So to expand on what Mijin is writing about Chaos Theory, it is impossible to have completely accurate measurements in many systems that are being modeled. Some times that leads to problems sometimes it doesn’t.
If we have a model that relatively accurately reflects reality and that model is something like an ellipse, or a line, or a circle, or a parabola then an error in measurement will have a known error in results. With a linear equation it will be proportional to the error. So that error in result while not optimal still results in a model that behaves intuitively with regards to differences in initial conditions.
Instead of x being 1 x is 1.01 and the error over time is known. Furthermore the bounds of outcome are also intuitive. If precision of measurement is x then the result will have an error but will lie in a known and constrained and intuitively understandable range.
Now plot a system of non-linear differential equations. The system might have general properties that can be studied but the outcome can be wildly divergent with tiny changes in initial parameters. So in the real world a system that is modeled with non-linear differential equations such as the weather, anything could actually be the difference between the tornado or the non-tornado if one went far enough back in time.
In other words the butterfly flapping its wings is a metaphor for a change in initial conditions in a complex model. Whether or not a real butterfly flapping its wings or not causes a tornado is completely incalculable and unknowable. We have no control universe to compare to.
And reality is pretty chaotic. Look at any form of turbulent flow.
Again, you’re talking about our ordinary – pre chaos theory – understanding of how events work. That small events can only cause large changes if there’s some set of improbable events connecting the two. This is not what chaos theory is saying at all.
The misconception exists because of the butterfly metaphor. I suggest you look at the research that inspired the metaphor to better understand the phenomenon.
Basically Lorenz was running a weather simulation and found by chance that if he re-ran the simulation, but with miniscule rounding errors in input values, the simulation would eventually result in totally different weather predictions.
…Not immediately; at first everything would look the same, but gradually some error would creep in and then suddenly the system would make completely different predictions, with no mathematical relationship to the original predictions at all.
And it doesn’t matter how small the error is, or what kind of error it is. There is no “load-bearing butterfly”. Any change will give a different result set (although the time before the result set diverges may be very, very long).
This was a shocking finding and a meteorologist compared this to the flap of a seagull’s wings causing the weather to change forever. Here the seagull represents an infinitesimal difference in the input conditions, and the weather changing forever is the system at some future time where it has diverged from the same system which did not have the seagull.
This later became the butterfly “causing” a tornado. It’s a great metaphor but it’s very misleading because as I say, while it’s true without that butterfly the tornado doesn’t happen, it’s probably true of countless millions of other entities.
It sure looks as if that would certainly be the case, right? Doesn’t every agree on that? But is that alone enough to definitively say that we are “SURE” and constitute as “PROOF”?
If it does then aren’t there OTHER things that we could use this new “Bar of Proof” to label as absolutely certain. Sure would come in handy in some court trials where you don’t have the ability to do anything other than say “THIS is the only way we know of that X could have happened. No… I don’t have a shred of evidence, but we know these people didn’t do it… You have no motive and we don’t know how you would have done it, but because we know they didn’t then it HAD to be you”.
A classic invocation of the butterfly effect occurred in “Isaac’s Storm” by Erik Larsen, when he described the tropical wave that eventually generated the great Galveston hurricane of 1900.
“The seas were busy. A few ships must have encountered the thunder and rain but apparently their crews did not see it as anything unusual. They hung canvas to catch the rain. Steamers raised sails to save coal. Frigate birds wheeled in the canteloupe dawn.
Galveston spun through space at nine hundred miles an hour. The trade winds blew. Great masses of air shifted without a sound.
Somewhere, a butterfly opened its wings.”
I realize this is a zombie, so Cal may not see this.
I think Bradbury’s point was that an extremely small change (one butterfly dead at the wrong time and not doing whatever it would have done (pollinate, provide a meal for some predator, etc)) still had a (fairly small but significant) change to the future.
So, kind of summer breeze in Casablanca instead of a tornado in Kansas.
Although, extending it to future (since the changes keep piling up in unpredictable ways), maybe the Hitler guy leads the world into a nuclear war. That presumably would be non-trivial.
