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Elvis Chidera

Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas? — Summary

summary, paper, chaos1 min read

Today's summary is about an article written in 1972 by Edward N Lorenz.


  1. In 2008, the last year of Lorenz's life, he said this when asked whether a butterfly can really cause a tornado. “Even today I am unsure of the proper answer”. The question is valuable because it begs the bigger question that nature is highly sensitive to infinitesimal changes. — Fermat’s Library

  2. If the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.

  3. The author is proposing that over the years minuscule disturbances neither increase nor decrease the frequency of occurrences of various weather events such as tornados; the most they may do is to modify the sequences in which they occur.
  4. The atmosphere is not a controlled experiment; if we disturb it and then observe what happens, we shall never know what would have happened if we did not disturb it.
  5. Although it hasn’t been proven that the atmosphere is unstable, the evidence that it is is overwhelming.
  6. Current equations compatible with present computer capabilities are just our best attempts to approximate the equations actually governing the atmosphere.
  7. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.
  8. This can happen even though these systems are deterministic:

    Chaos: When the present determines the future, but the approximate present does not approximately determine the future. — Lorenz

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