Hodges' theorem

Hodges' theorem states that if a string of digits (or numbers) is written in a way where each digit is entirely determined by the digits before it (a property called "self-reference"), then the only possible infinite sequences that fit this rule are either completely random or follow a very specific pattern, such as repeating the same digit endlessly. In essence, it shows that certain types of self-referential rules are very restrictive, leading to sequences that are either fully predictable or exhibit total randomness, with no middle ground.