I heard this song in the mid-60s and, being in a slightly more-than-usually conscious state of mind (coming down, that is), felt like the Stones were bending time. Taking time and goosing it, delaying it, playing with it.
Keith's book, Life, is surprisingly good. In it he talks about a record they made in a motel room with a tape deck, Charlie playing a kids' drum kit, that they achieved something with analog that you can't get with digital. (My recollection may not be entirely accurate.) But what's interesting is that digital recording is on or off, black or white, with nothing in between, if you will.
The idea of introducing (allowing) imperfections in your music, your art, your life. Richer.