Debunking the Butterfly Effect

[Severian]

Example?

 

A ball rolling into a stable minima is clearly not a chaotic system (since pretty much any starting condition will result in the same end position) but a ball rolling off an unstable maximum (in 3d) is a chaotic system since a small perturbation in initial conditions leads to a large change in the final state.

 

It is also clear that almost all very complicated real world situations have some potential to be chaotic to some extent. If some lunatic decides to assasinate George Bush, there may be a profound effect on world politics. A small change (one person's instability) leads to a big change.

[reverse]

Our weather man on TV is never correct.

It always rains on sports days when he says it will be fine.

 

This whole butterfly thing is obviously a conspiracy to shift the blame from bad weather reporting on to the poor little helpless butterflies.

[Red_Ninja]

Dr. Roger Pielke, head of the American Association of State Climatologists, debunks the Butterfly Effect:

 

Debunks the butterfly effect ? OK, debunked as a silly little phrase about butterflies causing tornadoes.

 

He certainly hasn't debunked sensitive dependence on initial conditions. If he had we'd know what weather to expect this Christmas.

 

The Lorenzian equations are telling because they are a deterministic, abstract simplification of a real system. And you still cannot tell what it's going to do, it will behave in an infinitely complex manner. The Lorenz attractor shows a system with three dimensions in phase space (or three variables) - how many dimensions does the real climate have ? The same number, in practical terms, as a small stream - infinite.

[starbug1]

A ball rolling into a stable minima is clearly not a chaotic system (since pretty much any starting condition will result in the same end position) but a ball rolling off an unstable maximum (in 3d) is a chaotic system since a small perturbation in initial conditions leads to a large change in the final state.

 

It is also clear that almost all very complicated real world situations have some potential to be chaotic to some extent. If some lunatic decides to assasinate George Bush' date=' there may be a profound effect on world politics. A small change (one person's instability) leads to a big change.[/quote']

 

My example was a fictitious real-life example. All systems are not chaotic, and while your "ball rolling into a stable minima" example shows this, you also stated "it is also clear that very complicated real world situations have potential to be chaotic to some extent."

 

While I may not have been exactly clear in my example about this, that is all I was getting across--the potential chaos of complicated, real world situations is present, even if in theory or if only to some extent of likelihood.

 

The example of an assination on the president has very real potential to have very real consequences. The potential, likewise, of small or insignificant events is much less, and for this reason they are always being cancelled out, so the whole "stepping on a butterfly in the prehistoric age will have insurmountable, diastrous affects on today" notion is more or less garbage.

 

I never meant to convey that everything was chaotic by nature.

 

EDIT: sorry for late reply

[SmallIsPower]

Histroical events are definately have the Butterfly Effect

 

Rosa Parks not standing up caused the Civil Rights Movement

The Assasination of the Archduke causes WW1

Martin Luthor's resentment of the Pope causes the Protestant Reformation

A conquerer chooses to battle a city where a defender just happens to be at the wrong place, changing the future of his empire, advancing or retarding a keyn technology

 

In fact, a quantuum glitch could start WW3!

[Chaotic1]

Why

[Chaotic1]

I'll try to be brief. Butterfly effect does *not* imply that a butterfly flapping its wings *will* cause/change-the-course-of a tornado. It only says that the system is sensitive to initial conditions and the sensitivity is such that even *really* small changes such as the flapping of a butterfly's wings will *affect* a tornado. Traditionally, one tends to beleive that the effect of a single butterfly is *negligible* and we are taught that such insignificant things as butterflies can be neglected. However, the discovery during Lorenz's time was that such Minor things cannot always be neglected because nonlinear systems are extremely sensitive to initial conditions. This fact can be fairly readily understood. The "Butterfly" is only a very crude metaphor for uncertainity of initial conditions. Since in real world, initial conditions are uncertain, and since systems (such as weather, stock market etc) are nonlinear, the outcome is bound to be impossible to predict with certainity. I do not see a reason why this should be difficult to digest. And I do not understand the eagerness to debunk the Butterfly effect. Please correct me if I am wrong anywhere...

[yrreg]

A small event like a drop of rain falling toward the ground in Washington D.C. will not lead eventually to a tsunami in Japan, because its force is dissipated in a split second time before it can (the force) travel later and farther and longer as to reach Japan.

 

However, it can and does cause an effect in a person's life lasting for his lifetime, for good or ill, if it leads to a freak accident in the person as to make him lose an eye, like this:

 

The drop of rain falls on the head of this person, let's call him Doe, and Doe feels it on his head and with one hand he reaches to his head to touch the wetness on top of his head to determine: whether it is rain or something else wet but unwelcome, like a drop of excrement or urine from a flying thing above, he gets distracted and does not see that he is stepping into a manhole with the cover removed and does step into it, and falls flat with his face on the pavement, and his left eye lands on a stone big and sharp enough to bust the eyeball: so he loses one eye -- for the rest of his lifetime.

 

That is someone losing an eyeball but it is not a tsunami in Japan later or elsewhere thousands of kilometers away.

 

 

 

Yrreg

[Joatmon]

 

Can you think of any small event or choice that you made that had a large knock on effect in your life.

.

 

I once met a girl 3 weeks before her 21st birthday. Money was short and I pondered whether to drop her immediately or use what money I had on a decent present. That was 53 years ago. If I had dropped her our two children, five grandchildren and six great grandchildren would never have been born.