Induced power from nearby lines??

I once visited somebody who lived almost right under the lines. For a magic demonstration, out on his back deck, he would hold a fluorescent tube in the air and it lit up (not at full brightness). When I dinked around with ham radio many years ago, I didn't know for a long time that the shut-off lights in the apartment below me would flicker dimly synchronized with my voice. Three girls lived there and it freaked them out pretty seriously.