The biggest surprise to me about this drama is that it really does want us to take the "science" in science fiction rather more seriously than one might expect it to. One some level the name dropping (eg. Schrodinger's Cat, Heisenberg's Uncertainty Principle etc) might just be window dressing... "Attention! Attention! You are watching a time travel-multiverse story" but the fact that the writer is making the effort, is almost commendable. There's almost enough gobbledegook to rival that of an episode of Star Trek: TNG. It's really rare in my experience to see a K drama go to go to all the trouble of analysing and discussing the moral intricacies of playing peek-o-boo with the past.
By now we're meant to understand that the Alice project is not all that it's cracked up to be. Good intentions are not always matched by reality and outcomes. While Alice might not be an abject failure (yet), it can't entirely live up to its lofty aims of wanting to better the lives of people or alleviate suffering. It also appears, rather worryingly that the people behind the Alice project aren't entirely cognizant of all things time travel, much less about the competing interests within that space. There's talk about parallel universes and other selves in existence but there's no notion of paradoxes of future selves becoming part of the past and integrating their footprint in a single timeline. If there had been (at least) two separate timelines before, they seem to have now collapsed into one apparently because of Tae-yi's decision to remain in 1992. Seok O-won seems to have some awareness of this having the benefit of hindsight taken from the so-called Book of Prophecy.
Prophetic utterances and oracles within this universe seem to the ramblings and chronicles of time travellers who have witnessed the future firsthand, recorded key events and left them behind for posterity. How the book found its way into Dr Jang Do-shik originally and Seok O-won's hands eventually at various times are still mysteries that need to be revealed in due time. Playing pass the parcel with the book itself seems to imply that there is one timeline at play rather than multiple ones. Unless of course there are multiple ones circulating in parallel worlds.
The contestability of time travel may prove to be the most fascinating aspect of the drama. It's also a new twist to Kdramaland's increasing macabre fixation with serial murders. A good excuse to raise the body count. It isn't just the tourism murders that call into the question the entire enterprise but there are other murders involving rough looking men with long hair and leather jackets who have a thing about dead cats. Who are they taking their orders from? It seemed initially that Seok O-won might be behind this and yet it is possible that there's a third party calling the shots. The contestability of time travel will undoubtedly turn it into the pandora's box that Seok O-won hints darkly at. It's a double-edged sword depending on who's wielding it.
The time card brings Min-hyuk face to face with the woman he loves and is stopped in his tracks. Is she his Tae-yi? According to Schrodinger's thought experiment... the answer is no... and yes. He knows her but not her as she is now but as she will be. But to add insult to injury he thinks she's another Tae-yi from a parallel universe, out of his reach. Are we all sufficiently discombobulated yet?
Min-hyuk is wrestling with the same issues Jin-gyeom does. Who is this woman? Should he care? As long as she doesn't have memories of him, she can't be his Tae-yi. Just as Jin-gyeom has concluded that the professor can't be his mother. Appearances, habits and personality aren't everything if they have no shared memories. According to the premise laid down here, her identity is not necessarily determined by who she thinks she is or what she does alone BUT by how she is perceived by the people who know her best. Tae-yi from 2050 apart from being a scientist was also someone's lover and then someone's mother.
The time card is the key... not just for accessing the temporal mechanism but the key to all those involved in this relationship web to find out the truth about the past. 1992 and 2010. Min-hyuk's entry at this point in 2020 Tae-yi's existence suggests that the show might be avoiding an icky Oedipal scenario. Although the constant sparring between father and son might indicate otherwise. Certainly on Jin-gyeom's side, his interest in present-day Tae-yi is purely for the fact she resembles his mother in striking ways. He must also feel some responsibility for drawing her into this dragnet of inexplicable danger that grows even more inexplicable as the web of intrigue expands to include a whole assortment of unsavoury characters that have come from nowhere.
Oh Shi-young is a curious and suspicious figure. One wonders about her role and possible presence on the night of Tae-yi's death in 2010... as signalled by the drone. But the really curious thing is why she's been feeding Min-hyuk porkies about Tae-yi moving on and living the good life and the death of their baby. To help him forget and move on so that he would turn his attention to her? That's a likely explanation. And he is undoubtedly walking eye-candy in a suit.
More than that, she must know that Tae-yi left behind a son. His and her son. Whatever she might be trying to convince herself of regarding parallel universes it doesn't change the fact that Park Jin-gyeom is Min-hyuk's son from that particular timeline.
The reality is that Min-hyuk hasn't moved on despite running around busily with a stoic resolve. Neither has Jin-gyeom despite his innate expression of stoicism. The passage of time apparently doesn't heal all wounds. Perhaps this explains Min-hyuk's quiet sympathy for his murderous clients. He himself is only too aware of his own grief that he keeps well-hidden from public gaze.
However, the use of the past as a psychotherapeutic playground continues to throw up all kinds of troubling ethical questions. For an oligarchy with all their emotional baggage, not matter how well-intentioned, to adjudicate this life and death process, continues to be disturbing.
There's no denying the well-used tropes making their appearances here. It is still a recognizably K drama after all. However, credit should be given to the showrunners for using them in playful, innovative ways as it pertains to the time travel multiverse madness. It may be true that underneath all the other worldly elements beats the heart of a good old fashion K melodrama.