CaF Introduction
Tuesday, February 5th, 2008
I’m going to divide the introduction into sections. The titles are mine, rather than the authors’, unless stated otherwise.
Warmup
- Comparison of predictable tides to unpredictable weather (forecasts good for much shorter intervals).
- Chaos is deterministic (future completely determined by past) - but small uncertainties can snowball.
- Mention of
methodologies which have been designed for a precise scientific evaluation of the presence of chaotic behavior in mathematical models as well as in real phenomena
and says that they can be used to estimate the “predictability horizon” of a system - mathematical/physical/time limit within which predictability is ideally possible. - Predictability horizon for weather is not more than 2-3 weeks.
History of chaos theory
- Calculus developed by Newton and Leibniz.
- Laplace’s demon
- Uncertainty principle
- Lewis Fry Richardson’s book Weather Prediction by Numerical Process
- John von Neumann began building ENIAC (1st electronic computer) to try to put Richardson’s ideas about weather prediction into practice.
- It was found (by whom?) that Richardson hadn’t succeeded because the
space and time increments used in his work had not met a computational stability criterion (Courant-Friedrichs-Lewy Criterion)
. - Edward Norton Lorenz and the butterfly effect (aka “sensitive dependence on initial conditions”) mentioned.
- Near the end:
determinism and predictability are not equivalent
.
Also:
In other words, one of the lessons coming out of chaos theory is that the validity of the causality principle is narrowed by the uncertainty principle from one end as well as by the intrinsic instability properties of the underlying natural laws from the other end.
Notes
A Google search for “Courant-Friedrichs-Lewy Criterion” turned up only for-pay journal articles, all focused narrowly on particular applications/instances of its use. A Google Book search turned up a book that I’ve added to my Amazon wishlist, The Emergence of Numerical Weather Prediction: Richardson’s Dream (ISBN-13 978-0521857291), Richardson’s book, and the second volume of the authors other work, Fractals in the Classroom, which seems to have the same introduction, word for word, as CaF.
The edition of Richardson’s book cited in a footnote in the introduction is the 1965 Dover edition.