Wikipedia:Reference desk/Archives/Mathematics/2012 January 7

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January 7

standard scrabble points

E=1, M=3, O=1, R=1, Y=4

so why E=1, M=2, O=1, R=1 Y=10? http://www.bbc.co.uk/news/health-16425522 — Preceding unsigned comment added by 81.147.58.70 (talk) 12:28, 7 January 2012 (UTC)

Scrabble has many editions for different languages, each with different letter distributions and points. The photo clearly isn't of an English-language edition. From the points shown, it could be a French edition. Qwfp (talk) 12:50, 7 January 2012 (UTC)

In fact of the scrabble editions mentioned, French is the only one that matches up. French and German both have 10 point 'Y's, but an 'M' in German is 3 points, not 2.

Two- or three-dimensional chaotic system or map with at least two parameters

The section header pretty much says it. I would prefer the system or map (I don't know if there is a difference between the two terms) to be continuous. I am currently taking calculus in high school so I don't understand how to apply terms like dyadic transformation and eigenvalues, so I would prefer the system to be in an explicit form. --Melab±1 ☎ 15:26, 7 January 2012 (UTC)

What have you attempted and where did you get stuck? Bo Jacoby (talk) 20:38, 7 January 2012 (UTC).

I am not stuck due to this is not being an assignment. I am interested in experimenting with initial conditions and I would rather use a continuous system with an exact and explicit solution as opposed to any of the discrete systems I could find that have exact and explicit solution. Connecting points generated discretely using a continuous equation just isn't satisfactory. --Melab±1 ☎ 20:50, 7 January 2012 (UTC)

Your question was posed and answered here[1], remember. Bo Jacoby (talk) 08:23, 8 January 2012 (UTC).

Perhaps we could help you better if you explained some of your goals. There is plenty of fun to be had playing with chaotic systems, but why the need for a three dimensional state variable and continuity? Why do you wish for exact solutions? Exact solutions for chaotic systems are usually found only in simple "toy" models, and even then are not so common. There is a reason most of this stuff was not studied well until modern computation for numeric integration became cheap. As an aside, I'd highly recommend this book, "Nonlinear dynamics and chaos" [2]. You should be able to handle at least the first few chapters, and it gives some very nice intuitive approaches. It deals with chaos, but also other important features of nonlinear dynamics, such as stable limit cycles. SemanticMantis (talk) 15:09, 8 January 2012 (UTC)

The classical analysis of the Geiger-Marsden experiment may be relevant. The orbit in 3-dimensional space depend critically on the impact parameter, so the actual orbit is unpredictable, even if the formula is well known. Bo Jacoby (talk) 12:42, 9 January 2012 (UTC).

I want it to be continuous because I want to be able to evaluate for any $t$ and not have to use only specific values and I want an exact solution simply because I do not like errors to have any chance of propagating. --Melab±1 ☎ 13:10, 9 January 2012 (UTC)

I just checked the book, some of the notation looks to be beyond me. Like on page 235, I don't understand what $h(x,{\dot {x}})$ solves. I also don't understand how $x(0=a)$ and ${\dot {x}}(0)=0$ fit into ${\ddot {x}}+x+\varepsilon h(x,{\dot {x}})$. --Melab±1 ☎ 22:06, 9 January 2012 (UTC)

The system doesn't need to model a physical process. --Melab±1 ☎ 22:16, 9 January 2012 (UTC)

Your enthusiasm is inspiring, but we must walk before we run. Strogatz starts from a (somewhat) elementary perspective, but you need to read (and fully understand) the first 234 pages before you tackle p. 235. Make sure you are confident with ch.1-3, and feel free to ask a new question if you need help with the book. As to the original question, I don't have the time to search out what you're looking for right now, nor am I totally sure that it exists. Perhaps after you've read a bit more (and made sure you ace your HS math class this semester), you can re-post the question :) SemanticMantis (talk) 22:59, 9 January 2012 (UTC)

Thank you, very much. :) I want to say that I think I may have come up with a discrete chaotic system a while ago, it just doesn't satisfy my requirements. --Melab±1 ☎ 23:16, 9 January 2012 (UTC)