What did Eckels from the short story "A Sound of Thunder" written by Ray Bradbury do to jeopardize the safari and the future? Was it when he stepped off the path and stepped on the butterfly? (spoiler alert) If that's the case then I already know, but if it's not please tell me. Thanks.
Generally, "spoiler alert" comes before you write the spoiler :) It's a good thing I've read this story before.
You have it correct. The future is put in jeopardy when Eckels steps off of the floating sidewalk thing (awesome) and kills the butterfly. He changed something in the past that wasn't supposed to change. That butterfly didn't get to pass on its genes, so its future descendants never lived, which somehow caused the entire future government system to be changed in the present (future?).
The concept of changing one tiny thing that would result in massive changes has been around since about the year 1900. Bradbury gave the idea a cool setting and story in "A Sound of Thunder." Bradbury used a butterfly in his story. About a decade later, a meteorologist named Edward Lorenz changed a minuscule amount of in a weather prediction model, and the result was way different than the initial result. Lorenz made the logical connection that a butterfly's wing flap could alter the end result of a developing weather pattern. Long story short, Bradbury and Lorenz helped develop the concept which has today become known as "The Butterfly Effect."
Probably the most famous showing of The Butterfly Effect" is the original "Back to the Future" movie. Marty Mcfly causes one tiny change and almost wipes out his existence. Speaking of movies, there is a film version of "A Sound of Thunder." Don't bother with it. It doesn't follow Bradbury's story at all.
Let me leave you with this butterfly effect paradox. Suppose I went back in time and killed my grandfather before he had a chance to have my father. If my father never existed, I never existed. So if I never existed, who went back in time to kill my grandfather?