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Note: I wrote this about a decade ago, when the Earth's population was about six billion people. At this point it's around seven billion people, but the rest of the data hasn't changed much.

The Dumbest "Argument"

Lately I've been hearing, from several places, the idea that the world is not overpopulated. For example, I was driving home one day from work, and was listening to NPR, as was my wont. I heard Mr. Dinesh D'Souza make a statement that I had heard before elsewhere, which is reproduced on his website at "http://www.dineshdsouza.com/overpop.htm".

"Apocalyptic writers warn that the world's population has crossed 6 billion. So what? If all those 6 billion people lived in Texas, each family of four would have an average of an eighth of an acre of land - and the rest of the globe would be vacant. If you're [sic] been told that the world is running out of space, reflect on that for a moment."

Do The Math

Obviously, this isn't an argument, it's a non sequitur. If that's not obvious, let's take it all the way to the limit, and see if it still seems convincing. Let's assume 4.5 ft^3/person. There's 1.47x10^11 ft^3/mile^3. Divide that by 4.5 and then by 6x10^9 and you get ~.20 mi^3 to hold the world's population! Heck, we only need a cube ~3000 ft on a side! We can stack everyone in a corner of the Grand Canyon and leave the rest of the planet untouched!

Okay, who wants to volunteer to be on the bottom layer?

The Magic Wand (More Math)

Even if it's silly, this oft-repeated line still might serve an illustrative purpose. We'll take it literally and see where it leads. Let's assume we have a magic wand. We can wave it and solve the literally billions of political problems involved in getting everyone to move to one region of the Earth. We do the wave.

Now, where do we move them to? Texas is right out - huge amounts of desert make it impractical to support 6x10^9 people. Like California, they already have problems distributing water to a population several orders of magnitude smaller than 6x10^9. Heck, is there any place on Earth that can supply that much fresh water? According to the Merck manual (http://www.merck.com/pubs/mmanual/section2/chapter12/12b.htm"), people need a minimum of 700ml of water per day to stay alive and avoid kidney failure. So, for 6 billion people, we need... 4.2x10^9 liters of fresh water/day.

Hmmm. I've got it! It seems that 100,000 ft^3 of water flows over Niagra Falls per second (http://www.great-lakes.net/lakes/). That's about 2.8 million liters/second, so it works out to about 4x10^9 liters per day. Well, it's two hundred million liters short, but if we divert the entire St. Lawrence river then we're pretty close. Of course, people engaging in vigorous physical activity will use a lot more water than that. A lot more.

However, people use water for more than drinking. What about, at minimum, toilets and showers? We have to back up and consider water again... specifically, sewage. Think of the plumbing that can carry the wastes of six billion people. Let's do a little research... oh, cripes.

The best case I found, using the critical emergency water usage restrictions for a town near Vancouver, limits people to 25 gallons of water per day. (http://www.fridayharbor.org/title13.htm) That's 135 times the (unrealistically small) amount of water we calculated we needed for drinking. It's worth following that link and seeing the kinds of activities that are forbidden during such an emergency. Heck, even Singapore, not exactly known for elbow room, assumes (http://www.env.gov.sg/cop/sd/cop1v1/Part%202.html) about 60 gallons per person (230 liters) minimum and designs for three times that (690 liters, 182 gallons, or 985 times what we originally assumed).

So we need at least 135 times the runoff from the Great Lakes just to keep people alive and to carry off their wastes. So far we've been able to keep up, but people aren't concentrated in an area the size of Texas. I won't even attempt to figure out how to handle that plumbing problem. But for the sake of the argument, let's pretend that somehow someone can.

So, we pick a Texas-size area of a nice temperate clime, let's say the southeast United States, around the Carolinas. Now, how much land do people get? Texas is 261,914 mi^2. That's 167,624,960 acres, at 640 acre/mi^2. So, with 6x10^9 people, that's .0279 acre/person, or .1117 acre/family of four. Hmmm, Mr. D'Souza was wrong, that's only about a ninth of an acre, or a square 70 feet on a side.

Of course, we can't just leave them there. We have to feed them, right? To do that, we need arable land. Assuming .07 hectare/person/year (http://www.cnie.org/pop/conserving/landuse2b.htm) - which is (ahem) rather optimistic - that's .1729 acres/person... hmmm. That's 6x10^9 * .1729 = 1,037,400,000, or about 1x10^9 acres. Which is 1,620,937.5 mi^2, or a square that's 1273 miles on a side.

(Note that http://dieoff.com/page55.htm cites .5ha/person as "minimum requirement for a diverse diet of animal and plant food products", or seven times as much as we've assumed above. A test of this is Anuta Island, a Polynesian island one quarter mile in diameter that has supported about 200 people at a time throughout its history, which works out to .25ha/person - but their diet isn't particularly diverse.)

The whole continental United States is 3,700,000 mi^2 (9,158,960 km^2). I.e., for a purely vegetarian diet, feeding only humans (no pets allowed in New Texas), using extremely aggressive agricultural technology (which, by the way, needs water too - according to this, 74% of water use worldwide is for irrigation, with 18% for hydropower and 8% for households), we need 43% of the land area of the United States. And that's the best case.

What if our magic wand doesn't make everyone vegetarians? Assume people eat, on average, 1/4 lb of beef only 3 times a week. Well, http://www.gov.on.ca/OMAFRA/english/research/researchfund/rmdocs/rm3037.htm claims that beef production in Ontario gets a max of 750kg/hectare/year, with an average of 250kg/ha. (That's 303.6kg/acre max, 101.2 kg/acre average.) Let's take that as typical, it's the best data I could find. It's certainly accurate enough for our ballpark estimate.

Now, we need 17.7 kg/person/year. So, one acre can, at best, feed 17.15 people per year. So, to feed beef to 6x10^9 people, we need... 349,800,000 acres. That's 546,566 mi^2, or a square 739 miles on a side. (That's best case. Assuming only 250 kg/hectare, we need 1.049x10^9 acres, 1,640,000 mi^2, or a 1280 mile x 1280 mile square.)

I won't bother going through the calculations for people wanting mutton, or pork, or chicken, or what have you. I think we can assume that we'll be needing more room, eh? Oh, and water, too. Cattle need to drink... a lot. Referring back to that link above, "a calorie of food took roughly 1 liter (0.2200 Imp gallons) of water to produce. But a kilo of grain needed only 500-4,000 liters while a kilo of industrially produced meat took 10,000 liters."

Our best case above adds up to 60% of the continental US to feed everyone a minimal diet. The "realistic" (and still wildly optimistic) case... 3.5 times the surface area of the U.S. Hmmm... only 19% of the US is arable land, and 25% is grazing land. (That's from the CIA's 1993 stats, which are available at http://www.odci.gov/cia/publications/factbook/us.html#geo). We're going to need some more room.

Say, don't you have to let some agricultural land lie fallow every year? We haven't accounted for that. I have no idea how to estimate that, but keep it in the back of your mind that there's yet another significant land usage we're not including.

We haven't even clothed them yet. We aren't keeping sheep, so we can't use wool. Clothing the whole world in leather (from the cows) has its kinky aspects, but we aren't raising enough cows. We should probably use some kind of plant fiber.

Cotton is very agriculture-intensive. We could use flax, that is, linen. We can even feed some of the flax to the cows. But we'll need space to grow it. According to http://www.ag.ndsu.nodak.edu/aginfo/procrop/flx/fxly9808.htm, we get about 30 bushels/acre/year of flax. So far I've been unable to find out how much cloth you can get per bushel. Somehow I think we're going to need at least another half-a-United-States to clothe everyone, though.

Of course, we can use nylon and such, too, but we need petrochemicals for that. That takes up less space than agriculture, but still needs room. (Hmmm. How many trees do we need to supply everyone with toilet paper, anyway?)

Besides, we have all these people on 70x70 plots of land. How will they move about? We're going to need roads, unless we assume teleportation or personal helicopters or something. At the very least, we'll need a railway system for mass transit.

Then, of course, we'll need hospitals. And police stations. And fire stations. (I guess we'll assume underground plumbing and wiring and such.) Hmmm. We're going to need schools. If not local stores, then at least centralized shopping malls. And office buildings. And factories, warehouses, and so forth. Are there going to be any parks or stadiums or museums or movie theaters in New Texas?

We worked out that New Texas would have .0279 acres/person. It's interesting to note that this is almost exactly the population density of New York City (321 square miles, 8 million people, i.e. .0256 acres/person.) Think of it, almost eight hundred New York Cities side by side...

Let's be generous and assume that our area is zoned 2/3 residential and 1/3 other. (New York is quite a bit less, currently 43% residential. Even if we add the 12% vacant land, that still only gets us 55% residential.) So, we're really going to need half again the size of Texas to hold all these people. Or else every family of four gets a "ranch" 57 feet on a side.

(Say... where does all the trash go?)

Something else... it's worth noting that, with the current best figures (60% of the US to feed everyone on Earth, which we determined was a hopeless underestimate, .5 times the size of Texas for support and distribution, and Texas to hold everyone) the actual space homes take up is less than 10% of the total space needed. Based on the "more realistic" figures (3.5 times the US for food, .5 times the US for clothes, .5 Texas for support, Texas for homes) the figure's closer to 1.7%.

So even at a wildly optimistic guess, 98.3% of the space you take up is just in support. Where you live is your least important use of space.

A recent Scientific American article claimed that, on average, Americans need 24 acres of supporting land per person. How does that square with our figures?

Now, there's 640 acres per square mile, and 5280 feet in a mile, so that means average American support space is (5280^2)/640*24 or 1,045,440 square feet. Using that as a basis, and assuming again that they live on 70x70 plots of land per family of four (so (70^2)/4 or 1,225 sq. ft.), living space makes up 1,225/1,045,440 = 0.00117 or 0.117% of the total land area needed to support them.

So, as expected, our guesses above were optimistic. By about an order of magnitude.

Using present technology, how much land would it take so that everyone on Earth could live like an American? Let's see... 24 acres, times 6*10^9, divided by 640 to get the area in square miles... 225 million square miles. What's the surface area of the Earth? 197,000,000 square miles. And only 57,268,900 square miles of that is land at all, much less arable land.

Forget New Texas. We're going to need three or four New Earths.

Now, there are people who will argue that it's just a problem of technology. With better tech, we can support more people in the lifestyle to which Americans have become accustomed. I think this is, in fact, possible. However, it will require, as amply illustrated above, at least an order of magnitude improvement in agricultural and manufacturing techniques, probably two orders or better.

This is possible, using nanotechnology, the science of building machines out of individual atoms. Really, that's what living things are. A plant is a machine that turns dirt and water and sunlight into, say, corn or grass. A cow is a machine that turns grass into beef. Theoretically, we could build (or genetically engineer, or whatever) something that could turn sunlight and dirt directly into beef, presumably more efficiently.

Of course, the "science of building things out of individual atoms" doesn't really exist yet. They've been predicting great strides in the field since I first heard about it in the late 1980s. It's been about twenty years and we still do not have the kinds of things that they were predicting we'd have by now (diamond ropes, microscopic medical robots, etc.)

I think we probably will have nanotech someday. But it's going to take a while. They've been predicting an artificial intelligence since the 1950's and we still don't have anything as smart as a two-year-old human. We've just about got things as smart as insects. I hope I live to see real nanotech, but I'm not betting the farm (literally) on it.

Implications

Hopefully the above analysis has sparked some thinking on your part. The key implication is not "We can't pack everyone into Texas and anyone who talks about doing that either doesn't know whereof they speak or is being deliberately deceptive." (Though that's a valid conclusion.)

The key implication I'd hope you take away from this is that humans use a lot more land than just the square feet they are standing on. Think about how much space your house or apartment takes up, and your car and/or bike, and the place where you work, and the parks where you play, and the restaurants you go to, and the movies theaters you visit, and so on and so on. People take up a heck of a lot of room.

Then think about how much water you use, and food you eat, and various objects you use and buy and wear out. Think about the fact that space and resources are needed to supply those.

No, I don't want people to feel guilty about living. But if we're going to sensibly discuss overpopulation, we need to understand how much land people really use, and reason from that.

For example, Mr. D'Souza states on the webpage cited above that "Most of this country is completely uninhabited." From the point of view of most of the animals who live here, this is manifestly not so.

Don't get me wrong - as good ol' Robert Heinlein said, "I am a human, not a beaver." I don't put animal "rights" above human rights. But, aside from the obvious fact that we need other living things on this planet if for no other reason than to eat them, and aside from the fact that I like having places to go with no humans around, the distribution of people is, er, suboptimal.

I was lucky enough a few years back to work by several acres of woodland and wetlands. I saw up to thirty deer outside our windows. There were also beaver, groundhogs, squirrels beyond number, geese, etc. But it had been several years since anyone there on any shift last saw a fox to hunt them.

Yes, they are notoriously shy, but the consensus was that the foxes died out, simply not having a large enough territory to be sure of catching enough food. Perhaps there's enough room left to support one or two foxes, but not a family. (Let alone a bear, omnivorous though they are.)

While there are many places that don't have people actually living on them in this county, seen from above you can tell that they don't connect up very well. Look out from a plane, and see if you can find a wooded area larger than a square mile which does not have a road running through it.

My children are not going to see the same state parks that I did while growing up. We'll take them camping, but there's less room for that all the time, and fewer plants and animals to see, and more people who want to see them.

I think it's in our best human interest to consider how much space we take up and where we take it.

Exercises For The Reader