hundred thousand to a few million years (to study the impact of Milankovitch cycles on the global climate, for instance). Similarly, we’re usually perfectly comfortable with predictions that introduce errors of (say) a few thousand kilometers in the position of Mercury in the next century[1]. The fact that we can’t give a reliable prediction about where Mercury will be in its orbit at around the time Sol ceases to be a main-sequence star--or similarly that we can’t give a prediction about Mercury’s position in its orbit in five years that gets things right down to the centimeter--doesn’t really trouble us most of the time. This suggests that we can fruitfully approximate the solar system’s behavior as non-chaotic, given a few specifications about our predictive goals.
Norton (2012) argues that we can leverage this sort of example to generate a robust distinction between approximation and idealization, terms which are often used interchangeably. He defines the difference as follows: “approximations merely describe a target system inexactly” while “[i]dealizations refer to new systems whose properties approximate those of the target system.” Norton argues that the important distinction here is one of reference, with “idealizations...carry[ing] a novel semantic import not carried by approximations.”[2] The distinction between approximation and idealization, on Norton’s view, is that idealization involves the construction of an entirely novel system, which is then studied as a proxy for the actual system of interest. Approximation, on the other hand, involves only particular parameterizations of the target system--parameterizations in which assigned values describe the
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