Some notes, by John Burkardt
The chain letter is the cockroach of communication, an unwanted visitor that interrupts our routine with a strange voodoo incantation, promising luck and threatening misfortune. But for some reason, we pass this parasite on to the future, happy to see it go, little thinking that we are really only mailing it back to ourselves. Before it strikes me again, I take a few moments to think about this mysterious thread, passing through our lives repeatedly, as it weaves its way into a kind of immortality denied to us.
The first chain letter I ever saw came to me when I was a graduate student at the Mathematics department at the University of Pittsburgh. There, in my mail box, was what looked like a personal letter. But when I opened it up, I read a strange message, that began:
With Love All Things are PossibleIt was my very own "Good Luck" letter written by a South American missionary I'd never heard of. The letter promised me good luck, if only I made twenty copies and sent them on. But as I read on, the happy promises darkened. It was clear that the letter, while wishing me luck, could easily dole out unpleasant consequences to me if I thoughtlessly cast it away and broke the chain. I had never received such a strange communication before, and I carefully folded up the letter and placed it inside a book.
Several years later, another flock of chain letters flew through the Math department. I managed to get my hands on a copy, and was intrigued to see that the letter seemed, as best I could remember, the same as the one I had received earlier. Did an evil genius somewhere send out a new burst of messages every so often? Or was it possible that the chain letter had been "alive" all this time, passing from stranger to stranger?
I took my new chain letter home and compared it to my first specimen. Laying them out side by side, I realized that while the letters were very close, there were some strange little changes, that might reflect the wear and tear of repeated copyings.
For instance, the two chain letters both agreed that something bad happend in the Philippines; but the bad thing may have happened to "Gen. Walsh" or perhaps to "Gene Welch". Moreover, what happened to him wasn't clear, differing by a single crucial letter; either he had "lost his wife" or "lost his life". This sort of variation struck me as so funny and interesting that I was eager to receive more chain letters for comparison.
As I found out, there is little that one can do to encourage the receipt of chain letters, although perhaps I might have spread a rumor that I was in dire need of good luck. However, I did force various friends to swear that instead of throwing away the next chain letter they received (no one admitted to passing one on!) they'd save it for me.
In the last few years, I have found a few places where information about chain letters is available. My first source was some electronic bulletin boards, the USENET newsgroups, in particular rec.humor. Over a year during which I browsed through the articles on this bulletin board, it was repeatedly "hit directly" by a chain letter I'd never seen before, the "Dave Rhodes" message.
Like the ring of mushrooms that were supposed to spring up around the site of a lightning strike, a bolt of Rhodes would immediately call forth a fabulous bouquet of violent opinions. Many responses suggested that everyone send an angry note to the fool who had posted the Dave Rhodes letter, or to the person in charge of the fool's computer system. Other responses were crabby, nitpicking annotations of the chain letter, mocking each sentence. The most interesting responses treated the annoying recurrences of the chain letter as an irrational, unavoidable feature of life, and tried to find something to laugh about in this.
As I monitored the new postings to rec.humor, I occasionally came across yet another message, the "Cookie Recipe", sent in by many different people, none of who seemed to be aware of how many times this story had been told. This letter never caused the anger that "Dave Rhodes" would, but usually someone would post a debunking response. I had to laugh though, when after a particularly wearisome lecture was posted, someone sprightly replied "I don't care if it really happened or not. These cookies are good!"
Later, I also began to read postings in the alt.folklore.urban newsgroup, which devotes itself to the discussion of "urban legends" and popular culture. I was hoping to see either the "Good Luck" or "Dave Rhodes" letters discussed, but they didn't show up. Instead, I found out about Craig Shergold, a boy you can claim was cured of brain cancer by chain letters, but now is cursed with an unstoppable stream of get-well cards.
As I watched these four chain letters wandering ceaselessly across the network, I began to feel a sense of wonder, to imagine the chain letter as a sort of perpetual motion machine, a pathway to infinity, an elixir of immortality. But unlike those notions of perfection, chain letters have definite histories, personalities and flaws. And I resolved to gather some of that information together in recognition of the immense amount of hope, superstition, greed and good will that has been swarming across the country in great flocks of paper.
On the face of it, the "Good Luck" letter is a blessing. "You will receive good luck in the mail," it promises. That might be the first kind thing someone has sent you in a long time. And what does this letter ask in return for this good luck? You just have to help it make its way around the world, spreading the good luck to others.
The "Good Luck" chain letter has been nicknamed the ``dreaded Good Luck letter" on the USENET bulletin board alt.folklore.urban. Who could dread good luck? Perhaps people with enough superstitious friends find that they receive copies of this letter almost regularly. The charm of its first visit is considerably reduced the third or fourth time it shows up in the mail. On top of that, the "Good Luck" letter promises as much bad luck as good. Let's just get out the old Canopic balance here and see: in one pan, we have $10,065,00 in cold cash, a better job, and a new car. In the other, we have lost $40,000, a lost wife or life, a lost job, a definite lost life, various problems and car repairs. One wonders indeed if there isn't a better name for a letter which demands action on pain of death and disruption. Maybe blackmail is what we're really dealing with here; after all, no one signs that stuff either!
Granting the veneer of skepticism that adorns our generation, though, perhaps the dread of finding the "Good Luck" letter in the mail is simply the unhappy contemplation of the necessary duplication and mailing of twenty copies of a letter.
Or is it that simple? It seems like the letter is addressing your good side, trusting that you will help it, and offering a reward in return. But the letter has a very pronounced dark side, and it speaks the dark language of fear. That language is a magical incantation, which awakens a sleeping part of our soul. It's hardly a part we're proud of.
"I am magical," says the chain letter, and a drooling child with a mind from the Stone Age nods, because what is said must be so.
"Go out and make copies of me! Otherwise, you might die, like these have already!" says the chain letter, and the child feels a little death, trembles, and promises.
Who has not felt a wave of superstition, and acted impulsively, helplessly, like a child? If the chain letter reminds us of those moments of weakness, even showing us again how weak we are, then the word "dread" is well deserved!
The "Dave Rhodes" letter claims to have been written some time after 1988. I have never seen a copy in the mail, only on computer bulletin boards. The letter itself explicitly suggests that a computer be used to send the copies, and that the copies be posted on various computer bulletin boards. The letter even suggests that the subject heading of the bulletin board posting be MAKE.MONEY.FAST, the name by which the letter has now become notorious.
The "Dave Rhodes" letter has a number of classic chain letter features missing from the "Good Luck" letter. In particular, there is the promise of cash. There is the magical list of ten names, with instructions that the recipient is to send money to the top name, and send out copies of the letter with the top name removed, the other names moved up one position, and the recipient's name appended to the bottom. There is a specious discussion of how this chain letter is "really" a business generating mailing lists, and the people sending their money back up the chain are paying for the privilege of being added to the list. This, says "Dave", means that the letter is not some kind of cheap, phoney get-rich-quick pyramid scheme that the Post Office might want to shut down. Doesn't that put one's mind at ease!
The letter opens with a lengthy introduction from "Dave", telling of how he was struck low with poverty, and had nothing but his PC to keep him company. He received a chain letter in the mail, and thought about how tedious it would be to make 20 copies, and fold them up into envelopes, address and stamp each one. Why go to all that trouble when he had a PC right there, and the electronic addresses of loads of friends? In no time, he had composed his own chain letter (apparently throwing away the one he had received in the mail, with no resulting bad luck!) and quickly realized the modest sum of $50,000. (Chain letters seem to think that a sum of $50,000 to $100,000 is "plausible", while $1,000,000 might be suggesting a little too much to be believable!) As a hilarious sidenote, "Dave" mentions that whenever he needs more cash, he just sends out another copy of his chain letter. I guess it's more convenient than an ATM machine, with those ridiculous low limits of $100 or $200!
Perhaps the most amusing feature of "Dave's" letter is the list of personal testimonials tacked on to the end. The suckers are pitiful in their blind trust that all is going to work out, and yet they're wise enough to realize that they've got to excite the people later down the line if they want to get a substantial return.
A friend hands you a folded piece of paper. Unfolding it, you find a barely readable message that begins:
My daughter and I had just finished a salad at Neiman-Marcus Cafe in Dallas, & decided to have a small desert.The story goes on that the victim orders a plate of the store brand cookies, and when asking the price of the "secret" recipe, is told she can have it for "Two-fifty". This is acceptable, and she has the price added to her VISA bill, only to discover a month later that the waitress meant $250. After futilely arguing with the management of the store, the victim has decided to wreak her revenge by passing the recipe around the country, and breaking the store's monopoly.
That's it, just a story and a recipe. And yet this scrap of paper is a single bit of ore from a mighty mother lode that runs across the country, and back in time for decades. It has enough plausibility that it has appeared in the Anne Landers column. A booth advertising "original Neiman-Marcus recipe cookies" showed up at the Newton, Massachusetts kid's festival.
When this story was posted on rec.humor, one indignant reader wrote in with some advice for the victim. Phone VISA, he suggested, write the chairman of Neiman-Marcus, then go to the Better Business Bureau. Meanwhile, of course, the sympathizer had passed on copies of the letters to friends.
Yet Neiman-Marcus has never sold cookies in their restaurants, and they don't take VISA. Moreover, recipes from their restaurants are given out free to anyone who asks for them. Seems like the only thing wrong with this story is the facts!
And yet, there are many people who will testify that this story is true. It didn't happen to them, personally, mind you. No, but they know someone who could give you all the facts if you really wanted them... One person wrote in to rec.humor, for instance, "About 5 years ago a lady came into the library that my Mom used to work at and told everyone who would listen a story about how she had ordered some cookies..." Only problem was that this lady was talking about Mrs Fields's cookies. And Mrs Fields doesn't give out her recipes.
But if Mrs Fields is the culprit, how do you explain the recipe in the cookbook of the Charity League of Martinsville, Virginia, in 1963? No, it's not for $250 cookies but for $100 cake. Let me tell you the story. It seems that a North Carolinian, on visiting the Waldorf-Astoria in New York, was very impressed with the cake served - oh, you've heard this one before?
Here is an example of a chain letter which has managed to survive without threatening bad luck, or tempting the reader with money. What keeps the chain letter alive? Certainly, the letter tries to pass itself off as a free $250; moreover, it suggests that the recipient can essentially "print money" by passing along copies to friends. But the strongest reason this letter keeps going is the story element, which has become a so-called urban legend. You would hardly ever think of paraphrasing the "Good Luck" or "Dave Rhodes" letters to a friend, but the "Cookie Recipe" is just the kind of idle tale that naturally makes its reader want to share it. The letter tells us to make copies, but its story makes us want to.
The case of Craig Shergold demonstrates the spontaneous generation of chain letters. Craig was a seven year old British boy, who was suffering from a brain tumor. In 1989, he made a request that people send him get-well cards, in the hope of breaking the record for the most number of cards received by one person. Craig's request attracted attention, first in the British press and television, and then in the United States, through the Children's Wish Foundation. These initial appeals were so successful that Shergold received 16 million cards in a year, easily breaking the previous record.
The problem was that Craig's plea had spread so widely that it was impossible to call it off. Craig was actually taken to the United States and apparently cured in 1991, and yet the cards keep coming. They are no longer spreading because of newspaper or television coverage. Instead, they have entered the collective underground, and now, like the coal mine fires beneath Centralia, Pennsylvania, they smolder on, completely impossible to ever extinguish.
Craig's plea has been spread in the form of a chain letter. It has even been spread via fax machine, with the request for a letter replaced by a request for a business card. The messages still describe Craig as being seven years old, with incurable cancer. The letters and cards come pouring in, as much as 300,000 a week. They will surely continue coming for years.
Of course, although the Shergold appeal is now immortal, it is still subject to the laws of mutability. For instance, Craig's name has been spelled "Craig Sherwood" or "Craige Sherwood". The street address of the luckless foundation is now given as "Terimetera Center East", "Parlimenter Court, Suite 500", and "Perimeter Center East, Suite 500". Perhaps we're lucky that fax machines make such poor copies that we're guaranteed interesting variations like this!
The denizens of alt.folklore.urban actually feel it is their duty to carry out "Shergold spotting". If they see an appeal in their local newspaper or television or place of work, they resolutely send a standard debunking message explaining that no more cards are needed whatsoever. Nonetheless, the letters keep coming, and the unlucky foundation whose address is given in the appeals has had to pay for a full time hotline to deal with the misguided calls of concerned well-wishers.
In the days before copying machines, making five or ten copies of a chain letter was a tedious operation. The only easily available aid to such work would have been carbon paper. In general, a person making the copies would have to retype the entire text, and would be likely to make a few mistakes in the copying.
Once a mistake has entered the text of a copy of a chain letter, the next person to receive the letter might correct the mistake, if it was an obvious error, or pass it on, perhaps with even a few more errors.
In one way, this process is like the game called "Gossip" or "Telephone", where a group of people sit in a line, and a person at one end whispers a sentence to the next person, who repeats it to the next person and so on. When the last person receives the message and stands up and reports it, it is often mangled beyond all recognition. I remember our third grade teacher had about ten of us do this, and the best we could do was to turn "Noel's coming around" to "No elves are coming to town."
Luckily, chain letters aren't transmitted by whispers, or the original version would be beyond recall. And now that copy machines are available, and electronic mail can be used, the number of copying mistakes has presumably greatly decreased.
However, enough errors have been introduced into the chain letter "gene pool" that we can try to classify the errors, and to draw a "family tree" of any group of chain letters. In a later section of this paper, I print several copies of the "Good Luck" letter, to allow such studies to start.
Is a chain letter alive? Surely this is a silly question! When I was a child, I would have laughed, and said "Of course not! Where is the letter's heart, how does it think, what does it eat?" But the philosophy of biology has changed since I was a child. Some think of a living organism as anything which reproduces itself; in this way, the "genetic" information becomes most important, and an organism is reduced to a simple mechanism for transmitting that information into the future.
If you take such a view of life, it isn't too hard to imagine a simple chain letter as a living creature. If you really find yourself struggling to take this point of view, you might try thinking about viruses. Viruses inhabit a peculiar halfway zone between the biological and the "merely" chemical. And yet they know how to play our game when they need to! They pop up out of nowhere, invade a cell, and force it to make copies of them, which then take off, spreading to other cells. Does seem a little analogous, doesn't it?
Since reproduction is pretty much the only biological function that the chain letter can be considered to carry out, let us put on our wading boots and go out to where the wild chain letter nests, and find out what we can about this peculiar bird!
The chain letter reproduces asexually. After all, the odds are pretty slim that someone would get two chain letters on the same day, and somehow merging them. If you like to daydream, though, you might imagine chain letters mating this way, with the recipient randomly taking a sentence from one or the other to build an "offspring".
After reproducing, the chain letter, like a salmon, dies. Unless someone is really cheap, and makes 19 copies and then mails out the original!
Some chain letters have children, and some are barren. Chain letters that are received by a cooperative person reproduce twenty-fold. But I assume this is the exceptional case, and that most chain letters are simply tossed away. We can treat such chain letters as being "infertile". This infertility is the main control on the otherwise disastrous fecundity of chain letters.
The chain letter reproduces exponentially. That is, if we suppose that everyone follows the rules exactly, and for convenience assume that it takes a week for the copies to be made and received by the next person, then every week the number of chain letters added to the total increases by a factor of 20.
Clearly, such a rate of growth is not sustainable. But what we may not realize is that all a chain letter has to do is "linger" on. There have to be enough copies in circulation that, on average, the new copies replace the old ones that die out each week. So what advantage is the exponential growth rate? I would argue that the main advantage occurred when the chain letter was first sent. Most chain letters probably die out in the very early stages, before they reach a "critical mass" that allows them to sustain a reproductive existence indefinitely. By reproducing 20 at a time, a chain letter can take advantage of a lucky string of cooperaters to quickly ramp up from a few copies to the critical number. The actual effect of varying the reproductive rate and the prevalence of cooperators remains to be looked at.
The chain letter has a few natural enemies that actively seek it out and destroy it. We aren't talking about the "non-cooperators" who refuse to reproduce the letter. Instead, we are talking about postal inspectors, FBI agents, and network administrators.
The chain letter reproduces with a mild mutation rate. Back in the old days when a chain letter really had to be retyped, this rate was much higher. Now copiers and faxes and EMAIL have brought it down greatly, but none of these methods are quite perfect. So over time, we expect a certain amount of "genetic drift", meaning that in one year, for instance, a chain letter might have lost a sentence, or had a proper name misspelled, but in ten years we might expect the chain letter to have "grown" a new paragraph inserted for unknown reasons by a copier.
As copies of the same chain letter evolve, they will be subject to a form of competition for survival. All we have to assert here is that some chain letters make a better case to be copied. Some appeal to fear, some to greed or sympathy. Some are well written, some are mysterious. But if we have a sufficiently varied population of chain letters, then we expect that, over time, some chain letters will begin to predominate, presumably because they did a better job of convincing people to copy them. (Of course, you could always argue that the most effective mutation would be to have the words "make twenty copies" mutate into "make fifty copies"!)
In this struggle for survival, we might be especially interested to observe whether benign or malignant letters would do best. In our current world, we've seen a mix of these approaches. The "Good Luck" letter promises good or bad, depending on how it is treated. We might rename this letter the "Tit for Tat", therefore. The "Dave Rhodes" letter promises a simple reward, even though it demands a small payment.
At one time it was possible to believe in the "spontaneous generation" of certain creatures. Inobservant biologists explained the rotting of meat by claiming that maggots would simply appear in dead meat, without any intervention by a parent fly. While this theory is long discredited when applied to biology, chain letters themselves certainly seem to appear this way, out of nowhere. It is reasonable to believe that, for instance, there was no Craig Shergold chain letter until Craig Shergold's mother issued her appeal for get-well cards. Even then, she didn't explicitly call forth chain letters; no, but somehow, something brought them forth, sometime after 1989, and we surely can't explain them as mutants or products of some other chain letter!
Another biological concept mirrored by chain letters is the "Cambrian explosion". Supposedly, if you read the fossil record from the first records of life, there is a stretch of hundreds of millions of years where nothing interesting was produced but blue-green algae and extremely simple life forms. Suddenly, in the Cambrian period, there was a fantastic increase in the numbers and kinds of living creatures, as though some creative force had been suddenly released. Then came a great dying off, as the world settled down, to a far smaller, but sustainable set of creatures. Perhaps it is surprising, but many communities have historically gone through a similar sort of explosion and dying off of chain letters. For instance, Andrew Tobias describes a chain letter craze, which was started in Springfield, Missouri as a joke, and quotes an Associated Press report:
Chain letter "factories", with $18,000 changing hands at three of them within five hours, turned this southwestern Missouri city into a money-mad maelstrom today. Society women, waitresses, college students, taxi drivers and hundreds of others jammed downtown streets.By the following evening, though,
...sad-faced men and women walked around in a daze...seeking vainly for someone to buy their chain letters...The craze which swept over this city yesterday subsided because almost everybody had a letter to sell, thus draining the buyer market dry.
Of course, this wasn't the end of the chain letter craze. It simply moved on to new cities, such as Omaha, Kansas City, and Los Angeles. And even when the craze had peaked and moved on, a small pool of letters continued to circulate, ready to burst out at any time.
It is said that researchers in the Gulf of Mexico were able to date layers of mud by the transition from layers of bottle caps to the layers of pop tops. Perhaps in the future, when our civilization has been buried under the tons of paper it produces and discards each year, the bug eyed investigators who dug us up again will have a solid clue for dating us by studying the variations in the copies of the chain letters that surround us!
A famous representation of a chain is the play "Reigen", by Arthur Schnitzler. The first scene shows a man and woman going through an elaborate seduction. In the next scene, the same woman meets a different man, with the same result. Next, that man has a scene with yet another woman, and so on, until in the tenth scene, the chain actually closes back on itself, with the last woman pairing off with the man from the first scene. One theme of the play is the hypocrasy of the affirmations of love made so often by the characters, a point that derives its power from the relentless repetitiveness of the chain of the action.
A variation on the theme of the chain letter occurred in a story by Robert Louis Stevenson, called "The Bottle Imp". The story goes that Prester John bought a magical bottle from the devil, for unimaginable wealth. The imp in the bottle would satisfy the owner's every wish. But if the owner died in possession of the bottle, he would burn in hell forever.
The only escape from this fate was to sell the bottle to another person, at a lower price than had been paid for it. In this way, the bottle passed to Captain Cook, then Napoleon, and later to a man living in San Francisco. Stevenson begins the story as a Hawaiian visitor learns the story of the bottle from the San Franciscan, buys the bottle for $50, gets the house of his dreams by wishing, sells the bottle, and then discovers a spot of leprosy on his skin. Now he has to chase the bottle, which has already wandered through many people. He assumes he will know if he has caught up to the bottle, because that person will be in despair. Sure enough, he meets a man who has bought the bottle for two cents. This, of course, is hardly the end of the story.
What a strange twist on chain letters! Again, we have the theme of an object that promises both good and bad fortune, but now the good fortune lasts while the object is kept, and the bad fortune occurs only if the object is kept too long. We also see an object passed from one person to the next in a great chain, said to have originated far in the past. The fact that the bottle must be sold at a loss means that we could call this story "Lose Money Fast". The power of the story is derived from our growing dread at the dwindling price of the bottle and the unavoidable moment of retribution.
Another variation on chain letters that has recently become popular is the idea of "chain fiction", in which several authors each write a chapter of a novel; Dorothy Sayers was part of a "Detection Club" that produced several mysteries this way; Dave Barry was part of a group that wrote "Naked Came the Manatee", and the back of Esquire magazine has exhibited the various stages of a dreary chain "short story" cobbled together by Frank McCourt and others.
A famous catch phrase of recent years goes something like "Whenever you sleep with someone, you're also sleeping with everyone that person every slept with. And so on." The point, quite deliberately, is to suggest a dizzying and unending succession of people you've never met, and never would want to meet, and from whom you might just have caught something nasty.
In fact, sexually transmitted diseases are a very nice metaphor for chain letters, or vice versa. An ordinary disease can be caught unknowingly, but an STD requires a sexual encounter, and a certain amount of acquiescence. And once the unlucky recipient has been infected, the "copying" of the virus goes on automatically.
Like a chain letter, a sexually transmitted disease links hundreds and thousands of people in a chain of cause and effect; one that frequently crosses itself. As copies of the virus travel along this chain, they naturally mutate in a way that mimics the garbling of the chain letter. In some cases this makes it possible to tell, from a blood sample, who infected whom.
A bizarre sexual practice known as a "daisy chain" supposedly involves a group of people forming a circle and sexually interlocking with each other.
To a mathematician, a chain letter is a very simple example of geometric growth. If, for instance, each recipient of a chain letter makes 5 copies, and sends them on, then the number of letters in circulation grows as follows:
1, 5, 25, 125, 625, 3125, 15625, 78125, and so on.
Assuming everyone cooperates, and counting steps starting at zero, the number of letters in circulation at step N is 5^N. There is even a formula for the total number of letters mailed through step N:
( 5^(N+1) - 1) / (5-1)The next thing a mathematician will point out is that any such sequence "blows up" very quickly, reaching millions and billions in just a few steps. A mathematician may take this as sufficient proof that chain letters are a scam: even if we assume everyone cooperates, a chain letter can't continue very long before everyone on the earth will have received a copy. And then who do they send copies to?
Another way of looking at this is to consider the base of the pyramid. Let's say that you have just received a chain letter, and you mail your 5 to the person at the top of the pyramid, putting yourself on the bottom, as the tenth name. That means that, right now, there are 5^10 or 9,765,625 people sending him money. Now you want to reach the top in just 10 steps. But so do all the other people in your group of 9,765,625. Let's call it 9 million for now! Since each person who reaches the top does so by recruiting 9 million people for the base, it's going to take 81 trillion people to get you and all the other people on your level up to the top. We could translate the letter into other languages, mail it to the stars, or hope that some people are so stupid that they will join the chain as many times as they can. Even so, the chances just aren't very good that we're going to see our money. And this is true for the people at the base of the pyramid on the very first copy of the chain letter! They will never see any money!
Now it's much more reasonable to assume that most people simply toss the letter into the trash, but some small percentage follow the rules, send the money, mail the copies, and hope. We will look at this case in the section on Computer Modeling. But we will note right now that this fact has two main effects: the chain can last a very long time, even indefinitely, and the money, if any, that reaches the person at the top tends to be piddling. However, this means that the mathematician's initial assessment of a chain letter as "impossible" is really not very helpful. It's true that chain letters don't work the way they say they do; we know they can't work that way. Nonetheless, there's something in a chain letter that doesn't want to die!
A computer can help us test some simple ideas about chain letters. For instance, chain letters seem to be strangely stable. The "Good Luck" letter has been around for decades, so apparently, you could work backwards and find a chain of perhaps several thousand people, each of whom obeyed the instructions and passed the letter on to the next person. This is hard to believe, and at the very least, suggests that there is a fairly large group of "receptive" people.
But there can't be too many receptives, or we'd be swamped with copies of the letters in no time. Why doesn't the chain letter die out, or explosively jam the mail?
Without thinking about it very much, I guessed that the fact that the letter asked for twenty copies to be made meant that the receptive population must be about 5%. To see why, imagine that you are given a handful of dice, and you play the following game. You toss all the dice, and count the number of 6's you roll. Now you figure out how many dice you can throw on your next turn. It's just 6 times the number of 6's you rolled the last time. You keep doing this until you roll no 6's at all, and stop, or perhaps do so well that you win all the dice.
If you start with just one die, or even just a few, it's very likely that you will stop, by rolling no 6's, in just a few throws. But if you have a large enough set of dice to start with, then on average 1/6 of the dice you roll will be 6's, and so the dice you throw away will just be balanced by the dice you add. Such a "balanced" game can last a very long time.
The balance, of course, comes about because each die you roll has a 1/6 chance of being replaced by 6 dice, so you can expect that roughly speaking you will have as many dice on the next roll as on this one.
If chain letters work this way, then we should guess that there is about a 5% receptive audience, so that, on average, the incoming letters are replaced by roughly the same number of outgoing letters; in other words, for every 20 letters that are received, 19 people ignore them, and 1 person makes 20 copies and sends them out.
Let's consider some very simple questions:
While the computer isn't going to prove anything for us, it may make us more comfortable with some of the ideas we've had so far. Looking at the first question, let's suppose that the original author of the chain letter has just sent off 20 copies of the chain letter, and that, on average, about 5% of the population chosen at random will obey the request to copy the letter.
Surprisingly, about half the time, the chain dies immediately. All the copies of the first letter are discarded. In almost all the other cases, the letter dies very quickly, in less than 10 steps. However, after trying this experiment 150 times, I saw two cases that came close to "taking off", one where the chain went for 147 steps, and another of 243 steps:
When letter died Cases
---------------- -----
Step 1 58
Between 2 and 10 67
Between 11 and 100 21
Between 101 and 1000 4
Still going at 1000 0
This is hardly an encouraging result! I realized that the odds weren't very good at all that I would get a chain letter that lasted for 1,000 steps, the point at which I had decided I would declare a chain letter "immortal". Perhaps there was some way of changing the problem slightly, so that it would be more likely that a chain letter could keep going.
The simplest change I could think of was to increase the number of copies made on just the very first step. I imagined this corresponding to the author of the chain letter trying very hard to get it established. So instead of 20 copies, I assumed the author sent out 400, although all the recipients from then on were only asked to make 20 copies, as before.
This makes it likely that about 20 people will accept the request and make copies. Of course it won't be exactly 20, but that's the point. If the number is a little below, say 18 or 15 or even 10, we still have some leeway. For the first experiment, we expected roughly 1 person to accept the request, but anything less was a disaster, killing the chain.
Sending out 400 copies on the first step, I got these results:
When letter died Cases
---------------- -----
Step 1 0
Between 2 and 10 6
Between 11 and 100 102
Between 101 and 1000 38
Still going at 1000 2
All of a sudden, it's very unlikely that a chain letter will die early, not unlikely that it will last into the hundreds of generations, and not impossible for it to get to the thousands. One of the letters that was still going at step 1000 had just been copied by 1,687 people!
It looks like, if you give a chain letter a big enough initial "kick", it will keep going for a long time. So the initial condition} is an important determinant of the expected lifetime of a chain.
What about the receptivity probability? We can make several simple experiments, where we repeat the first two, but use a receptivity of 0.049 and 0.051. That's quite a small change in the probability. Is it likely to have any effect on the outcome?
Here's the results if I drop the probability to 0.049:
When letter died Cases
---------------- -----
Step 1 0
Between 2 and 10 3
Between 11 and 100 126
Between 101 and 1000 21
Still going at 1000 0
Here's the results if I raise the probability to 0.051:
When letter died Cases
---------------- -----
Step 1 0
Between 2 and 10 5
Between 11 and 100 55
Between 101 and 1000 5
Still going at 1000 85
It really looks like we are in an unstable situation here. A probability of 0.049 means most letters die before the 100th step, a probability of 0.050 means just a very few make it to 1000 steps or 1000 copies, and a probability of 0.051 means suddenly that most letters reach 1000 copies. This is reasonable evidence for the hypothesis that, given enough copies to start with, the key to the behavior of our chain letter is the product of the probability of copying and the number of copies requested.
We won't go into this matter any further in this paper. However, it's clearly easy to generate a few more test cases for this hypothesis. On the other hand, it's hard to see how a chain letter could work quite the way we have described here. Is it really plausible that the "Good Luck" letter picked 20 copies which just hapens
If we try to take the letter seriously, it raises some strange questions of self reference. Take the simple statement "It has been around the world nine times." Assuming the letter started its journey at some fixed time, this sentence could not have been in the original. How did it get there? Even if we assumed that recipients are allowed to update the letter, no recipient could know that the letter had been around the world even once, unless we imagine absurd or contrived circumstances.
Perhaps the most amusing way to explain this sentence is to assume that the letter itself is talking to us, telling us its history and powers. Another satisfying thing about such an explanation is that then we could expect that the letter would be able to update itself at the appropriate time: "It has been around the world ten times."
The letter must have a consciousness of itself. How else can we explain that it describes the actions of a young woman in California, and what happened to her after she sent the letter out?
The letter makes a famous philosophic joke: "This is true whether or not you are superstitious." A similar joke, with the same point, was attributed to Niels Bohr, who is supposed to have been asked why he kept a lucky horseshoe in his laboratory.
Chain letters are so widely known and easily recognized that they have provided humorists with a handy form for phrasing jokes. A "joke" chain letter is really a joke, and not a chain letter. The stern warnings about making the right number of copies and not breaking the chain are not the main point of the joke, but simply set the chain letter scene. Within this scene, some humorous situation or punchline is developed.
The simplest takeoffs involve minor changes to the text of the original letter, or to the general idea. Some of the takeoffs include:
My name is David Senovich. In August 1989, the kommunist government was overthrown, my Lada was repossessed and the KGB were hounding me like you wouldn't believe...
Hi! My name is Mark Jason Dominus and in 1934 I was UNEMPLOYED and out on the STREET. I had a bad case of SCURVY and nobody would talk to me because I was constantly FLAKING and SPITTING BLOOD...The letter mocks the magic operation of the Dave Rhodes letter by directing the recipient to mail all their valuables to Mr Dominus. In a funny ending, the author warns that Craig Shergold broke the chain, and came down with terminal cancer, then found the letter again, followed the instructions and was cured. This last little joke represents a bizarre crossing of three separate chain letters!
Twenty years ago, I was a hopeless loser with no money, a disfunctional marriage, and a 1962 car with a big hole in the oil casing...If you too are interested in success, Bill asks you to vote for the person at the top of the list in the next election, and add your name at the end.
Other takeoffs try to achieve a humorous effect by moving the chain letter idea to a very unusual situation.
Some people who use electronic mail take advantage of a feature that allows one to write a response that includes the text of the original message. The recipient of such a response must presume himself presumed so dim-witted that without the text of his original message he'd be unable to figure out what the reply was about. Oddly, these same people don't respond to a written letter by stuffing that letter into the same envelope as their response. Then again, who responds to written letters at all?
But a new level of crassness is reached by those who don't merely enclose the original, but actually interleave their responses between the lines of the original. Great pains are taken to minimize the apparently colossal effort of typing, while presenting the appearance of thoughtful consideration, by writing nothing more than "YES" or "TUT-TUT" after a few lines of the text.
Naturally, there's no bad idea that can't be made worse. This same "echo" feature has been included in the USENET news groups, so that if one person posts a comment to the group, acephalic persons can reply to that comment by annotating the running text. The comments are usually insulting, and the person being commented upon will occasionally angrily comment the comments. This Talmudic deliberation can go to ludicrous degrees. A whole class of postings on rec.humor is devoted to so called "cascades" where each person adds a single line to a posting, and reposts it. I won't quote any of these efforts, and you may trust me that you're not missing a single iota of pleasure.
An odd, and more interesting, parallel to this UNIX running commentary feature occurs at the famous Gizmonics Institute, the setting for Mystery Science Theater 3000 or MST3K. This television show presents bad old movies, with the heads of several audience members (only one of them human) visible at the bottom of the screen. Throughout the movie, the audience heckles, mocks, and subverts the movie.
Thus, it is hardly surprising that some Internet users have taken on the role of the MST3K creatures, and produced mock versions of postings which have been snickered at by Tom, Crow and Joel. The Dave Rhodes chain letter has been a target of this sort of dissection at least twice. Perhaps the most extraordinary feature of these two commentaries is their great length. Both versions I have, which are completely different, go to 17 pages.
Here is the beginning of the version attributed to Jeffrey Shaffer:
Dear Friend,
Tom: Anyone's friend in particular? Or just generally well disposed?
My name is Dave Rhodes.
All: Hello Dave.
In September 1988 my car was repossessed}
Crow: Sorry Dave.
...and the bill collectors were hounding me like you wouldn't believe.
(Crow and Tom make barking noises.)
Joel: Big dogs. Jumping on my head.
I was laid off and my unemployment cheques had run out.
Tom: They made some comment about not spelling something right on the form, I don't know.
Joel: No, I think he's from England.
Crow: Oh? Well lookie what we have here boys! We got ourselves an alien!
The only escape I had
Tom: Was through a small trap door, and into the ventilation system. That night I was to board a boat just off the coast.
...from the pressure of failure was my Apple computer and my modem. I longed
Joel: For an IBM?
...to turn my advocation into my vocation.
Crow: What? Writing poor fiction? Sorry pal, Wood's dead.
This January 1989
Tom: As opposed to how many other January 1989's?
Joel: January 1989 BC?
Crow: Well, he did mention that he had an Apple computer...
...my family and I went on a ten day cruise to the tropics. }
Tom: And with some quick action the IRS was able to apprehend them before they arrived at their first port of call.
I bought a Lincoln Town Car for CASH
Joel: What a deal! Some guy named Vinny was in a parking lot selling it for $50!
...in February 1989. I am currently building a home on the West Coast of Florida,
Tom: Because the bank foreclosed on my previous home.
...with a private pool,
Crow: That's not a pool! That's a puddle in the street out front!
...boat slip,
Joel: And that's an old, collapsed dock!
...and a beautiful view of the bay
Tom: Out all four sides of the box!
...from my breakfast room table and patio. I will never have to work again.
Tom: Because now I eat the government cheese!
The Gospels of Matthew, Mark and Luke are known as synoptic, or "seen together", because they are close in organization and content. These three gospels are sometimes printed as three columns on one page, with the corresponding portions aligned, to emphasize their agreement. We will use a similar approach on a few varieties of the "Good Luck" chain letter. By the way, I'm sure you know that the word Gospel means "good news". Perhaps Christianity would have been different if Saint Paul had written chain epistles to the Corinthians!.
I originally tried printing each line of six chain letters, one beneath the other. While nicely scientific, this was boring as all hell and ugly to look at. Instead, I have conflated the various versions, as best I could, while trying to indicate alternate readings with parentheses, and omissions with square brackets. Thus, a "generic" chain letter would skip the parentheses and include the square brackets.
There is frequently an initial line, which is highly variable:
(With love all things are possible.)
(Trust in the Lord with all good faith (your heart and will); [and he will]
Acknowledge and he will light the way)
(Kiss someone you love when you get this letter and make magic.)
(Prayer. Believing, Ye shall receive, Math 21:22).
This paper (message) (prayer) (quote) was (has been) sent to you for good luck.
The original (copy) is in (from) New England (New Zealand) (the Netherlands).
It has been (sent) around the world [nine (many) times].
The luck has [now] been sent (brought) to you.
You will (are to) receive good luck within [the next] four (nine) days of
receiving this letter (message) [provided (pending) (providing) you, in return
(turn) send it on (back out) ].
This is no (not a) joke.
You will receive good luck (it) in the mail.
The (This) chain comes [to you] from Venezuela and was (is) [started and was]
written by Saul Anthony Degrow (Soul Anthony De Group) (Saint Anthony Da Grou)
(Saul De Groda) (Saul Anthony Degnas) (Saint Anthony de Codif)
(Saul Anthony DeGaold)
(Saul Anthody De Cavif) (Saul Anthony De Capif) (Saul Anthony DeCamp)
(Saul Anthony DeCroor) (Saul Anthony De Group), (Soul Anthony DeGroof)
a missionary from South America (Africa).
[I myself forward it to you] Since this (the) copy (chain) must [make a]
tour [of] [around] the world, you must take (make) (have) twenty (ten) copies
[identical to this one] and send them (it) to [your] friends, [parents] and
associates.
After a few days you will get a surprise.
This is true, even if you are not superstitious.
Do note (Take note of) the following:
Constantince (Constantine) (Constantina) (Constantin) (Contonare) Dine (Dina)
(Die) (Dias) (Diaz) (Dira) [had] received the chain [letter] in 1933 (1903)
(1985) (1983) (1957) (1958) (1963) (1953).
He asked his secretary to make twenty copies and send them [out].
A few days later he won a (the) lottery of [over] two (20) million dollars.
($20,000,000 on the lottery in his (this) country).
Carlo (Carlos) (Cario) (Coreo) (Carl) (Carolo) (Carol) (Arla) (Aria) Daddit
(Dapit) (Dobbit) (Doddit) (Deditt) (Dadirr) (Cradyit) (Bidett), an office
employee, [who] received the (this) letter (message) (chain) [and] [he] forgot
it [had to leave his hands in (within) 96 hours].
[And in a few days] He lost his job.
Later, [after] finding the letter (that message) again, he [made copies and]
mailed [the] 20 copies. (Later he found the chain and sent it to twenty people.)
Within a few days (A few days later) (Five days later) he got (found) [himself]
a better (an even better) job.
Dalen (Dalan) (Dallan) (Dolan) (David) (Darin) (Devan) (Salon) (Helen) Fairchild (Moirchild)
received the letter (chain) and not believing, [he] threw the letter (message) (it)
away.
Nine days later, he (she) died.
In 1987, the (this) letter (message) [was] received by a young lady (woman)
in California.
It was [very] faded and barely (hardly) readable.
She promised herself [that] she would retype the letter
and send it out (on)...
...but she put it aside to do [it] later [and forgot it].
She was plagued by (with) various problems, including expensive
car repairs (problems).
The letter did not leave her hands in (within) 96 hours.
She finally typed (retyped) the letter as promised and [within days] got (won) a
[brand] new car.
Remember, send no money.
[Good Luck but please remember: 10 copies of this message must
leave your hands in 96 hours.]
You must not sign on this message.
[Please] Do not ignore it (this).
[It's true and] It works.
St. Jude.
[Help me to remember Lord that nothing is going to happen
to me today that you and I cannot handle.]
[EXPECT A MIRACLE GOD BLESS YOU ST. JUDE WORKS]
[For no reason whatsoever should this chain be broken.]
Many chain letters require their recipients to send money to an earlier recipient, and promise, in turn, a much greater amount of money in due time. There are many "money-making" schemes that mimic this feature of chain letters, while not actually using a letter or message.
There is an entire burgeoning field of scams known as "MLM" or "multi-level marketing", based on the success of the shady corporations like Amway and NuSkin. In such systems, a person is induced to join a "distribution network", which purportedly markets a line of quality products. The person is told that he must pay a startup fee to his contact, to pay for the first set of goods. Then the person has two ways to make money: selling the goods, and "developing" new distributors. Part of the profits from each sale are passed back up the chain, as is the startup fee. Everyone upwards on the chain takes their own "commission" from the money.
In the seventies, there was a ludicrous craze that dispensed with the pretense of selling a product or doing a service of any kind, and got down to the essential mystifying magic of the classic pyramid scheme. You might be invited to attend what was called an "Airplane Party", and hear testimonials from people about how the airplane has made them rich. One person would be identified as the captain. There were also two co-pilots, four flight attendants. There was room for eight passengers, but these slots weren't taken yet, and the plane wouldn't "take off" until eight people in the party volunteered to take the flight. Of course, it cost you $100 to be a passenger. This money went straight to the pilot, who promptly retired. Everyone else on the plane was now promoted one level, meaning that there were now two planes, needing 16 new passengers.
Depending on the size of the crowd and the duration of the party, perhaps another plane would take off that night, or both. More typically, the participants would disband, agreeing to meet again in a week, at which time the new flight attendants were urged to bring several potential passengers so that everyone could move up. It's amusing to wonder if the party actually involved, say, setting up chairs to make a mock airplane. And I imagine many observers were mightily pressured by people already on the plane to "come on board so we can take off!" On the other hand, an airplane party seems to be an awful lot of work, with a pretty small profit, and a waiting period that might last a couple weeks.