Sometimes I notice people committing a fallacy that I may call the Butterfly Effect Fallacy. In trying to inspire people, they invoke the metaphor of a butterfly in Brazil causing a tornado in Ohio by flapping its wings. They then immediately imply this is similar to you, the listener, possibly causing great changes by your small art piece or political statement. This is done to provide inspiration and motivation. But in doing so they miss the point of the butterfly effect metaphor. The butterfly effect was conceived as a metaphor for chaotic dynamic systems, like Earth's weather. In weather simulations, a tiny deviation in the starting state eventually grew to completely change the state of the system compared to an alternative path. This sensibility to starting conditions imposes a harsh time horizon on any kind of dynamic simulation system, beyond which the system stops providing useful predictions of the exact state. (The system can still provide useful descriptions of the average state if you run many simulations with slight deviations of the starting state and average the results.) This abstract description of the butterfly effect reveals the ethical neutrality of it. In particular, a butterfly not flapping its wings can be said to be causing a tornado in Ohio just as much as the opposite. If the point of causality is prediction, then the butterfly effect strictly prevents us from predicting the long term consequences of our actions. Perhaps we should try to find a better metaphor for purposes of inspiration. I don't pretend to know anything catchy, but this is the way I think about causality. Small actions produce small impact. Large actions produce large impact. This mostly holds true, but if it was strict then we wouldn't have a world, we'd have a single pendulum as the entire universe. Instead, the exceptions to this principle drive the complexity we perceive as reality.
In modern solutions to the 3-body problem, there is a concept known as the gravitational keyhole. It is a region of space, an asteroid passing through which will lead to this asteroid hitting the Earth on a future orbit. This region is small, compared to our possible uncertainty of the asteroid's path, or the larger region we could bump the asteroid's orbit to, if we wish to prevent this collision. In other words, passing this keyhole creates a distinct change of state that is important to humans. The fact that keyholes are small is relevant here. "Small actions to small impact, large actions to large impact". In this grouping we see a clear hierarchy, or a continuous spectrum, or clear boundaries. This can even be interpreted as pessimistic, implying that your, the reader, small actions, cannot influence the world at large. But this is not even remotely true for chaotic dynamical systems such as our world. Small actions do in fact lead to large impacts, as is described by the butterfly effect metaphor. So how do we reconcile the apparent hierarchy of the impact scales with the chaotic behaviour? The solution lies in the fact that keyholes are small, but passing through one produces a big difference. While you can't map a particular butterfly flap to a particular tornado in Ohio, the same can be done to passing through keyholes and hitting the Earth. Where the butterfly effect metaphor originally tried to describe a rigorous inability to predict the future, the gravitational keyhole was invented as a tool for orbit prediction and impact defense. The butterfly effect, interpreted with understanding of dynamical systems, says, in effect: don't bother predicting the consequences of your actions, over a large enough time the predictions get completely useless. On the other hand, the gravitational keyhole gives a clear instruction: realize you're approaching a keyhole, and give just a tiny impulse to miss it. The change is tiny, but over the course of a couple of orbits it's going to grow large enough to completely miss the collision.