The Butterflies bit comes from weather forecasting and refers to the claim that weather systems are so interconnected that a butterfly in Mongolia can cause a cascade of events that leads to a hurricane in the North Atlantic.
What does that have to do with Alternate History? Alternate history butterfly advocates claim that history is similarly connected, that major changes, or even minor ones, from real history anywhere in the world would rapidly cascade, making the resulting world unrecognizable within a surprisingly short time.
For example, if someone went back in time and stepped on a bug, the impact on history might appear to be trivial. The bug dies a few hours or days earlier than it would have and the world goes on without much change. Don't count on that though. Let's say that in reality the bug dies an hour after the time traveler would have stepped on it. No big deal, right? Well, actually it could be a big deal. As a matter of fact, the odds are pretty good that it would eventually be a big deal, though it might take a thousand or ten thousand or even a million years before that's apparent.
Whenever it dies, the bug's body would be recycled, feeding some kind of predator or scavenger. The molecules of that bug's body get recycled time and time again throughout the rest of the life of the planet, but if it died an hour earlier and in a slightly different location it goes along a different set of pathways. How many recyclings does it take before the bug's molecules are or aren't part of something important, like the sperm or egg of the ancestral wolf that either did or didn't kill one of Columbus's remote ancestors? It probably takes thousands of recyclings, but given enough time those molecules will probably be involved in something crucial.
Also, the bug has a more direct impact. Something ate the bug or didn't eat it. Maybe a predator doesn't survive long enough to mate as a result of not eating the bug--it continues foraging and something bigger eats it. Or maybe it survives and has offspring whether or not it eats the bug, but at subtly different times--which, given the low likelihood of any given sperm being the one that fertilizes the egg, means that it has different offspring depending on whether or not the time-traveler stepped on the bug. Whatever ate the bug has a different life trajectory, probably chasing and eating different prey at different times than it did in real history. Each of those chases starts a new cascade of changes from historical reality. So does anything the bug's descendants and the predator's descendants do. Actually changes start cascading from two sources, not one, because something probably ate the bug that wouldn't have without the time traveler and something didn't eat the bug that otherwise would have.
The time traveler walks across a field, with every step starting a cascade of changes from his reality. Some of those changes may damp out, though the odds are against it. Some may be apparent only at the microscopic level for years or decades or even hundreds of years before changing something noticeable.
It's even possible that the time traveler's changes don't become noticeable until after his own time. That's a nightmare scenario: Go back a million years from 2016, take a walk in a field and come back to a seemingly unchanged world of 2016 where the microscopic changes you made eventually, long after your departure date. cause a nuclear war that wouldn't have happened if you hadn't gone back.
The structure of how things happened in reality is fragile. A point of divergence starts a cascade of changes, probably unpredictable beyond a decade or two at the most. Unfortunately, that takes a lot of interesting questions out of the realm of "hard" alternate history.
What would Columbus have found if most of the big North America animals hadn't died off at the end of the ice age? An interesting question, but all those animals existing over thousands of years would have almost certainly butterflied Columbus out of existence. They would probably take Spain and even a recognizable Europe with him. Too many fragile events went into the existence of that Europe. A Europe would undoubtedly exist and probably parallel the historic one in some ways, but with different languages and genetics.
Butterflies make it difficult to get to a lot of interesting questions. What if there had been a natural sea level Panama canal? No Columbus. No Spain. Probably not the same human species, though they might look a lot like us. The natural Panama canal closed several million years ago, changing climate across the world. If it hadn't closed, our ancestors might not have survived. Even if they survived, they wouldn't have gone along exactly the same path we did and genetic drift would mean that they probably couldn't produce fertile offspring with us after so many years.
That spoils a lot of alternate history (and time travel) doesn't it? How can we get to the interesting questions that butterflies make impossible? As a science fiction writer I don't let butterflies kill a good story. I get as much as I can right and ignore the logical holes butterflies rip in the story.
I did that to some extent in my novel All Timelines Lead to Rome. In All Timelines, primitive humans similar to the Flores Hobbits survived on a large Mediterranean island long enough that when Neolithic settlers reached the island around ten thousand years ago, those settlers decided to enslave the primitives rather than killing them off. So far, so good. The next step requires hand-waving though. The primitive humans remain slaves but don't spread through the ancient world and don't change the processes that led to the Roman Empire. Rome spreads them throughout the empire and remodels the empire around them, using them as crosses between slaves and pets. It's an interesting idea, but the chances of Rome creating a recognizably Roman Empire with a point of divergence over seven thousand years before the founding of Rome are slim.
I introduced a way to get around the butterflies in my novel Snapshot. Extraterrestrials with godlike powers make backups "snapshots" of Earth continents for tens of millions of years. Each Snapshot is an exact copy of a continent at some time in history. The Snapshots are each in a separate but interconnected universe. How does that get around butterflies? If you want a North America with Indians and big ice age animals, just time the Snapshot right. I'm currently writing stories set in a Snapshot taken of North America including Mexico in 1519, in the middle of the Spanish conquest of the Aztecs. The Snapshot cut off Spanish West Indies and Mexico from the Old World. Result: independent conquistador kingdoms in Mexico, which are hard to realistically get any other way. Future stories may involve a Snapshot of Europe taken in the summer of 1942--Europe isolated from the rest of the world and forced to cope with the Nazis on their own, Rainforest Australia, Africa before the dinosaurs went extinct and enough others that I can't do them all justice to in a lifetime.
The bottom line: Butterflies are a real issue if you're serious about your alternate history. They make some types of questions unrealistic. At the same time, we shouldn't allowed them to keep interesting questions from being explored, especially if they lead to interesting story settings.
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