Float like a butterfly, sting like a ... butterfly?

A metaphorical butterfly, that is.

In Ray Bradbury's classic (1954) "A Sound of Thunder," time traveling big-game hunters shoot dinosaurs that -- as known from previous viewing of the past -- are within moments of their deaths. The hunters must stay on and shoot from levitating metal walkways, lest their footsteps do anything to alter the past. Of course, one hunter does stray from the path (speaking of metaphors). The hunting party returns to its  own time to find the outcome of a presidential election changed and a fascist coming to power.

A crushed prehistoric butterfly is found in the mud beneath the straying hunter's boot ...

Fast-forward a couple decades, and the butterfly effect became the metaphor of choice for chaos theory, the branch of mathematics dealing with such complex aspects of the world as weather. The key thing to know about chaos theory is that some systems -- think a ball balanced at the top of a hill -- behave in ways exquisitely sensitive to initial conditions. If anything disturbs the balance of that ball, the path taken by the ball may vary with something as trivial and unpredictable as the bent of an individual blade of grass. Or, from the title of a 1972 scientific paper, "Does the flapping of a butterfly's wing in Brazil set off a tornado in Texas?"

To the extent that the butterfly causes a tornado, its flapping wings are -- of course -- but one energy source (and a trivial one) among many. But as in the case of the aforesaid ball gathering speed and kinetic energy as it careens downhill -- in an unpredictable direction -- in a chaotic system like the weather, even the slightest event may influence much larger forces.

As in "A Sound of Thunder,"  many time-travel stories deal with the unpredictable effects of the smallest events. So do parallel-universe stories such as -- sticking for now with the classics -- Keith Laumer's Imperium series (about to be reissued in one volume) and H. Beam Piper's Paratime series (already so collected).

The purest examination of the butterfly effect, however, is in a third SF subgenre: alternate history. As we know the American Civil War, a Confederate courier lost a copy of the battle plans for Robert E. Lee's 1862 invasion of the North. Union soldiers found the plan. Would Union general George McClellan have won the Battle of Antietam (Battle of Sharpsburg to Southerners) without that advantage? We'll never know -- but in How Few Remain, Harry Turtledove offers an alternate history in which plans weren't lost -- and so Lee's 1862 invasion led to Southern Independence. And from such a minor incident as mislaid cigars (the battle plan was found wrapped around three cigars), came -- in a later volume of this alternate history -- two feuding North American nations taking opposing sides in World War I.

Why are so many of us fascinated with alternate histories? Is it because we see ourselves at the mercy of events? Such lack of control might be scary -- and certainly horror is a popular enough genre.

And do some of us find that lack of control comforting? If the course of great nations can be redirected by chance, how much more random are our own lives? Why brood over a choice we made when the undesired outcome might have come about through the real or proverbial flapping of a butterfly's wings?

(Curious about more SF of the same ilk? Harry Turtledove has written a ton of it. Of course there's Philip K. Dick's classic (1962) The Man in the High Castle, in which Japan and Germany won World War II. There's Harry Harrison's Eden trilogy, beginning with West of Eden, in which a certain long-ago asteroid missed Earth, dinosaurs continued to evolve, and so intelligent species of saurians and humans came to compete for the planet. Or check out the Sideways Awards for Alternate History.

As for, specifically, "A Sound of Thunder," you can find it in A Sound of Thunder and Other Stories.

(Only try not to think about whether a dinosaur, killed even mere seconds before its time, might not have toppled upon and crushed the wrong butterflies. Or that levitating paths, presumably, exert an equal and opposite force upon the ground beneath, capable of crushing ... butterflies. Read Bradbury for the ideas and the beauty of his prose, not the rigor of his science.)