The result is cool, but it's not directly applicable to the traditional (sci-fi) scenario "I travel to the past and meet myself / my parents / my ancestors"
The reason is simple: the authors suppose a CLOSED timelike curve, i.e. something like a circle, where you travel back in time and BECOME your younger self - which by the way only exists because you traveled back in time in the first place.
A slightly different scenario would be much more interesting, but my guess is that it's much harder to analyze:
a NEARLY closed timelike curve, which arrives from the past, coils around itself one or more times - like a coil, indeed - allowing causal interaction between the different spires (i.e. one can interact with its future self/selves and with its past self/selves), and finally the last spire leaves toward the future.