I am studying calculus and statistics currently, and a possible relationship between them just occurred to me. I was thinking about two things: (i) is a differentiable function from R to R a manifold, and (ii) in what way is a random event really unpredictable? So I don't know much about either one, but manifolds and random variables seem to be related by their local vs. global or short-term vs. long-term behavior. I don't know how closely complexity and randomness are related, but assume that they are closely related (or perhaps recast this in terms of information-content and description-length). It seems interesting to me that a manifold can be relatively complex/random globally/long-term but relatively simple/predictable locally/short-term, and the value of a random variable can be complex/random locally/short-term but simple/predictable globally/long-term. They seem to be duals or opposites. If you just look closely enough or long enough, they both get simple and predictable and more efficiently describable. No? Comments? Is that a bad way to look at things?