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. 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.” 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
- Of course, there are situations in which we might demand significantly more accurate predictions than this. After all, the difference between an asteroid slamming into Manhattan and drifting harmlessly by Earth is one of only a few thousand kilometers!
- Norton (2012), pp. 207-208