what do you mean by the butterfly effect ? Give an example of this in recent times.
Answers
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.[1]
The term, closely associated with the work of Edward Lorenz, is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.[2]
The idea that small causes may have large effects in general and in weather specifically was earlier recognized by French mathematician and engineer Henri Poincaré and American mathematician and philosopher Norbert Wiener. Edward Lorenz's work placed the concept of instability of the earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.[3]
The butterfly effect can also be demonstrated by very simple systems.
Contents
History
In The Vocation of Man (1800), Johann Gottlieb Fichte says "you could not remove a single grain of sand from its place without thereby ... changing something throughout all parts of the immeasurable whole".
Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.[4] He later proposed that such phenomena could be common, for example, in meteorology.[5]
In 1898, Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature. Pierre Duhem discussed the possible general significance of this in 1908.[4]
The idea that one butterfly could eventually have a far-reaching ripple effect on subsequent historic events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury about time travel.[6]
In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.[7]
Lorenz wrote:
"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution." (E. N. Lorenz, The Essence of Chaos, U. Washington Press, Seattle (1993), page 134)[8]
In 1963 Lorenz published a theoretical study of this effect in a highly cited, seminal paper called Deterministic Nonperiodic Flow[9][10] (the calculations were performed on a Royal McBee LGP-30 computer).[11][12] Elsewhere he stated:
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Answer:
The term butterfly effect is closely associated with the work of Edward Lorenz. It is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier.