← chaosbook
Enter latest posts at the top, blog-style.
Predrag to Damon Lamb: Specifics?
Appendices:
Additional material:
Thanks! Whenever you can, please be specific, I need to know what is unclear in a particular in order to be able to improve it.
— Predrag Cvitanovic 2009-01-16
Damon Lamb to Predrag: Some general thoughts
Jargon: As some chapters make fairly heavy use of jargon, some of which is used in other fields but with different definitions or assumptions, it may be useful to have an appendix of terms and their specific definitions as used in this book.
More explicit algorithms: Perhaps as an addendum or an instructor resource, it would have been of great utility to have more explicit algorithms in several instances. Newton-Rhapson springs to mind, as many of us had problems with the particulars of the implementation - although, to be fair, this may have been problems on our end with fully understanding the nuances of the problem.
Derivations/Proofs of the more advanced formulae: While the first half (or so) of the course time, we covered material which, for me, followed from what I had seen in the past. The leap to the trace formulation, as well as some of the other more significant results we were presented with later in the course, were (and, to some extent, still are) far less clear. While I can say 'I trust that these are right', and apply them, I cannot derive them at will. This, for me, impedes my ability to apply them. I understand and appreciate the motivation to keep the proofs and mathematical minutae to a minimum, I strongly feel that they could greatly expand the utility and effectiveness of the book. Perhaps, as a compromise with efficiency and elegance in the main text, they could be relegated to appendices. Very, very useful appendices :)
Symbol uniformity: Several times my classmates and I found that the symbols used in a formula were unclear or inexact. This likely led to some of the aforementioned confusion or difficulty. It would be very helpful to have a single uniform symbolic set (especially if such a set of symbols was clearly defined prior to use, as well as gathered in yet another appendix of symbols). For me, having variables defined ahead of time is natural and expected.
All of these would broaden the impact of this book. I, for one, would be far more inclined to buy it if I could pick it up, quickly find the topic I wanted to review, and not need to re-read the entire book up to that point to understand the pages which apply. By pushing some of the additional material to an appendix, while slightly refining the primary presentation, I believe a balance can be struck which enables retention of the style of the book while rendering it more accessible and useful as a reference.
— Damon Lamb 2009-01-15
Discussion
Mohammad Ghorbani cusp2004 [snail] yahoo.com May 4, 2009
writes:
Dear Prof.Cvitanović,
I am Msc student in water engineering department of Tabriz University and am studying on prediction of river flow using chaos theory.
You know that Chaos theory applies to deterministic dynamical systems and also you know that all natural process such as rainfall, river flow, air temperature and .. is not deterministic systems. So why we use chaos theory in natural process modeling?
And what is the main advantage of Chaos theory in comparison with other methods such as artificial neural network (ANN)?
Excuse me for wasting your time. Memmed
Memmed
For you to answer parts of your question/statement will require years of concentrated study on graduate level; a single posting on the web will not do, but let's try anyway:
When you say “river flow … is not a deterministic system” you presumably mean that the deterministic Navier-Stokes equations together with the boundary conditions (river bed) do not suffice to describe the problem. Correct. For simple settings, such as the flow between two flat planes described in ChaosBook.org/tutorials deterministic Navier-Stokes is pretty good, and when it is worth the money, oceanographers and atmospheric physicists can extract much information by solving deterministic equations in realistic settings; see Emanuele Di Lorenzo's work as a typical good example of such work by a large community of scientists and engineers.
Ultimately no physical problem is “a deterministic system,” as there are always degrees of freedom you have not taken into account, be it rain or a galaxy showing up at the horizon of the visible universe. There the good science comes in. Sometimes the most important physics is captured by deterministic modelling, sometimes (like in the case of “fully developed turbulence”) you need to use probabilistic modelling, and most often you have to combine a variety of approaches. There is no royal road - every problem needs to be rethought from scratch. Your training should give you a basic tool kit: ODEs, PDEs, probability theory, statistical mechanics, ergodic theory (AKA chaos theory), theory of stochastic processes (AKA noise), algorithms such as ANN, and you should add to this by publishing advances you make in your own research.
None of us have time to philosophize about such broad questions as you pose here - so study hard, and if there is some very specific question relating to a specific section of ChaosBook.org, I might be able to help - providing the question is of sufficient importance for other students as well, and providing I find time for it (the last “providing” is a big if, so I appologize in advance)
Predrag