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Flatland: A Romance of Many Dimensions by Edwin Abbott
Reviewed by James Sogi
Flatland: A Romance of Many Dimensions is a short novel by Edwin Abbott published in London in 1884. Abbott described his interactions with beings who live in a flat plane of two spatial dimensions, and showed how we might perceive the existence of higher dimensions. We, with our two coordinate charts, two coordinate scatter diagrams and x and y spreadsheets live in Flatland. What new insights on the market would a multidimensional analysis reveal in the market galaxy?
Philip J. McDonnell Comments:
Jim has some very creative ideas relating physics and markets. Assuming that a multidimensional approach is ultimately the holy grail to trading markets I would question whether charts are of any value at all. Suppose for the sake of argument that the "true picture" is really 10-dimensional. Then projecting this 10-dimensional picture down to a 3-dimensional shadow of its reality will lose 7 dimensions. To get an intuitive idea of how much is lost suppose that each dimension is finite and of length 10. In that case losing 7 dimensions will cause us to lose 10 to the 7th power of the available information. We will only "see" 1 part in 10 million of the total picture in our 3D chart. My suggestion is to throw away your charts and go back to the original numbers. It seems going to the numbers is an idea which has been presented in this forum before.
Before we embrace the idea that if only we could find all the possible variables we could solve the market equation, let me remind all of another analogy from the history of physics. Newtonian physics said that the planets revolved around the Sun in elliptical orbits all of which could be described neatly in only 5 dimension - 3 of space, 1 of time and mass. For 300 years Newton could explain everything to many decimal places.
Then Einstein came along with a completely different theory in the same 5 dimensions which said that space is curved by gravity and the planets follow straight lines in curved space. It was a radically different theory which also fit the data to very many decimal places. However it made a unique prediction that Newton did not - that starlight passing by the nearby massive Sun would be bent by the curvature of space near the Sun. When the prediction was confirmed a few months later, Einstein's theory was widely accepted.
The point of the above discussion is that even a five-variable model allows many degrees of freedom which can result in a very good, but spurious data fit. There are many disparate models which can fit the data to a high degree of accuracy. My suggestion is to stick with simple one-variable predictive models. Only after a given variable is shown to be a reliable predictor on its own can another known predictor be combined. Even then, the two variables will always be somewhat correlated with each other. High-dimension models are fraught with pitfalls and spurious correlations and are best avoided. The simplest model is the best.
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