everything is still somebody's record: 77 areas from the 1920s, 50 wards from the last map, ZIPs from the mail.
  • None of them is uniform, none is regenerable, and only one is versioned, by accident, when it is redrawn.
  • What would the four principles give you one mile down?
Community areas and wards
5 · χGRID

χGRID: a square-mile geography for Chicago

  • Chicago Geographically Reductive Indexed Districts: the city tiled into roughly one-mile cells, "chis", anchored to the address-grid origin at State & Madison.
  • Limits are mile roads. Midpoints are the half-mile roads, on both axes.
  • A layer beneath neighborhoods and community areas, not a replacement: where a neighborhood name is fuzzy, a chi is exact, uniform and addressable.
  • On GitHub, MIT. Street-aligned cells follow street centerlines: Chicago publishes them; OpenStreetMap has them everywhere.

χ:5S3W = Damen–43rd chi = "Dam43"

wardwise.org chiGRID explainer
5 · χGRID

Naming: three forms, four rules

Ordinateχ:5S3W5th mile-band south, 3rd west of State & Madison: formal, sortable
NameDamen–43rd chithe avenue first, then the street: human-readable
LabelDam43compact, for maps and tables
5 · χGRID

v1 vs v2: 302 ideal squares or 288 real sets of blocks

v1 mile-squares beside v2 street-aligned
  • v1: perfect one-mile squares on the address grid. Every cell is exactly one square mile.
  • v2: cells bounded by the real mile-road centerlines, clipped to the city limit.
  • Built by rule: substitute the nearest aligned road where a mile road is missing; impute a straight line where no road exists; flag interior cells outside 0.9–1.1 sq mi; mark edge cells clipped by the limit.
  • The same trade-off as 2025 vs 2023: a cleaner rule or a truer map, and the version tells you which you chose.
5 · χGRID

In use, and how to do it where you are

  • Penlight rolls every measure to wards, neighborhoods and chis: 605,283 chi-level observations in the current civic-data snapshot.
  • byop/v1, bring your own polygons: a measure repo publishes points, a raster or polygon values with an aggregation spec, and the pipeline rolls it up. Four measures so far (sunscore, parkability, rentrate, microhappiness).
  • Your city: today's generators are Chicago's (v1 hard-codes State & Madison, v2 its mile roads). The recipe needs three inputs: an address-grid origin, a mile spacing, and your mile roads from OpenStreetMap or your own centerlines.
  • When a 1 km lattice beats a mile grid: comparing across cities or countries, use the UN's global lattice. Talking to the people who live there, use the grid they already navigate by.
Penlight map on χGRIDs: Wards, Neighborhoods and χGRIDs share one leaderboard
Five answers

Conclusions

  1. Every boundary has an author.Who draws the lines?
  2. A number must say which geography it is about.What do the lines cost us?
  3. A rule beats a record when you need to compare.Is there a rule instead?
  4. To the UN, Peoria is a town, and a rule away from being a city.What does the rule say about Illinois?
  5. A square mile is a neighborhood anyone can regenerate.Can a rule work at neighborhood scale?
Thank you

Links, slides, and a question for you

Does your organization report by ZIP, tract or municipality? The form asks only that, and whether a twenty-minute call would help.

QR: miccheck.media/ilgisamiccheck.media/ilgisa