In Fooled by Randomness, Nassim Nicholas Taleb gives the example of a person who wants to hire someone to type a copy of Homer’s Odyssey. Suppose an infinite number of monkeys are typing on an infinite number of typewriters. One of them comes up with a perfect copy of the Illiad. This enterprising monkey shows up at your door, applying for the job of Odyssey typist. But you’re a monkey, you reply skeptically. He takes out the perfect copy of the Illiad. You’re stunned. And you apologize and hire him on the spot, foolishly interpreting the perfect manuscript of the Illiad as an indication of the monkey’s skills.
Taleb’s point is that before you decide that monkeys are good at typing, you want to know more about the denominator—the number of monkeys trying to type the Illiad. When people claim that this stock-picker or that fund manager is a genius because he’s beaten the S&P 500 for 15 straight years, you should ask how many people are out there picking stocks and what proportion of those would be expected to beat the S&P for purely random reasons. It’s possible there are fund managers who are genuinely skilled but the fact that they do well over some limited time period is not proof.
A more mundane application is asking for references from a contractor. I always ask for two or three references. But a contractor who has been in business for any length of time will be able to find a few good ones—even a few raves—that may not be representative of the typical experience of the firm’s clients. The better strategy is to ask for references from the last three clients or clients from the last six months.
Here is a wonderful page on the infinite monkey metaphor. It will give you a healthy sense of what low-probability events really mean:
One computer program run by Dan Oliver of Scottsdale, Arizona, according to an article in The New Yorker,
came up with a result on August 4, 2004: After the group had worked for
42,162,500,000 billion billion years, one of the "monkeys" typed,
“VALENTINE. Cease toIdor:eFLP0FRjWK78aXzVOwm)-‘;8.t . . ." The first 19
letters of this sequence can be found in "The Two Gentlemen of Verona".
Other teams have reproduced 18 characters from "Timon of Athens", 17
from "Troilus and Cressida", and 16 from "Richard II".
A website entitled The Monkey Shakespeare Simulator, launched on July 1, 2003, contained a Java applet
that simulates a large population of monkeys typing randomly, with the
stated intention of seeing how long it takes the virtual monkeys to
produce a complete Shakespearean play from beginning to end. For
example, it produced this partial line from Henry IV, Part 2, reporting that it took "2,737,850 million billion billion billion monkey-years" to reach 24 matching characters:
- RUMOUR. Open your ears; 9r"5j5&?OWTY Z0d…
Even more entertaining is this study of actual monkeys:
In 2003, lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Sulawesi Crested Macaques in Paignton Zoo in Devon in England
for a month, with a radio link to broadcast the results on a website.
One researcher, Mike Phillips, defended the expenditure as being
cheaper than reality TV and still "very stimulating and fascinating
Not only did the monkeys produce nothing but five pages consisting largely of the letter S,
the lead male began by "bashing the hell out of" the keyboard with a
stone, and the monkeys continued by urinating and defecating on it. The
zoo’s scientific officer remarked that the experiment had "little
scientific value, except to show that the ‘infinite monkey’ theory is
flawed". Phillips said that the artist-funded project was primarily
performance art, and they had learned "an awful lot" from it. He
concluded that monkeys "are not random generators. They’re more complex
than that. … They were quite interested in the screen, and they saw
that when they typed a letter, something happened. There was a level of