The unstoppable conflict
The children wonder in vain if there is anything they can do to bring peace to the Vikings and the Parisians, but of course there isn't. The fight is eminent, and their only choice is whether to pick a side, and which side to choose. When they get separated, that elevates the stakes, because now at least one of the three will be on the losing side. The conflict is a symbol for historical conflicts of various kinds because they realize that history has an unstoppable way of moving forward through warfare.
The motif of innocence and experience
The kids represent an innocent point of view (because they are children), so their three experiences are a motif of different aspects of innocence that must be adjusted before empathy for the past can be attained. The novel presupposes that history students in school are mostly concerned with learning the facts of history. This novel teaches the experience of history as lived time, so that instead of hearing about a war and saying, "So what? It's just another war," the children actually scramble to save their own lives.
The symbolic "picking of sides"
One thing that experience teaches all three of these children is that their desire to pick sides as if history is one long chain of NFL teams competing for a prize—it doesn't actually work in practice, because the wars are violent and horrifying, and the children don't really understand the motivations behind either side. Also, they are from a different time, and they learn that picking sides doesn't amount to much, because they don't understand what it's like to be a Viking or a Parisian. The symbol is a reminder of the way one's present culture shapes opinion.
The kidnapping
Dak is abducted and forced to work for the Vikings, but the dilemma or helping them or working against them is still on his mind. He is in a position to sabotage them, but he can't know whether that is the right thing to do. This symbolizes his journey toward understanding the Vikings, because he feels one way, and then they accept him, and his loyalties quickly adapt. This represents the way loyalty emerges in dire situations.
The infinity ring
The ultimate purpose of the children's voyage back in time is to obtain this sacred relic for their own purposes. In their context, it means one thing, but to the reader, the infinity ring is a symbol. It certainly represents the continuity of time and the fluidity of the human experience (because it is a ring with an infinite nature), but beyond that, it represents insight and transformation in the characters, because they have to adventure through trials and tribulations to attain it.
