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Friday 11 October 2013

Population and Meaningless Math

In the daily barrage of needless coverage of TV celebrities, I note with vague disapproval the headline announcing that Michelle Duggar, mother and star of the TV reality show 19 Kids and Counting, has made waves this week with her announcement that she and her hubby Jim Bob are working at conceiving kid #20. Why this is even considered newsworthy is beyond me. Maybe, just maybe, if she were actually pregnant then that might be worth a footnote somewhere from the Hollywood press machine. But really now, do we need to know the Michelle and Jim Bob are having a good time making the bed springs squeak? Seriously folks, we know they are married, we know they are in good health; and we can safely conjecture therefore that they are indeed engaged in activities that may lead to pregnancy. We do not need a press release to inform us of that...

Folks with 19 kids usually aren't fodder for my blog. Really, people in such circumstance are more likely to receive my heartfelt sympathy more than anything else, and I have to concede a little admiration for utitlizing the size of their family to make a little money, despite my distaste for the tacky genre of reality TV.

I could not fail to note one statement made by Michelle Duggar in the news coverage that she and Jim Bob are looking to produce little kid No. 20. The article in question can be found at (accessed 10 Oct 2013). Here's the quote:

Michelle tells Celebrity Baby Scoop that she doesn't believe in overpopulation. "We have studied it and I believe that there is a misconception about overpopulation. I think that the whole mindset of overpopulation is really overrated," the Duggar family matriarch explains. "A few years back, we stated that the whole population of the world could be stood shoulder-to-shoulder in Jacksonville. That may have changed a little bit since we've heard that statistic."

I'm going to ignore the CYA pussy-footing around the world's population today vs. "a few years back" and just use current population figures. After all, I probably won't be off more than 500 million, which is less than an order of magnitude error, so let's wave our decent approximation arms in the air and proceed. To calculate how many people we could stuff into an area, I began by gathering population, population density and area data. The US government's websites that provide geographic and population data are down right now due to the government shut down so I had to rely on Wikipedia. For references, a list of all the wikipedia webpages I consulted are appended at the end of this blog post.

The current estimate for the world's population is 7,116,000,000 people. Our first calculation, a very crude one, assumes we can stuff one person in a square foot so long as that person stands with shoulders aligned along the diagonal of the square.

The amount of space needed for the world population is then:

Start with 711600000 people
Assume 1 person = 1 square foot 
So the world's estimated population will take up 7116000000 sq ft of space

There are 27,878,400 square feet in a square mile. 

We divide through by this amount to figure out how many square miles are needed to fit the world population.

7116000000 sq ft of space
divided by 27878400 sq ft per sq mile 
equals 255.3 sq miles

The square mileage of the City of Jacksonville, Florida, is 885 square miles. 

So far so good, right? Michelle Duggar wouldn't mislead her viewing public, now, would she?

Well, allocating a square foot per person is a bit tight. It would be much more reasonable to expand that a bit. The width of an airline seat in coach class is an average 18 inches. That's not a lot since shoulders, waists and arms are usually wider, especially on guys as the following picture illustrates.

Sean with ruler

The hapless victim, played by my talented spouse in the photo, is holding an accordian ruler expanded out to 30 inches. The ruler width just the other side of his left hand is 24 inches. So a more realistic width for making a gridded area filled with people would be 24 inches. Given that squares are not the most effective shape for maximizing effective specific area, we're going to switch to using the most efficient shape for packing uniform isometric equidimensional items in the least amount of space, namely the hexagonal cell in the arrangement known as hexagonal closest packing. This should be old hate (sic?) for all of you who've suffered through crystallography, advanced physical chemistry or solid state physics. For the rest of you, just take my word for it that hexagonal closest packing - or "hcp" - is the way to go, as looking at any honeycomb in a beehive can illustrate..

A hexagon with a width of 24 inches from apex to apex is equivalent in area to 6 equilateral triangles with sides of 12 inches. Using the area of a triangle formula of 1/2 the base times the height gives us an area of 62.35 sq inches per triangle, for a total area of 374.1 sq inches per hexagon. Dividing through by 144 square inches per square foot gives us an area of 2.6 square feet per hexagon. So using hexagonal closest packing with 24 inch hexagons gets us the following:

Assume 1 person = 2.6 square feet (24" hexagonal closest packing)

711600000 people x 2.6 sq ft/person = 18501600000 sq ft

18501600000 sq ft / (27878400 sq ft per sq mile) = 663.7 sq miles

Okay then, this is still less than the area of the City of Jacksonville, Florida. But of course, there's a catch - and here it is: Jacksonville, Florida, is the city in the entire United States of America with the largest area. Not even that queen of western US urban sprawl, Los Angeles, at 503 square miles, comes close. Let's look at LA real quick. LA is huge. Not only do you have downtown, which is actually quite small, but there's all of Griffith Park, Dodgers Stadium, most of the San Fernando Valley, parts of what's considered "Hollywood" including the famous sign, half of the Santa Monica Mountain Range, and the huge industrial area and rail yards east of downtown. In a state of big spawling cities, LA is the biggest. So in comparison, LA at 503 square miles, which includes that huge piece of suburbia called The Valley (like totally for sure...), is smaller than Jacksonville at a supersized 885.

Michelle Duggar picked the one city in the country with the biggest area. If the comparison used the second largest city in the country, which is LA, then the population of the world would take up more space on the basis of using hexagonal closest packing. Now we don't know what basis Mrs. Duggar used to estimate how much room a person takes up in terms of ground area but I'm assuming it isn't very different from what I've done here.

Of course, it does look a little suspicious that Mrs. Duggar used the one municipality with a really ridicuously huge area. So what's a more normal city look like? Here's a list of cities and towns with their ground area and their population density for your perusal:

NOTE: (My blogging software doesn't make it easy to do formatted tables so until I get off my butt to write the xhtml code to do the formatting, please forgive the crappy presentation below)

City..........................Area...........population density

Name....................Sq Miles.........population/sq mile

Los Angeles.............503..............225
New York..................302.6...........27550
Hong Kong...............426..............17024
Groton, Conn............45.3............890
Salt Lake City............110.4...........1666

Groton is where I grew up so I threw it onto the list. It's a typical town in coastal southern New England. I was surprised that Dehli was smaller than places like New York and Beijing. I was blown away that Macau and Manila were so tiny in terms of area, especially given their very large population densities.

Let's talk about population density. What Michelle Duggar's simplistic analysis lacks is the awareness that one can not judge whether the world is over-populated by examining how many people you can squeeze into the smallest possible area. All that does is tell you, well, how many poeple you can squeeze into the smallest possible area. It's a useless measure. It's smoke and Mirrors, folks. Why? Because it doesn't tell you anything real; for example, it can't tell you about how much area it takes to grow food for 7 billion people or how much fresh water has to fall out of the sky to grow that food and quench everyone's thirst. Stuffing everyone into the smallest possible space doesn't tell you how many people you can fit into an urban environment - an environment where you have to be able to bed all those people; to have transit systems to get them to work and to the market to buy food; to build and maintain roads and rail and canals and quays to move food and goods in and waste out; to construct water mains, storm water drains, sewer drains, water treatment plants and electric power lines; to plan and create parks and theaters and sports arenas. 

Figuring out how much room you need to fit the world's population on a tightly-packed grid doesn't tell you anything about how much room people need to actually LIVE. The thing that tells you about how many people you can stuff into a city where they can actually live and work and prosper will be population density.

We really don't know what the maximum population density might be before the critical infrastructure necessary to maintain urban life fails. We do know what the highest population densities are in the world's most populated cities. Given that an excess of thousands of people aren't dying everyday in cities all the time tells us that we have not yet exceeded a population density so great that modern infrastructure fails to provide our needs.

The number one most crowded urban space in the world right now is Manila in the Phillipines, with an astounding 111,002 people per square mile. The high population density of Dehli in India wasn't much of a surprise but the almost-as-high population density of Paris was, at least to me. That Paris has more than twice the population density of New York City was an eye opener and a bit of humble pie for this Yankee. I put both Vienna and Salt Lake City on the list as examples of moderate-sized urban places with good infrastructure and pleasant habitable environs. Vienna is considered one of the most desirable cities to live in, independent of my personal bias as a former resident. Salt Lake City is probably my favorite city in the left half of the US, with its stunning surroundings, comfortable size, exceptionally clean urban environs, and its active arts scene. I wasn't surprised at the population density in Vienna given that the city limits include the massive greenbelt known as the Wiener Walt or Vienna Woods, made famous by the Strauss waltz of the same name. I was surprised at the really low population density of Salt Lake City but that was before I looked at the city limits on a map. The city includes City Creek Canyon and Grandview Peak in the Wasatch Mountains, all of the airport and the much of the salt marsh north of the airport, the industrial area starting at the railyards and extending as far west as the Kennecott tailings, and most of the salt marsh west of the airport all the way out to the shore of the Great Salt Lake. Basically, the developed parts of the city are exceeded by undeveloped lands also within city limits. It's all that empty land that makes Salt Lake City's population density so low on paper. In a way, looking at population density for cities is a bit misleading since how you draw city limits can distort that number. Salt Lake City and Jacksonville have low population densities compared to places like New York and Hong Kong because both incorporate large amounts of empty land within city limits.

To make a measure that might better reflect the minimum amount of area needed to sustain the world's population, one approach would calculate how much land would be used if the world's population were confined to an area with a population density already sustained by one of the world's most populated cities. I have done just that. I took the population densities from the previous list and then using those numbers, figured out how much room 7,166,000,000 people would take up if we fit them into a space with, for example, the population density of Singapore or LA. Here's the list of those areas:

City..........................Area......  ...population.................area for world population this population density  

.............................Sq Miles........people/sq Sq Miles 

New York..................302.6...........27550...................258294
Hong Kong...............426..............17024...................417998
Los Angeles.............503..............225........................865167
Vienna.......................160.1.......... 10366...................686475
Salt Lake City............110.4...........1666.....................4271308
Jacksonville..............885..............1100.................... .6469091
Groton, Conn............45.3............890........................7995506

This list doesn't tell us much because there isn't anything to compare these areas against. So what I did next was to rewrite this list with the areas of various US states and some other places for comparison.

Place, Calculated or Actual Area in Sq Miles

  • Ohio                       44825
  • Manila                    64107
  • Missouri                 69704
  • Utah                       84899
  • Colorado                104094
  • Delhi                      107598
  • Paris                       129620
  • Macau                    147966
  • California                163696
  • New York               258294
  • Texas                     268581
  • Singapore              375653
  • Hong Kong             417998
  • Alaska                    663268
  • Vienna                   686475
  • Mexico                  759516
  • Greenland             836297
  • Los Angeles            865167
  • Argentina               1073518
  • Beijing                   2156364
  • Australia                2969907
  • Brazil                    3287597
  • USA                      3537110
  • Canada                 3854085
  • Europe                  3930000
  • Salt Lake City       4271308
  • Antarctica             5300000
  • Jacksonville          6469091
  • South America      6890000
  • Groton                   7995506
  • North America        9540000

What does this tell us? Well, if all the world's 7.116 billion people lived in one city as dense as Manila, that city would take up an area bigger than Ohio but smaller than Missouri.

It's useful at ths point to look at Jacksonville, the city that Michelle Duggar invoked in her "research" on the world's population. If all the world's 7.116 billion people lived in one city with the actual population density of Jacksonville, Florida, that city would take up an area bigger than the continent of Antarctica but smaller than South America. Of course, almost all of Antarctica is uninhabitable, but that's beside the point.

We still haven't looked at really important things like how much land you need to feed the world's population and what density you need of roads and rail and water shipping to move food and goods in and garbage out. These are big complex subjects with answers that aren't easy to calculate, as any geographer, earth scientist, or climatologist can tell you. The analysis we did here is really very simplistic. All we really did was show the inadequacy of using Michelle Duggar's approach for saying anything meaningful about over-population. We didn't come close to a real analysis of population sustainability. That would take a book or two, I suspect, and it might take more than that if one were to get really technical in a truly critical and scientific manner.

So, was Michelle Duggar wrong on the internet? I would answer that by first pointing out that she used a city so large in area that her analysis approached the threshold of lying with statistics; and depending on whether her faux pas was intensional, she possibly crossed that threshold of dishonesty. Was her analysis a meaningful measure of population vs. over-population? Well, do the, wait. We just did that, didn't we?


If subjects concerning population science intestest you, a good blog to follow is: I must tip my hat to Tim De Chant, its author, and note that I stole his really useful idea of expressing world population in terms of area vs. population density for this post. Crediting one's sources is good manners, after all.


  • (All accessed 10 October 2013)
City Sq Miles pop./sq mile
New York 302.6 27550

Wednesday 18 September 2013

Miscaptioning Atrazine

What a difference a few words makes. Today's offering is a figure caption from Wikipedia. Maybe it's unfair to pick on Wikipedia - but since it has become the launching point for many an inquiry, I don't think they should be exempted from scrutiny. All things considered, I think Wikipedia is a good thing. I'm a big fan of not having barriers to knowledge for people outside of academe. Given the open and egalitarian nature of Wikipedia, there's far more that's right with it than wrong. The downside of Wikipedia is that it takes time to craft quality articles from a neutral perspective when anyone at all can contribute to writing and editing. It will never be the Encyclopedia Britannica but it has become a great place to start a research project on the net.

I debated whether to even bother with a post about one small figure caption on Wikipedia. Then I realized that if the same figure caption had shown up in a scientific article that I had been asked to peer review for a journal, I would have no mercy on the article authors. Why? Because figure captions matter. A lot of science professionals read articles outside their discipline by skimming in the following manner: first one reads the abstract followed by the figures and figure captions. Depending on the ego and nastiness of any given scientist, some would include a third step which would be to check the references to see if one had been cited. After all, it really is a publish and perish world out there and citations matter.

Basically, figure captions matter. When you consider that journalists and bloggers often lift figures out of journal articles and reprint them in internet or newspaper content, then figure captions matter a whole lot more than one would think. So in this context, I decided that, yes, I would indeed pick on just one short figure caption in Wikipedia.

Earlier today, I was reading a string of comments on Facebook about a murderer and his victims. Someone made a comment speculating that the murderer could have poisoned one of his victims with atrazine. This immediately hit my HUH? filter big time and left me wondering how much atrazine comprised a lethal dose for an adult human.

These days, I tend to look at Wikipedia first for regulatory, physical chemistry and toxicology information since many chemical pages on Wikipedia often include that info. If the Wikipedia page is any good, there will be a link back to a public health, industrial hygene, health physics or envirnomental science authority or journal where cited numbers can be verified. For the record, unless I already know a number off the top of my head (for example, I know most of the EPA MCLs for heavy metals by heart), I almost always verify numbers, especially if I'm going to be commenting or blogging about it later. Just as a quick FYI, the CDC is even better than the EPA if you want to look up understandable environmental and toxicological info about pollutants.

Getting back to our main topic here, which is a figure caption on the English-language Wikipedia site for atrazine, I found the comment from Facebook rather odd since herbicides are not popular or widely used poisons for homicides. As I suspected after looking at the toxicology numbers for atrazine, the amount needed to poison someone would be several tablespoons. Nope, atrazine would make a lousy homicide poison on the basis of quantity required. I suspect it would also taste bad too. Arsenic and strychnine are in no danger of being displaced as effective human poisons by atrazine. I'm sure that's a great relief to know! You can sleep better tonight knowing that evil atrazine from the blue earth corn fields of Minnesota will not waylay you and bring you to death's door before you wake.

Of course, atrazine has its own little anti-fan club because of its use in American farming, for cereal crops and especially maize, the iconic crop of the Midwest. Like all other things that farmers put on their crops in liquid form, atrazine has infiltrated into drinking water aquifers wherever farming is big. If you believe that atrazine is a danger to public health or the environment, then this is a matter of concern.

Regardless of the real or imagined danger posed by atrazine, having good facts at hand on its spread, prevalence and impact is necessary for meaningful debate. For the people out there who go to Wikipedia - and no farther - for their information, getting the facts right on the page for Atrazine strikes me as highly desirable. Now there are a few things that could use some fixing on this wiki page, but the one and only figure caught my eye immediately. Here's what it looks like, straight off my monitor screen: atrazine2.png

Did you spot the caption below the figure? "Atrazine use in pounds per square mile by county."

I made the mistake of really getting eye tracks all over this figure BEFORE blowing it up for finer inspection. Right off the bat, I thought all that green-level use of atrazine in New England was off-base. Seriously, New England - the home of rocky ground and non-existent top soil - was using that much atrazine? You don't use atrazine if you're farming apples, potatoes, maple syrup, trees or cows - which are all the main aggie products in the New England states. Now look at California and southern Idaho - especially southern Idaho where one of the biggest crops is barley. I would have thought the atrazine use in these area would be much higher than on the figure.

So I enlarged the figure: atrazine.png

I just love how the highest usage area overlaps the Midwest corn belt. Check out the non-linear scale too. There's all sorts of fun on this figure.

The enlarged figure did two things for me. First, I could actually read the text inside the figure box. I couldn't before because I've reached that point of middle age where I should really be wearing reading glasses and I'm too vain to enlarge the type size like an old person. After enlarging the figure, I could read the rest of the text on the figure and saw that the original caption was "Average annual use of active ingredient (pounds per square mile of agricultural land in county)."

Wow! That's a big difference. Use per square mile of farm land in a county is a lot different than use per mile of all land in a county! This figure would never convey how much bulk atrazine was being spread around on a per area basis. It only tells you how likely it is that farms will use atrazine on a county by county basis, regardless of how much farm land is in any given county.

The bottom line is that the Wikipedia caption that's big enough for an old person like me to read is misleading. As soon as I can figure out how to send in edits to Wikipedia, I'll try to fix this caption.

The second thing that enlarging the figure did for me was confuse me terribly. If the figure is showing me usage BY COUNTY, then I should be able to discern county shapes in the data but I should not be able to pick up details smaller than counties. The problem here is that there are features in the data that are obviously smaller than whole counties.

For starters, you can pick out pieces of interstates, like I-80 west of Chicago and the I-39 corridor in northern Illinois. You can see the Platte River in eastern and central Nebraska. You can see Columbus, Indianapolis, Peoria, and Cleveland but not Toledo or Des Moines. Cities and rivers are at scales finer than counties. A figure that's captioned as presenting data on a "by county" basis is mislabeled if you're seeing details smaller than counties.

The explanation turns out that the figure really isn't on a per county basis in a weird sort of way but you have to go to the source of the data to find that out. The source of the figure turns out to be respectable and reputable. The data and the figure both are from a very recent USGS report on pesticide usage in the USA. The complete citation is: Thelin, G.P., and Stone, W.W., 2013, Estimation of annual agricultural pesticide use for counties of the conterminous United States, 1992–2009: U.S. Geological Survey Scientific Investigations Report 2013-5009. You can also find it online at (accessed 18 Sept 2013). The authors of this USGS report did something kinda strange with their data and I'm left wondering why they bothered since it strikes me as somewhat counter-intuitive. Here's their explanation from the USGS webpage that explains how they made the pesticide usage maps in their report:

Individual crop types....were reclassified to simply differentiate agricultural land (including pasture and hay) from non-agricultural land....then generalized to one square kilometer cell size and the percentage of agricultural land for each cell was calculated. The proportion of county agricultural land included in each one square kilometer cell was multiplied by the total county use for each pesticide to calculate the proportional amount of use allocated to each cell. To display pesticide use on the annual maps for each compound, all of the cell values nationwide for the entire period were divided into quintiles and a color-coded map was generated for each year; the quintile classes were converted to pounds per square mile.


You follow all of that? They proportioned out the farm land in each county by one kilometer cells, allocated to each cell the amount of pesticide known for the county multiplied by the proportion of farmland in the cell, and then rebinned it all to present it on one national map in units of pounds of pesticide used on a per square mile basis. At the scale of the entire country, this conversion from kilometers to miles is a monstrous amount of work which would not change the level of detail one could see on the maps in their report. For their purpose, the conversion step was essentially superfluous!

One last thing. If you sit down and actually read this USGS report, you'll discover that the usage numbers for almost all the pesticide and herbicide data broken out by county is estimated based on statewide data.

My brain hurts.

Friday 12 July 2013


If you recall - and even if you don't - I sometimes have a bit of fun exposing sloppy citations. There are various forms of sloppy citation on the internet. One that often turns up in news media blogs involves citing some other blog as a reliable source; however, the cited blog also got things wrong due to its own sloppy citations. It's possible to get a whole chain of sloppy citations like the one I discussed on March 6 (1). The problem here stems from the use of bad secondary and tertiary sources. The solution involves eschewing all but the most authoritative sources. The Encyclopedia Britannica is an authoritative source; Wikipedia is not.

Writers who use sloppy citations should be sent to the tenth pit of the eighth circle of Hell, along with impostors and perjurers (2). Just saying...

The following link will take you to a brilliant graphic that illustrates one mode of creating a sloppy citation:

(1), accessed 13 July 2013. (2) Dante, "The Falsifiers," Canto XXX, The Divine Comedy,, accessed 12 July 2013.