On TV shows where they have this sort of thing happening, a minute change in the far past has overreaching consequences in the future. Perhaps someone breaks the rules and others get sucked into it by trying to fix the initial problem. It usually involved saving someone who should have died. This caused their present to change radically, even out of all proportion.
One TV show I saw once had a guy go back to prehistoric times, did absolutely nothing and came back to his presence to find that the woman he was getting close to was now someone totally different with a completely different name. Everyone he knew expected him to know everything about that particular timeline. I suppose the name change could be possible if her parents waffled over her name, but this woman had a completely different surname and looked the same. I’m not sure that would have happened.
How changed the present would be depends on how far into the past that a person goes. Changes would be minimal the farther back a traveler goes, I think. When someone goes back in time, there is a danger of changing the present. That’s because the present depends on the past. What happened in the past shapes the present. Changing just one thing could make a difference to the present. You could go into the past, save someone’s life and come back to a completely different world.
My question is, would a tiny change, that far in the past, have devastating consequences in the present? A minute change in the past might well be just a minute change in the past. It could have no effect, a small effect, a large effect or even a catastrophically large effect. There would be no way to tell how that would work.
I guess it would depend on what was changed. Saving someone’s life could mean that someone born today would actually be someone else. The person changed might or might not be an important person, a doctor who saves the future president, the teacher who inspires a great writer. Or the person could just be a poor slob making a living the best he can. Influences can be shifted so easily, a small change in the past might make no difference to the present at all. If things are meant to be, then they will be and that is all there is to it.
Our mythical time traveler could have saved someone who turns around and kills another person who influenced history. However, would we have been able to predict that? I don’t think so. If that person died in the original timeline, we would have no record of him killing the second person. This is why we would be unable to predict the changes in the present resulting from a change in the past. There could be no change at all; there could be a huge change, maybe even for the better. There would be no way to tell.