The largest city in each 10x10 degree latitude/longitude box

The choice of geographic unit depends what questions you're interested in answering. If you're trying to answer questions about government, tax base, city services, etc., then you definitely want to use legal/administrative divisions as your unit of analysis. If you're interested in answering demographic questions, like population growth or labor pool, then statistical areas like CBSAs are more useful, because differences in administrative boundaries would introduce inconsistencies in your data.

You can also define a region as an area of (relatively) continuous density - the Census does this and labels them "urbanized areas". Any one of the 3 approaches (administrative boundaries, commuting zones, density) can be reasonable, depending on what sort of questions you'd like to answer.

> Can you really count the population of Newark, New Jersey as part of NYC, NY?

If you're looking at metro areas (which are defined by commuting regions), then you definitely should, because a sizable fraction of the residents of Newark and the surrounding communities commute into NYC for work. The Census does define a sub-unit called metropolitan division, and Newark, NJ is one of these.

> Is San Francisco part of san Jose?

If your unit of analysis is MSA, then no - "San Francisco-Oakland-Hayward, CA" and "San Jose-Sunnyvale-Santa Clara, CA". This division recognizes that the two have separate (but overlapping) commuting zones - very few people commute from Richmond to Sunnyvale, or from Milpitas to San Francisco.

However, they are both within the "San Jose-San Francisco-Oakland, CA" Combined Statistical Area, which is a broader unit which recognizes that there are commuting relationships between the two areas - they are just weaker than the commuting relationships within the MSAs.

> What about twin cities, like dallas and fort worth?

Dallas-Fort Worth-Arlington, TX is an MSA. For the purposes of maps like this, you can generally just take the name of the city that come first in the MSA name and people will understand what you're referring to.

This slide deck from the US Census Bureau is pretty interesting for understanding their geographic taxonomy, and the trade-offs of different levels of observation: https://www.census.gov/content/dam/Census/data/developers/ge...

A geographically curious conceptualization of the random error in sampling artifacts.

> Recall that all meridians intersect at the poles.

How is that relevant regarding “Parallels and meridians always meet at 90 degrees“?

Mostly an aside to your comment, but it's somewhat related. This post's divisions of 10° latitude/longitude is pretty close to the Maidenhead grid system, used heavily by amateur radio operators like myself.

The difference is that each top-level grid "square" (to your point, not actually square, but that's what they're called) is 20° longitude by 10° latitude represented by two letters. While the computation of a 4 or more character grid locator code is complex enough that most people can't quite do that in their head, because of them being treated as if they were coordinate "rectangles", it is simple enough to translate lat/lon coordinates to a grid code and vice versa with pen and paper if needed in the case of an emergency, if you know the algorithm or have a reference sheet. The 10° latitude size means that the parallels are the same in the Maidenhead system (for the first two letters of a code) as in this post. It also has the added benefit of knowing that DN is north of DM, which are both west of EM. I've gotten to where I can roughly place someone I hear on the radio based on a mental map of grid codes, and have memorized many grid codes of large population centers.

The beauty of the grid code system is that you can further refine an area by adding on subsequent numbers and letters, much like degrees/minutes/seconds in coordinates, but requiring significantly less characters to read to others over the radio. And, you can use phonetics for the letters, i.e. "delta mike seven niner" (DM79) is roughly the entire Denver metro area. Fort Collins, CO on this parent post falls under DN, above that 10°-sized parallel.

More info on the Maidenhead system: https://en.wikipedia.org/wiki/Maidenhead_Locator_System

Map with two-letter grid codes: https://www.mapability.com/ei8ic/maps/gridworld.php

You make a good point. What is an equal-area, tessellated shape that could be used in its place?

I guess a triangle. Or one of these:

https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Sp...

https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Sp...