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For an example, consider a data set on atmospheric temperature. Such a data set exhibits many different patterns (Bryant 1997). These include a pattern with a period of a day, associated with the earth’s rotation about its axis; patterns with periods of a few days, associated with the life span of individual weather systems; a pattern with a period of a year, associated with the earth’s orbit around the sun; a pattern with a period of 11 years, attributed to the sunspot cycle; a pattern with a period of approximately 21,000 years, attributed to the precession of the earth’s orbit; various patterns with periods of between 40,000 and 100,000 years, attributed to fluctuations in the inclination of the earth’s axis of rotation and the eccentricity of the earth’s orbit; and various patterns with periods of between 10$7$ and 10$9$ years, associated with variations in the earth’s rate of rotation, the major geography of the earth, the composition of the atmosphere, and the characteristics of the sun. Each of these patterns has a different algorithmic complexity and is exhibited in the data with a different noise level. Any of these patterns is eligible to be considered as the regularity of the data set. Depending on their cognitive and practical interests, weather forecasters, meteorologists, climatologists, palaeontologists, astronomers, and researchers in other scientific disciplines will regard different patterns in this series as constituting the regularity in the data. They will thus ascribe different values to the effective complexity of the data set."

McAllister’s observations are acute: this is indeed a consequence of effective complexity. I think McAllister is wrong in calling this a fatal flaw (or even a criticism) of the concept, though, for reasons that should be relatively obvious. The central thrust of McAllister’s criticism is that it is difficult to assign a determinate value to the effective complexity of any physical system, as that system might contain a myriad of patterns, and thus fail to be best represented by any single ensemble. The question of what effective complexity we assign a system will depend on what string we choose to represent the system. That choice, in turn, will depend on how we carve the system up—it will depend on our choice of which patterns to pay attention to. Choices like that are purpose-relative; as McAllister rightly says, they depend on our practical and cognitive interest.

Given the account of science I developed in Chapter One, though, this is precisely what we

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