Aug

8

The ratio of surface area to volume is a concept that is often used to optimize, e.g. the leaf has evolved to maximize this ratio. Are there applications of this to charting that might lead to insights and testable hypotheses?

Phil MPhil McDonnell replies: Hidden variables may be at work. When we see price and volume reported it is actually the result of up to four hidden variables. At any given time there is the book, the collection of all limit orders to sell and limits orders to buy. These two variables interact with two other unobservable variables which are the traders who are about to enter market orders to buy and to sell.

Market orders extinguish limit orders on the other side of the trade. Together the interaction of these results in the two observable numbers which are reported -price and volume. If we then add the third observable dimension of time we actually have a 3D space that can be quantified.

I am struck by the similarity of this line of thought to Kepler's Laws. Recall that Kepler's Laws are all expressed in terms of squares and cubes of the relevant variables.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008


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  1. Michael F. Martin on August 8, 2008 1:14 pm

    The study of extremization has its own mathematical theory — the calculus of variations.

    For a real treat, you should check out Feynman’s lecture on the same in Volume II of The Feynman Lectures. There is a special chapter with a verbatim transcript and photographs of the chalkboard. Feynman derived many of his most important insights from minimization principles.

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