In this talk I will discuss several topics of old research, much of it was joint with Fred Cohen, and all of it was inspired by him. All of these topics will have to do, in one way or another, with the two-fold loop space $\Omega^2 S^3$, one of Fred's favorite spaces (and also one of mine). I will be discussing bundles over configuration spaces and braid orientations of manifolds, the topology of spaces of rational mappings, and the ``Kervaire invariant 4" problem. I will end by describing a question and conjecture of Mark Mahowald, which I believe would make a very interesting topic for future research.