The theory is about the effect of initial conditions and slight changes in initial conditions that lead to greater impact in a large worldly scenario. In a layman's language, even the flapping of butterfly wings in a remote forest could have an effect on larger things such as a tornado.
The Men Behind:
- Edward Lorenz - mathematician and meteorologist
- Henri Poincare - mathematician and engineer
- Norbert Wiener - mathematician and philosopher
Pre-requisite to Understand:
NA
The Story of Origin:
In the year 1961, Lorenz was running a numerical computer model for weather prediction. He was using the computer LGP-30 for this purpose.
Fun Fact:
LGP-30 computer was priced at 47000 $ (back in 1956)
In today's equivalent- ₹ 3.5 crores
Weight of the machine- 360 kgs
Weather prediction usually depends on the initial conditions are given as input which the computer models run considering different parameters to predict the most probable weather outcome for the upcoming week. It is the same as predicting how long a car would run by taking input as fuel level and road conditions.
Lorenz ran the computer model from somewhere in the middle as a shortcut to avoid re-run from the beginning as it used to take the computer a few hours to compute given the large meteorological data for weather prediction.
He faced the same issue that we usually face while solving JEE numerical. If we use 0.1 instead of 0.11 somewhere in the middle of the calculation, as we go on multiplying with larger numbers the result would be way different from what would have been when the actual value 0.11 is used.
For example:
0.1*1000 = 100
0.11*1000 = 110
here the difference from the actual expected output (110) is 110-100 = 10
But the problem arises when we go on multiplying larger numbers
0.1*10000000 = 10 lakh
0.11*10000000 = 11 lakh
the same values multiplied by a larger number have given a difference of 100000.
This is where Lorenz made mistake while taking a shortcut and running the model from the middle which contained 12 equations and 12 variables in total.
In our terms, he hardcoded input as 0.506 instead of the actual value of 0.506127. This was not a deliberate approach. As we could see the computer screen had no display screen, a printer was used to print the output. The printer was capable of taking up to 3 decimal places whereas the computer used 6 decimals. Edward took the printer output and considered it as an input for his re-run of the computer model.
He went for a cup of coffee and came back after a couple of hours to see that the results of the prediction is nowhere near to that of the previous run. He then checked the computer hardware if it's in good condition and re-ran the model multiple times to get different outcomes each time.
You might be surprised why is this observation so fascinating. We also know that a slight change in the initial condition could make a huge difference in the final outcome. If we hold the gun with infinite ire range and just change the barrel angle by 1 degree, it would fire the bullet to a location 1000s of km away from the actual target.
Lorenz observed the variations carefully noted every tiny aspect, the fluctuations, and the initial conditions. After 2 years, in 1963 he decided to publish this study in the paper called Deterministic Nonperiodic Flow.
The butterfly effect got its name from the references made by various researchers as an apt metaphor as they could not find a more suitable and understandable phrase for the work.
Why is it called Butterfly Effect?
Lorenz's studies showed that when two similar activities are under experiment and started at the same time with a slight difference in the input values, showed a larger difference as the graph progressed.
However, the basic curvature of the mapping remained the same and resembled a butterfly structure.
Lorenz Attractor - curve (resembles a butterfly)
There have been 61 Hollywood movies so far having 'Butterfly effect' in their movie title.
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