When I was growing up, they would blame hurricanes on butterflies. One lonely butterfly would fly in circles and from that, the wind would get stronger and stronger and turn into a hurricane. Had that butterfly not flapped it wings at exactly the right time, the hurricane would not have happened. This "butterfly effect" is discussed seriously in chaos theory circles.
Yup. Those butterflies still cause a lot of problems.
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. [2]
Fascinating:
The term itself was coined by Edward Lorenz for the effect which had been known long before, and is derived from the metaphorical example of the details of a tornado (exact time of formation, 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. [3]
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:
One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.[12]
Following suggestions from colleagues, in later speeches and papers Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? as a title.[13] Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.[14] https://en.wikipedia.org/wiki/Butterfly_effect
Reminds me of a quote by Francis Thompson. While there is dispute over how much an effect is produced by small changes, including the most basic beginnings of a hurricane and all that directs it, the reality is that all is interrelated. Weather forecasters have come a long way, but they would have to be omniscient and omnipotent to know and make it all work to achieve a certain end, which is not their job anyway.