Finding an article on a scientific development is a consequence of our move – the discoveries just keep on coming! Today’s discovery is an article from a 1987 issue of Science, Vol. 238. Title: Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics.
Hat tip for this picture goes to: http://complex.upf.es/~josep/Chaos.html
Wait! Come back. That’s the most difficult part of this post – the rest is easy and enlightening. The article is a review of the field of “chaotic dynamics of dissipative systems.” Think of clouds. The little water drops in clouds are chaotic, not organized systems, and they dissipate or disappear with the wind. Whatever shapes we may imagine in clouds come from our own tendency to see patterns in everything we look at.
Anyway, chaotic dynamics had already been studied for many decades, according to authors Celso Grebogi, Edward Ott and James A. Yorke, but the field was “undergoing explosive growth” at the time they decided to write the article.
And we care because… ? Because scientists were beginning to apply the thinking about these ideas to their own fields in “ecology, economics, physics, chemistry, engineering, fluid mechanics.”
Specific examples the authors cited included simple models for the yearly variation of insect populations, stirred chemical reactor systems, “and the determination of limits on the length of reliable weather forecasting.” Aaah, hah.
We won’t go into the math, because it is waaayyy over our heads, but the reasoning appears to be sound, plus the article was clipped and saved by our genius DDH. After several pages of mysterious equations and cool diagrams, we arrived at the conclusion:
“According to Laplace, determination of the future depends only on the present state. Chaos adds a basic new aspect to this rule: small errors in our knowledge can grow exponentially with time, thus making the long-term prediction of the future impossible.”