Nearby points may have radically different fates under iteration. That's all — fishfry

Sorry, didn't want to misrepresent your view. My question is simple...

What is the connection between ''nearby points'' and ''different fates''?

I see. So, you do agree that a blink of an eye can cause weather changes.

Yes, perspective changes everything. I once lived in a small world - everything looked so daunting and so big. I still feel that way but this ''speck of dust'' really shakes up my world. I feel smaller of course but there's so many bigger things to appreciate. Does that sound odd? — TheMadFool

No, it sounds wonderful. There are things greater than you and you are no longer trapped in your own egotism, that all your social environment taught you to believe is reality no longer influences your decisions and where you get to thoroughly experience reality as it is. Superstition reverses this prospect and it is attractive because you shut reason and submit to irrational and nonsensical fears that merely amplify the prospect of ignoring the responsibility you have to make choices for yourself. A raw and fearless life is stunning and the only way to happiness.

I see. So, you do agree that a blink of an eye can cause weather changes. — TheMadFool

The weather will change, and there is no way, lack of eye blink included, to prevent that. So no, I don't agree with that statement.

No, it sounds wonderful — TimeLine

Thanks.

The weather will change, and there is no way, lack of eye blink included, to prevent that. So no, I don't agree with that statement — noAxioms

I think I understand now. Small differences in initial states have vastly different outcomes. For example, the temperature may differ by 0.000007 degrees but this tiny difference can mean the difference between fair weather and storms. The butterfly is simply a metaphor for this small difference in a variable.

I think I understand now. Small differences in initial states have vastly different outcomes. For example, the temperature may differ by 0.000007 degrees but this tiny difference can mean the difference between fair weather and storms. The butterfly is simply a metaphor for this small difference in a variable. — TheMadFool

Much better. The difference has no lower limit of triviality. One atom doing a radioactive decay or not is such a difference. The butterfly is an example, not just a metaphor.

The butterfly is an example, not just a metaphor. — noAxioms

Now I'm confused. Let me restate my understanding. See if I got it right this time.

The butterfly flapping its tiny wings represents the small changes in weather variables. It doesn't mean that a butterfly can actually affect the weather.

The butterfly flapping its tiny wings represents the small changes in weather variables. — TheMadFool

In two worlds with the only difference being the butterfly flap or not, the weather in these two worlds after some months will bear no resemblance to each other (except for that storm in 430 days). One butterfly does not constitute a difference. Two do. 'Changes' is not part of it.
Any small difference amplifies, which is characteristic of a chaotic system.

It doesn't mean that a butterfly can actually affect the weather.

Unless the butterfly is outside the light cone of some event, or in Schrodinger's box (yes, these exist but not ones that hold a butterfly), the butterfly affects that event. But many dynamic systems are not chaotic. Some small meteor slated to hit Earth in 2 years is going to do that no matter what the butterfly or the weather is like. The Earth's rotational orientation will not be significantly different in a century.

One example they used a lot to develop chaos theory is that of a dripping faucet. The drips are completely predictable at low flow, but become unpredictable at a fixed pace, but then become predicable again at a slightly higher pace, but with more complex drip patterns with different size drops.

(Y)

I think I understand now. Small differences in initial states have vastly different outcomes. For example, the temperature may differ by 0.000007 degrees but this tiny difference can mean the difference between fair weather and storms. The butterfly is simply a metaphor for this small difference in a variable. — TheMadFool

Yes exactly.

Our intuition is that a tiny change in the input conditions will smooth out over time and make no difference to the future evolution of the system. But it turns out that our intuition is wrong. Even a tiny change in the initial conditions can lead to a hugely different outcome in the future.

The butterfly story is misleading in that respect. It makes people think that the flapping wings "cause" a storm. That is not true. What is true is that the universe in which the butterfly flaps its wings, and the universe in which the butterfly does not flap its wings, may be profoundly different after a number of iterations of deterministic rules.

Wearing your lucky T-shirt to a game does cause small changes in the air around you. These small changes get magnified down the causal chain and transforms into a favorable wind/rain that can help your team to win. — TheMadFool

Getting back to the butterfly effect in relation to superstition, I think Efram had it right from the beginning:

There may be a possibility that wearing a certain shirt will have some impact on the game (e.g. you wear blue, someone who knows one of the players sees it while they pass you in the hallway and it puts them in a good mood, they then go and more convincingly encourage the team) but you don't know for sure what impact it will have — Efram

A superstition relies on a certain event having a certain impact, like expecting to experience bad luck if a black cat crosses your path. While the cat may cause you to pause, which later makes the difference in whether or not you step onto the street and get struck by a vehicle, you don't know if the cat's interference will improve the outcome or make it worse.

you don't know if the cat's interference will improve the outcome or make it worse. — CasKev

Ok but that still leaves the door wide open for personal bias to creep in, shaping the uncertainty that you mention into well-formed beliefs.

@TheMadFool

Right, but believing something to be true doesn't make it true. Personal bias will affect belief, but it won't change the ultimate truth of the matter.