Even though the composition of two rotations is a rotation on a standard sphere, the same is not true for higher dimensional spheres. Possibly even weirder, on a sphere the composition of two periodic rotations is not necessarily periodic.
Possibly even weirder, on a sphere the composition of two periodic rotations is not necessarily periodic.
This seems really unsurprising to me given the infinite dihedral group being generated by two reflections.
I recently flipped through the "Cartoon Guide to Physics", expecting an easy-to-understand rehash of ideas I was long familiar with; and that's what I got - right up to the last few pages, where I was presented with a fairly fundamental concept that's been absent from the popular science media I've enjoyed over the years. (Specifically, that the uncertainty principle, when expressed as linking energy and time, explains what electromagnetic fields actually /are/, as the propensity for virtual photons of various strengths to happen.) I find myself happy to try to integrate this new understanding - and at least mildly disturbed that I'd been missing it for so long, and with an increased curiosity about how I might find any other such gaps in my understanding of how the universe works.
So: what's the biggest, or most surprising, or most interesting concept /you/ have learned of, after you'd already gotten a handle on the basics?