Pop delusions and the madness of email October 29, 2001
Remember those chain letters that school kids used to send via mail?

Dear Friend,
Send a postcard (or a dollar, joke, comic book, etc.) to the person at the top of the list below. Then send this letter to five friends, leaving the top name off the list and adding your own. Within weeks, you should receive dozens of postcards.

Yours truly…

This is an innocent example of a form of communication that has been seen to serve all kinds of purposes, from the benign to the threatening. And now that email is so ubiquitous, the chain letter genre has expanded and taken on a new lease of life. On a daily basis, our email "in" boxes play host to bizarre urban legends, hoax schemes, and fake virus warnings.

You may recognize some of these classic stories that are popular in emails:

  • Someone got charged $250 for a cookie by an exclusive restaurant and is circulating the recipe as revenge.

  • Bill Gates is checking a new email-tracking program; if you forward the email to everyone you know, Microsoft will send you $1,000.

  • Send Nike your old sneakers — any brand — and the company will donate a new pair of shoes to a needy child.
Email allows messages to be distributed widely almost instantaneously. It's tailor-made for spreading rumors and playing pranks on vast numbers of information-hungry people.

Some of the stories circulating are harmless, like the story about the $250 cookie. Others can cause damage by harming a person or a company's reputation, by clogging a company or organization's computer system when the mail requests that readers send email responses to a certain address, or by flooding a company with some physical response, like thousands of pairs of shoes in the Nike prank.

Urban Legends
Ever hear the story about the Microsoft customer service employee who told a customer he was too stupid to own a computer? Or how an imported cactus exploded, dispersing hundreds of poisonous baby spiders? These pleasant tales are examples of one of the most popular forms of chain emails: the "urban legend." According to David Emery, the About.com guide to Urban Legends and Folklore, "Urban legends are popular narratives alleged to be true, transmitted from person to person by oral or written communication (including fax and email). Said stories always involve some combination of outlandish, humiliating, humorous, terrifying, or supernatural events — events which always happened to someone else."

Urban legends actually predate email, but the rise of email as a communication tool has brought them to new heights; a story can spread not just around the country but around the world in days. They become "true" stories in people's minds, even though they are largely falsified. Some stories may circulate for years, returning periodically to your "in" box.

At no time have Internet hoaxes been more exploited than in the month following the September terrorist attacks in the United States. Pranksters have been playing on the sensitivities of a decidedly nervous public by distributing false information on a variety of themes, from terrorist threats to anthrax. Here are the most well-known examples from recent times:

The rumor: Avoid shopping malls and commercial flights on Hallowe'en, because they may be subject to terrorist attacks.

The truth: Following an investigation, the FBI found that there is no reason to believe a real threat exists.

The rumor: Multiple trucks from Ryder, U-Haul, and Verizon have been stolen. It is feared that they may be used in some sort of terrorist attack.

The truth: None of the aforementioned companies reported trucks being stolen.

The rumor: Ironing your mail will kill anthrax spores.

The truth: ABC's Nightline investigated and found that exposing anthrax spores to the kind of heat generated by an iron or microwave oven would not be sufficient to kill the spores.

The prank: A photograph was taken of a tourist in the World Trade Center just before one of the planes hit

The truth: The photo was digitally manipulated, and for many reasons is easily recognizable as fake.

The prank: NASA requested that all Americans go outside with a candle on the night of September 18 for a satellite photo.

The truth: NASA made no such request.

For a complete list of rumors, visit Snopes.com, the urban legends Web site. The content of this site is very well written, but note that some of it is of a more mature nature.

Before sending a chain email to friends and family, you may want to determine if it is true and if it is likely to harm someone. The authenticity of a message can be difficult to determine. The Department of Energy's Hoaxbusters site offers excellent guidelines on how to distinguish fact from fiction.

Another good source is About.com, which offers one of the definitive sites on Urban Legends and Folklore. The Urban Legend Combat Kit provides both background information on legends and ready responses. You can copy the responses and send them to people who have emailed you an urban legend, in order to let them know that they are passing legends off as truth.
Learn About the Problem
Chain letters sent via the regular postal service start with five copies of a single letter and grow quickly — copies of the letter sent to five friends, who each send to five friends, who each send to five friends:
    Initial mailing:
    5 = 51 = 5 letters

    First recipients send:
    5 x 5 = 52 = 25 letters

    Second round of recipients send:
    5 x 5 x 5 = 53 = 125 letters

    Third round of recipients send:
    5 x 5 x 5 x 5 = 54 = 625 letters

Via email, the letters spread even more quickly. This type of increase is called exponential growth, because the growth is defined by a constantly increasing exponent.

Consider also how the distribution of emails might vary. The first person in a chain may only distribute the mail to five people. But those five people might each distribute the mail to many more people, depending on how many they have in their address book. It's easy to picture how messages can spread like wildfire.

Think About the Problem
 For each of the following types of growth, do you think the growth is basically linear (i.e., at a steadily climbing rate) or exponential (i.e., very rapid, geometric)? Consider general trends, not exact numbers:

  • a baby growing to adolescence

  • the world's human population between 1900 and 1999 the number of Internet users since 1995

  • the world record for number of home runs by a single batter in a baseball season

  • the number of cellphones in use in the U.S. between 1990 and 1999

  • for students who have used Biology Gateways: Exploring Populations or Biology Explorer: Population Ecology, which most closely represents exponential growth: an S-curve or a J-curve?
Extending the Problem
When applied in many disciplines — e.g., population studies — the concept of exponential growth is more complex than just the straightforward exponential function f(x) = xn.

For a detailed discussion aimed at teachers of grades 7-12, see the article "Activities for the Logistic Growth Model; or, Invasion of the Killer Moths", from Mathematics Teacher, Oct. 1, 1997.

A family tree starting back several generations approximates exponential growth, depending on the number of siblings in each generation. Have students draw a rough family tree starting with their eight great-grandparents. Have them explain why it is progressively harder to fit each generation onto the tree. Students who want to do a serious family tree can begin their research at the Yahoo Genealogy Research Club.

Students who are interested in folklore can:

  • Research folklore and discover how urban legends fit into the classification. They can start at the New York Folklore Society.

  • Choose a popular urban legend from the About.com site, and research the history of the legend.

  • Choose a legendary figure (e.g., King Arthur, Robin Hood, Buffalo Bill), and research the historical basis of the legend.