Issues with Comparing the Populations of Cities Proper

What are the most populous cities in the United States?

The list of the largest cities proper starts as so: New York, Los Angeles, Chicago, Houston, Philadelphia, Phoenix…

But there’s something hidden about the city population numbers that correspond to these cities: these cities come in vastly different sizes—as in, the land area they cover, how much is within their city limits. This wouldn’t make such a list of most populous cities so misleading if the city limits simply marked where people stopped living, but that is nowhere near the case. Pretty much all large cities have some quantity of suburbs, and many cities have twin cities right next to them. Inhabited areas around a city continuously flow into the cities next to them, and looking a map of nighttime city lights, for instance, one wouldn’t be able to tell where the actual city limits of one city stopped and those for the next city over began.

And in particular, cities across America are very inconsistent with how far out to the actual limits of their block of inhabitedness they stretch. And the actual city limits of some cities are amusingly pathological.

So what if we instead looked at the largest cities by population density? This list starts Guttenberg, Union City, West New York, Hoboken…

Okay, we can already see the problem here. A similar problem exists here as with looking at the most densely populated countries in the world. The beginning of the list is going to be filled with cities that are ridiculously tiny tracts of land that happen to be drawn to enclose a particularly densely populated area in a general region of high density. In the list above: why are they so densely populated? Because New York City.

So instead, let’s compare cities of approximately equal area, and see what cities make the top of the list in each general category.

Below are six lists of the 16 largest cities in the US smaller than an upper size limit. In the first five lists, cities that actually fit in a small enough area to go in the list for the next smaller size group are bolded. Population numbers are from the “2010” Census.

US Cities of Greatest Population with Area <1024 sq km
1. New York, NY (8175133)
2. Chicago, IL (2695598)
3. Philadelphia, PA (1567442)
4. San Diego, CA (1307402)
5. Dallas, TX (1197816)
6. San Jose, CA (945942)
7. Indianapolis, IN (820445)
8. San Francisco, CA (805235)
9. Austin, TX (790390)
10. Columbus, OH (787033)
11. Fort Worth, TX (741206)
12. Charlotte, NC (731424)
13. Detroit, MI (713777)
14. El Paso, TX (649121)
15. Memphis, TN (646889)
16. Baltimore, MD (620961)

US Cities of Greatest Population with Area <512 sq km
1. Philadelphia, PA (1567442)
2. San Jose, CA (945942)
3. San Francisco, CA (805235)
4. Detroit, MI (713777)
5. Baltimore, MD (620961)
6. Boston, MA (617594)
7. Seattle, WA (608660)
8. Washington, DC (601723)
9. Denver, CO (600158)
10. Milwaukee, WI (594833)
11. Portland, OR (583776)
12. Las Vegas, NV (583756)
13. Albuquerque, NM (545852)
14. Fresno, CA (494665)
15. Sacramento, CA (466488)
16. Long Beach, CA (462257)

US Cities of Greatest Population with Area <256 sq km
1. San Francisco, CA (805235)
2. Baltimore, MD (620961)
3. Boston, MA (617594)
4. Seattle, WA (608660)
5. Washington, DC (601723)
6. Milwaukee, WI (594833)
7. Sacramento, CA (466488)
8. Long Beach, CA (462257)
9. Miami, FL (399457)
10. Cleveland, OH (396815)
11. Oakland, CA (390724)
12. Minneapolis, MN (382578)
13. Arlington, TX (365438)
14. Honolulu, HI (337256)
15. Anaheim, CA (336265)
16. Santa Ana, CA (324528)

US Cities of Greatest Population with Area <128 sq km
1. San Francisco, CA (805235)
2. Boston, MA (617594)
3. Miami, FL (399457)
4. Santa Ana, CA (324528)
5. Newark, NJ (277140)
6. Buffalo, NY (261310)
7. Jersey City, NJ (247597)
8. Hialeah, FL (224669)
9. Rochester, NY (210565)
10. Modesto, CA (201165)
11. Oxnard, CA (197899)
11. Aurora, IL (197899)
13. Fontana, CA (196069)
14. Yonkers, NY (195976)
15. Glendale, CA (191719)
16. Huntington Beach, CA (189992)

US Cities of Greatest Population with Area <64 sq km
1. Newark, NJ (277140)
2. Jersey City, NJ (247597)
3. Hialeah, FL (224669)
4. Yonkers, NY (195976)
5. Providence, RI (178042)
6. Garden Grove, CA (170883)
7. Salinas, CA (150441)
8. Pomona, CA (149058)
9. Paterson, NJ (146199)
10. Torrance, CA (145438)
11. Bridgeport, CT (144229)
12. Sunnyvale, CA (140081)
13. Alexandria, VA (139966)
14. Pasadena, CA (137122)
15. Fullerton, CA (135161)
16. New Haven, CT (129779)

US Cities of Greatest Population with Area <32 sq km
1. Paterson, NJ (146199)
2. Elizabeth, NJ (124969)
3. El Monte, CA (113475)
4. Berkeley, CA (112580)
5. Inglewood, CA (109673)
6. Norwalk, CA (105549)
7. Cambridge, MA (105162)
8. Daly City, CA (101123)
9. South Gate, CA (96375)
10. Miami Beach, FL (87933)
11. Alhambra, CA (85804)
12. Cicero, IL (85616)
13. Trenton, NJ (85403)
14. Hawthorne, CA (84112)
15. Santa Monica, CA (84084)
16. Upper Darby, PA (81821)

Notice that some of the largest cities by population in the United States, like Los Angeles and Houston, are so large they can’t fit in the largest category shown here, 1024 sq km, which really is a plenty large tract of land (larger than 25 UN-recognized countries). And notice that the smallest area category is pretty much the festival of the suburbs (just in case I still need to clarify, by “suburb” in this post I am referring to the more generalized concept of a city on the periphery of a larger city, and am not exactly talking about “the suburbs” as a concept of a type of periphery city).

So here’s a way that one could answer the what’s-the-largest-city question in a way that lets go of city limits as defined a bit and looks a bit more at the general picture of the conglomeration of people: look for cities that are at the top of their area category, especially those with suburbs that pop up in lower area categories. Notice that New York can very well be rightfully recognized as truly the US’s largest city: it has a larger population density than all other cities of millions of people, and has numerous suburbs that appear in the lower lists. Notice that Miami, a city that would be ranked 44th in a city population ranking by size of city proper (where in fact in Florida it would be dwarfed by Jacksonville!) shows up as 3rd on one of these lists, and has multiple suburbs show up, one of which is 3rd on another list, whereas neither Jacksonville nor any of its suburbs shows up anywhere in these lists (indeed Jacksonville has nearly annexed its county in entirety). Your impression that Miami was one of the US’s largest cities and Jacksonville wasn’t was not unfounded—the population statistics were merely defined in ways that reflect reality misleadingly. On the other hand, note that even though Los Angeles spans a ridiculously large area, an impressive quantity of its suburbs make the lower lists, justifying that it is actually a very large population center.

This method, of course, still has areas where it falls short. Chicago is in fact a significant population center, but of its suburbs only Cicero shows up. The actual case is that the Chicago area is just dotted with a huge number of suburbs, such that many are too small to even make the smallest list here (where I decided to stop), but for which the consolidation of several of them would probably build a convincing suburb base for Chicago on these charts.

Incidentally, you may have read this far and wondered why I’m not instead looking at the populations of metropolitan areas. Ideally, that sounds like what we’re looking for here. Sadly, once one looks at a map of where the defined boundaries of metropolitan statistical areas actually are, one easily realizes that this may be an even worse idea than city limits for proxying the idea of the population of a city.


Pandemic: Legacy of the Sea

About a month ago, three friends and I did a playthrough of the campaign of Pandemic: Legacy. I strongly recommend it, in particular to those who enjoy cooperative strategizing and have a high tolerance for yelling at your teammates due to your miscommunications. (With the complexity of the rules, this will almost certainly plague your playthrough.)

In this post, however, I am talking not about diseases. I am instead talking about the world’s oceans.

Scientific estimates for how much the Earth will warm on average in one century if humans don’t do anything about their current carbon dioxide behaviors revolve around 4°C. Pessimal evaluations consider 4°C enough for the melting of the Greenlandic ice sheet. If the earth warms 10°C (which may well be the case if after one century humankind decides it can go another century before doing anything), not only the Greenlandic, but also the West Antarctic and East Antarctic ice sheets could all melt. The combination of the conversion of this massive quantity of continental ice to ocean water and the thermal expansion of water would cause sea levels to rise by 70 meters. The Earth has a lot of land above 70 meters in elevation, but remember, most humans live on the coast and more generally in low areas. And thus, rather than ask how many of 48 cities will survive a tumultous outbreak of diseases, I will here ask:

How do the 48 cities of Pandemic: Legacy fare in the ultimate sea level rise?

Blue Region
San Francisco, Chicago, Atlanta, Montréal, Washington, New York, London, Madrid, Paris, Essen, Milan, St. Petersburg

San Francisco: Most of Sunset, Mission, and Downtown are below the critical elevation. The highlands in the heart of San Francisco is now the only of San Francisco, aside from the various hills of the rest of San Francisco, which form an archipelago. City Hall and Union Square are both way underwater. For all practicality, San Francisco has perished. (Going north from San Francisco along the Pacific coast, the story is not happier. Portland, Seattle, and Vancouver also do not make it.)

Chicago: Fortunately, substantially high enough. Lake Ontario is barely above the seventy meter mark, but Lake Michigan is more than an entire Niagara Falls above Lake Ontario. Chicago survives.

Atlanta: Far enough inland to be high enough. Atlanta survives. (More-coastal Georgia and other southern states, though, do not make it. Charleston is gone. Houston sinks. New Orleans’ levees that couldn’t take Katrina cannot anywhere near take 70m of sea level rise. Memphis survives with minimal damage.)

Montréal: Only seemingly inland on a map, Montréal is too near to the mouth of the St. Lawrence River. Although the center of the island Montréal is on makes it, most of the populated regions of the city do not, and sink underwater. (Toronto survives, though.)

Washington: At about 20 meters of elevation for each, the White House and the Capitol don’t make it even if only Greenland melts. The Supreme Court survives Greenland melting but not Antarctica melting. Neither Georgetown University nor George Washington University stay unsoaked. Only some outermost regions of the District of Columbia remain above sea level.

New York: Well, the top of the Empire State Building is high enough. But almost nowhere on the ground on Manhattan is. Only a small speck of the north end of Manhattan is above the line. The Bronx does barely better. Queens does worse. Brooklyn does even worse, 100% reclaimed by the sea. Staten Island fares by far the best of the five boroughs, but even the vast majority of it does not make it. (Baltimore, Philadelphia, New Haven, and Boston also perish. Of all the colleges of the Boston area, even the more-inland Brandeis, Bentley, Tufts, and Boston College do not stay on land. Northeastern, Harvard, MIT, and Boston University do not survive even a Greenlandic melt.)

London: Most of London does not make it. (Edinburgh is split about in half between parts that stay dry and parts that sink.)

Madrid: Protected by quite a lot of land. The rising seas aren’t a problem here. (More coastal Barcelona is not as lucky. Over in Portugal, Lisbon is claimed by the sea.)

Paris: Like Madrid, far enough inland to not need to fear the waters.

Essen: Essen is mostly okay. Western regions of the city may succumb to the rising Rhine. (Hamburg is much less fine, and is lost in near entirety. Berlin does not too well. West of Germany, destruction is near total. Almost all of Netherlands is far too low to survive, and much of Belgium, including Antwerp and a substantial amount of Brussels, doesn’t either. The Nordic countries also suffer heavy damage, all five of their capitals—Reykjavik, Oslo, Copenhagen, Stockholm, and Helsinki—being lost to the sea.)

Milan: Milan is elevated enough to survive. (Rome isn’t. Venice isn’t even close to standing a chance. Elsewhere in Mediterranean peninsulas, about half of Athens is lost, but the Acropolis continues to stand proudly atop a safe hill.)

St. Petersburg: St. Petersburg is far too low to survive the rising seas. (Tallinn and Riga also succumb to the advancing waters of the Baltic.)

6/12 cities survive
San Francisco, Chicago, Atlanta, Montréal, Washington, New York, London, Madrid, Paris, Essen, Milan, St. Petersburg

Continue reading “Pandemic: Legacy of the Sea”


Home of the free
Messenger of democracy
Moral authority of the world
Retainer of slavery past Britain and France
Land proud of Tippecanoe
Sender of gunned boats to Japan
Paver of the Trail of Tears
Excluder of Chinese immigrants
Home of the Ku Klux Klan
Refuser of suffrage to women
Maker of Japanese Internment Camps
Backer of the Guatemalan and Bangladeshi genocides
Land of abortion clinic bombings
Oppressor of Palestinians
Killer of a hundred thousand Iraqi civilians
Home of the Waterboard
Home of the free
Messenger of democracy
Moral authority of the world

This YouTube Channel Achieves Fractal Wrongness in Data Misuse

This one. The channel of “GOOD Magazine”. I take it it’s one of those ironically named things, like how Fox News’ Slogan is “Fair & Balanced”, because the bad data is strong with this one.

Let’s take a look at one of their YouTube videos titled “Top 10 Most Powerful Hurricanes Ever“.

Let’s start at 0 seconds in. Do you see a problem?

I see a problem. The title of the video is “Top 10 Most Powerful Hurricanes Ever”. What does that mean? What is their metric for “Most Powerful”? Hmmm, maybe we’ll find out after watching this video for a while. Let’s see…

Okay, 15 seconds in, the text on screen tells us that they’re clarifying that “most powerful hurricanes” means “biggest hurricanes”.

…really? Because I think for most people “biggest” defaults to meaning “biggest by area”, and I’m not quite convinced at all how big a hurricane is tells anything about their power. (Watching the video a bit, one can see that in fact this is not the case and the video uses “biggest” in a more metaphorical sense.)

All right, let’s roll their top 10 through.

Done watching it? How many things bothered you? If your answer is zero, you should go and rewatch it again, until you find something fishy. No really, there are things in this top 10 that are fishy that do not require knowledge about hurricanes to detect.

Let’s start with realizing what their metric of hurricane power is: it’s the smallness of the central pressure. But even they decide to put this metric second in their data display, so certainly it should also be nonobvious to them that this is a nontrivial clarification to make?

But second of all, how reliable is their data on central pressure (which, incidentally, appears like it should have been labeled minimal central pressure—the central pressure of a hurricane changes over time)? Notice that they report one hurricane (the “Labor Day” Hurricane) from Gregorian calendar 1935, long before the other hurricanes mentioned. What was the quality of meteorological instruments back then?

It turns out the “Labor Day” Hurricane occurs significantly before accurate hurricane data became available, and “892 mb” is merely the hurricane’s pressure at landfall. As hurricanes tend to weaken around landfall, the storm was likely more powerful (and its central pressure a lower reading) at some point prior at sea. (Alternatively, since they didn’t explicitly say “minimal” on the data label, one could suggest that maybe they are reporting landfall central pressure rather than minimal central pressure, but in that case the landfall central pressures of other hurricanes are incorrect, so this is a theory of more discrepancy.) This fact was ignored simply because data was unavailable because of the state of meteorological technology eighty years ago, and the data point that was the strongest data available was presented as the strongest data. Other hurricanes from way-back-then were strong enough to potentially be close contenders for this list, but their data is unavailable, so their possibility is silently discarded.

They also present wind speeds. Like how they left out the “minimal” before “central pressure”, they also left out the “maximal” before “wind speed”. But also notice that all the wind speeds presented are divisible by 5 except for Katrina’s. Did it just happen that among the top 10 only Katrina’s maximum wind speed was not divisible by 5?

It turns out that hurricane wind speeds are typically reported to the nearest 5 mph in the US. I have no idea where they got their 174 figure for Katrina from, but it’s probably not from the same source as their figures for the other hurricanes on the list.

Speaking about mph and the US, isn’t it odd that all the strongest hurricanes decided to pick on North America? Do hurricanes have a thing against imperial units? (If this helps the US get off the imperial system, I don’t think I actually mind that much.)

It turns out they get away with a technicality here, because “hurricane” is a term that’s local to North America. There are more powerful cyclonic storms than the ones presented in the Western Pacific, but there they are not called “hurricanes”; they’re called “typhoons”. Still, this is a technicality against intuitive interpretation, and storms of the same meteorological nature that just happened to be called different names should not be discounted in the creation of such a list.

Okay, so circles appear on a map above this presented quantitative data. It looks like they mean to present the path of travel that each of the hurricanes took. But first of all, the paths are wrong. They do generally have the shape that the actual paths of the hurricanes had, but the paths are quite shifted from the actual paths the respective hurricanes took.

But also, one would suppose that the circles are equidistant in time. (They’re certainly not equidistant in space—note Gilbert’s path versus the paths of the others, for instance.) That is, one would think the amount of real-life time it took for the hurricane to move from one plotted location to the next location is the same as the amount of real-life time between the hurricane being at that second location and being at the one after that. But three days pass between the second and third circles shown for Hurricane Wilma whereas only six hours separate consecutive circles at the end of the path presented for Wilma (that is, if we assume that the presented path is just a position-shift from the correct path, and not something crazier).

Continue reading “This YouTube Channel Achieves Fractal Wrongness in Data Misuse”

A Day With Sporcle

I decided to spend a few hours with a site I once upon a time frequented: Sporcle.

Specifically, to find out the order of ten categories from my worst to my best, I played 16 games using the random button (skipping quizzes that were essentially multiple choices for four or less choices) in each of the ten and jotted down the results.

(Below the ten categories are in increasing order of how well I did.)


(Things turned out approximately how I expected them to turn out.)