Abstarct:
"You keep using that word. I do not think it means what you think it means. "
Inigo Montoya
"The butterfly effect" is called that, not because of some cockamamie story about a butterfly farting somewhere to create the next hurricane Catrina..
I was looking at a friend's FB wall today when I realized they made a reference to the so called "butterfly effect", I want to set some things straight regarding that effect.
Usually when people use the term "butterfly effect" they use it without actual knowledge about what it really stands for, and where and when it was coined.
So, a little history lesson is probably called for here:
Of strange attractors, and non linear effects:
Some of you may have at some point or the other, had a chance to have a fatal brush with physics studies, be it in high-school, university or college or you simply had a pesky friend who was into that kind of kinky stuff and insisted on explaining, oh I don't know, general relativity to you while insisting you most certainly possess the means to understand and assimilate everything he "taught" you right there and then. well that's me.
Warning: physics rant here:
<Physics rant>
Well it just so happens, that MOST physics areas we encounter, even as PHD students or actual researchers, are areas of LINEAR PHYSICS. for instance quantum physics is strongly embedded within the framework of linear algebra, with operators that are linear by definition, another field which is strongly linear is electrodynamics, which for the most part (but not always) relies heavily on linear algebra tools ,methods and operators to provide refutable results.
</Physics rant>.
The world isn't linear, or in the words of my namesake, "it ain't necessarily so".
Looking for the linear approximation of some dynamic, is not entirely different than looking for the proverbial coin under the street-light.
It so happened that in a cold day in the late 1950s an egghead, or otherwise called a scientist, sat in his lab, punched numbers in his then top-of-the-line computer, and got meters upon meters of output sheets, containing numbers that would represent a meteorological system.
By a fluke, the researcher went out for coffee, while the computer heaved and clicked and buzzed and chirped and spewed out sheets of numbers.
When he came back, the computer was silent. no more chirping, just plain cold data. but the experiment was not over!!! since in those days the internal memory of a computer was very limited it became necessary to punch in the last output you got,and so proceed with the number spewing.
But alas, the variables were saved in the computer to a precision of six decimal places, yet the output was given in only 3! So by default the researcher rounded off the last output and introduced it into the computer.
What he got was very strange, he projected a certain result but got a result differing greatly from expectation.
So like every respectable researcher he had tried to reproduce the experiment... getting results that differ greatly from both expected values, AND previous results!!!
See, if it were me in my first year at the academy I would have just drawn the damn graph I knew was expected, shrugged my shoulders, and go to sleep.
But not our epic protagonist! He set out to delve deeper into what had happened and stumbled upon a great discovery!!!
The protagonist was called Edward (Norton) Lorentz and he found out, that in some systems, an infinitesimal change in starting conditions, translate very quickly into a gross divergence in results.
To illustrate here is a picture of a Strange attractor:
Usually when people use the term "butterfly effect" they use it without actual knowledge about what it really stands for, and where and when it was coined.
So, a little history lesson is probably called for here:
Of strange attractors, and non linear effects:
Some of you may have at some point or the other, had a chance to have a fatal brush with physics studies, be it in high-school, university or college or you simply had a pesky friend who was into that kind of kinky stuff and insisted on explaining, oh I don't know, general relativity to you while insisting you most certainly possess the means to understand and assimilate everything he "taught" you right there and then. well that's me.
Warning: physics rant here:
<Physics rant>
Well it just so happens, that MOST physics areas we encounter, even as PHD students or actual researchers, are areas of LINEAR PHYSICS. for instance quantum physics is strongly embedded within the framework of linear algebra, with operators that are linear by definition, another field which is strongly linear is electrodynamics, which for the most part (but not always) relies heavily on linear algebra tools ,methods and operators to provide refutable results.
</Physics rant>.
The world isn't linear, or in the words of my namesake, "it ain't necessarily so".
Looking for the linear approximation of some dynamic, is not entirely different than looking for the proverbial coin under the street-light.
It so happened that in a cold day in the late 1950s an egghead, or otherwise called a scientist, sat in his lab, punched numbers in his then top-of-the-line computer, and got meters upon meters of output sheets, containing numbers that would represent a meteorological system.
By a fluke, the researcher went out for coffee, while the computer heaved and clicked and buzzed and chirped and spewed out sheets of numbers.
When he came back, the computer was silent. no more chirping, just plain cold data. but the experiment was not over!!! since in those days the internal memory of a computer was very limited it became necessary to punch in the last output you got,and so proceed with the number spewing.
But alas, the variables were saved in the computer to a precision of six decimal places, yet the output was given in only 3! So by default the researcher rounded off the last output and introduced it into the computer.
What he got was very strange, he projected a certain result but got a result differing greatly from expectation.
So like every respectable researcher he had tried to reproduce the experiment... getting results that differ greatly from both expected values, AND previous results!!!
See, if it were me in my first year at the academy I would have just drawn the damn graph I knew was expected, shrugged my shoulders, and go to sleep.
But not our epic protagonist! He set out to delve deeper into what had happened and stumbled upon a great discovery!!!
The protagonist was called Edward (Norton) Lorentz and he found out, that in some systems, an infinitesimal change in starting conditions, translate very quickly into a gross divergence in results.
 |
| Not the same Edward Norton |
To illustrate here is a picture of a Strange attractor:
|
|
Just to explain what's going on here, I'll disregard the right hand picture as the freak of nature that it is, and concentrate on the left hand picture.
This is a graph generated by this applet *, the applet simulates a Lorentz' system which is a meteorological model.
If you want to actually see it in action, just click anywhere on the white field, twice at the same place.
You will have generated 2 plots, or more if you have Parkinson's disease, that started at the exact same spot - or did they?
Actually no they didn't. see the computer saves the mouse pointer in a "float variable", thus it saves it to a degree of precision that we can't see, and I'm pretty sure the applet rounds off a couple of places after the decimal - thus recreating Lorentz' experiment actually...
So if you wait a while, you will see a divergence in paths taken by the two differently colored plots.
This graph is called "Lorentz' Butterfly" and THIS is why they call the effect "the butterfly effect", not because of some cockamamie story about a butterfly farting somewhere to create the next hurricane Catrina...
So this concludes the short history lesson, and here I go into proving the world is evil.
Well, no it's not, but I do have to make an attempt to show it is...
OK, so a lot of people use the so called "butterfly effect" to justify a line of reasoning that says something like this:
If you do something good now, for a certain person, it will generate more good deeds like the ripples on a pond, and like the butterfly effect, this will cause a major force for good in the world... or something like that.
Now let me be absolutely clear about this:
I DO subscribe to the notion of doing at least one random act of loving kindness a day, I think it's good for you, and if only I would remember this every day I would probably be a better human being right now.
BUT! (and it's a big butt) this line of reasoning sucks.
it's flawed in so many ways I can't even start counting all of them so I will just give up and point the one I was aiming at.
First off the butterfly effect is all about a small change in starting condition having a huge effect later on, what is described in the above dynamic is called a "chain-reaction".
A chain reaction is in essence a LINEAR dynamic, it has absolutely NOTHING to do with the butterfly effect (as far as I know).
Secondly and more importantly is this:
Invoking the butterfly effect assumes a non-linear system.
Assuming that if we do something good things get better in the world assumes strong linearity of the system.
These two assumptions are mutually exclusive and while the former is actually well documented, experimented and reproduced, the latter is a figment of our wishful thinking (that may be true in a convoluted way as far as I know, but is neither proven nor reproduced).
In general MOST dynamics in the world are non-linear, and we physicists make assumptions, and approximations to linear or at most quadratic cases in order to get prevailing approximate results we can later compare with experimental results.
For the most part I think most of us would agree that human behavior is non-linear as well thus, I tend to lean towards the first assumption rather than the second.
And if we take in account Murphy's law we instantly come to the grim realization that it is much more probable that if you do a good deed, something will go terribly wrong.
or differently put:
"No good deed goes unpunished" in-deed (see what I did there?).
But also, at the same time no bad deed goes unpunished, as almost EVERY change in starting conditions results in a huge divergence in results thus I propose that:
"No deed goes unpunished" - and so we are all constantly punished... whether we do something or not - thus the world is an evil place.
QED.
But to end this on a lighter note, two things.
the first: if we all do random acts of loving kindness every day, the whole graph jumps up on the scale of good vs. evil, and so the whole dynamic is shifted up by a constant, it might be just the constant that may save us as a species.
so don't stop doing good things!!!
the second is this...
If I learned anything in my 30 odd years of life experience it is that when it comes to physics I am usually wrong the first time around and I always need further study.
oh and something else - you can argue with your wife, but ultimately, she's right and you know it.
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| And I mean this in the best possible way.... *GULP* |
again, this was longer than expected... bummer.
I also almost died -again- yesterday, maybe I will tell you all about it in a future post...
* with permission. Copyright 1996, James P. Crutchfield. All rights reserved.
