“What has been will be again,
what has been done will be done again;
there is nothing new under the sun.” (Ecclesiastes 1:9)
"...The eternal hourglass of existence is turned over again and again, and you with it, speck of dust!" Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: "You are a god, and never have I heard anything more divine..." (Nietzsche, The Gay Science)
"Fellow man! Your whole life, like a sandglass, will always be reversed and will ever run out again, - a long minute of time will elapse until all those conditions out of which you were evolved return in the wheel of the cosmic process." (Nietzsche, Thus Spake Zarathustra)
Time paradoxes have been a staple of speculative fiction for nearly a hundred years. The most famous paradox (used in the novel) has been famously explained by Isaac Asimov: journeying to the past and shooting his grandfather...which would mean that he hadn't been born in the future and therefore could not travel to the past to shoot his grandfather, so he
was
born and then could travel into the past
again
... (the "grandfather paradox," which also appears in the "what if Hitler were shot when he was an artist" version).
Another version was famously used by Ray Bradbury, who popularized the term "butterfly effect" in his short story "The Sound of Thunder," in which a time traveler in a prehistoric jungle accidentally steps on a butterfly, thus changing the future to which they return (the Back to the Future effect, which, unfortunately, would be impossible given the fact that the future from which the travelers originated no longer existed...or did it?).
Then again, maybe travel into the past would create new strands of time, or new dimensions or universes (the novel terms this "branch theory"). Which would mean travel into the past is a one-way ticket (think Back to the Future again...and why it failed as a plausible SF movie), because the original future would no longer come into existence, at least from the point of change in the past.
But what if everything had already happened, and was happening again, ad infinitum?
This would make time/space a "loop" or a "circle." This, too, has been explored in science fiction - most famously by Robert Heinlein ("By His Bootstraps" and "All You Zombies," source of the 2014 movie Predestination). In philosophy and religion, this is termed "eternal recurrence" or "eternal return," and has been a concept for literally thousands of years, dating back to the Vedas and the Bhagavad Gita of ancient India.
"On arrival of day, all manifestations originate from "Unmanifest"; On arrival of night they annihilate into [what is] known as "Unmanifest" only. This [same] elementary world only happens again & again; Annihilates upon arrival of night, [and] originates upon arrival of day." (BG, 8:18-19)
In taking on the concept of "circles" in time travel, Beyond Yesterday enters into a deep philosophical conversation and pushes the reader to the limit. While reading the first two novels of the series is not entirely necessary to comprehend the story, a reader who has read those two books (Beyond Cloud Nine and Beyond the Horizon) will have a much deeper appreciation of the intricate plotting and characterizing in this wonderfully complex story.
If you see a bit of Heroes in Katayama, Shin, and Zeke, you may not be too far off. If you see a bit of Battlestar Galactica (the new one) and Aliens in the androids Eve and Bob, again, that might not be too farfetched (though they represent opposites). If you see a little Stargate and "Ancient Aliens" in the Onaki, you may not be incorrect (keeping in mind, of course, that this is all fiction!). I'm also tempted to think that the Vril, as supreme manipulators of human history, are named after Vril Dox of L.E.G.I.O.N. (later R.E.B.E.L.S.) fame: arrogant, genius, sneaky, ruthless, immoral - and almost always right. But it's (Admiral) Brooke and (Captain) Maya who are the real focus of the story - both heroic and tragic - and by far the most original, and interesting characters of the series.
"Alien" species and their interactions with both futuristic and ancient humans - past, present, future, or would that be past(s), present(s), and future(s)? - is a circle, not a straight line. Aside from a few minor bumps here and there in the language usage (everyone has a style preference for scene descriptions!), this book comes just as highly recommended as the previous books in the series. Maybe even more so.
"The picture of the real infinite...is the circle...which is closed and entirely present." (Hegel, Logik, I, 173)
Disclaimer: I received a free copy of this book for an honest review. I purchased the previous two books of the series. I can't wait for the fourth (and final?) book of the series.