Patterns hidden from simple algorithms

Abstract

Is the number 9021960864034418159813 random? Educated opinions might vary from “No! No single string can be random,” to the more contemptuous ”Come on! Those are just the 714th to 733rd digits of π.” Yet, to my limited mind, the string did appear random. Is there a way to use some formal mathematics to justify my naïveté? The modern theory of pseudorandomness indeed manages to explain such phenomena, where strings appear random to simple minds. The key, this theory argues, is that randomness is really in the “eyes of the beholder,” or rather in the computing power of the tester of randomness. More things appear random to simpler, or resource limited, algorithms than to complex, powerful, algorithms.