Editing Chaos theory (section)

== A popular but inaccurate analogy for chaos ==
The sensitive dependence on initial conditions (i.e., butterfly effect) has been illustrated using the following folklore:<ref name=":8" />

<poem style="margin-left: 2em;">
For want of a nail, the shoe was lost.
For want of a shoe, the horse was lost.
For want of a horse, the rider was lost.
For want of a rider, the battle was lost.
For want of a battle, the kingdom was lost.
And all for the want of a horseshoe nail.
</poem>

Based on the above, many people mistakenly believe that the impact of a tiny initial perturbation monotonically increases with time and that any tiny perturbation can eventually produce a large impact on numerical integrations. However, in 2008, Lorenz stated that he did not feel that this verse described true chaos but that it better illustrated the simpler phenomenon of instability and that the verse implicitly suggests that subsequent small events will not reverse the outcome.<ref name=":9">{{Cite web |last=Lorenz |first=E. N. |date=December 2008 |title=The butterfly effect. In Premio Felice Pietro Chisesi E Caterina Tomassoni Award Lecture; University of Rome: Rome, Italy. |url=https://eapsweb.mit.edu/sites/default/files/Tomassoni_2008.pdf |archive-url=https://web.archive.org/web/20230610171122/https://eapsweb.mit.edu/sites/default/files/Tomassoni_2008.pdf |access-date=January 29, 2023 |website= |archive-date=June 10, 2023 |url-status=dead }}</ref> Based on the analysis, the verse only indicates divergence, not boundedness.<ref name=":7" /> Boundedness is important for the finite size of a butterfly pattern.<ref name=":7" /> The characteristic of the aforementioned verse was described as "finite-time sensitive dependence".<ref>{{Cite journal |last1=Saiki |first1=Yoshitaka |last2=Yorke |first2=James A. |date=2023-05-02 |title=Can the Flap of a Butterfly's Wings Shift a Tornado into Texas&mdash;Without Chaos? |journal=Atmosphere |language=en |volume=14 |issue=5 |pages=821 |doi=10.3390/atmos14050821 |bibcode=2023Atmos..14..821S |issn=2073-4433 |doi-access=free }}</ref>