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		2.5.10— Problems: How Much Data?

		How many values in time are needed in order to accurately construct the phase space set and to evaluate its fractal dimension?

		Different groups proposed different methods to estimate the amount of data needed.

		Each of these methods is based on a reasonable mathematical argument. The validity of each of these methods was confirmed by computer tests on sample problems done by the group that proposed the method.

		To compare the results of the different methods, we used each method to compute the number of values in the time series needed to confirm the existence of a 6-dimensional attractor. The estimates of the number of values needed range from 10 to 5,000,000,000.

		This range of uncertainty makes it very difficult to design experiments.

		It is not clear how much data is needed. The highest estimates may be too high. However, our experience is that about 10D measurements are needed for us to identify an attractor of dimension D. This is a lot of data. It raises the question of how a biological system can be maintained under constant experimental conditions long enough to record such a large amount of data.

 

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