Edward Lorenz (May 23, 1917 – April 16, 2008)
was the father of "chaos theory," also known as the "butterfly effect." He explained how something as small as the flutter of a butterfly's wings could lead to a big change elsewhere in the world, like a tornado. He died Wednesday at age 90.

American mathematician and meteorologist, and a pioneer of chaos theory.



Edward Norton Lorenz
Born May 23, 1917
West Hartford, Connecticut, United States
Died April 16, 2008 (aged 90)
Cambridge, Massachusetts, United States
Fields Mathematics and Meteorology
Institutions MIT
Alma mater Dartmouth College
Harvard University
Massachusetts Institute of Technology
Doctoral adviser James Murdoch Austin
Known for Chaos theory

Butterfly effect
Notable awards Kyoto Prize (1991)

The Butterfly Effect

Weather prediction is an extremely difficult problem. Meteorologists can predict the weather for short periods of time, a couple days at most, but beyond that predictions are generally poor.

Edward Lorenz was a mathematician and meteorologist at the Massachusetts Institute of Technology who loved the study of weather. With the advent of computers, Lorenz saw the chance to combine mathematics and meteorology. He set out to construct a mathematical model of the weather, namely a set of differential equations that represented changes in temperature, pressure, wind velocity, etc. In the end, Lorenz stripped the weather down to a crude model containing a set of 12 differential equations.

On a particular day in the winter of 1961, Lorenz wanted to re-examine a sequence of data coming from his model. Instead of restarting the entire run, he decided to save time and restart the run from somewhere in the middle. Using data printouts, he entered the conditions at some point near the middle of the previous run, and re-started the model calculation. What he found was very unusual and unexpected. The data from the second run should have exactly matched the data from the first run. While they matched at first, the runs eventually began to diverge dramatically — the second run losing all resemblance to the first within a few "model" months. A sample of the data from his two runs in shown below:
Lorenz's Sample Data


At first Lorenz thought that a vacuum tube had gone bad in his computer, a Royal McBee — an extremely slow and crude machine by today's standards. After discovering that there was no malfunction, Lorenz finally found the source of the problem. To save space, his printouts only showed three digits while the data in the computer's memory contained six digits. Lorenz had entered the rounded-off data from the printouts assuming that the difference was inconsequential. For example, even today temperature is not routinely measured within one part in a thousand.

This led Lorenz to realize that long-term weather forecasting was doomed. His simple model exhibits the phenomenon known as "sensitive dependence on initial conditions." This is sometimes referred to as the butterfly effect, e.e. a butterfly flapping its wings in South America can affect the weather in Central Park. The question then arises — why does a set of completely deterministic equations exhibit this behavior? After all, scientists are often taught that small initial perturbations lead to small changes in behavior. This was clearly not the case in Lorenz's model of the weather. The answer lies in the nature of the equations; they were nonlinear equations. While they are difficult to solve, nonlinear systems are central to chaos theory and often exhibit fantastically complex and chaotic behavior.

https://www.pha.jhu.edu/~ldb/seminar/butterfly.html
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n many cases, minor and seemingly inconsequential actions in the past are extrapolated over time and can have radical effects on the present time of the main characters. In the movie The Butterfly Effect, Evan Treborn (Ashton Kutcher), when reading from his adolescent journals, is able to essentially "redo" parts of his past. As he continues to do this, he realizes that even though his intentions are good, the actions he takes always have unintended consequences.

Theories abound as to real-life examples of this phenomenon:

1. The weather: small changes in weather effect larger patterns.
2. The stock market: slight fluctuations in one market can effect many others.
3. Biology: A small change in a virus in monkeys in Africa creates a "thunderstorm" of an effect on the human population around the world with the appearance of the AIDs virus.
4. Evolution: small changes in the chemistry of the early Earth gives rise to life.
5. Psychology: Thought patterns and consciousness altered by small changes in brain chemistry or small changes in physical environmental stimuli.

The butterfly effect occurs under two conditions:
1. The system is nonlinear.
2. Each state of the system is determined by the previous state. In other words, the output at each moment is repeatedly entered back into the system for another cycle through the mathematical functions that determine the system.

The result of the butterfly effect is unpredictability. Small differences in initial input can have dramatically different results after several cycles through the system. In the fractals pictured above, points that are very close together can be different colors. The results can tend toward infinity at different rates or toward zero, even though the initial points are very close together.
The Metaphysical perspective..
https://www.crystalinks.com/chaos.html