Entropy means many different things in different contexts, but there is a wonderful notion of entropy which is purely topological. It only requires a space, and a map on it. It is independent of geometry, or any other arbitrary features — it is a purely intrinsic concept. This notion, not surprisingly, is known as topological entropy.
In the spirit of hilariously advanced baby books like Chris Ferrie’s Quantum Physics for Babies, I have taken to incorporating absurdly sophisticated concepts into nursery rhymes.
In which I recall, via neurologist Oliver Sacks, some musings of Sylvester from 1877 on the limitlessness of mathematics.