"With love all things are possible. This paper has been sent to you for good luck. The original is in New England. It has been around the world nine times. You will receive good luck within four days of receiving this letter provided you, in turn, send it on. Please send 20 copies and see what happens in four days."
Chances are you've received a "chain letter" like this, perhaps from a well-meaning friend. You may even have been tempted to forward it. The copy I received came with a cover note saying, "For obvious reasons, I wouldn't dare not pass it on." But I know that the vast majority of recipients have ignored the instructions.
How do I know? If everyone had followed the law of the letter, you and I and the rest of the world would be buried in copies. The math isn't hard to figure. Consider, for instance, that 20 copies of the letter are to be sent out within four days of receipt. So, on the first mailing, 20 copies hit the street. Four days later, each of those 20 recipients sends copies to 20 "friends," providing a wave of mail consisting of 20 x 20 = 400 pieces. The chart below shows what happens for the next month:
| Mailing | Day | Number of Copies |
|---|---|---|
| 1 | 1 | 20 |
| 2 | 4 | 20x20 = 400 |
| 3 | 8 | 203 = 8,000 |
| 4 | 12 | 204 = 160,000 |
| 5 | 16 | 205 = 3.2 million |
| 6 | 20 | 206 = 64 million |
| 7 | 24 | 207 = 1.3 billion |
| 8 | 28 | 208 = 26 billion copies! |
The world's population is about 5.5 billion. In less than a month, this chain letter should have produced copies in quintuplicate for every man, woman and child on Earth. That wouldn't bury all of us, but read on.
The letter I received claims that someone named Constantine Dias received a copy in 1953. Dias supposedly passed on 20 copies and promptly won a $2 million lottery. The 42-year period since then represents 15,340 days or 3,835 waves of mailing. Had the chain remained unbroken, the last ripple of the wave would consist of 203835 pieces for the Postal Service to shoulder. That's more than my calculator can compute, but a little approximation puts the grand total at more than 104500. In other words, more than a 1 followed by 4,500 zeroes. "Bulk mail" indeed!
It's hard to conceive of numbers so large, especially since the known stars in the sky number only about 1022. If this chain letter were truly unbroken, it would have produced more letters than there are atoms in the known universe - a mere 1019, give or take a few zillion.
We can make a few crude guesses as to how many folks actually are perpetuating the letter. For the last few years, I've seen some version of this particular letter about twice a year.
Taking my personal experience at face value, sometimes a bad idea, we might guess that the total number of chain letters in the mail is about constant. If the number of copies in circulation were really increasing in a chain reaction, the number reaching me should grow rapidly from year to year.
The steady state that I see would happen if one of every 20 recipients followed the letter's instructions, while the other 19 tossed it in the recycling bin.
How many copies in circulation does this mean? We can determine that if we assume that my twice-a-year experience is typical.
We could multiply the chances of getting this chain letter on a given day of the year (2 out of 365 or 2/365) times the number of people able to use the mail, say 150 million of the 250 million people in the United States. Do the math, and you have about 820,000 recipients on any given day.
Thus, it looks as if 41,000 people, less than .02 percent of the U.S. population, generating 20 fresh copies daily, could account for the volume I'm seeing.
This particular letter is basically innocuous. It doesn't ask us to send money or even to believe in superstitions. All we have to do is copy and mail it and wait for good stuff to happen. "This is true even if you are not superstitious," it promises. It is no more pernicious than the newspaper's daily horoscope, and few people would let it run their lives.
New technologies offer new opportunities. Electronic mail makes it even easier for otherwise rational folks to indulge their superstitions. A few keystrokes and that letter has been copied and forwarded to 20 cybervictims.
Even without stamps to lick, the math still holds. There aren't enough electrons in the universe to support this mass behavior. Even on a small scale, such electronic mailings consume limited resources, slow other mail traffic and generally waste "bandwidth."
Similar poor appreciation of math lies behind much more costly and insidious schemes. Some chain letters try to sucker dupes into sending money to the head of a pyramid in the hope that eventually, if the chain remains unbroken, the lucky players will more than recoup their stake as they reach the top and collect cash from new players.
A small-scale version a few years ago suggested building a music library by sending compact disks rather than cash, but it shared the same shaky pyramid structure. The Postal Service considers such schemes illegal games of chance and will prosecute for mail fraud. If you receive such a letter, postal authorities ask that you contact your postmaster.
Similar bad math underlies pyramid investment schemes. A recent example is the collapse of the Foundation for New Era Philanthropy last spring. Hundreds of nonprofit and charitable organizations, including a Boy Scout troop in Pennsylvania and a group providing mentors for disadvantaged youths in the District, bought into this plan.
New Era promised a 100 percent return within six months but, unknown to investors, was a pyramid that depended on new waves of investors to pay their predecessors.
The earliest investors saw their hopes come true. But in all such schemes, eventually there are fewer new participants, and the chain is broken. Those who join late lose their upfront investment. This kind of chain is called a Ponzi scheme, in dubious honor of Charles Ponzi, who made and lost fortunes in Boston in 1919. Such "pyramid power" is about as likely to bring you luck and wealth as any other kind of magic charm - that is to say, not at all.
Chip Denman is manager of the Statistics Laboratory at the University of Maryland where he also teaches "Science vs. Pseudoscience" for the University Honors Program. He is past president of the National Capital Area Skeptics, a not-for-profit educational group promoting critical and scientific thinking.