graner@ut-ngp.UUCP (Nicolas Graner) (04/14/85)
from gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>): > > What is the next number in the series > > 2, 3, 5, 7, ... > > > > My point was that there IS no "right answer". Any of the following > could be the next number in the sequence: > [...] > > Appeals to simplicity do not help, since my first answer is > simpler in a strict formal sense than the "obvious" one. > How do you define 'simplicity' in such series? I vaguely remember an old article on the subject in Scientific American. The idea was that the simplest series is the one that can be generated by a program using the fewest instructions. Of course, the answer depends on the language you choose. For instance, to reflect the way most people reason about the above example, the language should have a single instruction to test if a number is a prime (and thus make 11 the simplest answer). But people who have never heard of primes would not have this instruction in their language and would find another 'simplest' answer. I wonder if this definition can lead to paradoxes, as with "the smallest number that cannot be defined in less than fifteen words". Nic. {ihnp4,seismo,...}!ut-ngp!graner *If Murphy's law can go wrong, it won't*