This turned out to be a popular thread, so I thought I’d share it over here.
This is a good example of a common misconception: that physical space per person matters.
Things that actually matter:
1. Water per person
2. Farmland per person
3. Cost of housing near city centers
4. Commuting time to city centers
Thing is, while we still eat food, our economy has been, since the late 1800s, something we describe as “industrial” (and now “post-industrial”). This means that the vast majority of people have to live in cities instead of farms, because industries are in cities.
Don’t get your political information from anyone who doesn’t know we live in an industrial (post-industrial) economy, folks.
One of the side effects of living in an industrial/post-industrial economy is that, by necessity, you end up with uneven population densities. We don’t plop cities down on farmland (not if you want to eat) and you don’t try to grow potatoes in city medians.
So a pure measure of “density” is meaningless.
In an agrarian economy, land is the most important resource. In an industrial/post-industrial economy, proximity to industry is itself a kind of resource. People have to actually be able to get to their jobs. This is why in places like Silicon Valley, where housing is artificially restricted, the price of housing skyrockets. You can probably find some super cheap (relatively speaking) land a mere hundred miles away from SF, but people can’t commute that far, so they bid up the prices on what housing there is.
Of course it would be great if people could just build more housing in CA, but that’s a separate issue–regardless, if people could just move to one of those less populated areas, they would.
(By the way, South Africa is also a modern, industrial economy, which is why the idea of taking people’s farms and redistributing them to the masses is absurd from an economic point of view. South Africa is not an agrarian society, and very few people there actually want to be farmers. The goal is not economic growth, but simply to hurt the farmers.)
Many of our other resources are similarly “invisible”–that is, difficult to quantify easily on a map. Where does your water come from? Rain? Rivers? Aquifer?
How much water can your community use before you run out?
Water feels infinite because it just pours out of the faucet, but it isn’t. Each area has so much water it can obtain easily, a little more that can be obtained with effort, and after that, you’re looking at very large energy expenditures for more.

Groundwater Depletion in the United States (1900–2008). A natural consequence of groundwater withdrawals is the removal of water from subsurface storage, but the overall rates and magnitude of groundwater depletion in the United States are not well characterized. This study evaluates long-term cumulative depletion volumes in 40 separate aquifers or areas and one land use category in the United States, bringing together information from the literature and from new analyses. Depletion is directly calculated using calibrated groundwater models, analytical approaches, or volumetric budget analyses for multiple aquifer systems. Estimated groundwater depletion in the United States during 1900–2008 totals approximately 1,000 cubic kilometers (km3). Furthermore, the rate of groundwater depletion has increased markedly since about 1950, with maximum rates occurring during the most recent period (2000–2008) when the depletion rate averaged almost 25 km3 per year (compared to 9.2 km3 per year averaged over the 1900–2008 timeframe).
We’re not just “full”; we’re eating our seed corn. When the aquifers run out, well, the farms are just fucked.
There are some ways to prevent total aquifer collapse, like planting crops that require less water. We’re not totally doomed. But the idea that we can keep our present lifestyles/consumption levels while continuously expanding the population is nonsense.

Eventually something has to give. Someone has to scale back their consumption. Maybe it’s no more almonds. Maybe it’s less meat. Maybe it’s longer commutes or smaller houses.
No matter how you slice it, resources aren’t infinite and you can’t feed cities on deserts.
One more thought:
This is all technical, addressing the question of “How do we measure whether we are really full or not?”
No one has addressed the question of whether being “full” or not is even important.
You could look at my house and say, “Hey, your house isn’t full! There’s plenty of room for two more people in your living room,” and I can say “Excuse me? Who are you and why are you looking in my windows?”
This is my house, and it’s not my responsibility to justify to some stranger why I want X number of people living here and not Y number of people.
If I want to live alone, that’s my business. I am not obligated to take a roommate. If I want my sister and her husband and five kids to move in here with my husband and kids and their dogs, too, that’s also my business (well, and theirs.)
It is not a stranger’s.
Just because we can cram a lot of people into Nevada does not mean anyone is obligated to do so.