I agree about the butterfly effect being not totally legit, but that doesn't mean that I don't have a huge warm spot in my heart for Bradbury's The Sound of Thunder - the first story I ever read that made me catch my breath in surprise at the ending, and the standard by which all other stories, whether heard, read, or watched, are held. I want the "OH" feeling. The plunging down a roller coaster surprise. Sixth Sense - like that. But when I think about the actual butterfly effect, I figure, like say Hitler had not been born, somebody would have filled that void. That void was created so hugely. And so on.

However wide acceptance of the Butterfly effect would in this world probably result in president Cheeto declaring war on weather terrorist butterflies everywhere and his building a huge net over the USA.
The straw that broke the camel's back will like wise result in the Health and safety executive making camels wear anti-straw back braces when engaged in agricultural labour or of them being banned from all hay, straw, grass and associate products production bases all together.

Chaos Theory is simple maths. There's no denying it any more than you can deny that there's an infinite supply of prime numbers or that pi is irrational. Certainly large parts of our world are modeled by stable equilibria. However that is not universally the case. Some systems are chaotic. This simply means that a small change in the input results in a large change in the output.

Here's an example. Say I was mathematically modeling a game of pooh sticks. We have a channel of water and the water is flowing in a regular non-chaotic manner. If I throw a twig into the water it hits the water at a specific spot at a specific time (that's the input) and I work out where it will be in 60 seconds time. (that's the output)
If I were to change the input location by one centimeter then the output would change in an easily predictable manner, and the smaller the change I made to the input, the smaller the change we'd see on the output.

However if the water running fast enough to become turbulent then chaos would rule. Change the input by less than an atom's width and the maths will throw out an entirely different result.

Your interpretation of the butterfly effect is not which i have heard. The version which I endorse tyakes the position that in huge, multifaceted systems, such a the earth's weather, the beating of a butterfly's wings, at the right time and place, in conjunction with the confluence of other events and forces, can set into motion a chain of effects which creates huge changes -- such as a violent storm.

Your version comes directly from Ray Bradbury's short story, "The Sound of Thunder."

What you've described is actually a correct understanding of the butterfly effect, as first described by MIT meteorologist Edward Lorenz.

Lorenz's actual finding was that tiny changes in an initial state (at the start of an experiment or weather record) can lead to enormous differences later, but that it's impossible to connect a particular initial change to a particular outcome change. The butterfly flapping its wings could cause a tornado or prevent one, and there is no way of knowing.

To put it another way, Lorenz's butterfly effect states that certain systems are simply not predictable, no matter how precise the initial measurements are.

Panicked for a moment!

Yes, there are many factors and dynamic forces affecting everything in the universe. Chaos theory involves a lot of these things. Why can't you balance a pencil on its point? This is the reason determinism fails at some point. There can be no absolute determinism. That is why when people assert that there can be no free will because of determinism they are wrong. At some point, probably at the quantum level chaos reigns.

Absolutely agree, the “butterfly effect” only applies to non-linear systems where even small changes can have a drastic effect on the subsequent evolution of a system. My favorite example of this is given by the multiple pendulum: just a slight change in the other the starting velocity or position can drastically effect the subsequent evolution of the system; however, for a single pendulum small changes in the initial conditions don’t result in behavior that is too different.

It is important to understand when such systems are being dealt with and when a system is simply linear. It’s also important to understand under what parameters a system will operate in a linear fashion. Good post.

I like the post.

I think at least sometimes, these expressions are meant metaphorically, and not literally. But I agree with what you're saying.