• By
  • Carl Bialik

Two weeks ago, I asked readers to try answering questions from a new book called “Guesstimation,” which gathers the sort of head scratchers that job applicants may find tossed at them in interviews in an effort to find out how they’d tackle seemingly impossible problems. The post drew several dozen comments attempting to estimate the amount of space that all humans in the world would take up if crammed side by side, and the external surface area of a typical person. And today we’ll go through the book’s solutions to those questions, in addition to some ingenious ones suggested by readers.

John A. Adam and Lawrence Weinstein

John A. Adam and Lawrence Weinstein at an Old Dominion physics lab. Hair effects courtesy of an off-camera van de Graaf generator. (Photo by C.J. Oakley)

First, though, a few commenters questioned the whole exercise, with one calling such questions “another fad.” So I asked the book’s authors — Old Dominion University’s Lawrence Weinstein and John A. Adam, a physicist and a mathematician, respectively — whether such questions really help find good job candidates.

“They do test how interviewees think on their feet, although the circumstances are not necessarily the most conducive to clarity of thought,” Prof. Adam said. “I’d probably have floundered badly.” Prof. Weinstein added that such questions are particularly useful for jobs that require “intellectual versatility.” I’d add that these questions aren’t typically posed to applicants for journalism jobs, but perhaps they should. Reporters routinely are confronted with numbers, and the ability to sniff out suspect ones should be valued — though if more people started doing that, I might have less to write about for this blog.

On to the questions:

Question: If all the humans in the world were crammed together, how much area would we require? How does that compare to the area of Rhode Island? How much area would we need if we gave every family a house and a yard (i.e., a small plot of land)?

Answer: Job applicants could be expected to know that there are between six and seven billion people in the world. The authors used the figure six billion; the U.S. Census Bureau puts it, a bit too precisely, at 6,673,731,135 as of Thursday morning. Several Numbers Guy commenters went with 6.6 billion.

The authors assume that six people can fit into a space three feet by three feet, so that’s 1.5 square feet per person. Most commenters gave people more space, between two square feet and nine (“don’t really want to be touching”). These are also reasonable, though the first part of the question isn’t really asking about a real-life scenario; if it were, we’d have to allow for breathing room, food and water sources, and latrines. (In that vein, one reader went vertical, turning the world’s population into one big cheerleading troupe, 10 layers high.) Using the authors’ figures, it works out to an area of around 400 square miles. Readers who gave the world’s people more space came up with bigger areas such as 2,000 square miles. Within the book’s parameters, that’s correct, as they’re looking for an answer that’s neither more than 10 times too big nor 10 times too small.

How about Rhode Island? Several readers guessed at its size by picturing its length and width, and multiplying them; others remembered it’s about 1,000 square miles. Another way to go would be to remember the United States is between three and four million square miles, or about 60,000 to 80,000 square miles per state, but Rhode Island is much smaller than average. So give it a few thousand. (What’s the real area? Even Rhode Islanders can’t agree.)

When we more-generously allocate each family a small plot of land, that means giving more space to about two billion units, assuming an average family size of three, as the authors do. The authors gave each family one-quarter of an acre, within close range of most commenters’ lot sizes. That works out to about one million square miles, or less than one-third the land mass of the U.S.

Question: What is the external surface area of a typical person? (Include only the outward-facing part of the body — i.e. skin, hair and nails — and not, say, the digestive tract.)

Answer: The authors assume we are a cylinder, with radius of eight inches and height is about six feet. The area of a cylinder, not counting the top and bottom, is 2*pi*r*h. That yields an area of 2.4 square meters, which the authors round up to three square meters to account for the top, bottom, corners and curves. They also try a much simpler model, of a flat sheet six feet high and 1.5 feet wide, and get a surface area of two square meters, not far off. (As a reality check, online body-surface-area calculators, used for calculating certain medicine doses, yield surface areas of about two square meters for a six-foot-tall male.) One square meter is a little over 10 square feet, the preferred unit for commenters, most of whom got answers in close range of the authors’ solution, using similar methods.

Three notable reader comments: Several pointed out that the human body is uneven on its surface, complicating the true area calculation and perhaps even requiring fractals. This is reasonable but beyond the kind of calculations sought in most job interviews and online quizzes. One reader ingeniously started with weight, assumed the body’s density is equal to that of water, and then modeled the body as a cube, adding a fudge factor because of our un-cube-like characteristics. And another remembered a comment by his high-school physics teacher that the pressure on the human body is equal to four elephants, which, combined with his knowledge of air pressure at sea level and a good guess at the weight of an elephant, led him to a reasonable answer. The lesson to physics teachers: Use elephants as units if you want your lessons to stay with students.

It was comments like that one that made Prof. Adam remark, “I was both impressed and delighted with the range of approaches, and ingenuity of many of them.” So go ahead and pat yourselves on your five-square-foot back.

Profs. Weinstein and Adams enjoyed the exercise enough to want to do it again, so here are a couple more questions from the book for you, and them, to hash out in the comments.

1. What volume of gas does a typical automobile use during its lifetime?

2. What is the risk in America of dying per mile traveled in a large airplane?