Butterfly Effect...

Autolite

Graduate Poster
Autolite
Joined
Jul 26, 2007
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I had just recently watched the movie "The Butterfly Effect" again for the first time in a couple of years. I then Googled-up the Wikipedia explanation of the 'Chaos Theory' but I admittedly have a somewhat less than a tenacious grasp of the subject matter.

So I would like to ask those of you who are more familiar with such ideas. Is this 'Chaos Theory' a valid and widely accepted concept? Or is it woo? What are your thoughts...

(Or we could just have another 'gun control' thread. Your call...)
 
Autolite said:
I had just recently watched the movie "The Butterfly Effect" again for the first time in a couple of years. I then Googled-up the Wikipedia explanation of the 'Chaos Theory' but I admittedly have a somewhat less than a tenacious grasp of the subject matter.

So I would like to ask those of you who are more familiar with such ideas. Is this 'Chaos Theory' a valid and widely accepted concept? Or is it woo? What are your thoughts...

(Or we could just have another 'gun control' thread. Your call...)
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There are many interpretations/iterations of it but from the engineering sciences side.

The theory itself in the most "literal" interpretation is generally accepted as true as long as the essence is strictly adhered to.

For example, the butterfly and the wings.

It is completely possible that when the tornado is in its barest state of forming- a "minute" shift in a building block could alter it in many ways.


In layman's English- the theory would be better stated as:

In the beginning of anything- a random ( or deliberate) influx of external force(s) at "the" specific point necessary can ( and probably will) have an affect and effect on the prior programmed outcome had there been no such influx.

The theory is sound but the "woo" comes in, not from the theory, but its improper application and usage in popular pseudoscience by those who willing or unknowingly misapply it.
 
LONGTABBER PE said:
In the beginning of anything- a random ( or deliberate) influx of external force(s) at "the" specific point necessary can ( and probably will) have an affect and effect on the prior programmed outcome had there been no such influx.

The theory is sound but the "woo" comes in, not from the theory, but its improper application and usage in popular pseudoscience by those who willing or unknowingly misapply it.
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Many thanks LONGTABBER PE. That gives me a better understanding.

Here's the Wiki link for anyone who might be interested...

http://en.wikipedia.org/wiki/Chaos_theory
 
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Autolite said:
Many thanks LONGTABBER PE. That gives me a better understanding.

Here's the Wiki link for anyone who might be interested...

http://en.wikipedia.org/wiki/Chaos_theory
Click to expand...

Let me give you an example of the application of the theory I used 3 yrs ago on a mining conveyor root cause analysis.

There was a conveyor another compant spec.d a flywheel out to carry the load 3 full revolutions by using the inertia of the wheel as a automatic controlled braking device.

It was mathmatically sound and worked on paper and in application.

The variable was the load of rock on the belt and the harmonics transmitted to the bearings damaged them.

Conventional wisdom beefed up the bearings then the entire structure fell over.

Had the original designers employed the chaos theory on every reasonable variable and extrapolated to its end effect- they would have seen that the weakest link in the process was the welds on the structural steel and as part of the installation also reinforced the joints as well as added expansion joints to nullify the effect.
 
LONGTABBER PE said:
Had the original designers employed the chaos theory on every reasonable variable and extrapolated to its end effect- they would have seen that the weakest link in the process was the welds on the structural steel and as part of the installation also reinforced the joints as well as added expansion joints to nullify the effect.
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Sure, this I can understand. I was having difficulty finding where the line was drawn between basic 'cause and effect' and the 'butterfly wings influencing a tornado' thing. Can I assume that the butterfly analogy is just a gross exaggeration to illustrate the Chaos Theory itself?

Your explanation works for me...

However, between posts I am working in my shop fabricating these little custom metal attaching 'thingies' to be used to secure a tent structure to the ground. I read your post about the conveyor incident and went back and doubled up my welds.

Coincidence? I dunno. Perhaps there's more of a 'woo' angle in this 'Chaos Theory' than we care to consider... :)
 
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Autolite said:
Sure, this I can understand. I was having difficulty finding where the line was drawn between basic 'cause and effect' and the 'butterfly wings influencing a tornado' thing. Can I assume that the butterfly analogy is just a gross exaggeration to illustrate the Chaos Theory itself?
Your explanation works for me...

However, between posts I am working in my shop fabricating these little custom metal attaching 'thingies' to be used to secure a tent structure to the ground. I read your post about the conveyor incident and went back and doubled up my welds.

Coincidence? I dunno. Perhaps there's more of a 'woo' angle in this 'Chaos Theory' than we care to consider... :)
Click to expand...

I cannot speak for the math and other disciplines ( out of my area) but thats essentially it.

Its representative of the most "gross' example possible of a minor thing having a major effect downrange which should at least make an Engineer think of at least 3-5 levels of affect/effect of every computation.

True, the potential and possibilities are infinite and nobody could forsee them all but its a real world lesson to look a few steps beyond whats in front of your face.

There is no "line" per se but the general understanding is to consider the small details.

When one does a lot of RCFA's and failure analysis- you come to realize that overt and obvious initial failures ( the infant mortality part of the bathtub curve) happen but they are rare- its the 2nd and 3rd echelon failures that occur elsewhere that often get overlooked in relation to the root cause.

2 examples that come to mind from way back

Warped brake rotors are normally blamed on the caliper/pad/road conditions but studies show the most likely cause was improper torque when you buy tires- but it doesnt show up because its so slow but the butterfly flapped its wings when the tire jockey didnt use a torque stick.

Tire failure in the form of a separation blowout- Michilen tests showed that the most common type of that specific failure had to do with failing to use a "patch plug" instead of the normal cold patch allowing moisture/road salts to get in the steel belts thus corroding them and making them fail.

The butterfly flapped its wings on the remaining hole and not on the obvious air holding patch on the inside.

In both cases, the normal progressive life of the part was affected by some obscure and unrelated influence that nobody noticed or even thought about.
 
Consider this as one point of chaotic injection: Inside a female's body, just outside the ovary, an egg has emerged, and is surrounded by hundreds of thousands of sperm. Only one shall win; the rest of egg's many brothers- and sisters-potential will not be realized and are of no consequence. But which one? At this cusp, the slightest shift, scratch, touch or squirm by the mother will totally rethrow the dice. A butterfly exciting the hairs on her arm and causing her to scratch where she would not have otherwise results in a similar sibling being born than one who might have been, but by far, not the same person, and thus Alison Einstein is born rather than Albert. Something as gross as causing her to be in a different place last night speaks for itself.
 
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shadron said:
Consider this as one point of chaotic injection: Inside a female's body, just outside the ovary, an egg has emerged, and is surrounded by hundreds of thousands of sperm. Only one shall win; the rest of egg's many brothers- and sisters-potential will not be realized and are of no consequence. But which one? At this cusp, the slightest shift, scratch, touch or squirm by the mother will totally rethrow the dice. A butterfly exciting the hairs on her arm and causing her to scratch where she would not have otherwise results in a similar sibling being born than one who might have been, but by far, not the same person, and thus Alison Einstein is born rather than Albert. Something as gross as causing her to be in a different place last night speaks for itself.
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Interesting! Perhaps that could be a screen play for "ButterFly Effect II"... ;)
 
Autolite said:
Interesting! Perhaps that could be a screen play for "ButterFly Effect II"... ;)
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Titles aside, the movie I thought best illustrated the Butterfly Effect was "Run Lola Run". Very much worth renting.

Linda
 
I read the James Gleick book a few months back. What stuck in my mind was his description of a computer model for something (I forget what--weather or populations or some such).

Note: this is from my very crappy memory, so I've probably got a lot of the particulars wrong.

It was in the bad old days of limited computer memory, so data was dumped to cards or paper printouts which had to be fed back in. During one of these runs, the computer crashed or otherwise failed. Rather than re-run the whole thing, the guy just re-entered the last known conditions and started it from there. Surprisingly, this run quickly diverged from previous runs with the same starting conditions.

What happened was that when he re-entered the mid-point "starting" conditions, he used the values from a printout which were actually rounded off values. I disremember the details, but he found that rounding off a number that was already carried out to 4 decimal places became highly significant. This is the butterfly effect. A very small change in conditions quickly results in vastly divergent conditions.

ETA: I don't know that I would call the "butterfly" analogy an exaggeration as much as a poetic illustration of the principle. It seems that very tiny differences in conditions at one point in time will result in widely different conditions before too long. Previously the thought was that these tiny differences, the flapping of a butterfly's wings, would dampen out and be insignificant.
 
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fls said:
Titles aside, the movie I thought best illustrated the Butterfly Effect was "Run Lola Run". Very much worth renting.

Linda
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That looks interesting too! The IMDB gives it a good rating.

http://www.imdb.com/title/tt0130827/

It brings to mind an old Mickey Rooney movie called "Quicksand" where a series of seemingly minor acts on the part of the lead character lead to an array of increasingly disastrous consequences. Every time Rooney's character tries to 'undo' each mistake, his problems are compounded with even more calamitous results.

Sort of a "Butterfly Effect - The Prequel"...

http://www.imdb.com/title/tt0042869/
 
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Run Lola Run is a great movie indeed.

One idea of the butterfly effect and of chaotic systems in general, as has been explained to some degree already, is that any change in the starting conditions of a chaotic system will lead, eventually, to completely different conditions. Chaotic systems can be quite simple, one seemingly predictable system is a double pendulum. (Check out the animated gif on the right had side of the page to view the chaotic behavior.)

Another big idea is that aside from a sensitivity to initial values of the variables in the system, chaotic systems are not periodic. If I change the length of a simple pendulum by a small amount, for example, the period of that pendulum changes and the particulars of the pendulum's behavior will be completely different from that of the original. However, both pendulums will have very similar, highly predictable and periodic behaviors that are closely related. In a double pendulum, this is not the case. If I put a graph of the positions of the two pendulums next to each other, the connection between them would not be apparent. There are other ways of analyzing a system like this to try to find connections, but they would not necessarily exist at all.

The butterfly effect is definitely chosen for its "poetic illustration" but it does appear to be real. The problem is that there is no way to predict the way in which a particular flap will actually affect the rest of the system. Heck, if I choose to repave my driveway with asphalt as opposed to using limestone gravel, or if I fart now or hold it for a minute, it will eventually change Earth's weather.

A simple mathematical example is
xn+1 = r (xn - xn2)
For 0 < x < 1 and 0 < r < 4 this system is a good example of chaotic behavior. If you play with the values, for small r the values are periodic, but as r approaches a particular value, the system appears to oscillate more and more rapidly, until eventually it becomes apparently random. I made a simple excel spreadsheet with a graph to demonstrate this system.

View attachment simple chaotic system.zip
 
JoeTheJuggler said:
I read the James Gleick book a few months back. What stuck in my mind was his description of a computer model for something (I forget what--weather or populations or some such).

Note: this is from my very crappy memory, so I've probably got a lot of the particulars wrong.

It was in the bad old days of limited computer memory, so data was dumped to cards or paper printouts which had to be fed back in. During one of these runs, the computer crashed or otherwise failed. Rather than re-run the whole thing, the guy just re-entered the last known conditions and started it from there. Surprisingly, this run quickly diverged from previous runs with the same starting conditions.

What happened was that when he re-entered the mid-point "starting" conditions, he used the values from a printout which were actually rounded off values. I disremember the details, but he found that rounding off a number that was already carried out to 4 decimal places became highly significant. This is the butterfly effect. A very small change in conditions quickly results in vastly divergent conditions.

ETA: I don't know that I would call the "butterfly" analogy an exaggeration as much as a poetic illustration of the principle. It seems that very tiny differences in conditions at one point in time will result in widely different conditions before too long. Previously the thought was that these tiny differences, the flapping of a butterfly's wings, would dampen out and be insignificant.
Click to expand...



I read about something similar in a book called Storm Warning: the Story of a Killer Tornado by Nancy Mathis. It's about the May 3rd, 1999 tornados in Oklahoma and a researcher in the book does what you described. Great book, it also gives background on the F-scale.
 
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.​
 
The Greater Fool said:
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.​
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And the loss of the kingdom resulted in world wide nuclear arms proliferation! That 'Butterfly Effect' can get real nasty if you don't get a handle on it... :D
 
This reminds me of a story I think read a long time ago. Something about someone going back in time, and all they did while there was kill a spider. When they came back to the present, some of the letters in our alphabet had been switched (like Ks were now Ls, or something). And I believe it involved Robert the Bruce somehow...anyone know what I'm talking about?
 
ugot2bekidding said:
This reminds me of a story I think read a long time ago. Something about someone going back in time, and all they did while there was kill a spider. When they came back to the present, some of the letters in our alphabet had been switched (like Ks were now Ls, or something). And I believe it involved Robert the Bruce somehow...anyone know what I'm talking about?
Click to expand...

"The Sound of Thunder" by Ray Bradbury perhaps?

http://www.lasalle.edu/~didio/courses/hon462/hon462_assets/sound_of_thunder.htm

It was, appropriately, a butterfly rather than a spider.
 
IIRC, chaos is one of the reasons weather forecasting can be so wrong on occasion - OK, it's not particularly accurate at the best of times because it's very complex phenomenon, but often it enters a chaotic state where it becomes completely unpredictable even over relatively short timescales. No matter how good the instrumentation and the modelling, there's really no way to improve forecasts when the weather is in this state - but, of course, the meterologists still have to provide the forecasts (I bet their ears burn when they realise they're basically just giving out pure guesswork).
 
On a perfectly balanced see-saw, the addition of one snow flake on one side or the other will cause a decidedly different effect.
 
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