"Compression" is one result. But this is sometimes referred to as the "inverse problem": Given a set of data tell me a function which fits it (or fits it to some tolerance.) It's important in statistics and all kinds of data analyses.
Another area is fourier transforms which basically sums sine waves of different amp/freq until you reach the desired fit. This is also the basis of a lot of noise filtering algorithms, throw out the frequencies you don't want, such as 60HZ or 50HZ, or all those smaller than you consider interesting, high-freq "noise", or low freq noise, whatever. Another buzz term is "data entropy", randomness. If the data were perfectly random then there exists no such function which can be represented in less bits than the original data, which is why you can't compress a compressed file indefinitely and also why it's recommended you compress files before encrypting them, it's hard to begin cracking a file which is pretty close to random. And this is what you do when you give something like a MARC or ISBN or Dewey Decimal index to a librarian and s/he brings you the book you want. Effectively you've represented the entire book as that small "number". Imagine if you had to recite the entire text of a book to find it unambiguously! See: Transfinite Number Systems. -- -Barry Shein The World | b...@theworld.com | http://www.TheWorld.com Purveyors to the Trade | Voice: 800-THE-WRLD | Dial-Up: US, PR, Canada Software Tool & Die | Public Access Internet | SINCE 1989 *oo*