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		2.5.13— Problems: The Meaning of a Low Dimensional Attractor

		It is always hard in science to prove that an explanation is the explanation. The existence of a low dimensional attractor means that a deterministic process could have generated all the values of the measurements found in the experiment. It does not mean that the deterministic process did generate these values.

		For example, let's say we have a set of a million numbers, each of which happens to be 6. We pick numbers from this set at random. The time series will be: 6, 6, 6, 6, 6, . . . . The phase space set will be a zero-dimensional point. The low fractal dimension of the phase space set accurately indicates that a deterministic mechanism can generate these data. For example, the deterministic mechanism could be: (1) let the value of the first number be equal to 6, and (2) let the value of each subsequent number be equal to the value of the previous one. The problem is that even though a deterministic mechanism could have generated the data, in this case it didn't. These data were generated by a random mechanism.

		We are more likely to believe in the uniqueness of an explanation in science when that explanation predicts new values, explains previously unrelated facts, or allows us to see things in a new light that helps us make further discoveries.

 

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