I'm a big fan of combinatory logic. The rabbit hole goes really deep, with connections to quantum computing (via the linear combinators mentioned in the article

I'm a big fan of combinatory logic. The rabbit hole goes really deep, with connections to quantum computing (via the linear combinators mentioned in the article), philosophy (e.g. John Tromp's investigation of Kolmogorov Complexity using binary combinatory logic and lambda calculus), and also to type theory and fundamental mathematics (e.g. illative combinatory logic, which I've played with on my blog http://chriswarbo.net/blog/2012-12-01-typed_combinators.html http://chriswarbo.net/blog/2012-12-01-typed_combinators.html ).