In the mid 19th century, a strange idea was growing heavy in the ether: There might be dimensions beyond the three we experience. To some—including eminent scientists of the day—these were the realms of spirits and the supernatural, accessed through tabletop seances. To Charles Hinton, a British mathematician and science-fiction writer at the time, it was something that could be puzzled out, modeled in things like his “tesseract” four-dimensional cube. In the intervening century and a half, spir...