The Stopping Problem

The 37% Rule derives from optimal stopping’s most famous puzzle, which has come to be known as the “secretary problem.” Its setup is much like the apartment hunter’s dilemma that we considered earlier. Imagine you’re interviewing a set of applicants for a position as a secretary, and your goal is to maximize the chance of hiring the single best applicant in the pool. While you have no idea how to assign scores to individual applicants, you can easily judge which one you prefer. (A mathematici...

 The Explore VS Exploit Problem

In English, the words “explore” and “exploit” come loaded with completely opposite connotations. But to a computer scientist, these words have much more specific and neutral meanings. Simply put, exploration is gathering information, and exploitation is using the information you have to get a known good result. [...] [...] A sobering property of trying new things is that the value of exploration, of finding a new favorite, can only go down over time, as the remaining opportunities to savor...

 The Dreariness of Curation

Part of what’s nice about music, for instance, is that there are constantly new things to listen to. Or, if you’re a music journalist, part of what’s terrible about music is that there are constantly new things to listen to. Being a music journalist means turning the exploration dial all the way to 11, where it’s nothing but new things all the time. Music lovers might imagine working in music journalism to be paradise, but when you constantly have to explore the new you can never enjoy the fr...

 Caching in Public Libraries

...libraries are a natural example of a memory hierarchy when used in concert with our own desk space. In fact, libraries in themselves, with their various sections and storage facilities, are a great example of a memory hierarchy with multiple levels. As a consequence, they face all sorts of caching problems. They have to decide which books to put in the limited display space at the front of the library, which to keep in their stacks, and which to consign to offsite storage. The policy for w...

 Prime Numbers and Cryptography

Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then cross out all the numbers that are multiples of 2, besides itself (4, 6, 8, 10, 12, and so on). Take the next smallest number that hasn’t been crossed out (in this case, 3), and ...

 Fruitless Recursion as a Strategy

Luring an opponent into fruitless recursion can be an effective strategy in other games, too. One of the most colorful, bizarre, and fascinating episodes in the history of man-vs.-machine chess came in a 2008 blitz showdown between American grandmaster Hikaru Nakamura and leading computer chess program Rybka. In a game where each side got just three minutes on the clock to play all of their moves or automatically lose, the advantage surely seemed to be on the side of the computer—capable of e...