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Treebeard's Stumper Answer
15 October 1999

World Party

The United Nations designated Tuesday, October 12 as the "Day of 6 Billion," the likely day when the world population will reach that mark. (There's more info at the PBS TV site That's a lot of people! If all 6 billion of us agreed to get together for a world party, where would we have to go? What country or landmass would just hold us all? Make reasonable assumptions about crowding, don't worry about details like comfort or bathrooms, and (as a science teacher, I love saying this) show your work! What if we all jumped in the air at once?

World Party image by Orin.
World Party image by DMS student Orin for the
Dunn Middle School 20th anniversary reunion next June!

If every person had just a 2 foot square to stand in, our total area would be 2 ft x 2 ft x 6 billion people = 24 billion square feet. Square miles are easier, so we can convert:

                              1 mile    1 mile
square miles = 24 billion ft2 x ------- x ------- 
                               5280 ft   5280 ft
That's about 900 square miles. That seems too small, but it's right! We're bigger than LA, but smaller than Rhode Island or Zanzibar. Jumping would have less effect than last week's 7.1 earthquake. We impact the world with our actions more than our bulk.


I did this simple area calculation, and the answer didn't seem possible. So I did it again (and again), and I'm sure it's right. Assembled in the tight but possible crowd of 4 square feet per person (2 by 2), the human population of earth would only occupy about 900 square miles, with a population density of about 7 million per square mile. That's the ultimate mosh pit! By comparison, Hong Kong has an area of about 400 square miles and a population density of about 10,800 per square mile. But people actually live there!

John Brunner wrote the classic sci-fi novel Stand on Zanzibar in 1968 describing life in the near future world of 2010 when the over-stressed population on the earth could just stand on the island of Zanzibar (950 square miles). He got that right.

Stand on Zanzibar book cover

Graybear sent this interesting analysis with more reasonable assumptions:

As a construction engineer, I consulted the "Life Safety Code" to determine how densely we can assemble ourselves. Of course, I assumed it would be an outdoor gathering. At a rock music concert in Toronto on July 16, 1980, approximately 35,000 people occupied an area of 125,000 square feet, a density of about 3.5 square feet per person. Officials say that the density close to the stage was about 2 square feet per person, causing problems when people could not expand their chests enough to breathe. The "Life Safety Code" says to use 7 square feet per person for 'festival seating' where people sit on the ground with enough space for aisleways to occur. That seems a little more comfortable. Using this number, I get the following: 6,000,000,000 people x 7 square feet/person / 27,878,400 square feet/square mile = 1,506.5427 square miles. Santa Barbara County has 2,738 square miles (according to my atlas), and has nice weather, so it might be a good spot to have the party while giving about 12.7 square feet per person. I realize that some of Santa Barbara County is occupied by water, forests or buildings, but we will need some of those buildings especially the restrooms, hospitals, and mortuaries. If our party lasted one (24 hour) day, we could expect around 380,000 births and 144,000 deaths that day.

If we all jumped at the same time, we wouldn't knock the Earth out of orbit or anything, but I wonder if it might trigger an earthquake. Guessing that the average person weighs 100 pounds, 600,000,000,000 pounds equals 300,000,000 tons, compared to the 6,588,000,000,000,000,000,000 ton mass of the Earth.

One side note, I remember in the late sixties or maybe 1970, the world population was about to reach 4 billion and doomsday environmentalists (as opposed to the other kind) were alarming people with predictions of mass starvation. Now they are saying the Earth can support about 12 billion - maybe some of your students will be alive to see that prediction broken - or maybe we will live on other planets by that time.

Population biologists talk about the carrying capacity of the land for a species, but this is a tricky concept to use with humans because of technology and social disparities. I worry that over-population is being used as a smokescreen. In fact, one small group's high-consumption (us) can have a greater effect on global environmental standards than that huge population elsewhere. Population is not the only problem in the world, and maybe not the greatest. I think the real stumper is: can everyone be rich and live well?

It's interesting to turn this stumper around. Instead of squeezing the earth's population into a small area, let's spread out across the earth. How much space do we each get? I figure (with some rounding):

Earth's diameter = 7926.41 miles
Surface Area (pi d2) = 200,000,000 square miles
The oceans cover about 70% = 140,000,000 square miles
So about 30% is land = 60,000,000 square miles
6 billion people / 60 million square miles = 100 people per square mile
1 square mile = 640 acres
That's about 640 acres / 100 people = 6 acres per person

Six acres is a nice homestead in the right place. But consider the alternatives. It could be impossible.

Two follow-up stumpers:

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